Bayesian Model Averaging for Propensity Score Analysis
Kaplan, David; Chen, Jianshen
2013-01-01
The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…
A new approach for Bayesian model averaging
Institute of Scientific and Technical Information of China (English)
TIAN XiangJun; XIE ZhengHui; WANG AiHui; YANG XiaoChun
2012-01-01
Bayesian model averaging (BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization (EM) and the Markov Chain Monte Carlo (MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the additional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA (referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algorithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is almost equivalent to that for EM.
Model uncertainty and Bayesian model averaging in vector autoregressive processes
R.W. Strachan (Rodney); H.K. van Dijk (Herman)
2006-01-01
textabstractEconomic forecasts and policy decisions are often informed by empirical analysis based on econometric models. However, inference based upon a single model, when several viable models exist, limits its usefulness. Taking account of model uncertainty, a Bayesian model averaging procedure i
Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling
Vrugt, J.A.; Diks, C.G.H.; Clark, M.
2008-01-01
Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In t
De Luca, G.; Magnus, J.R.
2011-01-01
This article is concerned with the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals which implement, respectively, the exact Bayesian Model Averaging (BMA) estimator and the Weighted Average Least Squa
Predictive RANS simulations via Bayesian Model-Scenario Averaging
Energy Technology Data Exchange (ETDEWEB)
Edeling, W.N., E-mail: W.N.Edeling@tudelft.nl [Arts et Métiers ParisTech, DynFluid laboratory, 151 Boulevard de l' Hospital, 75013 Paris (France); Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft (Netherlands); Cinnella, P., E-mail: P.Cinnella@ensam.eu [Arts et Métiers ParisTech, DynFluid laboratory, 151 Boulevard de l' Hospital, 75013 Paris (France); Dwight, R.P., E-mail: R.P.Dwight@tudelft.nl [Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft (Netherlands)
2014-10-15
The turbulence closure model is the dominant source of error in most Reynolds-Averaged Navier–Stokes simulations, yet no reliable estimators for this error component currently exist. Here we develop a stochastic, a posteriori error estimate, calibrated to specific classes of flow. It is based on variability in model closure coefficients across multiple flow scenarios, for multiple closure models. The variability is estimated using Bayesian calibration against experimental data for each scenario, and Bayesian Model-Scenario Averaging (BMSA) is used to collate the resulting posteriors, to obtain a stochastic estimate of a Quantity of Interest (QoI) in an unmeasured (prediction) scenario. The scenario probabilities in BMSA are chosen using a sensor which automatically weights those scenarios in the calibration set which are similar to the prediction scenario. The methodology is applied to the class of turbulent boundary-layers subject to various pressure gradients. For all considered prediction scenarios the standard-deviation of the stochastic estimate is consistent with the measurement ground truth. Furthermore, the mean of the estimate is more consistently accurate than the individual model predictions.
Predictive RANS simulations via Bayesian Model-Scenario Averaging
Edeling, W. N.; Cinnella, P.; Dwight, R. P.
2014-10-01
The turbulence closure model is the dominant source of error in most Reynolds-Averaged Navier-Stokes simulations, yet no reliable estimators for this error component currently exist. Here we develop a stochastic, a posteriori error estimate, calibrated to specific classes of flow. It is based on variability in model closure coefficients across multiple flow scenarios, for multiple closure models. The variability is estimated using Bayesian calibration against experimental data for each scenario, and Bayesian Model-Scenario Averaging (BMSA) is used to collate the resulting posteriors, to obtain a stochastic estimate of a Quantity of Interest (QoI) in an unmeasured (prediction) scenario. The scenario probabilities in BMSA are chosen using a sensor which automatically weights those scenarios in the calibration set which are similar to the prediction scenario. The methodology is applied to the class of turbulent boundary-layers subject to various pressure gradients. For all considered prediction scenarios the standard-deviation of the stochastic estimate is consistent with the measurement ground truth. Furthermore, the mean of the estimate is more consistently accurate than the individual model predictions.
Forecasting natural gas consumption in China by Bayesian Model Averaging
Directory of Open Access Journals (Sweden)
Wei Zhang
2015-11-01
Full Text Available With rapid growth of natural gas consumption in China, it is in urgent need of more accurate and reliable models to make a reasonable forecast. Considering the limitations of the single model and the model uncertainty, this paper presents a combinative method to forecast natural gas consumption by Bayesian Model Averaging (BMA. It can effectively handle the uncertainty associated with model structure and parameters, and thus improves the forecasting accuracy. This paper chooses six variables for forecasting the natural gas consumption, including GDP, urban population, energy consumption structure, industrial structure, energy efficiency and exports of goods and services. The results show that comparing to Gray prediction model, Linear regression model and Artificial neural networks, the BMA method provides a flexible tool to forecast natural gas consumption that will have a rapid growth in the future. This study can provide insightful information on natural gas consumption in the future.
Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors
Karl, Anna; Lenkoski, Alex
2012-01-01
We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct evaluation of model probabilities is intractable in this setting. We show that by nesting model moves inside the Gibbs sampler, model comparison can be performed via conditional Bayes factors, leading to straightforward calculations. This new Gibbs sampler is...
Evidence on Features of a DSGE Business Cycle Model from Bayesian Model Averaging
R.W. Strachan (Rodney); H.K. van Dijk (Herman)
2012-01-01
textabstractThe empirical support for features of a Dynamic Stochastic General Equilibrium model with two technology shocks is valuated using Bayesian model averaging over vector autoregressions. The model features include equilibria, restrictions on long-run responses, a structural break of unknown
Rings, J.; Vrugt, J.A.; Schoups, G.; Huisman, J.A.; Vereecken, H.
2012-01-01
Bayesian model averaging (BMA) is a standard method for combining predictive distributions from different models. In recent years, this method has enjoyed widespread application and use in many fields of study to improve the spread-skill relationship of forecast ensembles. The BMA predictive probabi
Rings, J.; Vrugt, J.A.; Schoups, G.; Huisman, J.A.; Vereecken, H.
2012-01-01
Bayesian model averaging (BMA) is a standard method for combining predictive distributions from different models. In recent years, this method has enjoyed widespread application and use in many fields of study to improve the spread-skill relationship of forecast ensembles. The BMA predictive probabi
In this paper, the Genetic Algorithms (GA) and Bayesian model averaging (BMA) were combined to simultaneously conduct calibration and uncertainty analysis for the Soil and Water Assessment Tool (SWAT). In this hybrid method, several SWAT models with different structures are first selected; next GA i...
Multi-objective calibration of forecast ensembles using Bayesian model averaging
Vrugt, J.A.; Clark, M.P.; Diks, C.G.H.; Duan, Q.; Robinson, B.A.
2006-01-01
Bayesian Model Averaging (BMA) has recently been proposed as a method for statistical postprocessing of forecast ensembles from numerical weather prediction models. The BMA predictive probability density function (PDF) of any weather quantity of interest is a weighted average of PDFs centered on the
Bayesian Model Averaging of Artificial Intelligence Models for Hydraulic Conductivity Estimation
Nadiri, A.; Chitsazan, N.; Tsai, F. T.; Asghari Moghaddam, A.
2012-12-01
This research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in the AI model outputs stems from error in model input as well as non-uniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. BAIMA employs Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights were determined using the Bayesian information criterion (BIC) that follows the parsimony principle. BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty due to model non-uniqueness. We employed Takagi-Sugeno fuzzy logic (TS-FL), artificial neural network (ANN) and neurofuzzy (NF) to estimate hydraulic conductivity for the Tasuj plain aquifer, Iran. BAIMA combined three AI models and produced better fitting than individual models. While NF was expected to be the best AI model owing to its utilization of both TS-FL and ANN models, the NF model is nearly discarded by the parsimony principle. The TS-FL model and the ANN model showed equal importance although their hydraulic conductivity estimates were quite different. This resulted in significant between-model variances that are normally ignored by using one AI model.
Prioritizing Policies for Pro-Poor Growth : Applying Bayesian Model Averaging to Vietnam
Klump, R.; Prüfer, P.
2006-01-01
Pro-Poor Growth (PPG) is the vision of combining high growth rates with poverty reduction.Due to the myriad of possible determinants of growth and poverty a unique theoretical model for guiding empirical work on PPG is absent, though.Bayesian Model Averaging is a statistically robust framework for t
Application of Bayesian model averaging to measurements of the primordial power spectrum
Parkinson, David
2010-01-01
Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale 0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper limit, depending on prior assumptions.
Inferring cellular regulatory networks with Bayesian model averaging for linear regression (BMALR).
Huang, Xun; Zi, Zhike
2014-08-01
Bayesian network and linear regression methods have been widely applied to reconstruct cellular regulatory networks. In this work, we propose a Bayesian model averaging for linear regression (BMALR) method to infer molecular interactions in biological systems. This method uses a new closed form solution to compute the posterior probabilities of the edges from regulators to the target gene within a hybrid framework of Bayesian model averaging and linear regression methods. We have assessed the performance of BMALR by benchmarking on both in silico DREAM datasets and real experimental datasets. The results show that BMALR achieves both high prediction accuracy and high computational efficiency across different benchmarks. A pre-processing of the datasets with the log transformation can further improve the performance of BMALR, leading to a new top overall performance. In addition, BMALR can achieve robust high performance in community predictions when it is combined with other competing methods. The proposed method BMALR is competitive compared to the existing network inference methods. Therefore, BMALR will be useful to infer regulatory interactions in biological networks. A free open source software tool for the BMALR algorithm is available at https://sites.google.com/site/bmalr4netinfer/.
Shou, Yiyun; Smithson, Michael
2015-03-01
Conventional measures of predictor importance in linear models are applicable only when the assumption of homoscedasticity is satisfied. Moreover, they cannot be adapted to evaluating predictor importance in models of heteroscedasticity (i.e., dispersion), an issue that seems not to have been systematically addressed in the literature. We compare two suitable approaches, Dominance Analysis (DA) and Bayesian Model Averaging (BMA), for simultaneously evaluating predictor importance in models of location and dispersion. We apply them to the beta general linear model as a test-case, illustrating this with an example using real data. Simulations using several different model structures, sample sizes, and degrees of multicollinearity suggest that both DA and BMA largely agree on the relative importance of predictors of the mean, but differ when ranking predictors of dispersion. The main implication of these findings for researchers is that the choice between DA and BMA is most important when they wish to evaluate the importance of predictors of dispersion.
Reconstruction of large-scale gene regulatory networks using Bayesian model averaging.
Kim, Haseong; Gelenbe, Erol
2012-09-01
Gene regulatory networks provide the systematic view of molecular interactions in a complex living system. However, constructing large-scale gene regulatory networks is one of the most challenging problems in systems biology. Also large burst sets of biological data require a proper integration technique for reliable gene regulatory network construction. Here we present a new reverse engineering approach based on Bayesian model averaging which attempts to combine all the appropriate models describing interactions among genes. This Bayesian approach with a prior based on the Gibbs distribution provides an efficient means to integrate multiple sources of biological data. In a simulation study with maximum of 2000 genes, our method shows better sensitivity than previous elastic-net and Gaussian graphical models, with a fixed specificity of 0.99. The study also shows that the proposed method outperforms the other standard methods for a DREAM dataset generated by nonlinear stochastic models. In brain tumor data analysis, three large-scale networks consisting of 4422 genes were built using the gene expression of non-tumor, low and high grade tumor mRNA expression samples, along with DNA-protein binding affinity information. We found that genes having a large variation of degree distribution among the three tumor networks are the ones that see most involved in regulatory and developmental processes, which possibly gives a novel insight concerning conventional differentially expressed gene analysis.
Bayesian Model Averaging for Ensemble-Based Estimates of Solvation Free Energies
Gosink, Luke J; Reehl, Sarah M; Whitney, Paul D; Mobley, David L; Baker, Nathan A
2016-01-01
This paper applies the Bayesian Model Averaging (BMA) statistical ensemble technique to estimate small molecule solvation free energies. There is a wide range methods for predicting solvation free energies, ranging from empirical statistical models to ab initio quantum mechanical approaches. Each of these methods are based on a set of conceptual assumptions that can affect a method's predictive accuracy and transferability. Using an iterative statistical process, we have selected and combined solvation energy estimates using an ensemble of 17 diverse methods from the SAMPL4 blind prediction study to form a single, aggregated solvation energy estimate. The ensemble design process evaluates the statistical information in each individual method as well as the performance of the aggregate estimate obtained from the ensemble as a whole. Methods that possess minimal or redundant information are pruned from the ensemble and the evaluation process repeats until aggregate predictive performance can no longer be improv...
Energy Technology Data Exchange (ETDEWEB)
Zhao, Kaiguang; Valle, Denis; Popescu, Sorin; Zhang, Xuesong; Malick, Bani
2013-05-15
Model specification remains challenging in spectroscopy of plant biochemistry, as exemplified by the availability of various spectral indices or band combinations for estimating the same biochemical. This lack of consensus in model choice across applications argues for a paradigm shift in hyperspectral methods to address model uncertainty and misspecification. We demonstrated one such method using Bayesian model averaging (BMA), which performs variable/band selection and quantifies the relative merits of many candidate models to synthesize a weighted average model with improved predictive performances. The utility of BMA was examined using a portfolio of 27 foliage spectral–chemical datasets representing over 80 species across the globe to estimate multiple biochemical properties, including nitrogen, hydrogen, carbon, cellulose, lignin, chlorophyll (a or b), carotenoid, polar and nonpolar extractives, leaf mass per area, and equivalent water thickness. We also compared BMA with partial least squares (PLS) and stepwise multiple regression (SMR). Results showed that all the biochemicals except carotenoid were accurately estimated from hyerspectral data with R2 values > 0.80.
Energy Technology Data Exchange (ETDEWEB)
Yang, Hongwei [APEC Climate Center, Busan (Korea, Republic of); Wang, Bin [University of Hawaii at Manoa, Department of Meteorology, Honolulu, HI (United States); University of Hawaii at Manoa, International Pacific Research Center, Honolulu, HI (United States); Wang, Bin [Chinese Academy of Sciences, LASG, Institute of Atmospheric Physics, Beijing (China)
2012-11-15
Reduction of uncertainty in large-scale lateral-boundary forcing in regional climate modeling is a critical issue for improving the performance of regional climate downscaling. Numerical simulations of 1998 East Asian summer monsoon were conducted using the Weather Research and Forecast model forced by four different reanalysis datasets, their equal-weight ensemble, and Bayesian model averaging (BMA) ensemble means. Large discrepancies were found among experiments forced by the four individual reanalysis datasets mainly due to the uncertainties in the moisture field of large-scale forcing over ocean. We used satellite water-vapor-path data as observed truth-and-training data to determine the posterior probability (weight) for each forcing dataset using the BMA method. The experiment forced by the equal-weight ensemble reduced the circulation biases significantly but reduced the precipitation biases only moderately. However, the experiment forced by the BMA ensemble outperformed not only the experiments forced by individual reanalysis datasets but also the equal-weight ensemble experiment in simulating the seasonal mean circulation and precipitation. These results suggest that the BMA ensemble method is an effective method for reducing the uncertainties in lateral-boundary forcing and improving model performance in regional climate downscaling. (orig.)
Directory of Open Access Journals (Sweden)
I. Soltanzadeh
2011-07-01
Full Text Available Using Bayesian Model Averaging (BMA, an attempt was made to obtain calibrated probabilistic numerical forecasts of 2-m temperature over Iran. The ensemble employs three limited area models (WRF, MM5 and HRM, with WRF used with five different configurations. Initial and boundary conditions for MM5 and WRF are obtained from the National Centers for Environmental Prediction (NCEP Global Forecast System (GFS and for HRM the initial and boundary conditions come from analysis of Global Model Europe (GME of the German Weather Service. The resulting ensemble of seven members was run for a period of 6 months (from December 2008 to May 2009 over Iran. The 48-h raw ensemble outputs were calibrated using BMA technique for 120 days using a 40 days training sample of forecasts and relative verification data.
The calibrated probabilistic forecasts were assessed using rank histogram and attribute diagrams. Results showed that application of BMA improved the reliability of the raw ensemble. Using the weighted ensemble mean forecast as a deterministic forecast it was found that the deterministic-style BMA forecasts performed usually better than the best member's deterministic forecast.
Robust determinants of OECD FDI in developing countries: Insights from Bayesian model averaging
Directory of Open Access Journals (Sweden)
Nikolaos Antonakakis
2015-12-01
Full Text Available In this paper, we examine the determinants of outward FDI from four major OECD investors, namely, the US, Germany, France, and the Netherlands, to 129 developing countries classified under five regions over the period 1995–2008. Our goal is to distinguish whether the motivation for FDI differs among these investors in developing countries. Rather than relying on specific theories of FDI determinants, we examine them all simultaneously by employing Bayesian model averaging (BMA. This approach permits us to select the most appropriate model (or combination of models that governs FDI allocation and to distinguish robust FDI determinants. We find that no single theory governs the decision of OECD FDI in developing countries but a combination of theories. In particular, OECD investors search for destinations with whom they have established intensive trade relations and that offer a qualified labor force. Low wages and attractive tax rates are robust investment criteria too, and a considerable share of FDI is still resource-driven. Overall, investors show fairly similar strategies in the five developing regions.
Comparison of Two Gas Selection Methodologies: An Application of Bayesian Model Averaging
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Renholds, Andrea S.; Thompson, Sandra E.; Anderson, Kevin K.; Chilton, Lawrence K.
2006-03-31
One goal of hyperspectral imagery analysis is the detection and characterization of plumes. Characterization includes identifying the gases in the plumes, which is a model selection problem. Two gas selection methods compared in this report are Bayesian model averaging (BMA) and minimum Akaike information criterion (AIC) stepwise regression (SR). Simulated spectral data from a three-layer radiance transfer model were used to compare the two methods. Test gases were chosen to span the types of spectra observed, which exhibit peaks ranging from broad to sharp. The size and complexity of the search libraries were varied. Background materials were chosen to either replicate a remote area of eastern Washington or feature many common background materials. For many cases, BMA and SR performed the detection task comparably in terms of the receiver operating characteristic curves. For some gases, BMA performed better than SR when the size and complexity of the search library increased. This is encouraging because we expect improved BMA performance upon incorporation of prior information on background materials and gases.
R.W. Strachan (Rodney); H.K. van Dijk (Herman)
2008-01-01
textabstractA Bayesian model averaging procedure is presented that makes use of a finite mixture of many model structures within the class of vector autoregressive (VAR) processes. It is applied to two empirical issues. First, stability of the Great Ratios in U.S. macro-economic time series is inves
Duc, Hiep Nguyen; Rivett, Kelly; MacSween, Katrina; Le-Anh, Linh
2017-01-01
Rainfall in New South Wales (NSW), located in the southeast of the Australian continent, is known to be influenced by four major climate drivers: the El Niño/Southern Oscillation (ENSO), the Interdecadal Pacific Oscillation (IPO), the Southern Annular Mode (SAM) and the Indian Ocean Dipole (IOD). Many studies have shown the influences of ENSO, IPO modulation, SAM and IOD on rainfall in Australia and on southeast Australia in particular. However, only limited work has been undertaken using a multiple regression framework to examine the extent of the combined effect of these climate drivers on rainfall. This paper analysed the role of these combined climate drivers and their interaction on the rainfall in NSW using Bayesian Model Averaging (BMA) to account for model uncertainty by considering each of the linear models across the whole model space which is equal to the set of all possible combinations of predictors to find the model posterior probabilities and their expected predictor coefficients. Using BMA for linear regression models, we are able to corroborate and confirm the results from many previous studies. In addition, the method gives the ranking order of importance and the probability of the association of each of the climate drivers and their interaction on the rainfall at a site. The ability to quantify the relative contribution of the climate drivers offers the key to understand the complex interaction of drivers on rainfall, or lack of rainfall in a region, such as the three big droughts in southeastern Australia which have been the subject of discussion and debate recently on their causes.
Bayesian model comparison and model averaging for small-area estimation
Aitkin, Murray; Liu, Charles C.; Chadwick, Tom
2009-01-01
This paper considers small-area estimation with lung cancer mortality data, and discusses the choice of upper-level model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. We give a general methodology for both evaluating the data evidence for different models and averaging over plausible models to give robust area effect distributions. We reanalyze the data of Tsutak...
Gosink, Luke; Bensema, Kevin; Pulsipher, Trenton; Obermaier, Harald; Henry, Michael; Childs, Hank; Joy, Kenneth I
2013-12-01
Numerical ensemble forecasting is a powerful tool that drives many risk analysis efforts and decision making tasks. These ensembles are composed of individual simulations that each uniquely model a possible outcome for a common event of interest: e.g., the direction and force of a hurricane, or the path of travel and mortality rate of a pandemic. This paper presents a new visual strategy to help quantify and characterize a numerical ensemble's predictive uncertainty: i.e., the ability for ensemble constituents to accurately and consistently predict an event of interest based on ground truth observations. Our strategy employs a Bayesian framework to first construct a statistical aggregate from the ensemble. We extend the information obtained from the aggregate with a visualization strategy that characterizes predictive uncertainty at two levels: at a global level, which assesses the ensemble as a whole, as well as a local level, which examines each of the ensemble's constituents. Through this approach, modelers are able to better assess the predictive strengths and weaknesses of the ensemble as a whole, as well as individual models. We apply our method to two datasets to demonstrate its broad applicability.
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Vrugt, Jasper A [Los Alamos National Laboratory; Wohling, Thomas [NON LANL
2008-01-01
Most studies in vadose zone hydrology use a single conceptual model for predictive inference and analysis. Focusing on the outcome of a single model is prone to statistical bias and underestimation of uncertainty. In this study, we combine multi-objective optimization and Bayesian Model Averaging (BMA) to generate forecast ensembles of soil hydraulic models. To illustrate our method, we use observed tensiometric pressure head data at three different depths in a layered vadose zone of volcanic origin in New Zealand. A set of seven different soil hydraulic models is calibrated using a multi-objective formulation with three different objective functions that each measure the mismatch between observed and predicted soil water pressure head at one specific depth. The Pareto solution space corresponding to these three objectives is estimated with AMALGAM, and used to generate four different model ensembles. These ensembles are post-processed with BMA and used for predictive analysis and uncertainty estimation. Our most important conclusions for the vadose zone under consideration are: (1) the mean BMA forecast exhibits similar predictive capabilities as the best individual performing soil hydraulic model, (2) the size of the BMA uncertainty ranges increase with increasing depth and dryness in the soil profile, (3) the best performing ensemble corresponds to the compromise (or balanced) solution of the three-objective Pareto surface, and (4) the combined multi-objective optimization and BMA framework proposed in this paper is very useful to generate forecast ensembles of soil hydraulic models.
Pannullo, Francesca; Lee, Duncan; Waclawski, Eugene; Leyland, Alastair H
2016-08-01
The long-term impact of air pollution on human health can be estimated from small-area ecological studies in which the health outcome is regressed against air pollution concentrations and other covariates, such as socio-economic deprivation. Socio-economic deprivation is multi-factorial and difficult to measure, and includes aspects of income, education, and housing as well as others. However, these variables are potentially highly correlated, meaning one can either create an overall deprivation index, or use the individual characteristics, which can result in a variety of pollution-health effects. Other aspects of model choice may affect the pollution-health estimate, such as the estimation of pollution, and spatial autocorrelation model. Therefore, we propose a Bayesian model averaging approach to combine the results from multiple statistical models to produce a more robust representation of the overall pollution-health effect. We investigate the relationship between nitrogen dioxide concentrations and cardio-respiratory mortality in West Central Scotland between 2006 and 2012.
Fang, Xin; Li, Runkui; Kan, Haidong; Bottai, Matteo; Fang, Fang
2016-01-01
Objective To demonstrate an application of Bayesian model averaging (BMA) with generalised additive mixed models (GAMM) and provide a novel modelling technique to assess the association between inhalable coarse particles (PM10) and respiratory mortality in time-series studies. Design A time-series study using regional death registry between 2009 and 2010. Setting 8 districts in a large metropolitan area in Northern China. Participants 9559 permanent residents of the 8 districts who died of respiratory diseases between 2009 and 2010. Main outcome measures Per cent increase in daily respiratory mortality rate (MR) per interquartile range (IQR) increase of PM10 concentration and corresponding 95% confidence interval (CI) in single-pollutant and multipollutant (including NOx, CO) models. Results The Bayesian model averaged GAMM (GAMM+BMA) and the optimal GAMM of PM10, multipollutants and principal components (PCs) of multipollutants showed comparable results for the effect of PM10 on daily respiratory MR, that is, one IQR increase in PM10 concentration corresponded to 1.38% vs 1.39%, 1.81% vs 1.83% and 0.87% vs 0.88% increase, respectively, in daily respiratory MR. However, GAMM+BMA gave slightly but noticeable wider CIs for the single-pollutant model (−1.09 to 4.28 vs −1.08 to 3.93) and the PCs-based model (−2.23 to 4.07 vs −2.03 vs 3.88). The CIs of the multiple-pollutant model from two methods are similar, that is, −1.12 to 4.85 versus −1.11 versus 4.83. Conclusions The BMA method may represent a useful tool for modelling uncertainty in time-series studies when evaluating the effect of air pollution on fatal health outcomes. PMID:27531727
Bayesian Averaging is Well-Temperated
DEFF Research Database (Denmark)
Hansen, Lars Kai
2000-01-01
Bayesian predictions are stochastic just like predictions of any other inference scheme that generalize from a finite sample. While a simple variational argument shows that Bayes averaging is generalization optimal given that the prior matches the teacher parameter distribution the situation...
Morales-Casique, E.; Neuman, S.P.; Vesselinov, V.V.
2010-01-01
We use log permeability and porosity data obtained from single-hole pneumatic packer tests in six boreholes drilled into unsaturated fractured tuff near Superior, Arizona, to postulate, calibrate and compare five alternative variogram models (exponential, exponential with linear drift, power, trunca
Xiao, H; Wang, J -X; Sun, R; Roy, C J
2015-01-01
Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering applications. For many practical flows, the turbulence models are by far the most important source of uncertainty. In this work we develop an open-box, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Si...
Xiao, H.; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C. J.
2016-11-01
Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has
Directory of Open Access Journals (Sweden)
Jiaming Liu
2016-01-01
Full Text Available Many downscaling techniques have been developed in the past few years for projection of station-scale hydrological variables from large-scale atmospheric variables to assess the hydrological impacts of climate change. To improve the simulation accuracy of downscaling methods, the Bayesian Model Averaging (BMA method combined with three statistical downscaling methods, which are support vector machine (SVM, BCC/RCG-Weather Generators (BCC/RCG-WG, and Statistics Downscaling Model (SDSM, is proposed in this study, based on the statistical relationship between the larger scale climate predictors and observed precipitation in upper Hanjiang River Basin (HRB. The statistical analysis of three performance criteria (the Nash-Sutcliffe coefficient of efficiency, the coefficient of correlation, and the relative error shows that the performance of ensemble downscaling method based on BMA for rainfall is better than that of each single statistical downscaling method. Moreover, the performance for the runoff modelled by the SWAT rainfall-runoff model using the downscaled daily rainfall by four methods is also compared, and the ensemble downscaling method has better simulation accuracy. The ensemble downscaling technology based on BMA can provide scientific basis for the study of runoff response to climate change.
General and Local: Averaged k-Dependence Bayesian Classifiers
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Limin Wang
2015-06-01
Full Text Available The inference of a general Bayesian network has been shown to be an NP-hard problem, even for approximate solutions. Although k-dependence Bayesian (KDB classifier can construct at arbitrary points (values of k along the attribute dependence spectrum, it cannot identify the changes of interdependencies when attributes take different values. Local KDB, which learns in the framework of KDB, is proposed in this study to describe the local dependencies implicated in each test instance. Based on the analysis of functional dependencies, substitution-elimination resolution, a new type of semi-naive Bayesian operation, is proposed to substitute or eliminate generalization to achieve accurate estimation of conditional probability distribution while reducing computational complexity. The final classifier, averaged k-dependence Bayesian (AKDB classifiers, will average the output of KDB and local KDB. Experimental results on the repository of machine learning databases from the University of California Irvine (UCI showed that AKDB has significant advantages in zero-one loss and bias relative to naive Bayes (NB, tree augmented naive Bayes (TAN, Averaged one-dependence estimators (AODE, and KDB. Moreover, KDB and local KDB show mutually complementary characteristics with respect to variance.
R.W. Strachan (Rodney); H.K. van Dijk (Herman)
2007-01-01
textabstractA Bayesian model averaging procedure is presented within the class of vector autoregressive (VAR) processes and applied to two empirical issues. First, stability of the "Great Ratios" in U.S. macro-economic time series is investigated, together with the presence and e¤ects of permanent s
Model Diagnostics for Bayesian Networks
Sinharay, Sandip
2006-01-01
Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…
Directory of Open Access Journals (Sweden)
Kang Su Cho
Full Text Available To investigate whether skin-to-stone distance (SSD, which remains controversial in patients with ureter stones, can be a predicting factor for one session success following extracorporeal shock wave lithotripsy (ESWL in patients with upper ureter stones.We retrospectively reviewed the medical records of 1,519 patients who underwent their first ESWL between January 2005 and December 2013. Among these patients, 492 had upper ureter stones that measured 4-20 mm and were eligible for our analyses. Maximal stone length, mean stone density (HU, and SSD were determined on pretreatment non-contrast computed tomography (NCCT. For subgroup analyses, patients were divided into four groups. Group 1 consisted of patients with SSD<25th percentile, group 2 consisted of patients with SSD in the 25th to 50th percentile, group 3 patients had SSD in the 50th to 75th percentile, and group 4 patients had SSD≥75th percentile.In analyses of group 2 patients versus others, there were no statistical differences in mean age, stone length and density. However, the one session success rate in group 2 was higher than other groups (77.9% vs. 67.0%; P = 0.032. The multivariate logistic regression model revealed that shorter stone length, lower stone density, and the group 2 SSD were positive predictors for successful outcomes in ESWL. Using the Bayesian model-averaging approach, longer stone length, lower stone density, and group 2 SSD can be also positive predictors for successful outcomes following ESWL.Our data indicate that a group 2 SSD of approximately 10 cm is a positive predictor for success following ESWL.
Congdon, Peter
2014-01-01
This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBU
DEFF Research Database (Denmark)
Jensen, Finn Verner; Nielsen, Thomas Dyhre
2016-01-01
and edges. The nodes represent variables, which may be either discrete or continuous. An edge between two nodes A and B indicates a direct influence between the state of A and the state of B, which in some domains can also be interpreted as a causal relation. The wide-spread use of Bayesian networks...
Bayesian modeling using WinBUGS
Ntzoufras, Ioannis
2009-01-01
A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all ...
Bayesian stable isotope mixing models
In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...
Bayesian Evidence and Model Selection
Knuth, Kevin H; Malakar, Nabin K; Mubeen, Asim M; Placek, Ben
2014-01-01
In this paper we review the concept of the Bayesian evidence and its application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical techniques. Application to several practical examples within the context of signal processing are discussed.
Borsboom, D.; Haig, B.D.
2013-01-01
Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science primar
Bayesian variable selection for latent class models.
Ghosh, Joyee; Herring, Amy H; Siega-Riz, Anna Maria
2011-09-01
In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.
Bayesian model discrimination for glucose-insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Brooks, Stephen P.; Højbjerre, Malene
the reformulation of existing deterministic models as stochastic state space models which properly accounts for both measurement and process variability. The analysis is further enhanced by Bayesian model discrimination techniques and model averaged parameter estimation which fully accounts for model as well...
Nonparametric Bayesian Modeling of Complex Networks
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...... for complex networks can be derived and point out relevant literature....
Modeling Diagnostic Assessments with Bayesian Networks
Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego
2007-01-01
This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…
Bayesian inference for OPC modeling
Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.
2016-03-01
The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.
Bayesian Calibration of Microsimulation Models.
Rutter, Carolyn M; Miglioretti, Diana L; Savarino, James E
2009-12-01
Microsimulation models that describe disease processes synthesize information from multiple sources and can be used to estimate the effects of screening and treatment on cancer incidence and mortality at a population level. These models are characterized by simulation of individual event histories for an idealized population of interest. Microsimulation models are complex and invariably include parameters that are not well informed by existing data. Therefore, a key component of model development is the choice of parameter values. Microsimulation model parameter values are selected to reproduce expected or known results though the process of model calibration. Calibration may be done by perturbing model parameters one at a time or by using a search algorithm. As an alternative, we propose a Bayesian method to calibrate microsimulation models that uses Markov chain Monte Carlo. We show that this approach converges to the target distribution and use a simulation study to demonstrate its finite-sample performance. Although computationally intensive, this approach has several advantages over previously proposed methods, including the use of statistical criteria to select parameter values, simultaneous calibration of multiple parameters to multiple data sources, incorporation of information via prior distributions, description of parameter identifiability, and the ability to obtain interval estimates of model parameters. We develop a microsimulation model for colorectal cancer and use our proposed method to calibrate model parameters. The microsimulation model provides a good fit to the calibration data. We find evidence that some parameters are identified primarily through prior distributions. Our results underscore the need to incorporate multiple sources of variability (i.e., due to calibration data, unknown parameters, and estimated parameters and predicted values) when calibrating and applying microsimulation models.
GPstuff: Bayesian Modeling with Gaussian Processes
Vanhatalo, J.; Riihimaki, J.; Hartikainen, J.; Jylänki, P.P.; Tolvanen, V.; Vehtari, A.
2013-01-01
The GPstuff toolbox is a versatile collection of Gaussian process models and computational tools required for Bayesian inference. The tools include, among others, various inference methods, sparse approximations and model assessment methods.
Bayesian Uncertainty Analyses Via Deterministic Model
Krzysztofowicz, R.
2001-05-01
Rational decision-making requires that the total uncertainty about a variate of interest (a predictand) be quantified in terms of a probability distribution, conditional on all available information and knowledge. Suppose the state-of-knowledge is embodied in a deterministic model, which is imperfect and outputs only an estimate of the predictand. Fundamentals are presented of three Bayesian approaches to producing a probability distribution of the predictand via any deterministic model. The Bayesian Processor of Output (BPO) quantifies the total uncertainty in terms of a posterior distribution, conditional on model output. The Bayesian Processor of Ensemble (BPE) quantifies the total uncertainty in terms of a posterior distribution, conditional on an ensemble of model output. The Bayesian Forecasting System (BFS) decomposes the total uncertainty into input uncertainty and model uncertainty, which are characterized independently and then integrated into a predictive distribution.
Bayesian models a statistical primer for ecologists
Hobbs, N Thompson
2015-01-01
Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods-in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probabili
Bayesian Modeling of a Human MMORPG Player
Synnaeve, Gabriel
2010-01-01
This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.
Bayesian Modeling of a Human MMORPG Player
Synnaeve, Gabriel; Bessière, Pierre
2011-03-01
This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.
Multi-Fraction Bayesian Sediment Transport Model
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Mark L. Schmelter
2015-09-01
Full Text Available A Bayesian approach to sediment transport modeling can provide a strong basis for evaluating and propagating model uncertainty, which can be useful in transport applications. Previous work in developing and applying Bayesian sediment transport models used a single grain size fraction or characterized the transport of mixed-size sediment with a single characteristic grain size. Although this approach is common in sediment transport modeling, it precludes the possibility of capturing processes that cause mixed-size sediments to sort and, thereby, alter the grain size available for transport and the transport rates themselves. This paper extends development of a Bayesian transport model from one to k fractional dimensions. The model uses an existing transport function as its deterministic core and is applied to the dataset used to originally develop the function. The Bayesian multi-fraction model is able to infer the posterior distributions for essential model parameters and replicates predictive distributions of both bulk and fractional transport. Further, the inferred posterior distributions are used to evaluate parametric and other sources of variability in relations representing mixed-size interactions in the original model. Successful OPEN ACCESS J. Mar. Sci. Eng. 2015, 3 1067 development of the model demonstrates that Bayesian methods can be used to provide a robust and rigorous basis for quantifying uncertainty in mixed-size sediment transport. Such a method has heretofore been unavailable and allows for the propagation of uncertainty in sediment transport applications.
Bayesian Data-Model Fit Assessment for Structural Equation Modeling
Levy, Roy
2011-01-01
Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…
Bayesian modeling of unknown diseases for biosurveillance.
Shen, Yanna; Cooper, Gregory F
2009-11-14
This paper investigates Bayesian modeling of unknown causes of events in the context of disease-outbreak detection. We introduce a Bayesian approach that models and detects both (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A key contribution of this paper is that it introduces a Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has broad applicability in medical informatics, where the space of known causes of outcomes of interest is seldom complete.
Distributed Bayesian Networks for User Modeling
DEFF Research Database (Denmark)
Tedesco, Roberto; Dolog, Peter; Nejdl, Wolfgang
2006-01-01
by such adaptive applications are often partial fragments of an overall user model. The fragments have then to be collected and merged into a global user profile. In this paper we investigate and present algorithms able to cope with distributed, fragmented user models – based on Bayesian Networks – in the context...... of Web-based eLearning platforms. The scenario we are tackling assumes learners who use several systems over time, which are able to create partial Bayesian Networks for user models based on the local system context. In particular, we focus on how to merge these partial user models. Our merge mechanism...... efficiently combines distributed learner models without the need to exchange internal structure of local Bayesian networks, nor local evidence between the involved platforms....
A Bayesian Analysis of Spectral ARMA Model
Directory of Open Access Journals (Sweden)
Manoel I. Silvestre Bezerra
2012-01-01
Full Text Available Bezerra et al. (2008 proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967. The Bayesian computations, simulation via Markov Monte Carlo (MCMC is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.
Bayesian semiparametric dynamic Nelson-Siegel model
C. Cakmakli
2011-01-01
This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model where the density of the yield curve factors and thereby the density of the yields are estimated along with other model parameters. This is accomplished by modeling the error distributions of the factors according to a Diric
Posterior Predictive Model Checking in Bayesian Networks
Crawford, Aaron
2014-01-01
This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…
Bayesian calibration of car-following models
Van Hinsbergen, C.P.IJ.; Van Lint, H.W.C.; Hoogendoorn, S.P.; Van Zuylen, H.J.
2010-01-01
Recent research has revealed that there exist large inter-driver differences in car-following behavior such that different car-following models may apply to different drivers. This study applies Bayesian techniques to the calibration of car-following models, where prior distributions on each model p
Bayesian modeling of flexible cognitive control.
Jiang, Jiefeng; Heller, Katherine; Egner, Tobias
2014-10-01
"Cognitive control" describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation.
Bayesian modeling of flexible cognitive control
Jiang, Jiefeng; Heller, Katherine; Egner, Tobias
2014-01-01
“Cognitive control” describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation. PMID:24929218
Bayesian Approach to Neuro-Rough Models for Modelling HIV
Marwala, Tshilidzi
2007-01-01
This paper proposes a new neuro-rough model for modelling the risk of HIV from demographic data. The model is formulated using Bayesian framework and trained using Markov Chain Monte Carlo method and Metropolis criterion. When the model was tested to estimate the risk of HIV infection given the demographic data it was found to give the accuracy of 62% as opposed to 58% obtained from a Bayesian formulated rough set model trained using Markov chain Monte Carlo method and 62% obtained from a Bayesian formulated multi-layered perceptron (MLP) model trained using hybrid Monte. The proposed model is able to combine the accuracy of the Bayesian MLP model and the transparency of Bayesian rough set model.
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Energy Technology Data Exchange (ETDEWEB)
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
Bayesian Spatial Modelling with R-INLA
Finn Lindgren; Håvard Rue
2015-01-01
The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized) linear mixed to spatial and spatio-temporal models. Combined with the stochastic...
Modelling crime linkage with Bayesian networks
J. de Zoete; M. Sjerps; D. Lagnado; N. Fenton
2015-01-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model
Bayesian modelling of geostatistical malaria risk data
Directory of Open Access Journals (Sweden)
L. Gosoniu
2006-11-01
Full Text Available Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locations and independent of location. We relax this assumption and analyse malaria survey data in Mali using a Bayesian non-stationary model. Model fit and predictions are based on Markov chain Monte Carlo simulation methods. Model validation compares the predictive ability of the non-stationary model with the stationary analogue. Results indicate that the stationarity assumption is important because it influences the significance of environmental factors and the corresponding malaria risk maps.
Bayesian modelling of geostatistical malaria risk data.
Gosoniu, L; Vounatsou, P; Sogoba, N; Smith, T
2006-11-01
Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locations and independent of location. We relax this assumption and analyse malaria survey data in Mali using a Bayesian non-stationary model. Model fit and predictions are based on Markov chain Monte Carlo simulation methods. Model validation compares the predictive ability of the non-stationary model with the stationary analogue. Results indicate that the stationarity assumption is important because it influences the significance of environmental factors and the corresponding malaria risk maps.
A Bayesian nonparametric meta-analysis model.
Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G
2015-03-01
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall effect size, such models may be adequate, but for prediction, they surely are not if the effect-size distribution exhibits non-normal behavior. To address this issue, we propose a Bayesian nonparametric meta-analysis model, which can describe a wider range of effect-size distributions, including unimodal symmetric distributions, as well as skewed and more multimodal distributions. We demonstrate our model through the analysis of real meta-analytic data arising from behavioral-genetic research. We compare the predictive performance of the Bayesian nonparametric model against various conventional and more modern normal fixed-effects and random-effects models.
Testing linearity against nonlinear moving average models
de Gooijer, J.G.; Brännäs, K.; Teräsvirta, T.
1998-01-01
Lagrange multiplier (LM) test statistics are derived for testing a linear moving average model against an additive smooth transition moving average model. The latter model is introduced in the paper. The small sample performance of the proposed tests are evaluated in a Monte Carlo study and compared
FREQUENTIST MODEL AVERAGING ESTIMATION: A REVIEW
Institute of Scientific and Technical Information of China (English)
Haiying WANG; Xinyu ZHANG; Guohua ZOU
2009-01-01
In applications, the traditional estimation procedure generally begins with model selection.Once a specific model is selected, subsequent estimation is conducted under the selected model without consideration of the uncertainty from the selection process. This often leads to the underreporting of variability and too optimistic confidence sets. Model averaging estimation is an alternative to this procedure, which incorporates model uncertainty into the estimation process. In recent years, there has been a rising interest in model averaging from the frequentist perspective, and some important progresses have been made. In this paper, the theory and methods on frequentist model averaging estimation are surveyed. Some future research topics are also discussed.
Bayesian Model comparison of Higgs couplings
Bergstrom, Johannes
2014-01-01
We investigate the possibility of contributions from physics beyond the Standard Model (SM) to the Higgs couplings, in the light of the LHC data. The work is performed within an interim framework where the magnitude of the Higgs production and decay rates are rescaled though Higgs coupling scale factors. We perform Bayesian parameter inference on these scale factors, concluding that there is good compatibility with the SM. Furthermore, we carry out Bayesian model comparison on all models where any combination of scale factors can differ from their SM values and find that typically models with fewer free couplings are strongly favoured. We consider the evidence that each coupling individually equals the SM value, making the minimal assumptions on the other couplings. Finally, we make a comparison of the SM against a single "not-SM" model, and find that there is moderate to strong evidence for the SM.
Bayesian inference for pulsar timing models
Vigeland, Sarah J
2013-01-01
The extremely regular, periodic radio emission from millisecond pulsars make them useful tools for studying neutron star astrophysics, general relativity, and low-frequency gravitational waves. These studies require that the observed pulse time of arrivals are fit to complicated timing models that describe numerous effects such as the astrometry of the source, the evolution of the pulsar's spin, the presence of a binary companion, and the propagation of the pulses through the interstellar medium. In this paper, we discuss the benefits of using Bayesian inference to obtain these timing solutions. These include the validation of linearized least-squares model fits when they are correct, and the proper characterization of parameter uncertainties when they are not; the incorporation of prior parameter information and of models of correlated noise; and the Bayesian comparison of alternative timing models. We describe our computational setup, which combines the timing models of tempo2 with the nested-sampling integ...
Structure learning for Bayesian networks as models of biological networks.
Larjo, Antti; Shmulevich, Ilya; Lähdesmäki, Harri
2013-01-01
Bayesian networks are probabilistic graphical models suitable for modeling several kinds of biological systems. In many cases, the structure of a Bayesian network represents causal molecular mechanisms or statistical associations of the underlying system. Bayesian networks have been applied, for example, for inferring the structure of many biological networks from experimental data. We present some recent progress in learning the structure of static and dynamic Bayesian networks from data.
Average-passage flow model development
Adamczyk, John J.; Celestina, Mark L.; Beach, Tim A.; Kirtley, Kevin; Barnett, Mark
1989-01-01
A 3-D model was developed for simulating multistage turbomachinery flows using supercomputers. This average passage flow model described the time averaged flow field within a typical passage of a bladed wheel within a multistage configuration. To date, a number of inviscid simulations were executed to assess the resolution capabilities of the model. Recently, the viscous terms associated with the average passage model were incorporated into the inviscid computer code along with an algebraic turbulence model. A simulation of a stage-and-one-half, low speed turbine was executed. The results of this simulation, including a comparison with experimental data, is discussed.
Bayesian network modelling of upper gastrointestinal bleeding
Aisha, Nazziwa; Shohaimi, Shamarina; Adam, Mohd Bakri
2013-09-01
Bayesian networks are graphical probabilistic models that represent causal and other relationships between domain variables. In the context of medical decision making, these models have been explored to help in medical diagnosis and prognosis. In this paper, we discuss the Bayesian network formalism in building medical support systems and we learn a tree augmented naive Bayes Network (TAN) from gastrointestinal bleeding data. The accuracy of the TAN in classifying the source of gastrointestinal bleeding into upper or lower source is obtained. The TAN achieves a high classification accuracy of 86% and an area under curve of 92%. A sensitivity analysis of the model shows relatively high levels of entropy reduction for color of the stool, history of gastrointestinal bleeding, consistency and the ratio of blood urea nitrogen to creatinine. The TAN facilitates the identification of the source of GIB and requires further validation.
Bayesian Recurrent Neural Network for Language Modeling.
Chien, Jen-Tzung; Ku, Yuan-Chu
2016-02-01
A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.
Bayesian Network Based XP Process Modelling
Directory of Open Access Journals (Sweden)
Mohamed Abouelela
2010-07-01
Full Text Available A Bayesian Network based mathematical model has been used for modelling Extreme Programmingsoftware development process. The model is capable of predicting the expected finish time and theexpected defect rate for each XP release. Therefore, it can be used to determine the success/failure of anyXP Project. The model takes into account the effect of three XP practices, namely: Pair Programming,Test Driven Development and Onsite Customer practices. The model’s predictions were validated againsttwo case studies. Results show the precision of our model especially in predicting the project finish time.
Bayesian nonparametric duration model with censorship
Directory of Open Access Journals (Sweden)
Joseph Hakizamungu
2007-10-01
Full Text Available This paper is concerned with nonparametric i.i.d. durations models censored observations and we establish by a simple and unified approach the general structure of a bayesian nonparametric estimator for a survival function S. For Dirichlet prior distributions, we describe completely the structure of the posterior distribution of the survival function. These results are essentially supported by prior and posterior independence properties.
Bayesian structural equation modeling in sport and exercise psychology.
Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus
2015-08-01
Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.
Bayesian Inference of a Multivariate Regression Model
Directory of Open Access Journals (Sweden)
Marick S. Sinay
2014-01-01
Full Text Available We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.
Model averaging and muddled multimodel inferences.
Cade, Brian S
2015-09-01
Three flawed practices associated with model averaging coefficients for predictor variables in regression models commonly occur when making multimodel inferences in analyses of ecological data. Model-averaged regression coefficients based on Akaike information criterion (AIC) weights have been recommended for addressing model uncertainty but they are not valid, interpretable estimates of partial effects for individual predictors when there is multicollinearity among the predictor variables. Multicollinearity implies that the scaling of units in the denominators of the regression coefficients may change across models such that neither the parameters nor their estimates have common scales, therefore averaging them makes no sense. The associated sums of AIC model weights recommended to assess relative importance of individual predictors are really a measure of relative importance of models, with little information about contributions by individual predictors compared to other measures of relative importance based on effects size or variance reduction. Sometimes the model-averaged regression coefficients for predictor variables are incorrectly used to make model-averaged predictions of the response variable when the models are not linear in the parameters. I demonstrate the issues with the first two practices using the college grade point average example extensively analyzed by Burnham and Anderson. I show how partial standard deviations of the predictor variables can be used to detect changing scales of their estimates with multicollinearity. Standardizing estimates based on partial standard deviations for their variables can be used to make the scaling of the estimates commensurate across models, a necessary but not sufficient condition for model averaging of the estimates to be sensible. A unimodal distribution of estimates and valid interpretation of individual parameters are additional requisite conditions. The standardized estimates or equivalently the t
Model averaging and muddled multimodel inferences
Cade, Brian S.
2015-01-01
Three flawed practices associated with model averaging coefficients for predictor variables in regression models commonly occur when making multimodel inferences in analyses of ecological data. Model-averaged regression coefficients based on Akaike information criterion (AIC) weights have been recommended for addressing model uncertainty but they are not valid, interpretable estimates of partial effects for individual predictors when there is multicollinearity among the predictor variables. Multicollinearity implies that the scaling of units in the denominators of the regression coefficients may change across models such that neither the parameters nor their estimates have common scales, therefore averaging them makes no sense. The associated sums of AIC model weights recommended to assess relative importance of individual predictors are really a measure of relative importance of models, with little information about contributions by individual predictors compared to other measures of relative importance based on effects size or variance reduction. Sometimes the model-averaged regression coefficients for predictor variables are incorrectly used to make model-averaged predictions of the response variable when the models are not linear in the parameters. I demonstrate the issues with the first two practices using the college grade point average example extensively analyzed by Burnham and Anderson. I show how partial standard deviations of the predictor variables can be used to detect changing scales of their estimates with multicollinearity. Standardizing estimates based on partial standard deviations for their variables can be used to make the scaling of the estimates commensurate across models, a necessary but not sufficient condition for model averaging of the estimates to be sensible. A unimodal distribution of estimates and valid interpretation of individual parameters are additional requisite conditions. The standardized estimates or equivalently the
Bayesian model selection in Gaussian regression
Abramovich, Felix
2009-01-01
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized least squares estimation with a complexity penalty associated with a prior on the model size. We investigate the optimality properties of the resulting estimator. We establish the oracle inequality and specify conditions on the prior that imply its asymptotic minimaxity within a wide range of sparse and dense settings for "nearly-orthogonal" and "multicollinear" designs.
Bayesian mixture models for partially verified data
DEFF Research Database (Denmark)
Kostoulas, Polychronis; Browne, William J.; Nielsen, Søren Saxmose;
2013-01-01
for some individuals, in order to minimize this loss in the discriminatory power. The distribution of the continuous antibody response against MAP has been obtained for healthy, MAP-infected and MAP-infectious cows of different age groups. The overall power of the milk-ELISA to discriminate between healthy......Bayesian mixture models can be used to discriminate between the distributions of continuous test responses for different infection stages. These models are particularly useful in case of chronic infections with a long latent period, like Mycobacterium avium subsp. paratuberculosis (MAP) infection...
Average Bandwidth Allocation Model of WFQ
Directory of Open Access Journals (Sweden)
Tomáš Balogh
2012-01-01
Full Text Available We present a new iterative method for the calculation of average bandwidth assignment to traffic flows using a WFQ scheduler in IP based NGN networks. The bandwidth assignment calculation is based on the link speed, assigned weights, arrival rate, and average packet length or input rate of the traffic flows. We prove the model outcome with examples and simulation results using NS2 simulator.
Bayesian modeling of ChIP-chip data using latent variables.
Wu, Mingqi
2009-10-26
BACKGROUND: The ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations. RESULTS: In this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment) effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length. CONCLUSION: The Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results indicate that the
A Bayesian Shrinkage Approach for AMMI Models.
da Silva, Carlos Pereira; de Oliveira, Luciano Antonio; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves; Balestre, Marcio
2015-01-01
Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior
A Bayesian Shrinkage Approach for AMMI Models.
Directory of Open Access Journals (Sweden)
Carlos Pereira da Silva
Full Text Available Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI model, are widely applicable to genotype-by-environment interaction (GEI studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05 in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct
Sparse Event Modeling with Hierarchical Bayesian Kernel Methods
2016-01-05
SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model, is able to model the rate of occurrence of... kernel methods made use of: (i) the Bayesian property of improving predictive accuracy as data are dynamically obtained, and (ii) the kernel function
Spatial averaging infiltration model for layered soil
Institute of Scientific and Technical Information of China (English)
HU HePing; YANG ZhiYong; TIAN FuQiang
2009-01-01
To quantify the influences of soil heterogeneity on infiltration, a spatial averaging infiltration model for layered soil (SAI model) is developed by coupling the spatial averaging approach proposed by Chen et al. and the Generalized Green-Ampt model proposed by Jia et al. In the SAI model, the spatial heterogeneity along the horizontal direction is described by a probability distribution function, while that along the vertical direction is represented by the layered soils. The SAI model is tested on a typical soil using Monte Carlo simulations as the base model. The results show that the SAI model can directly incorporate the influence of spatial heterogeneity on infiltration on the macro scale. It is also found that the homogeneous assumption of soil hydraulic conductivity along the horizontal direction will overestimate the infiltration rate, while that along the vertical direction will underestimate the infiltration rate significantly during rainstorm periods. The SAI model is adopted in the spatial averaging hydrological model developed by the authors, and the results prove that it can be applied in the macro-scale hydrological and land surface process modeling in a promising way.
Spatial averaging infiltration model for layered soil
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
To quantify the influences of soil heterogeneity on infiltration, a spatial averaging infiltration model for layered soil (SAI model) is developed by coupling the spatial averaging approach proposed by Chen et al. and the Generalized Green-Ampt model proposed by Jia et al. In the SAI model, the spatial hetero- geneity along the horizontal direction is described by a probability distribution function, while that along the vertical direction is represented by the layered soils. The SAI model is tested on a typical soil using Monte Carlo simulations as the base model. The results show that the SAI model can directly incorporate the influence of spatial heterogeneity on infiltration on the macro scale. It is also found that the homogeneous assumption of soil hydraulic conductivity along the horizontal direction will overes- timate the infiltration rate, while that along the vertical direction will underestimate the infiltration rate significantly during rainstorm periods. The SAI model is adopted in the spatial averaging hydrological model developed by the authors, and the results prove that it can be applied in the macro-scale hy- drological and land surface process modeling in a promising way.
A Bayesian Model Committee Approach to Forecasting Global Solar Radiation
Lauret, Philippe; Muselli, Marc; David, Mathieu; Diagne, Hadja; Voyant, Cyril
2012-01-01
This paper proposes to use a rather new modelling approach in the realm of solar radiation forecasting. In this work, two forecasting models: Autoregressive Moving Average (ARMA) and Neural Network (NN) models are combined to form a model committee. The Bayesian inference is used to affect a probability to each model in the committee. Hence, each model's predictions are weighted by their respective probability. The models are fitted to one year of hourly Global Horizontal Irradiance (GHI) measurements. Another year (the test set) is used for making genuine one hour ahead (h+1) out-of-sample forecast comparisons. The proposed approach is benchmarked against the persistence model. The very first results show an improvement brought by this approach.
Bayesian Spatial Modelling with R-INLA
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Finn Lindgren
2015-02-01
Full Text Available The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA approach proposed by Rue, Martino, and Chopin (2009 is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized linear mixed to spatial and spatio-temporal models. Combined with the stochastic partial differential equation approach (SPDE, Lindgren, Rue, and Lindstrm 2011, one can accommodate all kinds of geographically referenced data, including areal and geostatistical ones, as well as spatial point process data. The implementation interface covers stationary spatial mod- els, non-stationary spatial models, and also spatio-temporal models, and is applicable in epidemiology, ecology, environmental risk assessment, as well as general geostatistics.
Bayesian Discovery of Linear Acyclic Causal Models
Hoyer, Patrik O
2012-01-01
Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accur...
A Hierarchical Bayesian Model for Crowd Emotions
Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias
2016-01-01
Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366
Hopes and Cautions in Implementing Bayesian Structural Equation Modeling
MacCallum, Robert C.; Edwards, Michael C.; Cai, Li
2012-01-01
Muthen and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero…
Jones, Matt; Love, Bradley C
2011-08-01
The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology - namely, Behaviorism and evolutionary psychology - that set aside mechanistic explanations or make use of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls
Dynamic Model Averaging in Large Model Spaces Using Dynamic Occam’s Window*
Onorante, Luca; Raftery, Adrian E.
2015-01-01
Bayesian model averaging has become a widely used approach to accounting for uncertainty about the structural form of the model generating the data. When data arrive sequentially and the generating model can change over time, Dynamic Model Averaging (DMA) extends model averaging to deal with this situation. Often in macroeconomics, however, many candidate explanatory variables are available and the number of possible models becomes too large for DMA to be applied in its original form. We propose a new method for this situation which allows us to perform DMA without considering the whole model space, but using a subset of models and dynamically optimizing the choice of models at each point in time. This yields a dynamic form of Occam’s window. We evaluate the method in the context of the problem of nowcasting GDP in the Euro area. We find that its forecasting performance compares well with that of other methods. PMID:26917859
Entropic Priors and Bayesian Model Selection
Brewer, Brendon J
2009-01-01
We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst ...
Bayesian Estimation of a Mixture Model
Directory of Open Access Journals (Sweden)
Ilhem Merah
2015-05-01
Full Text Available We present the properties of a bathtub curve reliability model having both a sufficient adaptability and a minimal number of parameters introduced by Idée and Pierrat (2010. This one is a mixture of a Gamma distribution G(2, (1/θ and a new distribution L(θ. We are interesting by Bayesian estimation of the parameters and survival function of this model with a squared-error loss function and non-informative prior using the approximations of Lindley (1980 and Tierney and Kadane (1986. Using a statistical sample of 60 failure data relative to a technical device, we illustrate the results derived. Based on a simulation study, comparisons are made between these two methods and the maximum likelihood method of this two parameters model.
Effect on Prediction when Modeling Covariates in Bayesian Nonparametric Models.
Cruz-Marcelo, Alejandro; Rosner, Gary L; Müller, Peter; Stewart, Clinton F
2013-04-01
In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparametric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
MERGING DIGITAL SURFACE MODELS IMPLEMENTING BAYESIAN APPROACHES
Directory of Open Access Journals (Sweden)
H. Sadeq
2016-06-01
Full Text Available In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades. It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Merging Digital Surface Models Implementing Bayesian Approaches
Sadeq, H.; Drummond, J.; Li, Z.
2016-06-01
In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades). It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Mendes, B. S.; Draper, D.
2008-12-01
The issue of model uncertainty and model choice is central in any groundwater modeling effort [Neuman and Wierenga, 2003]; among the several approaches to the problem we favour using Bayesian statistics because it is a method that integrates in a natural way uncertainties (arising from any source) and experimental data. In this work, we experiment with several Bayesian approaches to model choice, focusing primarily on demonstrating the usefulness of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) simulation method [Green, 1995]; this is an extension of the now- common MCMC methods. Standard MCMC techniques approximate posterior distributions for quantities of interest, often by creating a random walk in parameter space; RJMCMC allows the random walk to take place between parameter spaces with different dimensionalities. This fact allows us to explore state spaces that are associated with different deterministic models for experimental data. Our work is exploratory in nature; we restrict our study to comparing two simple transport models applied to a data set gathered to estimate the breakthrough curve for a tracer compound in groundwater. One model has a mean surface based on a simple advection dispersion differential equation; the second model's mean surface is also governed by a differential equation but in two dimensions. We focus on artificial data sets (in which truth is known) to see if model identification is done correctly, but we also address the issues of over and under-paramerization, and we compare RJMCMC's performance with other traditional methods for model selection and propagation of model uncertainty, including Bayesian model averaging, BIC and DIC.References Neuman and Wierenga (2003). A Comprehensive Strategy of Hydrogeologic Modeling and Uncertainty Analysis for Nuclear Facilities and Sites. NUREG/CR-6805, Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research, U. S. Nuclear Regulatory Commission
Improving randomness characterization through Bayesian model selection
R., Rafael Díaz-H; Martínez, Alí M Angulo; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Castillo, Isaac Pérez
2016-01-01
Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We...
Modeling Social Annotation: a Bayesian Approach
Plangprasopchok, Anon
2008-01-01
Collaborative tagging systems, such as del.icio.us, CiteULike, and others, allow users to annotate objects, e.g., Web pages or scientific papers, with descriptive labels called tags. The social annotations, contributed by thousands of users, can potentially be used to infer categorical knowledge, classify documents or recommend new relevant information. Traditional text inference methods do not make best use of socially-generated data, since they do not take into account variations in individual users' perspectives and vocabulary. In a previous work, we introduced a simple probabilistic model that takes interests of individual annotators into account in order to find hidden topics of annotated objects. Unfortunately, our proposed approach had a number of shortcomings, including overfitting, local maxima and the requirement to specify values for some parameters. In this paper we address these shortcomings in two ways. First, we extend the model to a fully Bayesian framework. Second, we describe an infinite ver...
3-Layered Bayesian Model Using in Text Classification
Directory of Open Access Journals (Sweden)
Chang Jiayu
2013-01-01
Full Text Available Naive Bayesian is one of quite effective classification methods in all of the text disaggregated models. Usually, the computed result will be large deviation from normal, with the reason of attribute relevance and so on. This study embarked from the degree of correlation, defined the node’s degree as well as the relations between nodes, proposed a 3-layered Bayesian Model. According to the conditional probability recurrence formula, the theory support of the 3-layered Bayesian Model is obtained. According to the theory analysis and the empirical datum contrast to the Naive Bayesian, the model has better attribute collection and classify. It can be also promoted to the Multi-layer Bayesian Model using in text classification.
Modelling crime linkage with Bayesian networks.
de Zoete, Jacob; Sjerps, Marjan; Lagnado, David; Fenton, Norman
2015-05-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model different evidential structures that can occur when linking crimes, and how they assist in understanding the complex underlying dependencies. That is, how evidence that is obtained in one case can be used in another and vice versa. The flip side of this is that the intuitive decision to "unlink" a case in which exculpatory evidence is obtained leads to serious overestimation of the strength of the remaining cases.
Bayesian Student Modeling and the Problem of Parameter Specification.
Millan, Eva; Agosta, John Mark; Perez de la Cruz, Jose Luis
2001-01-01
Discusses intelligent tutoring systems and the application of Bayesian networks to student modeling. Considers reasons for not using Bayesian networks, including the computational complexity of the algorithms and the difficulty of knowledge acquisition, and proposes an approach to simplify knowledge acquisition that applies causal independence to…
Implementing Relevance Feedback in the Bayesian Network Retrieval Model.
de Campos, Luis M.; Fernandez-Luna, Juan M.; Huete, Juan F.
2003-01-01
Discussion of relevance feedback in information retrieval focuses on a proposal for the Bayesian Network Retrieval Model. Bases the proposal on the propagation of partial evidences in the Bayesian network, representing new information obtained from the user's relevance judgments to compute the posterior relevance probabilities of the documents…
The average free volume model for liquids
Yu, Yang
2014-01-01
In this work, the molar volume thermal expansion coefficient of 59 room temperature ionic liquids is compared with their van der Waals volume Vw. Regular correlation can be discerned between the two quantities. An average free volume model, that considers the particles as hard core with attractive force, is proposed to explain the correlation in this study. A combination between free volume and Lennard-Jones potential is applied to explain the physical phenomena of liquids. Some typical simple liquids (inorganic, organic, metallic and salt) are introduced to verify this hypothesis. Good agreement from the theory prediction and experimental data can be obtained.
Advances in Bayesian Modeling in Educational Research
Levy, Roy
2016-01-01
In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…
Bayesian Model Selection for LISA Pathfinder
Karnesis, Nikolaos; Sopuerta, Carlos F; Gibert, Ferran; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Ferraioli, Luigi; Hewitson, Martin; Hueller, Mauro; Korsakova, Natalia; Plagnol, Eric; Vitale, and Stefano
2013-01-01
The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the LISA/eLISA concept. The Data Analysis (DA) team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment on-board LPF. These models are used for simulations, but more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the DA team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching to this problem is to recover the essential parameters of the LTP which describe the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes Factor between two competing models. In our analysis, we use three main different methods to estimate...
A guide to Bayesian model selection for ecologists
Hooten, Mevin B.; Hobbs, N.T.
2015-01-01
The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.
Nonparametric Bayesian Modeling for Automated Database Schema Matching
Energy Technology Data Exchange (ETDEWEB)
Ferragut, Erik M [ORNL; Laska, Jason A [ORNL
2015-01-01
The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametric Bayesian models.
Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants
Jin, Ick Hoon
2014-03-01
Statistical inference for the models with intractable normalizing constants has attracted much attention. During the past two decades, various approximation- or simulation-based methods have been proposed for the problem, such as the Monte Carlo maximum likelihood method and the auxiliary variable Markov chain Monte Carlo methods. The Bayesian stochastic approximation Monte Carlo algorithm specifically addresses this problem: It works by sampling from a sequence of approximate distributions with their average converging to the target posterior distribution, where the approximate distributions can be achieved using the stochastic approximation Monte Carlo algorithm. A strong law of large numbers is established for the Bayesian stochastic approximation Monte Carlo estimator under mild conditions. Compared to the Monte Carlo maximum likelihood method, the Bayesian stochastic approximation Monte Carlo algorithm is more robust to the initial guess of model parameters. Compared to the auxiliary variable MCMC methods, the Bayesian stochastic approximation Monte Carlo algorithm avoids the requirement for perfect samples, and thus can be applied to many models for which perfect sampling is not available or very expensive. The Bayesian stochastic approximation Monte Carlo algorithm also provides a general framework for approximate Bayesian analysis. © 2012 Elsevier B.V. All rights reserved.
Bayesian model reduction and empirical Bayes for group (DCM) studies.
Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter
2016-03-01
This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.
A Gaussian Mixed Model for Learning Discrete Bayesian Networks.
Balov, Nikolay
2011-02-01
In this paper we address the problem of learning discrete Bayesian networks from noisy data. Considered is a graphical model based on mixture of Gaussian distributions with categorical mixing structure coming from a discrete Bayesian network. The network learning is formulated as a Maximum Likelihood estimation problem and performed by employing an EM algorithm. The proposed approach is relevant to a variety of statistical problems for which Bayesian network models are suitable - from simple regression analysis to learning gene/protein regulatory networks from microarray data.
Bayesian approach to decompression sickness model parameter estimation.
Howle, L E; Weber, P W; Nichols, J M
2017-03-01
We examine both maximum likelihood and Bayesian approaches for estimating probabilistic decompression sickness model parameters. Maximum likelihood estimation treats parameters as fixed values and determines the best estimate through repeated trials, whereas the Bayesian approach treats parameters as random variables and determines the parameter probability distributions. We would ultimately like to know the probability that a parameter lies in a certain range rather than simply make statements about the repeatability of our estimator. Although both represent powerful methods of inference, for models with complex or multi-peaked likelihoods, maximum likelihood parameter estimates can prove more difficult to interpret than the estimates of the parameter distributions provided by the Bayesian approach. For models of decompression sickness, we show that while these two estimation methods are complementary, the credible intervals generated by the Bayesian approach are more naturally suited to quantifying uncertainty in the model parameters.
Mapping malaria risk in Bangladesh using Bayesian geostatistical models.
Reid, Heidi; Haque, Ubydul; Clements, Archie C A; Tatem, Andrew J; Vallely, Andrew; Ahmed, Syed Masud; Islam, Akramul; Haque, Rashidul
2010-10-01
Background malaria-control programs are increasingly dependent on accurate risk maps to effectively guide the allocation of interventions and resources. Advances in model-based geostatistics and geographical information systems (GIS) have enabled researchers to better understand factors affecting malaria transmission and thus, more accurately determine the limits of malaria transmission globally and nationally. Here, we construct Plasmodium falciparum risk maps for Bangladesh for 2007 at a scale enabling the malaria-control bodies to more accurately define the needs of the program. A comprehensive malaria-prevalence survey (N = 9,750 individuals; N = 354 communities) was carried out in 2007 across the regions of Bangladesh known to be endemic for malaria. Data were corrected to a standard age range of 2 to less than 10 years. Bayesian geostatistical logistic regression models with environmental covariates were used to predict P. falciparum prevalence for 2- to 10-year-old children (PfPR(2-10)) across the endemic areas of Bangladesh. The predictions were combined with gridded population data to estimate the number of individuals living in different endemicity classes. Across the endemic areas, the average PfPR(2-10) was 3.8%. Environmental variables selected for prediction were vegetation cover, minimum temperature, and elevation. Model validation statistics revealed that the final Bayesian geostatistical model had good predictive ability. Risk maps generated from the model showed a heterogeneous distribution of PfPR(2-10) ranging from 0.5% to 50%; 3.1 million people were estimated to be living in areas with a PfPR(2-10) greater than 1%. Contemporary GIS and model-based geostatistics can be used to interpolate malaria risk in Bangladesh. Importantly, malaria risk was found to be highly varied across the endemic regions, necessitating the targeting of resources to reduce the burden in these areas.
Bayesian selection of nucleotide substitution models and their site assignments.
Wu, Chieh-Hsi; Suchard, Marc A; Drummond, Alexei J
2013-03-01
Probabilistic inference of a phylogenetic tree from molecular sequence data is predicated on a substitution model describing the relative rates of change between character states along the tree for each site in the multiple sequence alignment. Commonly, one assumes that the substitution model is homogeneous across sites within large partitions of the alignment, assigns these partitions a priori, and then fixes their underlying substitution model to the best-fitting model from a hierarchy of named models. Here, we introduce an automatic model selection and model averaging approach within a Bayesian framework that simultaneously estimates the number of partitions, the assignment of sites to partitions, the substitution model for each partition, and the uncertainty in these selections. This new approach is implemented as an add-on to the BEAST 2 software platform. We find that this approach dramatically improves the fit of the nucleotide substitution model compared with existing approaches, and we show, using a number of example data sets, that as many as nine partitions are required to explain the heterogeneity in nucleotide substitution process across sites in a single gene analysis. In some instances, this improved modeling of the substitution process can have a measurable effect on downstream inference, including the estimated phylogeny, relative divergence times, and effective population size histories.
Average Annual Precipitation (PRISM model) 1961 - 1990
U.S. Geological Survey, Department of the Interior — This map layer shows polygons of average annual precipitation in the contiguous United States, for the climatological period 1961-1990. Parameter-elevation...
Robust Bayesian Regularized Estimation Based on t Regression Model
Directory of Open Access Journals (Sweden)
Zean Li
2015-01-01
Full Text Available The t distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso t regression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat the t distribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesian t regression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.
Measuring the Average Thickness of a Plate Using a Bayesian Method and Free Vibration Data
2011-09-01
form, the model is constructed with the implicit assumption that the corrosion is uniform. A more detailed model that included details of the pitting ...PROCEDURE The test specimen was a 0.76m by 0.60m (30” by 24”, 5:4 aspect ratio), 1.55mm (1/16”) thick 6061 -T6 aluminum plate. The density was...considering corrosion effect.” Marine Struc- tures, 21(4):402 – 419. [3] T. Nakai, H. Matsushita, N. Yamamoto, and H. Arai, 2004. “Effect of pitting
Modelling of JET diagnostics using Bayesian Graphical Models
Energy Technology Data Exchange (ETDEWEB)
Svensson, J. [IPP Greifswald, Greifswald (Germany); Ford, O. [Imperial College, London (United Kingdom); McDonald, D.; Hole, M.; Nessi, G. von; Meakins, A.; Brix, M.; Thomsen, H.; Werner, A.; Sirinelli, A.
2011-07-01
The mapping between physics parameters (such as densities, currents, flows, temperatures etc) defining the plasma 'state' under a given model and the raw observations of each plasma diagnostic will 1) depend on the particular physics model used, 2) is inherently probabilistic, from uncertainties on both observations and instrumental aspects of the mapping, such as calibrations, instrument functions etc. A flexible and principled way of modelling such interconnected probabilistic systems is through so called Bayesian graphical models. Being an amalgam between graph theory and probability theory, Bayesian graphical models can simulate the complex interconnections between physics models and diagnostic observations from multiple heterogeneous diagnostic systems, making it relatively easy to optimally combine the observations from multiple diagnostics for joint inference on parameters of the underlying physics model, which in itself can be represented as part of the graph. At JET about 10 diagnostic systems have to date been modelled in this way, and has lead to a number of new results, including: the reconstruction of the flux surface topology and q-profiles without any specific equilibrium assumption, using information from a number of different diagnostic systems; profile inversions taking into account the uncertainties in the flux surface positions and a substantial increase in accuracy of JET electron density and temperature profiles, including improved pedestal resolution, through the joint analysis of three diagnostic systems. It is believed that the Bayesian graph approach could potentially be utilised for very large sets of diagnostics, providing a generic data analysis framework for nuclear fusion experiments, that would be able to optimally utilize the information from multiple diagnostics simultaneously, and where the explicit graph representation of the connections to underlying physics models could be used for sophisticated model testing. This
Technical note: Bayesian calibration of dynamic ruminant nutrition models.
Reed, K F; Arhonditsis, G B; France, J; Kebreab, E
2016-08-01
Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling.
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Hu, Liangdong; Wang, Limin
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
Bayesian structural equation modeling method for hierarchical model validation
Energy Technology Data Exchange (ETDEWEB)
Jiang Xiaomo [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: xiaomo.jiang@vanderbilt.edu; Mahadevan, Sankaran [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: sankaran.mahadevan@vanderbilt.edu
2009-04-15
A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.
Analysis of Gumbel Model for Software Reliability Using Bayesian Paradigm
Directory of Open Access Journals (Sweden)
Raj Kumar
2012-12-01
Full Text Available In this paper, we have illustrated the suitability of Gumbel Model for software reliability data. The model parameters are estimated using likelihood based inferential procedure: classical as well as Bayesian. The quasi Newton-Raphson algorithm is applied to obtain the maximum likelihood estimates and associated probability intervals. The Bayesian estimates of the parameters of Gumbel model are obtained using Markov Chain Monte Carlo(MCMC simulation method in OpenBUGS(established software for Bayesian analysis using Markov Chain Monte Carlo methods. The R functions are developed to study the statistical properties, model validation and comparison tools of the model and the output analysis of MCMC samples generated from OpenBUGS. Details of applying MCMC to parameter estimation for the Gumbel model are elaborated and a real software reliability data set is considered to illustrate the methods of inference discussed in this paper.
Bayesian Calibration of the Community Land Model using Surrogates
Energy Technology Data Exchange (ETDEWEB)
Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Sargsyan, K.; Swiler, Laura P.
2015-01-01
We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditioned on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural error in CLM under two error models. We find that accurate surrogate models can be created for CLM in most cases. The posterior distributions lead to better prediction than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters’ distributions significantly. The structural error model reveals a correlation time-scale which can potentially be used to identify physical processes that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.
Bayesian calibration of the Community Land Model using surrogates
Energy Technology Data Exchange (ETDEWEB)
Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Swiler, Laura Painton
2014-02-01
We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural error in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.
Estimating Tree Height-Diameter Models with the Bayesian Method
Directory of Open Access Journals (Sweden)
Xiongqing Zhang
2014-01-01
Full Text Available Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS and the maximum likelihood method (ML. The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.
Bayesian Network Models for Local Dependence among Observable Outcome Variables
Almond, Russell G.; Mulder, Joris; Hemat, Lisa A.; Yan, Duanli
2009-01-01
Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task, which may be dependent. This article explores four design patterns for modeling locally dependent observations: (a) no context--ignores dependence among observables; (b) compensatory context--introduces…
Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.
Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa
2017-01-01
TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
A COMPOUND POISSON MODEL FOR LEARNING DISCRETE BAYESIAN NETWORKS
Institute of Scientific and Technical Information of China (English)
Abdelaziz GHRIBI; Afif MASMOUDI
2013-01-01
We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Post-model selection inference and model averaging
Directory of Open Access Journals (Sweden)
Georges Nguefack-Tsague
2011-07-01
Full Text Available Although model selection is routinely used in practice nowadays, little is known about its precise effects on any subsequent inference that is carried out. The same goes for the effects induced by the closely related technique of model averaging. This paper is concerned with the use of the same data first to select a model and then to carry out inference, in particular point estimation and point prediction. The properties of the resulting estimator, called a post-model-selection estimator (PMSE, are hard to derive. Using selection criteria such as hypothesis testing, AIC, BIC, HQ and Cp, we illustrate that, in terms of risk function, no single PMSE dominates the others. The same conclusion holds more generally for any penalised likelihood information criterion. We also compare various model averaging schemes and show that no single one dominates the others in terms of risk function. Since PMSEs can be regarded as a special case of model averaging, with 0-1 random-weights, we propose a connection between the two theories, in the frequentist approach, by taking account of the selection procedure when performing model averaging. We illustrate the point by simulating a simple linear regression model.
Raftery, Adrian E; Kárný, Miroslav; Ettler, Pavel
2010-02-01
We consider the problem of online prediction when it is uncertain what the best prediction model to use is. We develop a method called Dynamic Model Averaging (DMA) in which a state space model for the parameters of each model is combined with a Markov chain model for the correct model. This allows the "correct" model to vary over time. The state space and Markov chain models are both specified in terms of forgetting, leading to a highly parsimonious representation. As a special case, when the model and parameters do not change, DMA is a recursive implementation of standard Bayesian model averaging, which we call recursive model averaging. The method is applied to the problem of predicting the output strip thickness for a cold rolling mill, where the output is measured with a time delay. We found that when only a small number of physically motivated models were considered and one was clearly best, the method quickly converged to the best model, and the cost of model uncertainty was small; indeed DMA performed slightly better than the best physical model. When model uncertainty and the number of models considered were large, our method ensured that the penalty for model uncertainty was small. At the beginning of the process, when control is most difficult, we found that DMA over a large model space led to better predictions than the single best performing physically motivated model. We also applied the method to several simulated examples, and found that it recovered both constant and time-varying regression parameters and model specifications quite well.
Bayesian Estimation of the DINA Model with Gibbs Sampling
Culpepper, Steven Andrew
2015-01-01
A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…
A Bayesian Approach for Analyzing Longitudinal Structural Equation Models
Song, Xin-Yuan; Lu, Zhao-Hua; Hser, Yih-Ing; Lee, Sik-Yum
2011-01-01
This article considers a Bayesian approach for analyzing a longitudinal 2-level nonlinear structural equation model with covariates, and mixed continuous and ordered categorical variables. The first-level model is formulated for measures taken at each time point nested within individuals for investigating their characteristics that are dynamically…
Using Consensus Bayesian Network to Model the Reactive Oxygen Species Regulatory Pathway
Liangdong Hu; Limin Wang
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks...
Forecasting unconventional resource productivity - A spatial Bayesian model
Montgomery, J.; O'sullivan, F.
2015-12-01
Today's low prices mean that unconventional oil and gas development requires ever greater efficiency and better development decision-making. Inter and intra-field variability in well productivity, which is a major contemporary driver of uncertainty regarding resource size and its economics is driven by factors including geological conditions, well and completion design (which companies vary as they seek to optimize their performance), and uncertainty about the nature of fracture propagation. Geological conditions are often not be well understood early on in development campaigns, but nevertheless critical assessments and decisions must be made regarding the value of drilling an area and the placement of wells. In these situations, location provides a reasonable proxy for geology and the "rock quality." We propose a spatial Bayesian model for forecasting acreage quality, which improves decision-making by leveraging available production data and provides a framework for statistically studying the influence of different parameters on well productivity. Our approach consists of subdividing a field into sections and forming prior distributions for productivity in each section based on knowledge about the overall field. Production data from wells is used to update these estimates in a Bayesian fashion, improving model accuracy far more rapidly and with less sensitivity to outliers than a model that simply establishes an "average" productivity in each section. Additionally, forecasts using this model capture the importance of uncertainty—either due to a lack of information or for areas that demonstrate greater geological risk. We demonstrate the forecasting utility of this method using public data and also provide examples of how information from this model can be combined with knowledge about a field's geology or changes in technology to better quantify development risk. This approach represents an important shift in the way that production data is used to guide
Spatial and spatio-temporal bayesian models with R - INLA
Blangiardo, Marta
2015-01-01
Dedication iiiPreface ix1 Introduction 11.1 Why spatial and spatio-temporal statistics? 11.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 21.3 Why INLA? 31.4 Datasets 32 Introduction to 212.1 The language 212.2 objects 222.3 Data and session management 342.4 Packages 352.5 Programming in 362.6 Basic statistical analysis with 393 Introduction to Bayesian Methods 533.1 Bayesian Philosophy 533.2 Basic Probability Elements 573.3 Bayes Theorem 623.4 Prior and Posterior Distributions 643.5 Working with the Posterior Distribution 663.6 Choosing the Prior Distr
Uncertainty Modeling Based on Bayesian Network in Ontology Mapping
Institute of Scientific and Technical Information of China (English)
LI Yuhua; LIU Tao; SUN Xiaolin
2006-01-01
How to deal with uncertainty is crucial in exact concept mapping between ontologies. This paper presents a new framework on modeling uncertainty in ontologies based on bayesian networks (BN). In our approach, ontology Web language (OWL) is extended to add probabilistic markups for attaching probability information, the source and target ontologies (expressed by patulous OWL) are translated into bayesian networks (BNs), the mapping between the two ontologies can be digged out by constructing the conditional probability tables (CPTs) of the BN using a improved algorithm named I-IPFP based on iterative proportional fitting procedure (IPFP). The basic idea of this framework and algorithm are validated by positive results from computer experiments.
Bayesian probabilistic modeling for damage assessment in a bolted frame
Haynes, Colin; Todd, Michael
2012-04-01
This paper presents the development of a Bayesian framework for optimizing the design of a structural health monitoring (SHM) system. Statistical damage detection techniques are applied to a geometrically-complex, three-story structure with bolted joints. A sparse network of PZT sensor-actuators is bonded to the structure, using ultrasonic guided waves in both pulse-echo and pitch-catch modes to inspect the structure. Receiver operating characteristics are used to quantify the performance of multiple features (or detectors). The detection rate of the system is compared across different types and levels of damage. A Bayesian cost model is implemented to determine the best performing network.
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J
2010-12-01
Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies
Bayesian Modelling of fMRI Time Series
DEFF Research Database (Denmark)
Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward
2000-01-01
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte...
Advanced REACH tool: A Bayesian model for occupational exposure assessment
McNally, K.; Warren, N.; Fransman, W.; Entink, R.K.; Schinkel, J.; Van Tongeren, M.; Cherrie, J.W.; Kromhout, H.; Schneider, T.; Tielemans, E.
2014-01-01
This paper describes a Bayesian model for the assessment of inhalation exposures in an occupational setting; the methodology underpins a freely available web-based application for exposure assessment, the Advanced REACH Tool (ART). The ART is a higher tier exposure tool that combines disparate sourc
A Bayesian network approach to coastal storm impact modeling
Jäger, W.S.; Den Heijer, C.; Bolle, A.; Hanea, A.M.
2015-01-01
In this paper we develop a Bayesian network (BN) that relates offshore storm conditions to their accompagnying flood characteristics and damages to residential buildings, following on the trend of integrated flood impact modeling. It is based on data from hydrodynamic storm simulations, information
Bayesian online algorithms for learning in discrete Hidden Markov Models
Alamino, Roberto C.; Caticha, Nestor
2008-01-01
We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.
Research on Bayesian Network Based User's Interest Model
Institute of Scientific and Technical Information of China (English)
ZHANG Weifeng; XU Baowen; CUI Zifeng; XU Lei
2007-01-01
It has very realistic significance for improving the quality of users' accessing information to filter and selectively retrieve the large number of information on the Internet. On the basis of analyzing the existing users' interest models and some basic questions of users' interest (representation, derivation and identification of users' interest), a Bayesian network based users' interest model is given. In this model, the users' interest reduction algorithm based on Markov Blanket model is used to reduce the interest noise, and then users' interested and not interested documents are used to train the Bayesian network. Compared to the simple model, this model has the following advantages like small space requirements, simple reasoning method and high recognition rate. The experiment result shows this model can more appropriately reflect the user's interest, and has higher performance and good usability.
Bayesian estimation of parameters in a regional hydrological model
Directory of Open Access Journals (Sweden)
K. Engeland
2002-01-01
Full Text Available This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1 process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis
Energy Technology Data Exchange (ETDEWEB)
Kim, Joo Yeon; Lee, Seung Hyun; Park, Tai Jin [Korean Association for Radiation Application, Seoul (Korea, Republic of)
2016-06-15
Any real application of Bayesian inference must acknowledge that both prior distribution and likelihood function have only been specified as more or less convenient approximations to whatever the analyzer's true belief might be. If the inferences from the Bayesian analysis are to be trusted, it is important to determine that they are robust to such variations of prior and likelihood as might also be consistent with the analyzer's stated beliefs. The robust Bayesian inference was applied to atmospheric dispersion assessment using Gaussian plume model. The scopes of contaminations were specified as the uncertainties of distribution type and parametric variability. The probabilistic distribution of model parameters was assumed to be contaminated as the symmetric unimodal and unimodal distributions. The distribution of the sector-averaged relative concentrations was then calculated by applying the contaminated priors to the model parameters. The sector-averaged concentrations for stability class were compared by applying the symmetric unimodal and unimodal priors, respectively, as the contaminated one based on the class of ε-contamination. Though ε was assumed as 10%, the medians reflecting the symmetric unimodal priors were nearly approximated within 10% compared with ones reflecting the plausible ones. However, the medians reflecting the unimodal priors were approximated within 20% for a few downwind distances compared with ones reflecting the plausible ones. The robustness has been answered by estimating how the results of the Bayesian inferences are robust to reasonable variations of the plausible priors. From these robust inferences, it is reasonable to apply the symmetric unimodal priors for analyzing the robustness of the Bayesian inferences.
Lu, Dan; Ye, Ming; Meyer, Philip D.; Curtis, Gary P.; Shi, Xiaoqing; Niu, Xu-Feng; Yabusaki, Steve B.
2013-01-01
When conducting model averaging for assessing groundwater conceptual model uncertainty, the averaging weights are often evaluated using model selection criteria such as AIC, AICc, BIC, and KIC (Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, and Kashyap Information Criterion, respectively). However, this method often leads to an unrealistic situation in which the best model receives overwhelmingly large averaging weight (close to 100%), which cannot be justified by available data and knowledge. It was found in this study that this problem was caused by using the covariance matrix, CE, of measurement errors for estimating the negative log likelihood function common to all the model selection criteria. This problem can be resolved by using the covariance matrix, Cek, of total errors (including model errors and measurement errors) to account for the correlation between the total errors. An iterative two-stage method was developed in the context of maximum likelihood inverse modeling to iteratively infer the unknown Cek from the residuals during model calibration. The inferred Cek was then used in the evaluation of model selection criteria and model averaging weights. While this method was limited to serial data using time series techniques in this study, it can be extended to spatial data using geostatistical techniques. The method was first evaluated in a synthetic study and then applied to an experimental study, in which alternative surface complexation models were developed to simulate column experiments of uranium reactive transport. It was found that the total errors of the alternative models were temporally correlated due to the model errors. The iterative two-stage method using Cekresolved the problem that the best model receives 100% model averaging weight, and the resulting model averaging weights were supported by the calibration results and physical understanding of the alternative models. Using Cek
Empirical evaluation of scoring functions for Bayesian network model selection.
Liu, Zhifa; Malone, Brandon; Yuan, Changhe
2012-01-01
In this work, we empirically evaluate the capability of various scoring functions of Bayesian networks for recovering true underlying structures. Similar investigations have been carried out before, but they typically relied on approximate learning algorithms to learn the network structures. The suboptimal structures found by the approximation methods have unknown quality and may affect the reliability of their conclusions. Our study uses an optimal algorithm to learn Bayesian network structures from datasets generated from a set of gold standard Bayesian networks. Because all optimal algorithms always learn equivalent networks, this ensures that only the choice of scoring function affects the learned networks. Another shortcoming of the previous studies stems from their use of random synthetic networks as test cases. There is no guarantee that these networks reflect real-world data. We use real-world data to generate our gold-standard structures, so our experimental design more closely approximates real-world situations. A major finding of our study suggests that, in contrast to results reported by several prior works, the Minimum Description Length (MDL) (or equivalently, Bayesian information criterion (BIC)) consistently outperforms other scoring functions such as Akaike's information criterion (AIC), Bayesian Dirichlet equivalence score (BDeu), and factorized normalized maximum likelihood (fNML) in recovering the underlying Bayesian network structures. We believe this finding is a result of using both datasets generated from real-world applications rather than from random processes used in previous studies and learning algorithms to select high-scoring structures rather than selecting random models. Other findings of our study support existing work, e.g., large sample sizes result in learning structures closer to the true underlying structure; the BDeu score is sensitive to the parameter settings; and the fNML performs pretty well on small datasets. We also
FACIAL LANDMARKING LOCALIZATION FOR EMOTION RECOGNITION USING BAYESIAN SHAPE MODELS
Directory of Open Access Journals (Sweden)
Hernan F. Garcia
2013-02-01
Full Text Available This work presents a framework for emotion recognition, based in facial expression analysis using Bayesian Shape Models (BSM for facial landmarking localization. The Facial Action Coding System (FACS compliant facial feature tracking based on Bayesian Shape Model. The BSM estimate the parameters of the model with an implementation of the EM algorithm. We describe the characterization methodology from parametric model and evaluated the accuracy for feature detection and estimation of the parameters associated with facial expressions, analyzing its robustness in pose and local variations. Then, a methodology for emotion characterization is introduced to perform the recognition. The experimental results show that the proposed model can effectively detect the different facial expressions. Outperforming conventional approaches for emotion recognition obtaining high performance results in the estimation of emotion present in a determined subject. The model used and characterization methodology showed efficient to detect the emotion type in 95.6% of the cases.
Model averaging for semiparametric additive partial linear models
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
To improve the prediction accuracy of semiparametric additive partial linear models(APLM) and the coverage probability of confidence intervals of the parameters of interest,we explore a focused information criterion for model selection among ALPM after we estimate the nonparametric functions by the polynomial spline smoothing,and introduce a general model average estimator.The major advantage of the proposed procedures is that iterative backfitting implementation is avoided,which thus results in gains in computational simplicity.The resulting estimators are shown to be asymptotically normal.A simulation study and a real data analysis are presented for illustrations.
A note on moving average models for Gaussian random fields
DEFF Research Database (Denmark)
Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.
The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy...
A Bayesian ensemble of sensitivity measures for severe accident modeling
Energy Technology Data Exchange (ETDEWEB)
Hoseyni, Seyed Mohsen [Department of Basic Sciences, East Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of); Di Maio, Francesco, E-mail: francesco.dimaio@polimi.it [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Vagnoli, Matteo [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Zio, Enrico [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Chair on System Science and Energetic Challenge, Fondation EDF – Electricite de France Ecole Centrale, Paris, and Supelec, Paris (France); Pourgol-Mohammad, Mohammad [Department of Mechanical Engineering, Sahand University of Technology, Tabriz (Iran, Islamic Republic of)
2015-12-15
Highlights: • We propose a sensitivity analysis (SA) method based on a Bayesian updating scheme. • The Bayesian updating schemes adjourns an ensemble of sensitivity measures. • Bootstrap replicates of a severe accident code output are fed to the Bayesian scheme. • The MELCOR code simulates the fission products release of LOFT LP-FP-2 experiment. • Results are compared with those of traditional SA methods. - Abstract: In this work, a sensitivity analysis framework is presented to identify the relevant input variables of a severe accident code, based on an incremental Bayesian ensemble updating method. The proposed methodology entails: (i) the propagation of the uncertainty in the input variables through the severe accident code; (ii) the collection of bootstrap replicates of the input and output of limited number of simulations for building a set of finite mixture models (FMMs) for approximating the probability density function (pdf) of the severe accident code output of the replicates; (iii) for each FMM, the calculation of an ensemble of sensitivity measures (i.e., input saliency, Hellinger distance and Kullback–Leibler divergence) and the updating when a new piece of evidence arrives, by a Bayesian scheme, based on the Bradley–Terry model for ranking the most relevant input model variables. An application is given with respect to a limited number of simulations of a MELCOR severe accident model describing the fission products release in the LP-FP-2 experiment of the loss of fluid test (LOFT) facility, which is a scaled-down facility of a pressurized water reactor (PWR).
Bayesian modeling growth curves for quail assuming skewness in errors
Directory of Open Access Journals (Sweden)
Robson Marcelo Rossi
2014-06-01
Full Text Available Bayesian modeling growth curves for quail assuming skewness in errors - To assume normal distributions in the data analysis is common in different areas of the knowledge. However we can make use of the other distributions that are capable to model the skewness parameter in the situations that is needed to model data with tails heavier than the normal. This article intend to present alternatives to the assumption of the normality in the errors, adding asymmetric distributions. A Bayesian approach is proposed to fit nonlinear models when the errors are not normal, thus, the distributions t, skew-normal and skew-t are adopted. The methodology is intended to apply to different growth curves to the quail body weights. It was found that the Gompertz model assuming skew-normal errors and skew-t errors, respectively for male and female, were the best fitted to the data.
Quasi-Bayesian software reliability model with small samples
Institute of Scientific and Technical Information of China (English)
ZHANG Jin; TU Jun-xiang; CHEN Zhuo-ning; YAN Xiao-guang
2009-01-01
In traditional Bayesian software reliability models,it was assume that all probabilities are precise.In practical applications the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information of experts' judgments on sparse statistical data.In this paper,a quasi-Bayesian software reliability model using interval-valued probabilities to clearly quantify experts' prior beliefs on possible intervals of the parameters of the probability distributions is presented.The model integrates experts' judgments with statistical data to obtain more convincible assessments of software reliability with small samples.For some actual data sets,the presented model yields better predictions than the Jelinski-Moranda (JM) model using maximum likelihood (ML).
A Bayesian Alternative for Multi-objective Ecohydrological Model Specification
Tang, Y.; Marshall, L. A.; Sharma, A.; Ajami, H.
2015-12-01
Process-based ecohydrological models combine the study of hydrological, physical, biogeochemical and ecological processes of the catchments, which are usually more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov Chain Monte Carlo (MCMC) techniques. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological framework. In our study, a formal Bayesian approach is implemented in an ecohydrological model which combines a hydrological model (HyMOD) and a dynamic vegetation model (DVM). Simulations focused on one objective likelihood (Streamflow/LAI) and multi-objective likelihoods (Streamflow and LAI) with different weights are compared. Uniform, weakly informative and strongly informative prior distributions are used in different simulations. The Kullback-leibler divergence (KLD) is used to measure the dis(similarity) between different priors and corresponding posterior distributions to examine the parameter sensitivity. Results show that different prior distributions can strongly influence posterior distributions for parameters, especially when the available data is limited or parameters are insensitive to the available data. We demonstrate differences in optimized parameters and uncertainty limits in different cases based on multi-objective likelihoods vs. single objective likelihoods. We also demonstrate the importance of appropriately defining the weights of objectives in multi-objective calibration according to different data types.
Spatial Bayesian hierarchical modelling of extreme sea states
Clancy, Colm; O'Sullivan, John; Sweeney, Conor; Dias, Frédéric; Parnell, Andrew C.
2016-11-01
A Bayesian hierarchical framework is used to model extreme sea states, incorporating a latent spatial process to more effectively capture the spatial variation of the extremes. The model is applied to a 34-year hindcast of significant wave height off the west coast of Ireland. The generalised Pareto distribution is fitted to declustered peaks over a threshold given by the 99.8th percentile of the data. Return levels of significant wave height are computed and compared against those from a model based on the commonly-used maximum likelihood inference method. The Bayesian spatial model produces smoother maps of return levels. Furthermore, this approach greatly reduces the uncertainty in the estimates, thus providing information on extremes which is more useful for practical applications.
[A medical image semantic modeling based on hierarchical Bayesian networks].
Lin, Chunyi; Ma, Lihong; Yin, Junxun; Chen, Jianyu
2009-04-01
A semantic modeling approach for medical image semantic retrieval based on hierarchical Bayesian networks was proposed, in allusion to characters of medical images. It used GMM (Gaussian mixture models) to map low-level image features into object semantics with probabilities, then it captured high-level semantics through fusing these object semantics using a Bayesian network, so that it built a multi-layer medical image semantic model, aiming to enable automatic image annotation and semantic retrieval by using various keywords at different semantic levels. As for the validity of this method, we have built a multi-level semantic model from a small set of astrocytoma MRI (magnetic resonance imaging) samples, in order to extract semantics of astrocytoma in malignant degree. Experiment results show that this is a superior approach.
Quarterly Bayesian DSGE Model of Pakistan Economy with Informality
2013-01-01
In this paper we use the Bayesian methodology to estimate the structural and shocks‟ parameters of the DSGE model in Ahmad et al. (2012). This model includes formal and informal firms both at intermediate and final goods production levels. Households derive utility from leisure, real money balances and consumption. Each household is treated as a unit of labor which is a composite of formal (skilled) and informal (unskilled) labor. The formal (skilled) labor is further divided into types “r” a...
Energy Technology Data Exchange (ETDEWEB)
Ajami, N K; Duan, Q; Sorooshian, S
2006-05-05
This paper presents a new technique--Integrated Bayesian Uncertainty Estimator (IBUNE) to account for the major uncertainties of hydrologic rainfall-runoff predictions explicitly. The uncertainties from the input (forcing) data--mainly the precipitation observations and from the model parameters are reduced through a Monte Carlo Markov Chain (MCMC) scheme named Shuffled Complex Evolution Metropolis (SCEM) algorithm which has been extended to include a precipitation error model. Afterwards, the Bayesian Model Averaging (BMA) scheme is employed to further improve the prediction skill and uncertainty estimation using multiple model output. A series of case studies using three rainfall-runoff models to predict the streamflow in the Leaf River basin, Mississippi are used to examine the necessity and usefulness of this technique. The results suggests that ignoring either input forcings error or model structural uncertainty will lead to unrealistic model simulations and their associated uncertainty bounds which does not consistently capture and represent the real-world behavior of the watershed.
Arsenault, Richard; Gatien, Philippe; Renaud, Benoit; Brissette, François; Martel, Jean-Luc
2015-10-01
This study aims to test whether a weighted combination of several hydrological models can simulate flows more accurately than the models taken individually. In addition, the project attempts to identify the most efficient model averaging method and the optimal number of models to include in the weighting scheme. In order to address the first objective, streamflow was simulated using four lumped hydrological models (HSAMI, HMETS, MOHYSE and GR4J-6), each of which were calibrated with three different objective functions on 429 watersheds. The resulting 12 hydrographs (4 models × 3 metrics) were weighted and combined with the help of 9 averaging methods which are the simple arithmetic mean (SAM), Akaike information criterion (AICA), Bates-Granger (BGA), Bayes information criterion (BICA), Bayesian model averaging (BMA), Granger-Ramanathan average variant A, B and C (GRA, GRB and GRC) and the average by SCE-UA optimization (SCA). The same weights were then applied to the hydrographs in validation mode, and the Nash-Sutcliffe Efficiency metric was measured between the averaged and observed hydrographs. Statistical analyses were performed to compare the accuracy of weighted methods to that of individual models. A Kruskal-Wallis test and a multi-objective optimization algorithm were then used to identify the most efficient weighted method and the optimal number of models to integrate. Results suggest that the GRA, GRB, GRC and SCA weighted methods perform better than the individual members. Model averaging from these four methods were superior to the best of the individual members in 76% of the cases. Optimal combinations on all watersheds included at least one of each of the four hydrological models. None of the optimal combinations included all members of the ensemble of 12 hydrographs. The Granger-Ramanathan average variant C (GRC) is recommended as the best compromise between accuracy, speed of execution, and simplicity.
Nonparametric Bayesian inference of the microcanonical stochastic block model
Peixoto, Tiago P
2016-01-01
A principled approach to characterize the hidden modular structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: 1. Deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, that not only remove limitations that seriously degrade the inference on large networks, but also reveal s...
Application of a predictive Bayesian model to environmental accounting.
Anex, R P; Englehardt, J D
2001-03-30
Environmental accounting techniques are intended to capture important environmental costs and benefits that are often overlooked in standard accounting practices. Environmental accounting methods themselves often ignore or inadequately represent large but highly uncertain environmental costs and costs conditioned by specific prior events. Use of a predictive Bayesian model is demonstrated for the assessment of such highly uncertain environmental and contingent costs. The predictive Bayesian approach presented generates probability distributions for the quantity of interest (rather than parameters thereof). A spreadsheet implementation of a previously proposed predictive Bayesian model, extended to represent contingent costs, is described and used to evaluate whether a firm should undertake an accelerated phase-out of its PCB containing transformers. Variability and uncertainty (due to lack of information) in transformer accident frequency and severity are assessed simultaneously using a combination of historical accident data, engineering model-based cost estimates, and subjective judgement. Model results are compared using several different risk measures. Use of the model for incorporation of environmental risk management into a company's overall risk management strategy is discussed.
Application of the Bayesian dynamic survival model in medicine.
He, Jianghua; McGee, Daniel L; Niu, Xufeng
2010-02-10
The Bayesian dynamic survival model (BDSM), a time-varying coefficient survival model from the Bayesian prospective, was proposed in early 1990s but has not been widely used or discussed. In this paper, we describe the model structure of the BDSM and introduce two estimation approaches for BDSMs: the Markov Chain Monte Carlo (MCMC) approach and the linear Bayesian (LB) method. The MCMC approach estimates model parameters through sampling and is computationally intensive. With the newly developed geoadditive survival models and software BayesX, the BDSM is available for general applications. The LB approach is easier in terms of computations but it requires the prespecification of some unknown smoothing parameters. In a simulation study, we use the LB approach to show the effects of smoothing parameters on the performance of the BDSM and propose an ad hoc method for identifying appropriate values for those parameters. We also demonstrate the performance of the MCMC approach compared with the LB approach and a penalized partial likelihood method available in software R packages. A gastric cancer trial is utilized to illustrate the application of the BDSM.
Model Averaging Software for Dichotomous Dose Response Risk Estimation
Directory of Open Access Journals (Sweden)
Matthew W. Wheeler
2008-02-01
Full Text Available Model averaging has been shown to be a useful method for incorporating model uncertainty in quantitative risk estimation. In certain circumstances this technique is computationally complex, requiring sophisticated software to carry out the computation. We introduce software that implements model averaging for risk assessment based upon dichotomous dose-response data. This software, which we call Model Averaging for Dichotomous Response Benchmark Dose (MADr-BMD, ﬁts the quantal response models, which are also used in the US Environmental Protection Agency benchmark dose software suite, and generates a model-averaged dose response model to generate benchmark dose and benchmark dose lower bound estimates. The software fulﬁlls a need for risk assessors, allowing them to go beyond one single model in their risk assessments based on quantal data by focusing on a set of models that describes the experimental data.
The Optimal Selection for Restricted Linear Models with Average Estimator
Directory of Open Access Journals (Sweden)
Qichang Xie
2014-01-01
Full Text Available The essential task of risk investment is to select an optimal tracking portfolio among various portfolios. Statistically, this process can be achieved by choosing an optimal restricted linear model. This paper develops a statistical procedure to do this, based on selecting appropriate weights for averaging approximately restricted models. The method of weighted average least squares is adopted to estimate the approximately restricted models under dependent error setting. The optimal weights are selected by minimizing a k-class generalized information criterion (k-GIC, which is an estimate of the average squared error from the model average fit. This model selection procedure is shown to be asymptotically optimal in the sense of obtaining the lowest possible average squared error. Monte Carlo simulations illustrate that the suggested method has comparable efficiency to some alternative model selection techniques.
Introduction to Hierarchical Bayesian Modeling for Ecological Data
Parent, Eric
2012-01-01
Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts a
Bayesian Age-Period-Cohort Modeling and Prediction - BAMP
Directory of Open Access Journals (Sweden)
Volker J. Schmid
2007-10-01
Full Text Available The software package BAMP provides a method of analyzing incidence or mortality data on the Lexis diagram, using a Bayesian version of an age-period-cohort model. A hierarchical model is assumed with a binomial model in the first-stage. As smoothing priors for the age, period and cohort parameters random walks of first and second order, with and without an additional unstructured component are available. Unstructured heterogeneity can also be included in the model. In order to evaluate the model fit, posterior deviance, DIC and predictive deviances are computed. By projecting the random walk prior into the future, future death rates can be predicted.
Delineating the Average Rate of Change in Longitudinal Models
Kelley, Ken; Maxwell, Scott E.
2008-01-01
The average rate of change is a concept that has been misunderstood in the literature. This article attempts to clarify the concept and show unequivocally the mathematical definition and meaning of the average rate of change in longitudinal models. The slope from the straight-line change model has at times been interpreted as if it were always the…
Bayesian hierarchical modelling of weak lensing - the golden goal
Heavens, Alan; Jaffe, Andrew; Hoffmann, Till; Kiessling, Alina; Wandelt, Benjamin
2016-01-01
To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.
Averaging and exact perturbations in LTB dust models
Sussman, Roberto A
2012-01-01
We introduce a scalar weighed average ("q-average") acting on concentric comoving domains in spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. The resulting averaging formalism allows for an elegant coordinate independent dynamical study of the models, providing as well a valuable theoretical insight on the properties of scalar averaging in inhomogeneous spacetimes. The q-averages of those covariant scalars common to FLRW models (the "q-scalars") identically satisfy FLRW evolution laws and determine for every domain a unique FLRW background state. All curvature and kinematic proper tensors and their invariant contractions are expressible in terms of the q-scalars and their linear and quadratic local fluctuations, which convey the effects of inhomogeneity through the ratio of Weyl to Ricci curvature invariants and the magnitude of radial gradients. We define also non-local fluctuations associated with the intuitive notion of a "contrast" with respect to FLRW reference averaged values assigned to a...
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
year. Our goal is to develop an ensemble ocean forecast methodology, using Bayesian Hierarchical Modelling (BHM) tools . The ocean ensemble forecast...from above); i.e. we assume Ut ~ Z Λt1/2. WORK COMPLETED The prototype MFS-Wind-BHM was designed and implemented based on stochastic...coding refinements we implemented on the prototype surface wind BHM. A DWF event in February 2005, in the Gulf of Lions, was identified for reforecast
spTimer: Spatio-Temporal Bayesian Modeling Using R
Directory of Open Access Journals (Sweden)
Khandoker Shuvo Bakar
2015-02-01
Full Text Available Hierarchical Bayesian modeling of large point-referenced space-time data is increasingly becoming feasible in many environmental applications due to the recent advances in both statistical methodology and computation power. Implementation of these methods using the Markov chain Monte Carlo (MCMC computational techniques, however, requires development of problem-specific and user-written computer code, possibly in a low-level language. This programming requirement is hindering the widespread use of the Bayesian model-based methods among practitioners and, hence there is an urgent need to develop high-level software that can analyze large data sets rich in both space and time. This paper develops the package spTimer for hierarchical Bayesian modeling of stylized environmental space-time monitoring data as a contributed software package in the R language that is fast becoming a very popular statistical computing platform. The package is able to fit, spatially and temporally predict large amounts of space-time data using three recently developed Bayesian models. The user is given control over many options regarding covariance function selection, distance calculation, prior selection and tuning of the implemented MCMC algorithms, although suitable defaults are provided. The package has many other attractive features such as on the fly transformations and an ability to spatially predict temporally aggregated summaries on the original scale, which saves the problem of storage when using MCMC methods for large datasets. A simulation example, with more than a million observations, and a real life data example are used to validate the underlying code and to illustrate the software capabilities.
Broderick, Ciaran; Matthews, Tom; Wilby, Robert L.; Bastola, Satish; Murphy, Conor
2016-10-01
Understanding hydrological model predictive capabilities under contrasting climate conditions enables more robust decision making. Using Differential Split Sample Testing (DSST), we analyze the performance of six hydrological models for 37 Irish catchments under climate conditions unlike those used for model training. Additionally, we consider four ensemble averaging techniques when examining interperiod transferability. DSST is conducted using 2/3 year noncontinuous blocks of (i) the wettest/driest years on record based on precipitation totals and (ii) years with a more/less pronounced seasonal precipitation regime. Model transferability between contrasting regimes was found to vary depending on the testing scenario, catchment, and evaluation criteria considered. As expected, the ensemble average outperformed most individual ensemble members. However, averaging techniques differed considerably in the number of times they surpassed the best individual model member. Bayesian Model Averaging (BMA) and the Granger-Ramanathan Averaging (GRA) method were found to outperform the simple arithmetic mean (SAM) and Akaike Information Criteria Averaging (AICA). Here GRA performed better than the best individual model in 51%-86% of cases (according to the Nash-Sutcliffe criterion). When assessing model predictive skill under climate change conditions we recommend (i) setting up DSST to select the best available analogues of expected annual mean and seasonal climate conditions; (ii) applying multiple performance criteria; (iii) testing transferability using a diverse set of catchments; and (iv) using a multimodel ensemble in conjunction with an appropriate averaging technique. Given the computational efficiency and performance of GRA relative to BMA, the former is recommended as the preferred ensemble averaging technique for climate assessment.
Bayesian estimation of the network autocorrelation model
Dittrich, D.; Leenders, R.T.A.J.; Mulder, J.
2017-01-01
The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of
Bayesian prediction of placebo analgesia in an instrumental learning model
Jung, Won-Mo; Lee, Ye-Seul; Wallraven, Christian; Chae, Younbyoung
2017-01-01
Placebo analgesia can be primarily explained by the Pavlovian conditioning paradigm in which a passively applied cue becomes associated with less pain. In contrast, instrumental conditioning employs an active paradigm that might be more similar to clinical settings. In the present study, an instrumental conditioning paradigm involving a modified trust game in a simulated clinical situation was used to induce placebo analgesia. Additionally, Bayesian modeling was applied to predict the placebo responses of individuals based on their choices. Twenty-four participants engaged in a medical trust game in which decisions to receive treatment from either a doctor (more effective with high cost) or a pharmacy (less effective with low cost) were made after receiving a reference pain stimulus. In the conditioning session, the participants received lower levels of pain following both choices, while high pain stimuli were administered in the test session even after making the decision. The choice-dependent pain in the conditioning session was modulated in terms of both intensity and uncertainty. Participants reported significantly less pain when they chose the doctor or the pharmacy for treatment compared to the control trials. The predicted pain ratings based on Bayesian modeling showed significant correlations with the actual reports from participants for both of the choice categories. The instrumental conditioning paradigm allowed for the active choice of optional cues and was able to induce the placebo analgesia effect. Additionally, Bayesian modeling successfully predicted pain ratings in a simulated clinical situation that fits well with placebo analgesia induced by instrumental conditioning. PMID:28225816
Characterizing economic trends by Bayesian stochastic model specification search
DEFF Research Database (Denmark)
Grassi, Stefano; Proietti, Tommaso
We extend a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. In particular, we focus on autoregressive models with possibly time-varying intercept and slope and decide...... on whether their parameters are fixed or evolutive. Stochastic model specification is carried out to discriminate two alternative hypotheses concerning the generation of trends: the trend-stationary hypothesis, on the one hand, for which the trend is a deterministic function of time and the short run......, estimated by a suitable Gibbs sampling scheme, provides useful insight on quasi-integrated nature of the specifications selected....
AIC, BIC, Bayesian evidence against the interacting dark energy model
Energy Technology Data Exchange (ETDEWEB)
Szydlowski, Marek [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Krawiec, Adam [Jagiellonian University, Institute of Economics, Finance and Management, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Kurek, Aleksandra [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Kamionka, Michal [University of Wroclaw, Astronomical Institute, Wroclaw (Poland)
2015-01-01
Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative - the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock- Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam's razor we are inclined to reject this model. (orig.)
AIC, BIC, Bayesian evidence against the interacting dark energy model
Energy Technology Data Exchange (ETDEWEB)
Szydłowski, Marek, E-mail: marek.szydlowski@uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Krawiec, Adam, E-mail: adam.krawiec@uj.edu.pl [Institute of Economics, Finance and Management, Jagiellonian University, Łojasiewicza 4, 30-348, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Kurek, Aleksandra, E-mail: alex@oa.uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Kamionka, Michał, E-mail: kamionka@astro.uni.wroc.pl [Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-622, Wrocław (Poland)
2015-01-14
Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative—the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam’s principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock–Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam’s razor we are inclined to reject this model.
A Bayesian Nonparametric Meta-Analysis Model
Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G.
2015-01-01
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall…
Dissecting magnetar variability with Bayesian hierarchical models
Huppenkothen, D; Hogg, D W; Murray, I; Frean, M; Elenbaas, C; Watts, A L; Levin, Y; van der Horst, A J; Kouveliotou, C
2015-01-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behaviour, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favoured models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture afte...
Bayesian geostatistical modeling of leishmaniasis incidence in Brazil.
Directory of Open Access Journals (Sweden)
Dimitrios-Alexios Karagiannis-Voules
Full Text Available BACKGROUND: Leishmaniasis is endemic in 98 countries with an estimated 350 million people at risk and approximately 2 million cases annually. Brazil is one of the most severely affected countries. METHODOLOGY: We applied Bayesian geostatistical negative binomial models to analyze reported incidence data of cutaneous and visceral leishmaniasis in Brazil covering a 10-year period (2001-2010. Particular emphasis was placed on spatial and temporal patterns. The models were fitted using integrated nested Laplace approximations to perform fast approximate Bayesian inference. Bayesian variable selection was employed to determine the most important climatic, environmental, and socioeconomic predictors of cutaneous and visceral leishmaniasis. PRINCIPAL FINDINGS: For both types of leishmaniasis, precipitation and socioeconomic proxies were identified as important risk factors. The predicted number of cases in 2010 were 30,189 (standard deviation [SD]: 7,676 for cutaneous leishmaniasis and 4,889 (SD: 288 for visceral leishmaniasis. Our risk maps predicted the highest numbers of infected people in the states of Minas Gerais and Pará for visceral and cutaneous leishmaniasis, respectively. CONCLUSIONS/SIGNIFICANCE: Our spatially explicit, high-resolution incidence maps identified priority areas where leishmaniasis control efforts should be targeted with the ultimate goal to reduce disease incidence.
Bayesian comparisons of codon substitution models.
Rodrigue, Nicolas; Lartillot, Nicolas; Philippe, Hervé
2008-11-01
In 1994, Muse and Gaut (MG) and Goldman and Yang (GY) proposed evolutionary models that recognize the coding structure of the nucleotide sequences under study, by defining a Markovian substitution process with a state space consisting of the 61 sense codons (assuming the universal genetic code). Several variations and extensions to their models have since been proposed, but no general and flexible framework for contrasting the relative performance of alternative approaches has yet been applied. Here, we compute Bayes factors to evaluate the relative merit of several MG and GY styles of codon substitution models, including recent extensions acknowledging heterogeneous nonsynonymous rates across sites, as well as selective effects inducing uneven amino acid or codon preferences. Our results on three real data sets support a logical model construction following the MG formulation, allowing for a flexible account of global amino acid or codon preferences, while maintaining distinct parameters governing overall nucleotide propensities. Through posterior predictive checks, we highlight the importance of such a parameterization. Altogether, the framework presented here suggests a broad modeling project in the MG style, stressing the importance of combining and contrasting available model formulations and grounding developments in a sound probabilistic paradigm.
Probe Error Modeling Research Based on Bayesian Network
Institute of Scientific and Technical Information of China (English)
Wu Huaiqiang; Xing Zilong; Zhang Jian; Yan Yan
2015-01-01
Probe calibration is carried out under specific conditions; most of the error caused by the change of speed parameter has not been corrected. In order to reduce the measuring error influence on measurement accuracy, this article analyzes the relationship between speed parameter and probe error, and use Bayesian network to establish the model of probe error. Model takes account of prior knowledge and sample data, with the updating of data, which can reflect the change of the errors of the probe and constantly revised modeling results.
A Bayesian Network View on Nested Effects Models
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Fröhlich Holger
2009-01-01
Full Text Available Nested effects models (NEMs are a class of probabilistic models that were designed to reconstruct a hidden signalling structure from a large set of observable effects caused by active interventions into the signalling pathway. We give a more flexible formulation of NEMs in the language of Bayesian networks. Our framework constitutes a natural generalization of the original NEM model, since it explicitly states the assumptions that are tacitly underlying the original version. Our approach gives rise to new learning methods for NEMs, which have been implemented in the /Bioconductor package nem. We validate these methods in a simulation study and apply them to a synthetic lethality dataset in yeast.
Bayesian inference and model comparison for metallic fatigue data
Babuška, Ivo
2016-02-23
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios.
Bayesian Thurstonian models for ranking data using JAGS.
Johnson, Timothy R; Kuhn, Kristine M
2013-09-01
A Thurstonian model for ranking data assumes that observed rankings are consistent with those of a set of underlying continuous variables. This model is appealing since it renders ranking data amenable to familiar models for continuous response variables-namely, linear regression models. To date, however, the use of Thurstonian models for ranking data has been very rare in practice. One reason for this may be that inferences based on these models require specialized technical methods. These methods have been developed to address computational challenges involved in these models but are not easy to implement without considerable technical expertise and are not widely available in software packages. To address this limitation, we show that Bayesian Thurstonian models for ranking data can be very easily implemented with the JAGS software package. We provide JAGS model files for Thurstonian ranking models for general use, discuss their implementation, and illustrate their use in analyses.
A Bayesian Model for Discovering Typological Implications
Daumé, Hal
2009-01-01
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such implications are typically discovered by painstaking hand analysis over a small sample of languages. We propose a computational model for assisting at this process. Our model is able to discover both well-known implications as well as some novel implications that deserve further study. Moreover, through a careful application of hierarchical analysis, we are able to cope with the well-known sampling problem: languages are not independent.
Predicting coastal cliff erosion using a Bayesian probabilistic model
Hapke, C.; Plant, N.
2010-01-01
Regional coastal cliff retreat is difficult to model due to the episodic nature of failures and the along-shore variability of retreat events. There is a growing demand, however, for predictive models that can be used to forecast areas vulnerable to coastal erosion hazards. Increasingly, probabilistic models are being employed that require data sets of high temporal density to define the joint probability density function that relates forcing variables (e.g. wave conditions) and initial conditions (e.g. cliff geometry) to erosion events. In this study we use a multi-parameter Bayesian network to investigate correlations between key variables that control and influence variations in cliff retreat processes. The network uses Bayesian statistical methods to estimate event probabilities using existing observations. Within this framework, we forecast the spatial distribution of cliff retreat along two stretches of cliffed coast in Southern California. The input parameters are the height and slope of the cliff, a descriptor of material strength based on the dominant cliff-forming lithology, and the long-term cliff erosion rate that represents prior behavior. The model is forced using predicted wave impact hours. Results demonstrate that the Bayesian approach is well-suited to the forward modeling of coastal cliff retreat, with the correct outcomes forecast in 70-90% of the modeled transects. The model also performs well in identifying specific locations of high cliff erosion, thus providing a foundation for hazard mapping. This approach can be employed to predict cliff erosion at time-scales ranging from storm events to the impacts of sea-level rise at the century-scale. ?? 2010.
DPpackage: Bayesian Semi- and Nonparametric Modeling in R
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Alejandro Jara
2011-04-01
Full Text Available Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian nonparametric and semiparametric models in R, DPpackage. Currently, DPpackage includes models for marginal and conditional density estimation, receiver operating characteristic curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison and for eliciting the precision parameter of the Dirichlet process prior, and a general purpose Metropolis sampling algorithm. To maximize computational efficiency, the actual sampling for each model is carried out using compiled C, C++ or Fortran code.
Skilloscopy: Bayesian modeling of decision makers' skill
Di Fatta, Giuseppe; Haworth, Guy
2013-01-01
This paper proposes and demonstrates an approach, Skilloscopy, to the assessment of decision makers. In an increasingly sophisticated, connected and information-rich world, decision making is becoming both more important and more difficult. At the same time, modelling decision-making on computers is becoming more feasible and of interest, partly because the information-input to those decisions is increasingly on record. The aims of Skilloscopy are to rate and rank decision makers in a d...
Bayesian hierarchical modeling for detecting safety signals in clinical trials.
Xia, H Amy; Ma, Haijun; Carlin, Bradley P
2011-09-01
Detection of safety signals from clinical trial adverse event data is critical in drug development, but carries a challenging statistical multiplicity problem. Bayesian hierarchical mixture modeling is appealing for its ability to borrow strength across subgroups in the data, as well as moderate extreme findings most likely due merely to chance. We implement such a model for subject incidence (Berry and Berry, 2004 ) using a binomial likelihood, and extend it to subject-year adjusted incidence rate estimation under a Poisson likelihood. We use simulation to choose a signal detection threshold, and illustrate some effective graphics for displaying the flagged signals.
Bayesian parameter estimation for nonlinear modelling of biological pathways
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Ghasemi Omid
2011-12-01
Full Text Available Abstract Background The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. Results We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC method. We applied this approach to the biological pathways involved in the left ventricle (LV response to myocardial infarction (MI and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly
Study of TEC fluctuation via stochastic models and Bayesian inversion
Bires, A.; Roininen, L.; Damtie, B.; Nigussie, M.; Vanhamäki, H.
2016-11-01
We propose stochastic processes to be used to model the total electron content (TEC) observation. Based on this, we model the rate of change of TEC (ROT) variation during ionospheric quiet conditions with stationary processes. During ionospheric disturbed conditions, for example, when irregularity in ionospheric electron density distribution occurs, stationarity assumption over long time periods is no longer valid. In these cases, we make the parameter estimation for short time scales, during which we can assume stationarity. We show the relationship between the new method and commonly used TEC characterization parameters ROT and the ROT Index (ROTI). We construct our parametric model within the framework of Bayesian statistical inverse problems and hence give the solution as an a posteriori probability distribution. Bayesian framework allows us to model measurement errors systematically. Similarly, we mitigate variation of TEC due to factors which are not of ionospheric origin, like due to the motion of satellites relative to the receiver, by incorporating a priori knowledge in the Bayesian model. In practical computations, we draw the so-called maximum a posteriori estimates, which are our ROT and ROTI estimates, from the posterior distribution. Because the algorithm allows to estimate ROTI at each observation time, the estimator does not depend on the period of time for ROTI computation. We verify the method by analyzing TEC data recorded by GPS receiver located in Ethiopia (11.6°N, 37.4°E). The results indicate that the TEC fluctuations caused by the ionospheric irregularity can be effectively detected and quantified from the estimated ROT and ROTI values.
A study of finite mixture model: Bayesian approach on financial time series data
Phoong, Seuk-Yen; Ismail, Mohd Tahir
2014-07-01
Recently, statistician have emphasized on the fitting finite mixture model by using Bayesian method. Finite mixture model is a mixture of distributions in modeling a statistical distribution meanwhile Bayesian method is a statistical method that use to fit the mixture model. Bayesian method is being used widely because it has asymptotic properties which provide remarkable result. In addition, Bayesian method also shows consistency characteristic which means the parameter estimates are close to the predictive distributions. In the present paper, the number of components for mixture model is studied by using Bayesian Information Criterion. Identify the number of component is important because it may lead to an invalid result. Later, the Bayesian method is utilized to fit the k-component mixture model in order to explore the relationship between rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia. Lastly, the results showed that there is a negative effect among rubber price and stock market price for all selected countries.
A Bayesian subgroup analysis using collections of ANOVA models.
Liu, Jinzhong; Sivaganesan, Siva; Laud, Purushottam W; Müller, Peter
2017-03-20
We develop a Bayesian approach to subgroup analysis using ANOVA models with multiple covariates, extending an earlier work. We assume a two-arm clinical trial with normally distributed response variable. We also assume that the covariates for subgroup finding are categorical and are a priori specified, and parsimonious easy-to-interpret subgroups are preferable. We represent the subgroups of interest by a collection of models and use a model selection approach to finding subgroups with heterogeneous effects. We develop suitable priors for the model space and use an objective Bayesian approach that yields multiplicity adjusted posterior probabilities for the models. We use a structured algorithm based on the posterior probabilities of the models to determine which subgroup effects to report. Frequentist operating characteristics of the approach are evaluated using simulation. While our approach is applicable in more general cases, we mainly focus on the 2 × 2 case of two covariates each at two levels for ease of presentation. The approach is illustrated using a real data example.
Two Bayesian tests of the GLOMOsys Model.
Field, Sarahanne M; Wagenmakers, Eric-Jan; Newell, Ben R; Zeelenberg, René; van Ravenzwaaij, Don
2016-12-01
Priming is arguably one of the key phenomena in contemporary social psychology. Recent retractions and failed replication attempts have led to a division in the field between proponents and skeptics and have reinforced the importance of confirming certain priming effects through replication. In this study, we describe the results of 2 preregistered replication attempts of 1 experiment by Förster and Denzler (2012). In both experiments, participants first processed letters either globally or locally, then were tested using a typicality rating task. Bayes factor hypothesis tests were conducted for both experiments: Experiment 1 (N = 100) yielded an indecisive Bayes factor of 1.38, indicating that the in-lab data are 1.38 times more likely to have occurred under the null hypothesis than under the alternative. Experiment 2 (N = 908) yielded a Bayes factor of 10.84, indicating strong support for the null hypothesis that global priming does not affect participants' mean typicality ratings. The failure to replicate this priming effect challenges existing support for the GLOMO(sys) model. (PsycINFO Database Record
Objective Bayesian Comparison of Constrained Analysis of Variance Models.
Consonni, Guido; Paroli, Roberta
2016-10-04
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means [Formula: see text] through an analysis of variance (ANOVA), a model may specify that [Formula: see text], while another one may state that [Formula: see text], and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of nonnested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, requiring no prior specification from the user, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, suitably modified to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies. We also present an application to real data collected in a psychological experiment.
Bayesian item fit analysis for unidimensional item response theory models.
Sinharay, Sandip
2006-11-01
Assessing item fit for unidimensional item response theory models for dichotomous items has always been an issue of enormous interest, but there exists no unanimously agreed item fit diagnostic for these models, and hence there is room for further investigation of the area. This paper employs the posterior predictive model-checking method, a popular Bayesian model-checking tool, to examine item fit for the above-mentioned models. An item fit plot, comparing the observed and predicted proportion-correct scores of examinees with different raw scores, is suggested. This paper also suggests how to obtain posterior predictive p-values (which are natural Bayesian p-values) for the item fit statistics of Orlando and Thissen that summarize numerically the information in the above-mentioned item fit plots. A number of simulation studies and a real data application demonstrate the effectiveness of the suggested item fit diagnostics. The suggested techniques seem to have adequate power and reasonable Type I error rate, and psychometricians will find them promising.
Quantum-Like Bayesian Networks for Modeling Decision Making.
Moreira, Catarina; Wichert, Andreas
2016-01-01
In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.
Quantum-Like Bayesian Networks for Modeling Decision Making
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Catarina eMoreira
2016-01-01
Full Text Available In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.
Generalized linear models with coarsened covariates: a practical Bayesian approach.
Johnson, Timothy R; Wiest, Michelle M
2014-06-01
Coarsened covariates are a common and sometimes unavoidable phenomenon encountered in statistical modeling. Covariates are coarsened when their values or categories have been grouped. This may be done to protect privacy or to simplify data collection or analysis when researchers are not aware of their drawbacks. Analyses with coarsened covariates based on ad hoc methods can compromise the validity of inferences. One valid method for accounting for a coarsened covariate is to use a marginal likelihood derived by summing or integrating over the unknown realizations of the covariate. However, algorithms for estimation based on this approach can be tedious to program and can be computationally expensive. These are significant obstacles to their use in practice. To overcome these limitations, we show that when expressed as a Bayesian probability model, a generalized linear model with a coarsened covariate can be posed as a tractable missing data problem where the missing data are due to censoring. We also show that this model is amenable to widely available general-purpose software for simulation-based inference for Bayesian probability models, providing researchers a very practical approach for dealing with coarsened covariates.
BAYESIAN ESTIMATION IN SHARED COMPOUND POISSON FRAILTY MODELS
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David D. Hanagal
2015-06-01
Full Text Available In this paper, we study the compound Poisson distribution as the shared frailty distribution and two different baseline distributions namely Pareto and linear failure rate distributions for modeling survival data. We are using the Markov Chain Monte Carlo (MCMC technique to estimate parameters of the proposed models by introducing the Bayesian estimation procedure. In the present study, a simulation is done to compare the true values of parameters with the estimated values. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991 related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better frailty model out of two proposed frailty models.
Experimental validation of a Bayesian model of visual acuity.
LENUS (Irish Health Repository)
Dalimier, Eugénie
2009-01-01
Based on standard procedures used in optometry clinics, we compare measurements of visual acuity for 10 subjects (11 eyes tested) in the presence of natural ocular aberrations and different degrees of induced defocus, with the predictions given by a Bayesian model customized with aberrometric data of the eye. The absolute predictions of the model, without any adjustment, show good agreement with the experimental data, in terms of correlation and absolute error. The efficiency of the model is discussed in comparison with image quality metrics and other customized visual process models. An analysis of the importance and customization of each stage of the model is also given; it stresses the potential high predictive power from precise modeling of ocular and neural transfer functions.
Wu, Haiyan
2013-01-01
General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…
Theory-based Bayesian models of inductive learning and reasoning.
Tenenbaum, Joshua B; Griffiths, Thomas L; Kemp, Charles
2006-07-01
Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.
Bayesian Gaussian Copula Factor Models for Mixed Data.
Murray, Jared S; Dunson, David B; Carin, Lawrence; Lucas, Joseph E
2013-06-01
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.
Bayesian statistic methods and theri application in probabilistic simulation models
Directory of Open Access Journals (Sweden)
Sergio Iannazzo
2007-03-01
Full Text Available Bayesian statistic methods are facing a rapidly growing level of interest and acceptance in the field of health economics. The reasons of this success are probably to be found on the theoretical fundaments of the discipline that make these techniques more appealing to decision analysis. To this point should be added the modern IT progress that has developed different flexible and powerful statistical software framework. Among them probably one of the most noticeably is the BUGS language project and its standalone application for MS Windows WinBUGS. Scope of this paper is to introduce the subject and to show some interesting applications of WinBUGS in developing complex economical models based on Markov chains. The advantages of this approach reside on the elegance of the code produced and in its capability to easily develop probabilistic simulations. Moreover an example of the integration of bayesian inference models in a Markov model is shown. This last feature let the analyst conduce statistical analyses on the available sources of evidence and exploit them directly as inputs in the economic model.
BUMPER v1.0: a Bayesian user-friendly model for palaeo-environmental reconstruction
Holden, Philip B.; Birks, H. John B.; Brooks, Stephen J.; Bush, Mark B.; Hwang, Grace M.; Matthews-Bird, Frazer; Valencia, Bryan G.; van Woesik, Robert
2017-02-01
We describe the Bayesian user-friendly model for palaeo-environmental reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring ˜ 2 s to build a 100-taxon model from a 100-site training set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training sets under ideal assumptions. We then use these to demonstrate the sensitivity of reconstructions to the characteristics of the training set, considering assemblage richness, taxon tolerances, and the number of training sites. We find that a useful guideline for the size of a training set is to provide, on average, at least 10 samples of each taxon. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. An identically configured model is used in each application, the only change being the input files that provide the training-set environment and taxon-count data. The performance of BUMPER is shown to be comparable with weighted average partial least squares (WAPLS) in each case. Additional artificial datasets are constructed with similar characteristics to the real data, and these are used to explore the reasons for the differing performances of the different training sets.
Preferential sampling and Bayesian geostatistics: Statistical modeling and examples.
Cecconi, Lorenzo; Grisotto, Laura; Catelan, Dolores; Lagazio, Corrado; Berrocal, Veronica; Biggeri, Annibale
2016-08-01
Preferential sampling refers to any situation in which the spatial process and the sampling locations are not stochastically independent. In this paper, we present two examples of geostatistical analysis in which the usual assumption of stochastic independence between the point process and the measurement process is violated. To account for preferential sampling, we specify a flexible and general Bayesian geostatistical model that includes a shared spatial random component. We apply the proposed model to two different case studies that allow us to highlight three different modeling and inferential aspects of geostatistical modeling under preferential sampling: (1) continuous or finite spatial sampling frame; (2) underlying causal model and relevant covariates; and (3) inferential goals related to mean prediction surface or prediction uncertainty.
Uncovering Transcriptional Regulatory Networks by Sparse Bayesian Factor Model
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Qi Yuan(Alan
2010-01-01
Full Text Available Abstract The problem of uncovering transcriptional regulation by transcription factors (TFs based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF-regulated genes. The model admits prior knowledge from existing database regarding TF-regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems, and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the breast cancer microarray data of patients with Estrogen Receptor positive ( status and Estrogen Receptor negative ( status, respectively.
Efficient multilevel brain tumor segmentation with integrated bayesian model classification.
Corso, J J; Sharon, E; Dube, S; El-Saden, S; Sinha, U; Yuille, A
2008-05-01
We present a new method for automatic segmentation of heterogeneous image data that takes a step toward bridging the gap between bottom-up affinity-based segmentation methods and top-down generative model based approaches. The main contribution of the paper is a Bayesian formulation for incorporating soft model assignments into the calculation of affinities, which are conventionally model free. We integrate the resulting model-aware affinities into the multilevel segmentation by weighted aggregation algorithm, and apply the technique to the task of detecting and segmenting brain tumor and edema in multichannel magnetic resonance (MR) volumes. The computationally efficient method runs orders of magnitude faster than current state-of-the-art techniques giving comparable or improved results. Our quantitative results indicate the benefit of incorporating model-aware affinities into the segmentation process for the difficult case of glioblastoma multiforme brain tumor.
Uncovering Transcriptional Regulatory Networks by Sparse Bayesian Factor Model
Meng, Jia; Zhang, Jianqiu(Michelle); Qi, Yuan(Alan); Chen, Yidong; Huang, Yufei
2010-12-01
The problem of uncovering transcriptional regulation by transcription factors (TFs) based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM) is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF-regulated genes. The model admits prior knowledge from existing database regarding TF-regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems, and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the breast cancer microarray data of patients with Estrogen Receptor positive ([InlineEquation not available: see fulltext.]) status and Estrogen Receptor negative ([InlineEquation not available: see fulltext.]) status, respectively.
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen
2012-01-01
Many successful segmentation algorithms are based on Bayesian models in which prior anatomical knowledge is combined with the available image information. However, these methods typically have many free parameters that are estimated to obtain point estimates only, whereas a faithful Bayesian analysis would also consider all possible alternate values these parameters may take. In this paper, we propose to incorporate the uncertainty of the free parameters in Bayesian segmentation models more a...
Bayesian inference for generalized linear models for spiking neurons
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Sebastian Gerwinn
2010-05-01
Full Text Available Generalized Linear Models (GLMs are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate.
MODELING INFORMATION SYSTEM AVAILABILITY BY USING BAYESIAN BELIEF NETWORK APPROACH
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Semir Ibrahimović
2016-03-01
Full Text Available Modern information systems are expected to be always-on by providing services to end-users, regardless of time and location. This is particularly important for organizations and industries where information systems support real-time operations and mission-critical applications that need to be available on 24 7 365 basis. Examples of such entities include process industries, telecommunications, healthcare, energy, banking, electronic commerce and a variety of cloud services. This article presents a modified Bayesian Belief Network model for predicting information system availability, introduced initially by Franke, U. and Johnson, P. (in article “Availability of enterprise IT systems – an expert based Bayesian model”. Software Quality Journal 20(2, 369-394, 2012 based on a thorough review of several dimensions of the information system availability, we proposed a modified set of determinants. The model is parameterized by using probability elicitation process with the participation of experts from the financial sector of Bosnia and Herzegovina. The model validation was performed using Monte Carlo simulation.
Bayesian network as a modelling tool for risk management in agriculture
DEFF Research Database (Denmark)
Rasmussen, Svend; Madsen, Anders Læsø; Lund, Mogens
. In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be efficiently used to estimate conditional probabilities, which are the core elements in Bayesian network models....... We further show how the Bayesian network model RiBay is used for stochastic simulation of farm income, and we demonstrate how RiBay can be used to simulate risk management at the farm level. It is concluded that the key strength of a Bayesian network is the transparency of assumptions...
Enhancing debris flow modeling parameters integrating Bayesian networks
Graf, C.; Stoffel, M.; Grêt-Regamey, A.
2009-04-01
Applied debris-flow modeling requires suitably constraint input parameter sets. Depending on the used model, there is a series of parameters to define before running the model. Normally, the data base describing the event, the initiation conditions, the flow behavior, the deposition process and mainly the potential range of possible debris flow events in a certain torrent is limited. There are only some scarce places in the world, where we fortunately can find valuable data sets describing event history of debris flow channels delivering information on spatial and temporal distribution of former flow paths and deposition zones. Tree-ring records in combination with detailed geomorphic mapping for instance provide such data sets over a long time span. Considering the significant loss potential associated with debris-flow disasters, it is crucial that decisions made in regard to hazard mitigation are based on a consistent assessment of the risks. This in turn necessitates a proper assessment of the uncertainties involved in the modeling of the debris-flow frequencies and intensities, the possible run out extent, as well as the estimations of the damage potential. In this study, we link a Bayesian network to a Geographic Information System in order to assess debris-flow risk. We identify the major sources of uncertainty and show the potential of Bayesian inference techniques to improve the debris-flow model. We model the flow paths and deposition zones of a highly active debris-flow channel in the Swiss Alps using the numerical 2-D model RAMMS. Because uncertainties in run-out areas cause large changes in risk estimations, we use the data of flow path and deposition zone information of reconstructed debris-flow events derived from dendrogeomorphological analysis covering more than 400 years to update the input parameters of the RAMMS model. The probabilistic model, which consistently incorporates this available information, can serve as a basis for spatial risk
Bayesian experimental design for models with intractable likelihoods.
Drovandi, Christopher C; Pettitt, Anthony N
2013-12-01
In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables.
Recursive Bayesian recurrent neural networks for time-series modeling.
Mirikitani, Derrick T; Nikolaev, Nikolay
2010-02-01
This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.
Markov chain Monte Carlo simulation for Bayesian Hidden Markov Models
Chan, Lay Guat; Ibrahim, Adriana Irawati Nur Binti
2016-10-01
A hidden Markov model (HMM) is a mixture model which has a Markov chain with finite states as its mixing distribution. HMMs have been applied to a variety of fields, such as speech and face recognitions. The main purpose of this study is to investigate the Bayesian approach to HMMs. Using this approach, we can simulate from the parameters' posterior distribution using some Markov chain Monte Carlo (MCMC) sampling methods. HMMs seem to be useful, but there are some limitations. Therefore, by using the Mixture of Dirichlet processes Hidden Markov Model (MDPHMM) based on Yau et. al (2011), we hope to overcome these limitations. We shall conduct a simulation study using MCMC methods to investigate the performance of this model.
Bayesian Model Selection with Network Based Diffusion Analysis.
Whalen, Andrew; Hoppitt, William J E
2016-01-01
A number of recent studies have used Network Based Diffusion Analysis (NBDA) to detect the role of social transmission in the spread of a novel behavior through a population. In this paper we present a unified framework for performing NBDA in a Bayesian setting, and demonstrate how the Watanabe Akaike Information Criteria (WAIC) can be used for model selection. We present a specific example of applying this method to Time to Acquisition Diffusion Analysis (TADA). To examine the robustness of this technique, we performed a large scale simulation study and found that NBDA using WAIC could recover the correct model of social transmission under a wide range of cases, including under the presence of random effects, individual level variables, and alternative models of social transmission. This work suggests that NBDA is an effective and widely applicable tool for uncovering whether social transmission underpins the spread of a novel behavior, and may still provide accurate results even when key model assumptions are relaxed.
Bayesian Dose-Response Modeling in Sparse Data
Kim, Steven B.
This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a
Directory of Open Access Journals (Sweden)
Pengpeng Jiao
2014-11-01
Full Text Available Short-term prediction of dynamic turning movement proportions at intersections is very important for intelligent transportation systems, but it is impossible to detect turning flows directly through current traffic surveillance devices. Existing prediction models have proved to be rather accurate in general, but not precise enough during every time interval, and can only obtain the one-step prediction. This paper first presents a Bayesian combined model to forecast the entering and exiting flows at intersections, by integrating a nonlinear regression, a moving average, and an autoregressive model. Based on the forecasted traffic flows, this paper further develops an accurate backpropagation neural network model and an efficient Kalman filtering model to predict the dynamic turning movement proportions. Using Bayesian method with both historical information and currently prediction results for error adjustment, this paper finally integrates both the above two prediction models and proposes a Bi-Bayesian combined framework to achieve both one-step and two-step predictions. A case study is implemented based on practical survey data, which are collected at an intersection in Beijing city, including both historical and current data. The reported prediction results indicate that the Bi-Bayesian combined model is rather accurate and stable for on-line applications.
Perceptual decision making: Drift-diffusion model is equivalent to a Bayesian model
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Sebastian eBitzer
2014-02-01
Full Text Available Behavioural data obtained with perceptual decision making experiments are typically analysed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence towards a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses.
a Bayesian Synthesis of Predictions from Different Models for Setting Water Quality Criteria
Arhonditsis, G. B.; Ecological Modelling Laboratory
2011-12-01
Skeptical views of the scientific value of modelling argue that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure. In this regard, rather than picking the single "best-fit" model to predict future system responses, we can use Bayesian model averaging to synthesize the forecasts from different models. Hence, by acknowledging that models from different areas of the complexity spectrum have different strengths and weaknesses, the Bayesian model averaging is an appealing approach to improve the predictive capacity and to overcome the ambiguity surrounding the model selection or the risk of basing ecological forecasts on a single model. Our study addresses this question using a complex ecological model, developed by Ramin et al. (2011; Environ Modell Softw 26, 337-353) to guide the water quality criteria setting process in the Hamilton Harbour (Ontario, Canada), along with a simpler plankton model that considers the interplay among phosphate, detritus, and generic phytoplankton and zooplankton state variables. This simple approach is more easily subjected to detailed sensitivity analysis and also has the advantage of fewer unconstrained parameters. Using Markov Chain Monte Carlo simulations, we calculate the relative mean standard error to assess the posterior support of the two models from the existing data. Predictions from the two models are then combined using the respective standard error estimates as weights in a weighted model average. The model averaging approach is used to examine the robustness of predictive statements made from our earlier work regarding the response of Hamilton Harbour to the different nutrient loading reduction strategies. The two eutrophication models are then used in conjunction with the SPAtially Referenced Regressions On Watershed attributes (SPARROW) watershed model. The Bayesian nature of our work is used: (i) to alleviate problems of spatiotemporal
MATHEMATICAL RISK ANALYSIS: VIA NICHOLAS RISK MODEL AND BAYESIAN ANALYSIS
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Anass BAYAGA
2010-07-01
Full Text Available The objective of this second part of a two-phased study was to explorethe predictive power of quantitative risk analysis (QRA method andprocess within Higher Education Institution (HEI. The method and process investigated the use impact analysis via Nicholas risk model and Bayesian analysis, with a sample of hundred (100 risk analysts in a historically black South African University in the greater Eastern Cape Province.The first findings supported and confirmed previous literature (KingIII report, 2009: Nicholas and Steyn, 2008: Stoney, 2007: COSA, 2004 that there was a direct relationship between risk factor, its likelihood and impact, certiris paribus. The second finding in relation to either controlling the likelihood or the impact of occurrence of risk (Nicholas risk model was that to have a brighter risk reward, it was important to control the likelihood ofoccurrence of risks as compared with its impact so to have a direct effect on entire University. On the Bayesian analysis, thus third finding, the impact of risk should be predicted along three aspects. These aspects included the human impact (decisions made, the property impact (students and infrastructural based and the business impact. Lastly, the study revealed that although in most business cases, where as business cycles considerably vary dependingon the industry and or the institution, this study revealed that, most impacts in HEI (University was within the period of one academic.The recommendation was that application of quantitative risk analysisshould be related to current legislative framework that affects HEI.
Cross-validation analysis of bias models in Bayesian multi-model projections of climate
Huttunen, J. M. J.; Räisänen, J.; Nissinen, A.; Lipponen, A.; Kolehmainen, V.
2017-03-01
Climate change projections are commonly based on multi-model ensembles of climate simulations. In this paper we consider the choice of bias models in Bayesian multimodel predictions. Buser et al. (Clim Res 44(2-3):227-241, 2010a) introduced a hybrid bias model which combines commonly used constant bias and constant relation bias assumptions. The hybrid model includes a weighting parameter which balances these bias models. In this study, we use a cross-validation approach to study which bias model or bias parameter leads to, in a specific sense, optimal climate change projections. The analysis is carried out for summer and winter season means of 2 m-temperatures spatially averaged over the IPCC SREX regions, using 19 model runs from the CMIP5 data set. The cross-validation approach is applied to calculate optimal bias parameters (in the specific sense) for projecting the temperature change from the control period (1961-2005) to the scenario period (2046-2090). The results are compared to the results of the Buser et al. (Clim Res 44(2-3):227-241, 2010a) method which includes the bias parameter as one of the unknown parameters to be estimated from the data.
A hierarchical Bayesian GEV model for improving local and regional flood quantile estimates
Lima, Carlos H. R.; Lall, Upmanu; Troy, Tara; Devineni, Naresh
2016-10-01
We estimate local and regional Generalized Extreme Value (GEV) distribution parameters for flood frequency analysis in a multilevel, hierarchical Bayesian framework, to explicitly model and reduce uncertainties. As prior information for the model, we assume that the GEV location and scale parameters for each site come from independent log-normal distributions, whose mean parameter scales with the drainage area. From empirical and theoretical arguments, the shape parameter for each site is shrunk towards a common mean. Non-informative prior distributions are assumed for the hyperparameters and the MCMC method is used to sample from the joint posterior distribution. The model is tested using annual maximum series from 20 streamflow gauges located in an 83,000 km2 flood prone basin in Southeast Brazil. The results show a significant reduction of uncertainty estimates of flood quantile estimates over the traditional GEV model, particularly for sites with shorter records. For return periods within the range of the data (around 50 years), the Bayesian credible intervals for the flood quantiles tend to be narrower than the classical confidence limits based on the delta method. As the return period increases beyond the range of the data, the confidence limits from the delta method become unreliable and the Bayesian credible intervals provide a way to estimate satisfactory confidence bands for the flood quantiles considering parameter uncertainties and regional information. In order to evaluate the applicability of the proposed hierarchical Bayesian model for regional flood frequency analysis, we estimate flood quantiles for three randomly chosen out-of-sample sites and compare with classical estimates using the index flood method. The posterior distributions of the scaling law coefficients are used to define the predictive distributions of the GEV location and scale parameters for the out-of-sample sites given only their drainage areas and the posterior distribution of the
Aggregated Residential Load Modeling Using Dynamic Bayesian Networks
Energy Technology Data Exchange (ETDEWEB)
Vlachopoulou, Maria; Chin, George; Fuller, Jason C.; Lu, Shuai
2014-09-28
Abstract—It is already obvious that the future power grid will have to address higher demand for power and energy, and to incorporate renewable resources of different energy generation patterns. Demand response (DR) schemes could successfully be used to manage and balance power supply and demand under operating conditions of the future power grid. To achieve that, more advanced tools for DR management of operations and planning are necessary that can estimate the available capacity from DR resources. In this research, a Dynamic Bayesian Network (DBN) is derived, trained, and tested that can model aggregated load of Heating, Ventilation, and Air Conditioning (HVAC) systems. DBNs can provide flexible and powerful tools for both operations and planing, due to their unique analytical capabilities. The DBN model accuracy and flexibility of use is demonstrated by testing the model under different operational scenarios.
Extended Bayesian Information Criteria for Gaussian Graphical Models
Foygel, Rina
2010-01-01
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjunction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordi...
Development of a Bayesian Belief Network Runway Incursion Model
Green, Lawrence L.
2014-01-01
In a previous paper, a statistical analysis of runway incursion (RI) events was conducted to ascertain their relevance to the top ten Technical Challenges (TC) of the National Aeronautics and Space Administration (NASA) Aviation Safety Program (AvSP). The study revealed connections to perhaps several of the AvSP top ten TC. That data also identified several primary causes and contributing factors for RI events that served as the basis for developing a system-level Bayesian Belief Network (BBN) model for RI events. The system-level BBN model will allow NASA to generically model the causes of RI events and to assess the effectiveness of technology products being developed under NASA funding. These products are intended to reduce the frequency of RI events in particular, and to improve runway safety in general. The development, structure and assessment of that BBN for RI events by a Subject Matter Expert panel are documented in this paper.
Bayesian reduced-order models for multiscale dynamical systems
Koutsourelakis, P S
2010-01-01
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical interest is computationally infeasible or impractical. In complex systems, with limited physical insight on the coherent behavior of their constituents, the only available information is data obtained from simulations of the trajectories of huge numbers of degrees of freedom over microscopic time scales. This paper discusses a Bayesian approach to deriving probabilistic coarse-grained models that simultaneously address the problems of identifying appropriate reduced coordinates and the effective dynamics in this lower-dimensional representation. At the core of the models proposed lie simple, low-dimensional dynamical systems which serve as the building blocks of the global model. These approximate the latent, generating sources and parameterize the reduced-order dynamics. We d...
Performance and Prediction: Bayesian Modelling of Fallible Choice in Chess
Haworth, Guy; Regan, Ken; di Fatta, Giuseppe
Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration applications address questions frequently asked by the chess community regarding the stability of the rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The last include alleged under-performance, fabrication of tournament results, and clandestine use of computer advice during competition. Beyond the model world of games, the aim is to improve fallible human performance in complex, high-value tasks.
Advances in Bayesian Model Based Clustering Using Particle Learning
Energy Technology Data Exchange (ETDEWEB)
Merl, D M
2009-11-19
Recent work by Carvalho, Johannes, Lopes and Polson and Carvalho, Lopes, Polson and Taddy introduced a sequential Monte Carlo (SMC) alternative to traditional iterative Monte Carlo strategies (e.g. MCMC and EM) for Bayesian inference for a large class of dynamic models. The basis of SMC techniques involves representing the underlying inference problem as one of state space estimation, thus giving way to inference via particle filtering. The key insight of Carvalho et al was to construct the sequence of filtering distributions so as to make use of the posterior predictive distribution of the observable, a distribution usually only accessible in certain Bayesian settings. Access to this distribution allows a reversal of the usual propagate and resample steps characteristic of many SMC methods, thereby alleviating to a large extent many problems associated with particle degeneration. Furthermore, Carvalho et al point out that for many conjugate models the posterior distribution of the static variables can be parametrized in terms of [recursively defined] sufficient statistics of the previously observed data. For models where such sufficient statistics exist, particle learning as it is being called, is especially well suited for the analysis of streaming data do to the relative invariance of its algorithmic complexity with the number of data observations. Through a particle learning approach, a statistical model can be fit to data as the data is arriving, allowing at any instant during the observation process direct quantification of uncertainty surrounding underlying model parameters. Here we describe the use of a particle learning approach for fitting a standard Bayesian semiparametric mixture model as described in Carvalho, Lopes, Polson and Taddy. In Section 2 we briefly review the previously presented particle learning algorithm for the case of a Dirichlet process mixture of multivariate normals. In Section 3 we describe several novel extensions to the original
Bayesian network approach for modeling local failure in lung cancer
Oh, Jung Hun; Craft, Jeffrey; Al-Lozi, Rawan; Vaidya, Manushka; Meng, Yifan; Deasy, Joseph O; Bradley, Jeffrey D; Naqa, Issam El
2011-01-01
Locally advanced non-small cell lung cancer (NSCLC) patients suffer from a high local failure rate following radiotherapy. Despite many efforts to develop new dose-volume models for early detection of tumor local failure, there was no reported significant improvement in their application prospectively. Based on recent studies of biomarker proteins’ role in hypoxia and inflammation in predicting tumor response to radiotherapy, we hypothesize that combining physical and biological factors with a suitable framework could improve the overall prediction. To test this hypothesis, we propose a graphical Bayesian network framework for predicting local failure in lung cancer. The proposed approach was tested using two different datasets of locally advanced NSCLC patients treated with radiotherapy. The first dataset was collected retrospectively, which is comprised of clinical and dosimetric variables only. The second dataset was collected prospectively in which in addition to clinical and dosimetric information, blood was drawn from the patients at various time points to extract candidate biomarkers as well. Our preliminary results show that the proposed method can be used as an efficient method to develop predictive models of local failure in these patients and to interpret relationships among the different variables in the models. We also demonstrate the potential use of heterogenous physical and biological variables to improve the model prediction. With the first dataset, we achieved better performance compared with competing Bayesian-based classifiers. With the second dataset, the combined model had a slightly higher performance compared to individual physical and biological models, with the biological variables making the largest contribution. Our preliminary results highlight the potential of the proposed integrated approach for predicting post-radiotherapy local failure in NSCLC patients. PMID:21335651
Road network safety evaluation using Bayesian hierarchical joint model.
Wang, Jie; Huang, Helai
2016-05-01
Safety and efficiency are commonly regarded as two significant performance indicators of transportation systems. In practice, road network planning has focused on road capacity and transport efficiency whereas the safety level of a road network has received little attention in the planning stage. This study develops a Bayesian hierarchical joint model for road network safety evaluation to help planners take traffic safety into account when planning a road network. The proposed model establishes relationships between road network risk and micro-level variables related to road entities and traffic volume, as well as socioeconomic, trip generation and network density variables at macro level which are generally used for long term transportation plans. In addition, network spatial correlation between intersections and their connected road segments is also considered in the model. A road network is elaborately selected in order to compare the proposed hierarchical joint model with a previous joint model and a negative binomial model. According to the results of the model comparison, the hierarchical joint model outperforms the joint model and negative binomial model in terms of the goodness-of-fit and predictive performance, which indicates the reasonableness of considering the hierarchical data structure in crash prediction and analysis. Moreover, both random effects at the TAZ level and the spatial correlation between intersections and their adjacent segments are found to be significant, supporting the employment of the hierarchical joint model as an alternative in road-network-level safety modeling as well.
MAXIMUM LIKELIHOOD ESTIMATION FOR PERIODIC AUTOREGRESSIVE MOVING AVERAGE MODELS.
Vecchia, A.V.
1985-01-01
A useful class of models for seasonal time series that cannot be filtered or standardized to achieve second-order stationarity is that of periodic autoregressive moving average (PARMA) models, which are extensions of ARMA models that allow periodic (seasonal) parameters. An approximation to the exact likelihood for Gaussian PARMA processes is developed, and a straightforward algorithm for its maximization is presented. The algorithm is tested on several periodic ARMA(1, 1) models through simulation studies and is compared to moment estimation via the seasonal Yule-Walker equations. Applicability of the technique is demonstrated through an analysis of a seasonal stream-flow series from the Rio Caroni River in Venezuela.
Analytical network-averaging of the tube model:. Rubber elasticity
Khiêm, Vu Ngoc; Itskov, Mikhail
2016-10-01
In this paper, a micromechanical model for rubber elasticity is proposed on the basis of analytical network-averaging of the tube model and by applying a closed-form of the Rayleigh exact distribution function for non-Gaussian chains. This closed-form is derived by considering the polymer chain as a coarse-grained model on the basis of the quantum mechanical solution for finitely extensible dumbbells (Ilg et al., 2000). The proposed model includes very few physically motivated material constants and demonstrates good agreement with experimental data on biaxial tension as well as simple shear tests.
Modelling of population dynamics of red king crab using Bayesian approach
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Bakanev Sergey ...
2012-10-01
Modeling population dynamics based on the Bayesian approach enables to successfully resolve the above issues. The integration of the data from various studies into a unified model based on Bayesian parameter estimation method provides a much more detailed description of the processes occurring in the population.
Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data
Lee, Sik-Yum
2006-01-01
A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…
Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837
Levy, Roy
2014-01-01
Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…
Bayesian Framework for Water Quality Model Uncertainty Estimation and Risk Management
A formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based wat...
Nonparametric Bayesian inference of the microcanonical stochastic block model
Peixoto, Tiago P.
2017-01-01
A principled approach to characterize the hidden modular structure of networks is to formulate generative models and then infer their parameters from data. When the desired structure is composed of modules or "communities," a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints, i.e., the generated networks are not allowed to violate the patterns imposed by the model. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: (1) deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, which not only remove limitations that seriously degrade the inference on large networks but also reveal structures at multiple scales; (2) a very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges but also with an unlimited number of modules. We show also how this approach can be used to sample modular hierarchies from the posterior distribution, as well as to perform model selection. We discuss and analyze the differences between sampling from the posterior and simply finding the single parameter estimate that maximizes it. Furthermore, we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical SBM.
Bayesian geostatistical modeling of Malaria Indicator Survey data in Angola.
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Laura Gosoniu
Full Text Available The 2006-2007 Angola Malaria Indicator Survey (AMIS is the first nationally representative household survey in the country assessing coverage of the key malaria control interventions and measuring malaria-related burden among children under 5 years of age. In this paper, the Angolan MIS data were analyzed to produce the first smooth map of parasitaemia prevalence based on contemporary nationwide empirical data in the country. Bayesian geostatistical models were fitted to assess the effect of interventions after adjusting for environmental, climatic and socio-economic factors. Non-linear relationships between parasitaemia risk and environmental predictors were modeled by categorizing the covariates and by employing two non-parametric approaches, the B-splines and the P-splines. The results of the model validation showed that the categorical model was able to better capture the relationship between parasitaemia prevalence and the environmental factors. Model fit and prediction were handled within a Bayesian framework using Markov chain Monte Carlo (MCMC simulations. Combining estimates of parasitaemia prevalence with the number of children under we obtained estimates of the number of infected children in the country. The population-adjusted prevalence ranges from in Namibe province to in Malanje province. The odds of parasitaemia in children living in a household with at least ITNs per person was by 41% lower (CI: 14%, 60% than in those with fewer ITNs. The estimates of the number of parasitaemic children produced in this paper are important for planning and implementing malaria control interventions and for monitoring the impact of prevention and control activities.
Modeling Land-Use Decision Behavior with Bayesian Belief Networks
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Inge Aalders
2008-06-01
Full Text Available The ability to incorporate and manage the different drivers of land-use change in a modeling process is one of the key challenges because they are complex and are both quantitative and qualitative in nature. This paper uses Bayesian belief networks (BBN to incorporate characteristics of land managers in the modeling process and to enhance our understanding of land-use change based on the limited and disparate sources of information. One of the two models based on spatial data represented land managers in the form of a quantitative variable, the area of individual holdings, whereas the other model included qualitative data from a survey of land managers. Random samples from the spatial data provided evidence of the relationship between the different variables, which I used to develop the BBN structure. The model was tested for four different posterior probability distributions, and results showed that the trained and learned models are better at predicting land use than the uniform and random models. The inference from the model demonstrated the constraints that biophysical characteristics impose on land managers; for older land managers without heirs, there is a higher probability of the land use being arable agriculture. The results show the benefits of incorporating a more complex notion of land managers in land-use models, and of using different empirical data sources in the modeling process. Future research should focus on incorporating more complex social processes into the modeling structure, as well as incorporating spatio-temporal dynamics in a BBN.
Fully variational average atom model with ion-ion correlations.
Starrett, C E; Saumon, D
2012-02-01
An average atom model for dense ionized fluids that includes ion correlations is presented. The model assumes spherical symmetry and is based on density functional theory, the integral equations for uniform fluids, and a variational principle applied to the grand potential. Starting from density functional theory for a mixture of classical ions and quantum mechanical electrons, an approximate grand potential is developed, with an external field being created by a central nucleus fixed at the origin. Minimization of this grand potential with respect to electron and ion densities is carried out, resulting in equations for effective interaction potentials. A third condition resulting from minimizing the grand potential with respect to the average ion charge determines the noninteracting electron chemical potential. This system is coupled to a system of point ions and electrons with an ion fixed at the origin, and a closed set of equations is obtained. Solution of these equations results in a self-consistent electronic and ionic structure for the plasma as well as the average ionization, which is continuous as a function of temperature and density. Other average atom models are recovered by application of simplifying assumptions.
Japanese Dairy Cattle Productivity Analysis using Bayesian Network Model (BNM
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Iqbal Ahmed
2016-11-01
Full Text Available Japanese Dairy Cattle Productivity Analysis is carried out based on Bayesian Network Model (BNM. Through the experiment with 280 Japanese anestrus Holstein dairy cow, it is found that the estimation for finding out the presence of estrous cycle using BNM represents almost 55% accuracy while considering all samples. On the contrary, almost 73% accurate estimation could be achieved while using suspended likelihood in sample datasets. Moreover, while the proposed BNM model have more confidence then the estimation accuracy is lies in between 93 to 100%. In addition, this research also reveals the optimum factors to find out the presence of estrous cycle among the 270 individual dairy cows. The objective estimation methods using BNM definitely lead a unique idea to overcome the error of subjective estimation of having estrous cycle among these Japanese dairy cattle.
A Bayesian model of context-sensitive value attribution.
Rigoli, Francesco; Friston, Karl J; Martinelli, Cristina; Selaković, Mirjana; Shergill, Sukhwinder S; Dolan, Raymond J
2016-06-22
Substantial evidence indicates that incentive value depends on an anticipation of rewards within a given context. However, the computations underlying this context sensitivity remain unknown. To address this question, we introduce a normative (Bayesian) account of how rewards map to incentive values. This assumes that the brain inverts a model of how rewards are generated. Key features of our account include (i) an influence of prior beliefs about the context in which rewards are delivered (weighted by their reliability in a Bayes-optimal fashion), (ii) the notion that incentive values correspond to precision-weighted prediction errors, (iii) and contextual information unfolding at different hierarchical levels. This formulation implies that incentive value is intrinsically context-dependent. We provide empirical support for this model by showing that incentive value is influenced by context variability and by hierarchically nested contexts. The perspective we introduce generates new empirical predictions that might help explaining psychopathologies, such as addiction.
Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
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Pedersen, Niels Lovmand; Manchón, Carles Navarro; Badiu, Mihai Alin;
2015-01-01
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued m......In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex...
Diagnosing Hybrid Systems: a Bayesian Model Selection Approach
McIlraith, Sheila A.
2005-01-01
In this paper we examine the problem of monitoring and diagnosing noisy complex dynamical systems that are modeled as hybrid systems-models of continuous behavior, interleaved by discrete transitions. In particular, we examine continuous systems with embedded supervisory controllers that experience abrupt, partial or full failure of component devices. Building on our previous work in this area (MBCG99;MBCG00), our specific focus in this paper ins on the mathematical formulation of the hybrid monitoring and diagnosis task as a Bayesian model tracking algorithm. The nonlinear dynamics of many hybrid systems present challenges to probabilistic tracking. Further, probabilistic tracking of a system for the purposes of diagnosis is problematic because the models of the system corresponding to failure modes are numerous and generally very unlikely. To focus tracking on these unlikely models and to reduce the number of potential models under consideration, we exploit logic-based techniques for qualitative model-based diagnosis to conjecture a limited initial set of consistent candidate models. In this paper we discuss alternative tracking techniques that are relevant to different classes of hybrid systems, focusing specifically on a method for tracking multiple models of nonlinear behavior simultaneously using factored sampling and conditional density propagation. To illustrate and motivate the approach described in this paper we examine the problem of monitoring and diganosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.
A Bayesian Approach for Structural Learning with Hidden Markov Models
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Cen Li
2002-01-01
Full Text Available Hidden Markov Models(HMM have proved to be a successful modeling paradigm for dynamic and spatial processes in many domains, such as speech recognition, genomics, and general sequence alignment. Typically, in these applications, the model structures are predefined by domain experts. Therefore, the HMM learning problem focuses on the learning of the parameter values of the model to fit the given data sequences. However, when one considers other domains, such as, economics and physiology, model structure capturing the system dynamic behavior is not available. In order to successfully apply the HMM methodology in these domains, it is important that a mechanism is available for automatically deriving the model structure from the data. This paper presents a HMM learning procedure that simultaneously learns the model structure and the maximum likelihood parameter values of a HMM from data. The HMM model structures are derived based on the Bayesian model selection methodology. In addition, we introduce a new initialization procedure for HMM parameter value estimation based on the K-means clustering method. Experimental results with artificially generated data show the effectiveness of the approach.
Bayesian network models for error detection in radiotherapy plans.
Kalet, Alan M; Gennari, John H; Ford, Eric C; Phillips, Mark H
2015-04-07
The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network's conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.
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Rahul Tripathi
2014-01-01
Full Text Available Forecasting of rice area, production, and productivity of Odisha was made from the historical data of 1950-51 to 2008-09 by using univariate autoregressive integrated moving average (ARIMA models and was compared with the forecasted all Indian data. The autoregressive (p and moving average (q parameters were identified based on the significant spikes in the plots of partial autocorrelation function (PACF and autocorrelation function (ACF of the different time series. ARIMA (2, 1, 0 model was found suitable for all Indian rice productivity and production, whereas ARIMA (1, 1, 1 was best fitted for forecasting of rice productivity and production in Odisha. Prediction was made for the immediate next three years, that is, 2007-08, 2008-09, and 2009-10, using the best fitted ARIMA models based on minimum value of the selection criterion, that is, Akaike information criteria (AIC and Schwarz-Bayesian information criteria (SBC. The performances of models were validated by comparing with percentage deviation from the actual values and mean absolute percent error (MAPE, which was found to be 0.61 and 2.99% for the area under rice in Odisha and India, respectively. Similarly for prediction of rice production and productivity in Odisha and India, the MAPE was found to be less than 6%.
The stability of a zonally averaged thermohaline circulation model
Schmidt, G A
1995-01-01
A combination of analytical and numerical techniques are used to efficiently determine the qualitative and quantitative behaviour of a one-basin zonally averaged thermohaline circulation ocean model. In contrast to earlier studies which use time stepping to find the steady solutions, the steady state equations are first solved directly to obtain the multiple equilibria under identical mixed boundary conditions. This approach is based on the differentiability of the governing equations and especially the convection scheme. A linear stability analysis is then performed, in which the normal modes and corresponding eigenvalues are found for the various equilibrium states. Resonant periodic solutions superimposed on these states are predicted for various types of forcing. The results are used to gain insight into the solutions obtained by Mysak, Stocker and Huang in a previous numerical study in which the eddy diffusivities were varied in a randomly forced one-basin zonally averaged model. Resonant stable oscillat...
Designing and testing inflationary models with Bayesian networks
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Price, Layne C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics; Auckland Univ. (New Zealand). Dept. of Physics; Peiris, Hiranya V. [Univ. College London (United Kingdom). Dept. of Physics and Astronomy; Frazer, Jonathan [DESY Hamburg (Germany). Theory Group; Univ. of the Basque Country, Bilbao (Spain). Dept. of Theoretical Physics; Basque Foundation for Science, Bilbao (Spain). IKERBASQUE; Easther, Richard [Auckland Univ. (New Zealand). Dept. of Physics
2015-11-15
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
Designing and testing inflationary models with Bayesian networks
Price, Layne C; Frazer, Jonathan; Easther, Richard
2015-01-01
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use $N_f$--quadratic inflation as an illustrative example, finding that the number of $e$-folds $N_*$ between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
Bridging groundwater models and decision support with a Bayesian network
Fienen, Michael N.; Masterson, John P.; Plant, Nathaniel G.; Gutierrez, Benjamin T.; Thieler, E. Robert
2013-01-01
Resource managers need to make decisions to plan for future environmental conditions, particularly sea level rise, in the face of substantial uncertainty. Many interacting processes factor in to the decisions they face. Advances in process models and the quantification of uncertainty have made models a valuable tool for this purpose. Long-simulation runtimes and, often, numerical instability make linking process models impractical in many cases. A method for emulating the important connections between model input and forecasts, while propagating uncertainty, has the potential to provide a bridge between complicated numerical process models and the efficiency and stability needed for decision making. We explore this using a Bayesian network (BN) to emulate a groundwater flow model. We expand on previous approaches to validating a BN by calculating forecasting skill using cross validation of a groundwater model of Assateague Island in Virginia and Maryland, USA. This BN emulation was shown to capture the important groundwater-flow characteristics and uncertainty of the groundwater system because of its connection to island morphology and sea level. Forecast power metrics associated with the validation of multiple alternative BN designs guided the selection of an optimal level of BN complexity. Assateague island is an ideal test case for exploring a forecasting tool based on current conditions because the unique hydrogeomorphological variability of the island includes a range of settings indicative of past, current, and future conditions. The resulting BN is a valuable tool for exploring the response of groundwater conditions to sea level rise in decision support.
The average rate of change for continuous time models.
Kelley, Ken
2009-05-01
The average rate of change (ARC) is a concept that has been misunderstood in the applied longitudinal data analysis literature, where the slope from the straight-line change model is often thought of as though it were the ARC. The present article clarifies the concept of ARC and shows unequivocally the mathematical definition and meaning of ARC when measurement is continuous across time. It is shown that the slope from the straight-line change model generally is not equal to the ARC. General equations are presented for two measures of discrepancy when the slope from the straight-line change model is used to estimate the ARC in the case of continuous time for any model linear in its parameters, and for three useful models nonlinear in their parameters.
Lowman, L.; Barros, A. P.
2014-12-01
Computational modeling of surface erosion processes is inherently difficult because of the four-dimensional nature of the problem and the multiple temporal and spatial scales that govern individual mechanisms. Landscapes are modified via surface and fluvial erosion and exhumation, each of which takes place over a range of time scales. Traditional field measurements of erosion/exhumation rates are scale dependent, often valid for a single point-wise location or averaging over large aerial extents and periods with intense and mild erosion. We present a method of remotely estimating erosion rates using a Bayesian hierarchical model based upon the stream power erosion law (SPEL). A Bayesian approach allows for estimating erosion rates using the deterministic relationship given by the SPEL and data on channel slopes and precipitation at the basin and sub-basin scale. The spatial scale associated with this framework is the elevation class, where each class is characterized by distinct morphologic behavior observed through different modes in the distribution of basin outlet elevations. Interestingly, the distributions of first-order outlets are similar in shape and extent to the distribution of precipitation events (i.e. individual storms) over a 14-year period between 1998-2011. We demonstrate an application of the Bayesian hierarchical modeling framework for five basins and one intermontane basin located in the central Andes between 5S and 20S. Using remotely sensed data of current annual precipitation rates from the Tropical Rainfall Measuring Mission (TRMM) and topography from a high resolution (3 arc-seconds) digital elevation map (DEM), our erosion rate estimates are consistent with decadal-scale estimates based on landslide mapping and sediment flux observations and 1-2 orders of magnitude larger than most millennial and million year timescale estimates from thermochronology and cosmogenic nuclides.
West, Patti; Rutstein, Daisy Wise; Mislevy, Robert J.; Liu, Junhui; Choi, Younyoung; Levy, Roy; Crawford, Aaron; DiCerbo, Kristen E.; Chappel, Kristina; Behrens, John T.
2010-01-01
A major issue in the study of learning progressions (LPs) is linking student performance on assessment tasks to the progressions. This report describes the challenges faced in making this linkage using Bayesian networks to model LPs in the field of computer networking. The ideas are illustrated with exemplar Bayesian networks built on Cisco…
Lee, Sik-Yum; Song, Xin-Yuan; Tang, Nian-Sheng
2007-01-01
The analysis of interaction among latent variables has received much attention. This article introduces a Bayesian approach to analyze a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. This approach produces a Bayesian estimate that has the same statistical optimal properties as a…
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Canty Angelo
2007-09-01
Full Text Available Abstract Background This study compares the Bayesian and frequentist (non-Bayesian approaches in the modelling of the association between the risk of preterm birth and maternal proximity to hazardous waste and pollution from the Sydney Tar Pond site in Nova Scotia, Canada. Methods The data includes 1604 observed cases of preterm birth out of a total population of 17559 at risk of preterm birth from 144 enumeration districts in the Cape Breton Regional Municipality. Other covariates include the distance from the Tar Pond; the rate of unemployment to population; the proportion of persons who are separated, divorced or widowed; the proportion of persons who have no high school diploma; the proportion of persons living alone; the proportion of single parent families and average income. Bayesian hierarchical Poisson regression, quasi-likelihood Poisson regression and weighted linear regression models were fitted to the data. Results The results of the analyses were compared together with their limitations. Conclusion The results of the weighted linear regression and the quasi-likelihood Poisson regression agrees with the result from the Bayesian hierarchical modelling which incorporates the spatial effects.
Bayesian Multiscale Modeling of Closed Curves in Point Clouds.
Gu, Kelvin; Pati, Debdeep; Dunson, David B
2014-10-01
Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model's latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a 'central curve' that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem.
Pulsar average waveforms and hollow cone beam models
Backer, D. C.
1975-01-01
An analysis of pulsar average waveforms at radio frequencies from 40 MHz to 15 GHz is presented. The analysis is based on the hypothesis that the observer sees one cut of a hollow-cone beam pattern and that stationary properties of the emission vary over the cone. The distributions of apparent cone widths for different observed forms of the average pulse profiles (single, double/unresolved, double/resolved, triple and multiple) are in modest agreement with a model of a circular hollow-cone beam with random observer-spin axis orientation, a random cone axis-spin axis alignment, and a small range of physical hollow-cone parameters for all objects.
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Zhang Zhang
2009-06-01
Full Text Available A major analytical challenge in computational biology is the detection and description of clusters of specified site types, such as polymorphic or substituted sites within DNA or protein sequences. Progress has been stymied by a lack of suitable methods to detect clusters and to estimate the extent of clustering in discrete linear sequences, particularly when there is no a priori specification of cluster size or cluster count. Here we derive and demonstrate a maximum likelihood method of hierarchical clustering. Our method incorporates a tripartite divide-and-conquer strategy that models sequence heterogeneity, delineates clusters, and yields a profile of the level of clustering associated with each site. The clustering model may be evaluated via model selection using the Akaike Information Criterion, the corrected Akaike Information Criterion, and the Bayesian Information Criterion. Furthermore, model averaging using weighted model likelihoods may be applied to incorporate model uncertainty into the profile of heterogeneity across sites. We evaluated our method by examining its performance on a number of simulated datasets as well as on empirical polymorphism data from diverse natural alleles of the Drosophila alcohol dehydrogenase gene. Our method yielded greater power for the detection of clustered sites across a breadth of parameter ranges, and achieved better accuracy and precision of estimation of clusters, than did the existing empirical cumulative distribution function statistics.
Reprioritizing genetic associations in hit regions using LASSO-based resample model averaging.
Valdar, William; Sabourin, Jeremy; Nobel, Andrew; Holmes, Christopher C
2012-07-01
Significance testing one SNP at a time has proven useful for identifying genomic regions that harbor variants affecting human disease. But after an initial genome scan has identified a "hit region" of association, single-locus approaches can falter. Local linkage disequilibrium (LD) can make both the number of underlying true signals and their identities ambiguous. Simultaneous modeling of multiple loci should help. However, it is typically applied ad hoc: conditioning on the top SNPs, with limited exploration of the model space and no assessment of how sensitive model choice was to sampling variability. Formal alternatives exist but are seldom used. Bayesian variable selection is coherent but requires specifying a full joint model, including priors on parameters and the model space. Penalized regression methods (e.g., LASSO) appear promising but require calibration, and, once calibrated, lead to a choice of SNPs that can be misleadingly decisive. We present a general method for characterizing uncertainty in model choice that is tailored to reprioritizing SNPs within a hit region under strong LD. Our method, LASSO local automatic regularization resample model averaging (LLARRMA), combines LASSO shrinkage with resample model averaging and multiple imputation, estimating for each SNP the probability that it would be included in a multi-SNP model in alternative realizations of the data. We apply LLARRMA to simulations based on case-control genome-wide association studies data, and find that when there are several causal loci and strong LD, LLARRMA identifies a set of candidates that is enriched for true signals relative to single locus analysis and to the recently proposed method of Stability Selection.
A global climate model based, Bayesian climate projection for northern extra-tropical land areas
Arzhanov, Maxim M.; Eliseev, Alexey V.; Mokhov, Igor I.
2012-04-01
Projections with contemporary global climate models (GCMs) still markedly deviate from each other on magnitude of climate changes, in particular, in middle to subpolar latitudes. In this work, a climate projection based on the ensemble of 18 CMIP3 GCM models forced by SRES A1B scenario is performed for the northern extra-tropical land. To assess the change of soil state, off-line simulations are performed with the Deep Soil Simulator (DSS) developed at the A.M.Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences (IAP RAS). This model is forced by output of the above-mentioned GCM simulations. Ensemble mean and ensemble standard deviation for any variable are calculated by using Bayesian averaging which allows to enhance a contribution from more realistic models and diminish that from less realistic models. As a result, uncertainty for soil and permafrost variables become substantially narrower. The Bayesian weights for each model are calculated based on their performance for the present-day surface air temperature (SAT) and permafrost distributions, and for SAT trend during the 20th century. The results, except for intra-ensemble standard deviations, are not very sensitive to particular choice of Bayesian traits. Averaged over the northern extra-tropical land, annual mean surface air temperature in the ensemble increases by 3.1 ± 1.4 K (ensemble mean±intra-ensemble standard deviation) during the 21st century. Precipitation robustly increases in the pan-Arctic and decreases in the Mediterranean/Black Sea region. The models agree on near-surface permafrost degradation during the 21st century. The area underlain by near-surface permafrost decreases from the contemporary value 20 ± 3 mln sq. km to 14 ± 3 mln sq. km in the late 21st century. This leads to risk for geocryological hazard due to soil subsidence. This risk is classified as moderate to high in the southern and western parts of Siberia and Tibet in Eurasia, and in the region from Alaska
Bayesian nonparametric centered random effects models with variable selection.
Yang, Mingan
2013-03-01
In a linear mixed effects model, it is common practice to assume that the random effects follow a parametric distribution such as a normal distribution with mean zero. However, in the case of variable selection, substantial violation of the normality assumption can potentially impact the subset selection and result in poor interpretation and even incorrect results. In nonparametric random effects models, the random effects generally have a nonzero mean, which causes an identifiability problem for the fixed effects that are paired with the random effects. In this article, we focus on a Bayesian method for variable selection. We characterize the subject-specific random effects nonparametrically with a Dirichlet process and resolve the bias simultaneously. In particular, we propose flexible modeling of the conditional distribution of the random effects with changes across the predictor space. The approach is implemented using a stochastic search Gibbs sampler to identify subsets of fixed effects and random effects to be included in the model. Simulations are provided to evaluate and compare the performance of our approach to the existing ones. We then apply the new approach to a real data example, cross-country and interlaboratory rodent uterotrophic bioassay.
Bayesian-based Project Monitoring: Framework Development and Model Testing
Directory of Open Access Journals (Sweden)
Budi Hartono
2015-12-01
Full Text Available During project implementation, risk becomes an integral part of project monitoring. Therefore. a tool that could dynamically include elements of risk in project progress monitoring is needed. This objective of this study is to develop a general framework that addresses such a concern. The developed framework consists of three interrelated major building blocks, namely: Risk Register (RR, Bayesian Network (BN, and Project Time Networks (PTN for dynamic project monitoring. RR is used to list and to categorize identified project risks. PTN is utilized for modeling the relationship between project activities. BN is used to reflect the interdependence among risk factors and to bridge RR and PTN. A residential development project is chosen as a working example and the result shows that the proposed framework has been successfully applied. The specific model of the development project is also successfully developed and is used to monitor the project progress. It is shown in this study that the proposed BN-based model provides superior performance in terms of forecast accuracy compared to the extant models.
A Bayesian model for the analysis of transgenerational epigenetic variation.
Varona, Luis; Munilla, Sebastián; Mouresan, Elena Flavia; González-Rodríguez, Aldemar; Moreno, Carlos; Altarriba, Juan
2015-01-23
Epigenetics has become one of the major areas of biological research. However, the degree of phenotypic variability that is explained by epigenetic processes still remains unclear. From a quantitative genetics perspective, the estimation of variance components is achieved by means of the information provided by the resemblance between relatives. In a previous study, this resemblance was described as a function of the epigenetic variance component and a reset coefficient that indicates the rate of dissipation of epigenetic marks across generations. Given these assumptions, we propose a Bayesian mixed model methodology that allows the estimation of epigenetic variance from a genealogical and phenotypic database. The methodology is based on the development of a T: matrix of epigenetic relationships that depends on the reset coefficient. In addition, we present a simple procedure for the calculation of the inverse of this matrix ( T-1: ) and a Gibbs sampler algorithm that obtains posterior estimates of all the unknowns in the model. The new procedure was used with two simulated data sets and with a beef cattle database. In the simulated populations, the results of the analysis provided marginal posterior distributions that included the population parameters in the regions of highest posterior density. In the case of the beef cattle dataset, the posterior estimate of transgenerational epigenetic variability was very low and a model comparison test indicated that a model that did not included it was the most plausible.
Assessing fit in Bayesian models for spatial processes
Jun, M.
2014-09-16
© 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models\\' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.
Forecasts of time averages with a numerical weather prediction model
Roads, J. O.
1986-01-01
Forecasts of time averages of 1-10 days in duration by an operational numerical weather prediction model are documented for the global 500 mb height field in spectral space. Error growth in very idealized models is described in order to anticipate various features of these forecasts and in order to anticipate what the results might be if forecasts longer than 10 days were carried out by present day numerical weather prediction models. The data set for this study is described, and the equilibrium spectra and error spectra are documented; then, the total error is documented. It is shown how forecasts can immediately be improved by removing the systematic error, by using statistical filters, and by ignoring forecasts beyond about a week. Temporal variations in the error field are also documented.
Bayesian adaptive combination of short-term wind speed forecasts from neural network models
Energy Technology Data Exchange (ETDEWEB)
Li, Gong; Shi, Jing; Zhou, Junyi [Department of Industrial and Manufacturing Engineering, North Dakota State University, Dept. 2485, PO Box 6050, Fargo, ND 58108 (United States)
2011-01-15
Short-term wind speed forecasting is of great importance for wind farm operations and the integration of wind energy into the power grid system. Adaptive and reliable methods and techniques of wind speed forecasts are urgently needed in view of the stochastic nature of wind resource varying from time to time and from site to site. This paper presents a robust two-step methodology for accurate wind speed forecasting based on Bayesian combination algorithm, and three neural network models, namely, adaptive linear element network (ADALINE), backpropagation (BP) network, and radial basis function (RBF) network. The hourly average wind speed data from two North Dakota sites are used to demonstrate the effectiveness of the proposed approach. The results indicate that, while the performances of the neural networks are not consistent in forecasting 1-h-ahead wind speed for the two sites or under different evaluation metrics, the Bayesian combination method can always provide adaptive, reliable and comparatively accurate forecast results. The proposed methodology provides a unified approach to tackle the challenging model selection issue in wind speed forecasting. (author)
Iskandar, Ismed; Satria Gondokaryono, Yudi
2016-02-01
In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range
Averaged hole mobility model of biaxially strained Si
Institute of Scientific and Technical Information of China (English)
Song Jianjun; Zhu He; Yang Jinyong; Zhang Heming; Xuan Rongxi; Hu Huiyong
2013-01-01
We aim to establisha model of the averaged hole mobility of strained Si grown on (001),(101),and (111) relaxed Si1-xGex substrates.The results obtained from our calculation show that their hole mobility values corresponding to strained Si (001),(101) and (111) increase by at most about three,two and one times,respectively,in comparison with the unstrained Si.The results can provide a valuable reference to the understanding and design of strained Si-based device physics.
Bayesian modelling of compositional heterogeneity in molecular phylogenetics.
Heaps, Sarah E; Nye, Tom M W; Boys, Richard J; Williams, Tom A; Embley, T Martin
2014-10-01
In molecular phylogenetics, standard models of sequence evolution generally assume that sequence composition remains constant over evolutionary time. However, this assumption is violated in many datasets which show substantial heterogeneity in sequence composition across taxa. We propose a model which allows compositional heterogeneity across branches, and formulate the model in a Bayesian framework. Specifically, the root and each branch of the tree is associated with its own composition vector whilst a global matrix of exchangeability parameters applies everywhere on the tree. We encourage borrowing of strength between branches by developing two possible priors for the composition vectors: one in which information can be exchanged equally amongst all branches of the tree and another in which more information is exchanged between neighbouring branches than between distant branches. We also propose a Markov chain Monte Carlo (MCMC) algorithm for posterior inference which uses data augmentation of substitutional histories to yield a simple complete data likelihood function that factorises over branches and allows Gibbs updates for most parameters. Standard phylogenetic models are not informative about the root position. Therefore a significant advantage of the proposed model is that it allows inference about rooted trees. The position of the root is fundamental to the biological interpretation of trees, both for polarising trait evolution and for establishing the order of divergence among lineages. Furthermore, unlike some other related models from the literature, inference in the model we propose can be carried out through a simple MCMC scheme which does not require problematic dimension-changing moves. We investigate the performance of the model and priors in analyses of two alignments for which there is strong biological opinion about the tree topology and root position.
Bayesian nonparametric clustering in phylogenetics: modeling antigenic evolution in influenza.
Cybis, Gabriela B; Sinsheimer, Janet S; Bedford, Trevor; Rambaut, Andrew; Lemey, Philippe; Suchard, Marc A
2017-01-18
Influenza is responsible for up to 500,000 deaths every year, and antigenic variability represents much of its epidemiological burden. To visualize antigenic differences across many viral strains, antigenic cartography methods use multidimensional scaling on binding assay data to map influenza antigenicity onto a low-dimensional space. Analysis of such assay data ideally leads to natural clustering of influenza strains of similar antigenicity that correlate with sequence evolution. To understand the dynamics of these antigenic groups, we present a framework that jointly models genetic and antigenic evolution by combining multidimensional scaling of binding assay data, Bayesian phylogenetic machinery and nonparametric clustering methods. We propose a phylogenetic Chinese restaurant process that extends the current process to incorporate the phylogenetic dependency structure between strains in the modeling of antigenic clusters. With this method, we are able to use the genetic information to better understand the evolution of antigenicity throughout epidemics, as shown in applications of this model to H1N1 influenza. Copyright © 2017 John Wiley & Sons, Ltd.
Bayesian network model of crowd emotion and negative behavior
Ramli, Nurulhuda; Ghani, Noraida Abdul; Hatta, Zulkarnain Ahmad; Hashim, Intan Hashimah Mohd; Sulong, Jasni; Mahudin, Nor Diana Mohd; Rahman, Shukran Abd; Saad, Zarina Mat
2014-12-01
The effects of overcrowding have become a major concern for event organizers. One aspect of this concern has been the idea that overcrowding can enhance the occurrence of serious incidents during events. As one of the largest Muslim religious gathering attended by pilgrims from all over the world, Hajj has become extremely overcrowded with many incidents being reported. The purpose of this study is to analyze the nature of human emotion and negative behavior resulting from overcrowding during Hajj events from data gathered in Malaysian Hajj Experience Survey in 2013. The sample comprised of 147 Malaysian pilgrims (70 males and 77 females). Utilizing a probabilistic model called Bayesian network, this paper models the dependence structure between different emotions and negative behaviors of pilgrims in the crowd. The model included the following variables of emotion: negative, negative comfortable, positive, positive comfortable and positive spiritual and variables of negative behaviors; aggressive and hazardous acts. The study demonstrated that emotions of negative, negative comfortable, positive spiritual and positive emotion have a direct influence on aggressive behavior whereas emotion of negative comfortable, positive spiritual and positive have a direct influence on hazardous acts behavior. The sensitivity analysis showed that a low level of negative and negative comfortable emotions leads to a lower level of aggressive and hazardous behavior. Findings of the study can be further improved to identify the exact cause and risk factors of crowd-related incidents in preventing crowd disasters during the mass gathering events.
A Bayesian Generative Model for Learning Semantic Hierarchies
Directory of Open Access Journals (Sweden)
Roni eMittelman
2014-05-01
Full Text Available Building fine-grained visual recognition systems that are capable of recognizing tens of thousands of categories, has received much attention in recent years. The well known semantic hierarchical structure of categories and concepts, has been shown to provide a key prior which allows for optimal predictions. The hierarchical organization of various domains and concepts has been subject to extensive research, and led to the development of the WordNet domains hierarchy [18], which was also used to organize the images in the ImageNet [11] dataset, in which the category count approaches the human capacity. Still, for the human visual system, the form of the hierarchy must be discovered with minimal use of supervision or innate knowledge. In this work, we propose a new Bayesian generative model for learning such domain hierarchies, based on semantic input. Our model is motivated by the super-subordinate organization of domain labels and concepts that characterizes WordNet, and accounts for several important challenges: maintaining context information when progressing deeper into the hierarchy, learning a coherent semantic concept for each node, and modeling uncertainty in the perception process.
Xu, Yadong; Serre, Marc L; Reyes, Jeanette; Vizuete, William
2016-04-19
To improve ozone exposure estimates for ambient concentrations at a national scale, we introduce our novel Regionalized Air Quality Model Performance (RAMP) approach to integrate chemical transport model (CTM) predictions with the available ozone observations using the Bayesian Maximum Entropy (BME) framework. The framework models the nonlinear and nonhomoscedastic relation between air pollution observations and CTM predictions and for the first time accounts for variability in CTM model performance. A validation analysis using only noncollocated data outside of a validation radius rv was performed and the R(2) between observations and re-estimated values for two daily metrics, the daily maximum 8-h average (DM8A) and the daily 24-h average (D24A) ozone concentrations, were obtained with the OBS scenario using ozone observations only in contrast with the RAMP and a Constant Air Quality Model Performance (CAMP) scenarios. We show that, by accounting for the spatial and temporal variability in model performance, our novel RAMP approach is able to extract more information in terms of R(2) increase percentage, with over 12 times for the DM8A and over 3.5 times for the D24A ozone concentrations, from CTM predictions than the CAMP approach assuming that model performance does not change across space and time.
Institute of Scientific and Technical Information of China (English)
HU Zhao-yong
2005-01-01
Engineering diagnosis is essential to the operation of industrial equipment. The key to successful diagnosis is correct knowledge representation and reasoning. The Bayesian network is a powerful tool for it. This paper utilizes the Bayesian network to represent and reason diagnostic knowledge, named Bayesian diagnostic network. It provides a three-layer topologic structure based on operating conditions, possible faults and corresponding symptoms. The paper also discusses an approximate stochastic sampling algorithm. Then a practical Bayesian network for gas turbine diagnosis is constructed on a platform developed under a Visual C++ environment. It shows that the Bayesian network is a powerful model for representation and reasoning of diagnostic knowledge. The three-layer structure and the approximate algorithm are effective also.
Abdelkrim Moussaoui; Yacine Selaimia; Hadj A. Abbassi
2006-01-01
The authors discuss the combination of an Artificial Neural Network (ANN) with analytical models to improve the performance of the prediction model of finishing rolling force in hot strip rolling mill process. The suggested model was implemented using Bayesian Evidence based training algorithm. It was found that the Bayesian Evidence based approach provided a superior and smoother fit to the real rolling mill data. Completely independent set of real rolling data were used to evaluate the capa...
Bayesian inference for partially identified models exploring the limits of limited data
Gustafson, Paul
2015-01-01
Introduction Identification What Is against Us? What Is for Us? Some Simple Examples of Partially Identified ModelsThe Road Ahead The Structure of Inference in Partially Identified Models Bayesian Inference The Structure of Posterior Distributions in PIMs Computational Strategies Strength of Bayesian Updating, Revisited Posterior MomentsCredible Intervals Evaluating the Worth of Inference Partial Identification versus Model Misspecification The Siren Call of Identification Comp
Modeling hypoxia in the Chesapeake Bay: Ensemble estimation using a Bayesian hierarchical model
Stow, Craig A.; Scavia, Donald
2009-02-01
Quantifying parameter and prediction uncertainty in a rigorous framework can be an important component of model skill assessment. Generally, models with lower uncertainty will be more useful for prediction and inference than models with higher uncertainty. Ensemble estimation, an idea with deep roots in the Bayesian literature, can be useful to reduce model uncertainty. It is based on the idea that simultaneously estimating common or similar parameters among models can result in more precise estimates. We demonstrate this approach using the Streeter-Phelps dissolved oxygen sag model fit to 29 years of data from Chesapeake Bay. Chesapeake Bay has a long history of bottom water hypoxia and several models are being used to assist management decision-making in this system. The Bayesian framework is particularly useful in a decision context because it can combine both expert-judgment and rigorous parameter estimation to yield model forecasts and a probabilistic estimate of the forecast uncertainty.
Greiner, Matthias; Smid, Joost; Havelaar, Arie H; Müller-Graf, Christine
2013-05-15
Quantitative microbiological risk assessment (QMRA) models are used to reflect knowledge about complex real-world scenarios for the propagation of microbiological hazards along the feed and food chain. The aim is to provide insight into interdependencies among model parameters, typically with an interest to characterise the effect of risk mitigation measures. A particular requirement is to achieve clarity about the reliability of conclusions from the model in the presence of uncertainty. To this end, Monte Carlo (MC) simulation modelling has become a standard in so-called probabilistic risk assessment. In this paper, we elaborate on the application of Bayesian computational statistics in the context of QMRA. It is useful to explore the analogy between MC modelling and Bayesian inference (BI). This pertains in particular to the procedures for deriving prior distributions for model parameters. We illustrate using a simple example that the inability to cope with feedback among model parameters is a major limitation of MC modelling. However, BI models can be easily integrated into MC modelling to overcome this limitation. We refer a BI submodel integrated into a MC model to as a "Bayes domain". We also demonstrate that an entire QMRA model can be formulated as Bayesian graphical model (BGM) and discuss the advantages of this approach. Finally, we show example graphs of MC, BI and BGM models, highlighting the similarities among the three approaches.
Macroscopic Models of Clique Tree Growth for Bayesian Networks
National Aeronautics and Space Administration — In clique tree clustering, inference consists of propagation in a clique tree compiled from a Bayesian network. In this paper, we develop an analytical approach to...
Emulation Modeling with Bayesian Networks for Efficient Decision Support
Fienen, M. N.; Masterson, J.; Plant, N. G.; Gutierrez, B. T.; Thieler, E. R.
2012-12-01
Bayesian decision networks (BDN) have long been used to provide decision support in systems that require explicit consideration of uncertainty; applications range from ecology to medical diagnostics and terrorism threat assessments. Until recently, however, few studies have applied BDNs to the study of groundwater systems. BDNs are particularly useful for representing real-world system variability by synthesizing a range of hydrogeologic situations within a single simulation. Because BDN output is cast in terms of probability—an output desired by decision makers—they explicitly incorporate the uncertainty of a system. BDNs can thus serve as a more efficient alternative to other uncertainty characterization methods such as computationally demanding Monte Carlo analyses and others methods restricted to linear model analyses. We present a unique application of a BDN to a groundwater modeling analysis of the hydrologic response of Assateague Island, Maryland to sea-level rise. Using both input and output variables of the modeled groundwater response to different sea-level (SLR) rise scenarios, the BDN predicts the probability of changes in the depth to fresh water, which exerts an important influence on physical and biological island evolution. Input variables included barrier-island width, maximum island elevation, and aquifer recharge. The variability of these inputs and their corresponding outputs are sampled along cross sections in a single model run to form an ensemble of input/output pairs. The BDN outputs, which are the posterior distributions of water table conditions for the sea-level rise scenarios, are evaluated through error analysis and cross-validation to assess both fit to training data and predictive power. The key benefit for using BDNs in groundwater modeling analyses is that they provide a method for distilling complex model results into predictions with associated uncertainty, which is useful to decision makers. Future efforts incorporate
Energy Technology Data Exchange (ETDEWEB)
Elsheikh, Ahmed H., E-mail: aelsheikh@ices.utexas.edu [Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX (United States); Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Wheeler, Mary F. [Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX (United States); Hoteit, Ibrahim [Department of Earth Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal (Saudi Arabia)
2014-02-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems.
A Tutorial Introduction to Bayesian Models of Cognitive Development
2011-01-01
Bayesian reasoner in the long run (de Finetti , 1937). Even if the Bayesian framework captures optimal inductive inference, does that mean it is an...Johns Hopkins University Press. de Finetti , B. (1937). Prevision, its logical laws, its subjective sources. In H. Kyburg & H. Smokler (Eds.), In...studies in subjective probability (2nd ed.). New York: J. Wiley and Sons. de Finetti , B. (1974). Theory of probability (2nd ed.). New York: J. Wiley and
A Bayesian model of category-specific emotional brain responses.
Directory of Open Access Journals (Sweden)
Tor D Wager
2015-04-01
Full Text Available Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories--fear, anger, disgust, sadness, or happiness--is engaged by a study with 66% accuracy (43-86% across categories. Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a differential patterns of involvement in neocortical systems that differ between humans and other species, and (b distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches.
Reliability assessment using degradation models: bayesian and classical approaches
Directory of Open Access Journals (Sweden)
Marta Afonso Freitas
2010-04-01
Full Text Available Traditionally, reliability assessment of devices has been based on (accelerated life tests. However, for highly reliable products, little information about reliability is provided by life tests in which few or no failures are typically observed. Since most failures arise from a degradation mechanism at work for which there are characteristics that degrade over time, one alternative is monitor the device for a period of time and assess its reliability from the changes in performance (degradation observed during that period. The goal of this article is to illustrate how degradation data can be modeled and analyzed by using "classical" and Bayesian approaches. Four methods of data analysis based on classical inference are presented. Next we show how Bayesian methods can also be used to provide a natural approach to analyzing degradation data. The approaches are applied to a real data set regarding train wheels degradation.Tradicionalmente, o acesso à confiabilidade de dispositivos tem sido baseado em testes de vida (acelerados. Entretanto, para produtos altamente confiáveis, pouca informação a respeito de sua confiabilidade é fornecida por testes de vida no quais poucas ou nenhumas falhas são observadas. Uma vez que boa parte das falhas é induzida por mecanismos de degradação, uma alternativa é monitorar o dispositivo por um período de tempo e acessar sua confiabilidade através das mudanças em desempenho (degradação observadas durante aquele período. O objetivo deste artigo é ilustrar como dados de degradação podem ser modelados e analisados utilizando-se abordagens "clássicas" e Bayesiana. Quatro métodos de análise de dados baseados em inferência clássica são apresentados. A seguir, mostramos como os métodos Bayesianos podem também ser aplicados para proporcionar uma abordagem natural à análise de dados de degradação. As abordagens são aplicadas a um banco de dados real relacionado à degradação de rodas de trens.
DEFF Research Database (Denmark)
Quinonero, Joaquin; Girard, Agathe; Larsen, Jan
2003-01-01
The object of Bayesian modelling is predictive distribution, which, in a forecasting scenario, enables evaluation of forecasted values and their uncertainties. We focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaus....... The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.......The object of Bayesian modelling is predictive distribution, which, in a forecasting scenario, enables evaluation of forecasted values and their uncertainties. We focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models...... such as the Gaussian process and the relevance vector machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting...
Bayesian Safety Risk Modeling of Human-Flightdeck Automation Interaction
Ancel, Ersin; Shih, Ann T.
2015-01-01
Usage of automatic systems in airliners has increased fuel efficiency, added extra capabilities, enhanced safety and reliability, as well as provide improved passenger comfort since its introduction in the late 80's. However, original automation benefits, including reduced flight crew workload, human errors or training requirements, were not achieved as originally expected. Instead, automation introduced new failure modes, redistributed, and sometimes increased workload, brought in new cognitive and attention demands, and increased training requirements. Modern airliners have numerous flight modes, providing more flexibility (and inherently more complexity) to the flight crew. However, the price to pay for the increased flexibility is the need for increased mode awareness, as well as the need to supervise, understand, and predict automated system behavior. Also, over-reliance on automation is linked to manual flight skill degradation and complacency in commercial pilots. As a result, recent accidents involving human errors are often caused by the interactions between humans and the automated systems (e.g., the breakdown in man-machine coordination), deteriorated manual flying skills, and/or loss of situational awareness due to heavy dependence on automated systems. This paper describes the development of the increased complexity and reliance on automation baseline model, named FLAP for FLightdeck Automation Problems. The model development process starts with a comprehensive literature review followed by the construction of a framework comprised of high-level causal factors leading to an automation-related flight anomaly. The framework was then converted into a Bayesian Belief Network (BBN) using the Hugin Software v7.8. The effects of automation on flight crew are incorporated into the model, including flight skill degradation, increased cognitive demand and training requirements along with their interactions. Besides flight crew deficiencies, automation system
A Bayesian network model for predicting aquatic toxicity mode ...
The mode of toxic action (MoA) has been recognized as a key determinant of chemical toxicity but MoA classification in aquatic toxicology has been limited. We developed a Bayesian network model to classify aquatic toxicity mode of action using a recently published dataset containing over one thousand chemicals with MoA assignments for aquatic animal toxicity. Two dimensional theoretical chemical descriptors were generated for each chemical using the Toxicity Estimation Software Tool. The model was developed through augmented Markov blanket discovery from the data set with the MoA broad classifications as a target node. From cross validation, the overall precision for the model was 80.2% with a R2 of 0.959. The best precision was for the AChEI MoA (93.5%) where 257 chemicals out of 275 were correctly classified. Model precision was poorest for the reactivity MoA (48.5%) where 48 out of 99 reactive chemicals were correctly classified. Narcosis represented the largest class within the MoA dataset and had a precision and reliability of 80.0%, reflecting the global precision across all of the MoAs. False negatives for narcosis most often fell into electron transport inhibition, neurotoxicity or reactivity MoAs. False negatives for all other MoAs were most often narcosis. A probabilistic sensitivity analysis was undertaken for each MoA to examine the sensitivity to individual and multiple descriptor findings. The results show that the Markov blanket of a structurally
The dynamics of multimodal integration: The averaging diffusion model.
Turner, Brandon M; Gao, Juan; Koenig, Scott; Palfy, Dylan; L McClelland, James
2017-03-08
We combine extant theories of evidence accumulation and multi-modal integration to develop an integrated framework for modeling multimodal integration as a process that unfolds in real time. Many studies have formulated sensory processing as a dynamic process where noisy samples of evidence are accumulated until a decision is made. However, these studies are often limited to a single sensory modality. Studies of multimodal stimulus integration have focused on how best to combine different sources of information to elicit a judgment. These studies are often limited to a single time point, typically after the integration process has occurred. We address these limitations by combining the two approaches. Experimentally, we present data that allow us to study the time course of evidence accumulation within each of the visual and auditory domains as well as in a bimodal condition. Theoretically, we develop a new Averaging Diffusion Model in which the decision variable is the mean rather than the sum of evidence samples and use it as a base for comparing three alternative models of multimodal integration, allowing us to assess the optimality of this integration. The outcome reveals rich individual differences in multimodal integration: while some subjects' data are consistent with adaptive optimal integration, reweighting sources of evidence as their relative reliability changes during evidence integration, others exhibit patterns inconsistent with optimality.
A Bayesian Chance-Constrained Method for Hydraulic Barrier Design Under Model Structure Uncertainty
Chitsazan, N.; Pham, H. V.; Tsai, F. T. C.
2014-12-01
The groundwater community has widely recognized the model structure uncertainty as the major source of model uncertainty in groundwater modeling. Previous studies in the aquifer remediation design, however, rarely discuss the impact of the model structure uncertainty. This study combines the chance-constrained (CC) programming with the Bayesian model averaging (BMA) as a BMA-CC framework to assess the effect of model structure uncertainty in the remediation design. To investigate the impact of the model structure uncertainty on the remediation design, we compare the BMA-CC method with the traditional CC programming that only considers the model parameter uncertainty. The BMA-CC method is employed to design a hydraulic barrier to protect public supply wells of the Government St. pump station from saltwater intrusion in the "1,500-foot" sand and the "1-700-foot" sand of the Baton Rouge area, southeastern Louisiana. To address the model structure uncertainty, we develop three conceptual groundwater models based on three different hydrostratigraphy structures. The results show that using the traditional CC programming overestimates design reliability. The results also show that at least five additional connector wells are needed to achieve more than 90% design reliability level. The total amount of injected water from connector wells is higher than the total pumpage of the protected public supply wells. While reducing injection rate can be achieved by reducing reliability level, the study finds that the hydraulic barrier design to protect the Government St. pump station is not economically attractive.
Scalable Bayesian modeling, monitoring and analysis of dynamic network flow data
2016-01-01
Traffic flow count data in networks arise in many applications, such as automobile or aviation transportation, certain directed social network contexts, and Internet studies. Using an example of Internet browser traffic flow through site-segments of an international news website, we present Bayesian analyses of two linked classes of models which, in tandem, allow fast, scalable and interpretable Bayesian inference. We first develop flexible state-space models for streaming count data, able to...
A Bayesian approach for temporally scaling climate for modeling ecological systems.
Post van der Burg, Max; Anteau, Michael J; McCauley, Lisa A; Wiltermuth, Mark T
2016-05-01
With climate change becoming more of concern, many ecologists are including climate variables in their system and statistical models. The Standardized Precipitation Evapotranspiration Index (SPEI) is a drought index that has potential advantages in modeling ecological response variables, including a flexible computation of the index over different timescales. However, little development has been made in terms of the choice of timescale for SPEI. We developed a Bayesian modeling approach for estimating the timescale for SPEI and demonstrated its use in modeling wetland hydrologic dynamics in two different eras (i.e., historical [pre-1970] and contemporary [post-2003]). Our goal was to determine whether differences in climate between the two eras could explain changes in the amount of water in wetlands. Our results showed that wetland water surface areas tended to be larger in wetter conditions, but also changed less in response to climate fluctuations in the contemporary era. We also found that the average timescale parameter was greater in the historical period, compared with the contemporary period. We were not able to determine whether this shift in timescale was due to a change in the timing of wet-dry periods or whether it was due to changes in the way wetlands responded to climate. Our results suggest that perhaps some interaction between climate and hydrologic response may be at work, and further analysis is needed to determine which has a stronger influence. Despite this, we suggest that our modeling approach enabled us to estimate the relevant timescale for SPEI and make inferences from those estimates. Likewise, our approach provides a mechanism for using prior information with future data to assess whether these patterns may continue over time. We suggest that ecologists consider using temporally scalable climate indices in conjunction with Bayesian analysis for assessing the role of climate in ecological systems.
A Bayesian approach for temporally scaling climate for modeling ecological systems
Post van der Burg, Max; Anteau, Michael J.; McCauley, Lisa A.; Wiltermuth, Mark T.
2016-01-01
With climate change becoming more of concern, many ecologists are including climate variables in their system and statistical models. The Standardized Precipitation Evapotranspiration Index (SPEI) is a drought index that has potential advantages in modeling ecological response variables, including a flexible computation of the index over different timescales. However, little development has been made in terms of the choice of timescale for SPEI. We developed a Bayesian modeling approach for estimating the timescale for SPEI and demonstrated its use in modeling wetland hydrologic dynamics in two different eras (i.e., historical [pre-1970] and contemporary [post-2003]). Our goal was to determine whether differences in climate between the two eras could explain changes in the amount of water in wetlands. Our results showed that wetland water surface areas tended to be larger in wetter conditions, but also changed less in response to climate fluctuations in the contemporary era. We also found that the average timescale parameter was greater in the historical period, compared with the contemporary period. We were not able to determine whether this shift in timescale was due to a change in the timing of wet–dry periods or whether it was due to changes in the way wetlands responded to climate. Our results suggest that perhaps some interaction between climate and hydrologic response may be at work, and further analysis is needed to determine which has a stronger influence. Despite this, we suggest that our modeling approach enabled us to estimate the relevant timescale for SPEI and make inferences from those estimates. Likewise, our approach provides a mechanism for using prior information with future data to assess whether these patterns may continue over time. We suggest that ecologists consider using temporally scalable climate indices in conjunction with Bayesian analysis for assessing the role of climate in ecological systems.
Bayesian network as a modelling tool for risk management in agriculture
DEFF Research Database (Denmark)
Rasmussen, Svend; Madsen, Anders L.; Lund, Mogens
. In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be efficiently used to estimate conditional probabilities, which are the core elements in Bayesian network models....... We further show how the Bayesian network model RiBay is used for stochastic simulation of farm income, and we demonstrate how RiBay can be used to simulate risk management at the farm level. It is concluded that the key strength of a Bayesian network is the transparency of assumptions......The importance of risk management increases as farmers become more exposed to risk. But risk management is a difficult topic because income risk is the result of the complex interaction of multiple risk factors combined with the effect of an increasing array of possible risk management tools...
Bayesian parameter inference and model selection by population annealing in systems biology.
Murakami, Yohei
2014-01-01
Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named "posterior parameter ensemble". We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor.
Bayesian Proteoform Modeling Improves Protein Quantification of Global Proteomic Measurements
Energy Technology Data Exchange (ETDEWEB)
Webb-Robertson, Bobbie-Jo M.; Matzke, Melissa M.; Datta, Susmita; Payne, Samuel H.; Kang, Jiyun; Bramer, Lisa M.; Nicora, Carrie D.; Shukla, Anil K.; Metz, Thomas O.; Rodland, Karin D.; Smith, Richard D.; Tardiff, Mark F.; McDermott, Jason E.; Pounds, Joel G.; Waters, Katrina M.
2014-12-01
As the capability of mass spectrometry-based proteomics has matured, tens of thousands of peptides can be measured simultaneously, which has the benefit of offering a systems view of protein expression. However, a major challenge is that with an increase in throughput, protein quantification estimation from the native measured peptides has become a computational task. A limitation to existing computationally-driven protein quantification methods is that most ignore protein variation, such as alternate splicing of the RNA transcript and post-translational modifications or other possible proteoforms, which will affect a significant fraction of the proteome. The consequence of this assumption is that statistical inference at the protein level, and consequently downstream analyses, such as network and pathway modeling, have only limited power for biomarker discovery. Here, we describe a Bayesian model (BP-Quant) that uses statistically derived peptides signatures to identify peptides that are outside the dominant pattern, or the existence of multiple over-expressed patterns to improve relative protein abundance estimates. It is a research-driven approach that utilizes the objectives of the experiment, defined in the context of a standard statistical hypothesis, to identify a set of peptides exhibiting similar statistical behavior relating to a protein. This approach infers that changes in relative protein abundance can be used as a surrogate for changes in function, without necessarily taking into account the effect of differential post-translational modifications, processing, or splicing in altering protein function. We verify the approach using a dilution study from mouse plasma samples and demonstrate that BP-Quant achieves similar accuracy as the current state-of-the-art methods at proteoform identification with significantly better specificity. BP-Quant is available as a MatLab ® and R packages at https://github.com/PNNL-Comp-Mass-Spec/BP-Quant.
A spatially-averaged mathematical model of kidney branching morphogenesis
Zubkov, V.S.
2015-08-01
© 2015 Published by Elsevier Ltd. Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.
Comparison of Bayesian and Classical Analysis of Weibull Regression Model: A Simulation Study
Directory of Open Access Journals (Sweden)
İmran KURT ÖMÜRLÜ
2011-01-01
Full Text Available Objective: The purpose of this study was to compare performances of classical Weibull Regression Model (WRM and Bayesian-WRM under varying conditions using Monte Carlo simulations. Material and Methods: It was simulated the generated data by running for each of classical WRM and Bayesian-WRM under varying informative priors and sample sizes using our simulation algorithm. In simulation studies, n=50, 100 and 250 were for sample sizes, and informative prior values using a normal prior distribution with was selected for b1. For each situation, 1000 simulations were performed. Results: Bayesian-WRM with proper informative prior showed a good performance with too little bias. It was found out that bias of Bayesian-WRM increased while priors were becoming distant from reliability in all sample sizes. Furthermore, Bayesian-WRM obtained predictions with more little standard error than the classical WRM in both of small and big samples in the light of proper priors. Conclusion: In this simulation study, Bayesian-WRM showed better performance than classical method, when subjective data analysis performed by considering of expert opinions and historical knowledge about parameters. Consequently, Bayesian-WRM should be preferred in existence of reliable informative priors, in the contrast cases, classical WRM should be preferred.
A Bayesian hierarchical model for accident and injury surveillance.
MacNab, Ying C
2003-01-01
This article presents a recent study which applies Bayesian hierarchical methodology to model and analyse accident and injury surveillance data. A hierarchical Poisson random effects spatio-temporal model is introduced and an analysis of inter-regional variations and regional trends in hospitalisations due to motor vehicle accident injuries to boys aged 0-24 in the province of British Columbia, Canada, is presented. The objective of this article is to illustrate how the modelling technique can be implemented as part of an accident and injury surveillance and prevention system where transportation and/or health authorities may routinely examine accidents, injuries, and hospitalisations to target high-risk regions for prevention programs, to evaluate prevention strategies, and to assist in health planning and resource allocation. The innovation of the methodology is its ability to uncover and highlight important underlying structure of the data. Between 1987 and 1996, British Columbia hospital separation registry registered 10,599 motor vehicle traffic injury related hospitalisations among boys aged 0-24 who resided in British Columbia, of which majority (89%) of the injuries occurred to boys aged 15-24. The injuries were aggregated by three age groups (0-4, 5-14, and 15-24), 20 health regions (based of place-of-residence), and 10 calendar years (1987 to 1996) and the corresponding mid-year population estimates were used as 'at risk' population. An empirical Bayes inference technique using penalised quasi-likelihood estimation was implemented to model both rates and counts, with spline smoothing accommodating non-linear temporal effects. The results show that (a) crude rates and ratios at health region level are unstable, (b) the models with spline smoothing enable us to explore possible shapes of injury trends at both the provincial level and the regional level, and (c) the fitted models provide a wealth of information about the patterns (both over space and time
A Bayesian model of stereopsis depth and motion direction discrimination.
Read, J C A
2002-02-01
The extraction of stereoscopic depth from retinal disparity, and motion direction from two-frame kinematograms, requires the solution of a correspondence problem. In previous psychophysical work [Read and Eagle (2000) Vision Res 40: 3345-3358], we compared the performance of the human stereopsis and motion systems with correlated and anti-correlated stimuli. We found that, although the two systems performed similarly for narrow-band stimuli, broadband anti-correlated kinematograms produced a strong perception of reversed motion, whereas the stereograms appeared merely rivalrous. I now model these psychophysical data with a computational model of the correspondence problem based on the known properties of visual cortical cells. Noisy retinal images are filtered through a set of Fourier channels tuned to different spatial frequencies and orientations. Within each channel, a Bayesian analysis incorporating a prior preference for small disparities is used to assess the probability of each possible match. Finally, information from the different channels is combined to arrive at a judgement of stimulus disparity. Each model system--stereopsis and motion--has two free parameters: the amount of noise they are subject to, and the strength of their preference for small disparities. By adjusting these parameters independently for each system, qualitative matches are produced to psychophysical data, for both correlated and anti-correlated stimuli, across a range of spatial frequency and orientation bandwidths. The motion model is found to require much higher noise levels and a weaker preference for small disparities. This makes the motion model more tolerant of poor-quality reverse-direction false matches encountered with anti-correlated stimuli, matching the strong perception of reversed motion that humans experience with these stimuli. In contrast, the lower noise level and tighter prior preference used with the stereopsis model means that it performs close to chance with
Bayesian Network Based Fault Prognosis via Bond Graph Modeling of High-Speed Railway Traction Device
Directory of Open Access Journals (Sweden)
Yunkai Wu
2015-01-01
component-level faults accurately for a high-speed railway traction system, a fault prognosis approach via Bayesian network and bond graph modeling techniques is proposed. The inherent structure of a railway traction system is represented by bond graph model, based on which a multilayer Bayesian network is developed for fault propagation analysis and fault prediction. For complete and incomplete data sets, two different parameter learning algorithms such as Bayesian estimation and expectation maximization (EM algorithm are adopted to determine the conditional probability table of the Bayesian network. The proposed prognosis approach using Pearl’s polytree propagation algorithm for joint probability reasoning can predict the failure probabilities of leaf nodes based on the current status of root nodes. Verification results in a high-speed railway traction simulation system can demonstrate the effectiveness of the proposed approach.
Inherently irrational? A computational model of escalation of commitment as Bayesian Updating.
Gilroy, Shawn P; Hantula, Donald A
2016-06-01
Monte Carlo simulations were performed to analyze the degree to which two-, three- and four-step learning histories of losses and gains correlated with escalation and persistence in extended extinction (continuous loss) conditions. Simulated learning histories were randomly generated at varying lengths and compositions and warranted probabilities were determined using Bayesian Updating methods. Bayesian Updating predicted instances where particular learning sequences were more likely to engender escalation and persistence under extinction conditions. All simulations revealed greater rates of escalation and persistence in the presence of heterogeneous (e.g., both Wins and Losses) lag sequences, with substantially increased rates of escalation when lags comprised predominantly of losses were followed by wins. These methods were then applied to human investment choices in earlier experiments. The Bayesian Updating models corresponded with data obtained from these experiments. These findings suggest that Bayesian Updating can be utilized as a model for understanding how and when individual commitment may escalate and persist despite continued failures.
Gelman, Andrew; Stern, Hal S; Dunson, David B; Vehtari, Aki; Rubin, Donald B
2013-01-01
FUNDAMENTALS OF BAYESIAN INFERENCEProbability and InferenceSingle-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian ApproachesHierarchical ModelsFUNDAMENTALS OF BAYESIAN DATA ANALYSISModel Checking Evaluating, Comparing, and Expanding ModelsModeling Accounting for Data Collection Decision AnalysisADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional ApproximationsREGRESSION MODELS Introduction to Regression Models Hierarchical Linear
Ferragina, A; de los Campos, G; Vazquez, A I; Cecchinato, A; Bittante, G
2015-11-01
The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict "difficult-to-predict" dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm(-1) were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from
Institute of Scientific and Technical Information of China (English)
Farid Zayeri; Masoud Salehi; Hasan Pirhosseini
2011-01-01
Objective:To present the geographical map of malaria and identify some of the important environmental factors of this disease in Sistan and Baluchistan province, Iran.Methods:We used the registered malaria data to compute the standard incidence rates (SIRs) of malaria in different areas of Sistan and Baluchistan province for a nine-year period (from 2001 to 2009). Statistical analyses consisted of two different parts: geographical mapping of malaria incidence rates, and modeling the environmental factors. The empirical Bayesian estimates of malaria SIRs were utilized for geographical mapping of malaria and a Poisson random effects model was used for assessing the effect of environmental factors on malaria SIRs.Results:In general, 64 926 new cases of malaria were registered in Sistan and Baluchistan Province from 2001 to 2009. Among them, 42 695 patients (65.8%) were male and 22 231 patients (34.2%) were female. Modeling the environmental factors showed that malaria incidence rates had positive relationship with humidity, elevation, average minimum temperature and average maximum temperature, while rainfall had negative effect on malaria SIRs in this province.Conclusions:The results of the present study reveals that malaria is still a serious health problem in Sistan and Baluchistan province, Iran. Geographical map and related environmental factors of malaria can help the health policy makers to intervene in high risk areas more efficiently and allocate the resources in a proper manner.
Applied Bayesian Hierarchical Methods
Congdon, Peter D
2010-01-01
Bayesian methods facilitate the analysis of complex models and data structures. Emphasizing data applications, alternative modeling specifications, and computer implementation, this book provides a practical overview of methods for Bayesian analysis of hierarchical models.
Directory of Open Access Journals (Sweden)
Abel Palafox
2014-01-01
Full Text Available We address a prototype inverse scattering problem in the interface of applied mathematics, statistics, and scientific computing. We pose the acoustic inverse scattering problem in a Bayesian inference perspective and simulate from the posterior distribution using MCMC. The PDE forward map is implemented using high performance computing methods. We implement a standard Bayesian model selection method to estimate an effective number of Fourier coefficients that may be retrieved from noisy data within a standard formulation.
Directory of Open Access Journals (Sweden)
Mihaela Simionescu
2014-12-01
Full Text Available There are many types of econometric models used in predicting the inflation rate, but in this study we used a Bayesian shrinkage combination approach. This methodology is used in order to improve the predictions accuracy by including information that is not captured by the econometric models. Therefore, experts’ forecasts are utilized as prior information, for Romania these predictions being provided by Institute for Economic Forecasting (Dobrescu macromodel, National Commission for Prognosis and European Commission. The empirical results for Romanian inflation show the superiority of a fixed effects model compared to other types of econometric models like VAR, Bayesian VAR, simultaneous equations model, dynamic model, log-linear model. The Bayesian combinations that used experts’ predictions as priors, when the shrinkage parameter tends to infinite, improved the accuracy of all forecasts based on individual models, outperforming also zero and equal weights predictions and naïve forecasts.
Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W
2007-07-01
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.
Model Criticism of Bayesian Networks with Latent Variables.
Williamson, David M.; Mislevy, Robert J.; Almond, Russell G.
This study investigated statistical methods for identifying errors in Bayesian networks (BN) with latent variables, as found in intelligent cognitive assessments. BN, commonly used in artificial intelligence systems, are promising mechanisms for scoring constructed-response examinations. The success of an intelligent assessment or tutoring system…
Bayesian log-periodic model for financial crashes
DEFF Research Database (Denmark)
Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar
2014-01-01
This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions...
Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model
Mo, Qianxing
2010-01-29
ChIP-chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein-DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP-chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP-chip data through an Ising model with high-order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios. © 2010, The International Biometric Society.
Lesaffre, Emmanuel
2012-01-01
The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introd
Energy Technology Data Exchange (ETDEWEB)
La Russa, D [The Ottawa Hospital Cancer Centre, Ottawa, ON (Canada)
2015-06-15
Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributions found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.
Shen, Yanna; Cooper, Gregory F
2012-09-01
This paper investigates Bayesian modeling of known and unknown causes of events in the context of disease-outbreak detection. We introduce a multivariate Bayesian approach that models multiple evidential features of every person in the population. This approach models and detects (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A contribution of this paper is that it introduces a multivariate Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has general applicability in domains where the space of known causes is incomplete.
Energy Technology Data Exchange (ETDEWEB)
Placek, Ben; Knuth, Kevin H. [Physics Department, University at Albany (SUNY), Albany, NY 12222 (United States); Angerhausen, Daniel, E-mail: bplacek@albany.edu, E-mail: kknuth@albany.edu, E-mail: daniel.angerhausen@gmail.com [Department of Physics, Applied Physics, and Astronomy, Rensselear Polytechnic Institute, Troy, NY 12180 (United States)
2014-11-10
EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian model selection, a unique aspect of EXONEST is the potential capability to distinguish between reflective and thermal contributions to the light curve. A case study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the nontransiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.
A Bayesian hierarchical diffusion model decomposition of performance in Approach-Avoidance Tasks.
Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan
2015-01-01
Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach-Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest.
Placek, Ben; Angerhausen, Daniel
2013-01-01
EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian Inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian Model Selection, a unique aspect of EXONEST is the capability to distinguish between reflective and thermal contributions to the light curve. A case-study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the non-transiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically-relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentric...
Placek, Ben; Knuth, Kevin H.; Angerhausen, Daniel
2014-11-01
EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian model selection, a unique aspect of EXONEST is the potential capability to distinguish between reflective and thermal contributions to the light curve. A case study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the nontransiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.
Another look at Bayesian analysis of AMMI models for genotype-environment data
Josse, J.; Eeuwijk, van F.A.; Piepho, H.P.; Denis, J.B.
2014-01-01
Linear–bilinear models are frequently used to analyze two-way data such as genotype-by-environment data. A well-known example of this class of models is the additive main effects and multiplicative interaction effects model (AMMI). We propose a new Bayesian treatment of such models offering a proper
Time-series gas prediction model using LS-SVR within a Bayesian framework
Institute of Scientific and Technical Information of China (English)
Qiao Meiying; Ma Xiaoping; Lan Jianyi; Wang Ying
2011-01-01
The traditional least squares support vector regression (LS-SVR) model, using cross validation to determine the regularization parameter and kernel parameter, is time-consuming. We propose a Bayesian evidence framework to infer the LS-SVR model parameters. Three levels Bayesian inferences are used to determine the model parameters, regularization hyper-parameters and tune the nuclear parameters by model comparison. On this basis, we established Bayesian LS-SVR time-series gas forecasting models and provide steps for the algorithm. The gas outburst data of a Hebi 10th mine working face is used to validate the model. The optimal embedding dimension and delay time of the time series were obtained by the smallest differential entropy method. Finally, within a MATLAB7.1 environment, we used actual coal gas data to compare the traditional LS-SVR and the Bayesian LS-SVR with LS-SVMlab1.5 Toolbox simulation. The results show that the Bayesian framework of an LS-SVR significantly improves the speed and accuracy of the forecast
Bayesian network modeling method based on case reasoning for emergency decision-making
Directory of Open Access Journals (Sweden)
XU Lei
2013-06-01
Full Text Available Bayesian network has the abilities of probability expression, uncertainty management and multi-information fusion.It can support emergency decision-making, which can improve the efficiency of decision-making.Emergency decision-making is highly time sensitive, which requires shortening the Bayesian Network modeling time as far as possible.Traditional Bayesian network modeling methods are clearly unable to meet that requirement.Thus, a Bayesian network modeling method based on case reasoning for emergency decision-making is proposed.The method can obtain optional cases through case matching by the functions of similarity degree and deviation degree.Then,new Bayesian network can be built through case adjustment by case merging and pruning.An example is presented to illustrate and test the proposed method.The result shows that the method does not have a huge search space or need sample data.The only requirement is the collection of expert knowledge and historical case models.Compared with traditional methods, the proposed method can reuse historical case models, which can reduce the modeling time and improve the efficiency.
Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno
2016-01-01
Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
The Determinants of Gini Coefficient in Iran Based on Bayesian Model Averaging
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Mohsen Mehrara
2015-03-01
Full Text Available This paper has tried to apply BMA approach in order to investigate important influential variables on Gini coefficient in Iran over the period 1976-2010. The results indicate that the GDP growth is the most important variable affecting the Gini coefficient and has a positive influence on it. Also the second and third effective variables on Gini coefficient are respectively the ratio of government current expenditure to GDP and the ratio of oil revenue to GDP which lead to an increase in inequality. This result is corresponding with rentier state theory in Iran economy. Injection of massive oil revenue to Iran's economy and its high share of the state budget leads to inefficient government spending and an increase in rent-seeking activities in the country. Economic growth is possibly a result of oil revenue in Iran economy which has caused inequality in distribution of income.
The Determinants of Gini Coefficient in Iran Based on Bayesian Model Averaging
Mohsen Mehrara; Mojtaba Mohammadian
2015-01-01
This paper has tried to apply BMA approach in order to investigate important influential variables on Gini coefficient in Iran over the period 1976-2010. The results indicate that the GDP growth is the most important variable affecting the Gini coefficient and has a positive influence on it. Also the second and third effective variables on Gini coefficient are respectively the ratio of government current expenditure to GDP and the ratio of oil revenue to GDP which lead to an increase in inequ...
A Bayesian Surrogate Model for Rapid Time Series Analysis and Application to Exoplanet Observations
Ford, Eric B; Veras, Dimitri
2011-01-01
We present a Bayesian surrogate model for the analysis of periodic or quasi-periodic time series data. We describe a computationally efficient implementation that enables Bayesian model comparison. We apply this model to simulated and real exoplanet observations. We discuss the results and demonstrate some of the challenges for applying our surrogate model to realistic exoplanet data sets. In particular, we find that analyses of real world data should pay careful attention to the effects of uneven spacing of observations and the choice of prior for the "jitter" parameter.
Directory of Open Access Journals (Sweden)
Moritz eBoos
2016-05-01
Full Text Available Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modelling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities by two (likelihoods design. Five computational models of cognitive processes were compared with the observed behaviour. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model’s success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modelling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modelling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Gong, Maozhen
Selecting an appropriate prior distribution is a fundamental issue in Bayesian Statistics. In this dissertation, under the framework provided by Berger and Bernardo, I derive the reference priors for several models which include: Analysis of Variance (ANOVA)/Analysis of Covariance (ANCOVA) models with a categorical variable under common ordering constraints, the conditionally autoregressive (CAR) models and the simultaneous autoregressive (SAR) models with a spatial autoregression parameter rho considered. The performances of reference priors for ANOVA/ANCOVA models are evaluated by simulation studies with comparisons to Jeffreys' prior and Least Squares Estimation (LSE). The priors are then illustrated in a Bayesian model of the "Risk of Type 2 Diabetes in New Mexico" data, where the relationship between the type 2 diabetes risk (through Hemoglobin A1c) and different smoking levels is investigated. In both simulation studies and real data set modeling, the reference priors that incorporate internal order information show good performances and can be used as default priors. The reference priors for the CAR and SAR models are also illustrated in the "1999 SAT State Average Verbal Scores" data with a comparison to a Uniform prior distribution. Due to the complexity of the reference priors for both CAR and SAR models, only a portion (12 states in the Midwest) of the original data set is considered. The reference priors can give a different marginal posterior distribution compared to a Uniform prior, which provides an alternative for prior specifications for areal data in Spatial statistics.
Maximum Likelihood Estimation of Multivariate Autoregressive-Moving Average Models.
1977-02-01
maximizing the same have been proposed i) in time domain by Box and Jenkins [41. Astrom [3J, Wilson [23 1, and Phadke [161, and ii) in frequency domain by...moving average residuals and other convariance matrices with linear structure ”, Anna/s of Staustics, 3. 3. Astrom , K. J. (1970), Introduction to
Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective
Barker, Richard J.; Link, William A.
2015-01-01
Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.
Factors contributing to academic achievement: a Bayesian structure equation modelling study
Payandeh Najafabadi, Amir T.; Omidi Najafabadi, Maryam; Farid-Rohani, Mohammad Reza
2013-06-01
In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in their education despite their excellent performance on the Konkoor and in high school; (2) graduate with a grade point average (GPA) that is considerably lower than their high school GPA; (3) continue their master's education in majors other than statistics and (4) try to find jobs unrelated to statistics. This article employs the well-known and powerful statistical technique, the Bayesian structural equation modelling (SEM), to study the academic success of recent graduates who have studied statistics at Shahid Beheshti University in Iran. This research: (i) considered academic success as a latent variable, which was measured by GPA and other academic success (see below) of students in the target population; (ii) employed the Bayesian SEM, which works properly for small sample sizes and ordinal variables; (iii), which is taken from the literature, developed five main factors that affected academic success and (iv) considered several standard psychological tests and measured characteristics such as 'self-esteem' and 'anxiety'. We then study the impact of such factors on the academic success of the target population. Six factors that positively impact student academic success were identified in the following order of relative impact (from greatest to least): 'Teaching-Evaluation', 'Learner', 'Environment', 'Family', 'Curriculum' and 'Teaching Knowledge'. Particularly, influential variables within each factor have also been noted.
Bayesian modelling of the emission spectrum of the JET Li-BES system
Kwak, Sehyun; Brix, M; Ghim, Y -c; Contributors, JET
2015-01-01
A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy (Li-BES) system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The p...
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Che Wan Jasimah bt Wan Mohamed Radzi
2016-11-01
Full Text Available Several factors may influence children’s lifestyle. The main purpose of this study is to introduce a children’s lifestyle index framework and model it based on structural equation modeling (SEM with Maximum likelihood (ML and Bayesian predictors. This framework includes parental socioeconomic status, household food security, parental lifestyle, and children’s lifestyle. The sample for this study involves 452 volunteer Chinese families with children 7–12 years old. The experimental results are compared in terms of root mean square error, coefficient of determination, mean absolute error, and mean absolute percentage error metrics. An analysis of the proposed causal model suggests there are multiple significant interconnections among the variables of interest. According to both Bayesian and ML techniques, the proposed framework illustrates that parental socioeconomic status and parental lifestyle strongly impact children’s lifestyle. The impact of household food security on children’s lifestyle is rejected. However, there is a strong relationship between household food security and both parental socioeconomic status and parental lifestyle. Moreover, the outputs illustrate that the Bayesian prediction model has a good fit with the data, unlike the ML approach. The reasons for this discrepancy between ML and Bayesian prediction are debated and potential advantages and caveats with the application of the Bayesian approach in future studies are discussed.
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J. P. Werner
2015-03-01
Full Text Available Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.
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J. P. Werner
2014-12-01
Full Text Available Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches to accounting for time uncertainty are generally limited to repeating the reconstruction using each of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here we demonstrate how Bayesian Hierarchical climate reconstruction models can be augmented to account for time uncertain proxies. Critically, while a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age-model probabilities decreases uncertainty in the climate reconstruction, as compared with the current de-facto standard of sampling over all age models, provided there is sufficient information from other data sources in the region of the time-uncertain proxy. This approach can readily be generalized to non-layer counted proxies, such as those derived from marine sediments.
Nonparametric Bayesian Sparse Factor Models with application to Gene Expression modelling
Knowles, David
2010-01-01
A nonparametric Bayesian extension of Factor Analysis (FA) is proposed where observed data Y is modeled as a linear superposition, G, of a potentially infinite number of hidden factors, X. The Indian Buffet Process (IBP) is used as a prior on G to incorporate sparsity and to allow the number of latent features to be inferred. The model's utility for modeling gene expression data is investigated using randomly generated datasets based on a known sparse connectivity matrix for E. Coli, and on three biological datasets of increasing complexity.
Hierarchical Bayesian Model for Simultaneous EEG Source and Forward Model Reconstruction (SOFOMORE)
DEFF Research Database (Denmark)
Stahlhut, Carsten; Mørup, Morten; Winther, Ole;
2009-01-01
In this paper we propose an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model is motivated by the many uncertain contributions that form the forward propagation model including the tissue conductivity distribution, the cortical surface, and ele......In this paper we propose an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model is motivated by the many uncertain contributions that form the forward propagation model including the tissue conductivity distribution, the cortical surface......, and electrode positions. We first present a hierarchical Bayesian framework for EEG source localization that jointly performs source and forward model reconstruction (SOFOMORE). Secondly, we evaluate the SOFOMORE model by comparison with source reconstruction methods that use fixed forward models. Simulated...... and real EEG data demonstrate that invoking a stochastic forward model leads to improved source estimates....
Tang, An-Min; Tang, Nian-Sheng
2015-02-28
We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within-subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew-normal distribution to specify the within-subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within-subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies.
A Bayesian network model for assessing natural estrogen fate and transport in a swine waste lagoon.
Lee, Boknam; Kullman, Seth W; Yost, Erin; Meyer, Michael T; Worley-Davis, Lynn; Williams, C Michael; Reckhow, Kenneth H
2014-10-01
Commercial swine waste lagoons are regarded as a major reservoir of natural estrogens, which have the potential to produce adverse physiological effects on exposed aquatic organisms and wildlife. However, there remains limited understanding of the complex mechanisms of physical, chemical, and biological processes that govern the fate and transport of natural estrogens within an anaerobic swine lagoon. To improve lagoon management and ultimately help control the offsite transport of these compounds from swine operations, a probabilistic Bayesian network model was developed to assess natural estrogen fate and budget and then compared against data collected from a commercial swine field site. In general, the model was able to describe the estrogen fate and budget in both the slurry and sludge stores within the swine lagoon. Sensitivity analysis within the model demonstrated that the estrogen input loading from the associated barn facility was the most important factor in controlling estrogen concentrations within the lagoon slurry storage, whereas the settling rate was the most significant factor in the lagoon sludge storage. The degradation reactions were shown to be minor in both stores based on prediction of average total estrogen concentrations. Management scenario evaluations demonstrated that the best possible management options to reduce estrogen levels in the lagoon are either to adjust the estrogen input loading from swine barn facilities or to effectively enhance estrogen bonding with suspended solids through the use of organic polymers or inorganic coagulants.
Which level of model complexity is justified by your data? A Bayesian answer
Schöniger, Anneli; Illman, Walter; Wöhling, Thomas; Nowak, Wolfgang
2016-04-01
When judging the plausibility and utility of a subsurface flow or transport model, the question of justifiability arises: which level of model complexity can still be justified by the available calibration data? Although it is common sense that more data are needed to reasonably constrain the parameter space of a more complex model, there is a lack of tools that can objectively quantify model justifiability as a function of the available data. We propose an approach to determine model justifiability in the context of comparing alternative conceptual models. Our approach rests on Bayesian model averaging (BMA). BMA yields posterior model probabilities that point the modeler to an optimal trade-off between model performance in reproducing a given calibration data set and model complexity. To find out which level of complexity can be justified by the available data, we disentangle the complexity component of the trade-off from its performance counterpart. Technically, we remove the performance component from the BMA analysis by replacing the actually observed data values with potential measurement values as predicted by the models. Our proposed analysis results in a "model confusion matrix". Based on this matrix, the modeler can identify the maximum level of model complexity that could possibly be justified by the available amount and type of data. As a side product, model (dis-)similarity is revealed. We have applied the model justifiability analysis to a case of aquifer characterization via hydraulic tomography. Four models of vastly different complexity have been proposed to represent the heterogeneity in hydraulic conductivity of a sandbox aquifer, ranging from a homogeneous medium to geostatistical random fields. We have used drawdown data from two to six pumping tests to condition the models and to determine model justifiability as a function of data set size. Our test case shows that a geostatistical parameterization scheme requires a substantial amount of
Lee, Sik-Yum
2012-01-01
This book provides clear instructions to researchers on how to apply Structural Equation Models (SEMs) for analyzing the inter relationships between observed and latent variables. Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduce
Planning of O&M for Offfshore Wind Turbines using Bayesian Graphical Models
DEFF Research Database (Denmark)
Nielsen, Jannie Jessen; Sørensen, John Dalsgaard
2010-01-01
The costs to operation and maintenance (O&M) for offshore wind turbines are large, and riskbased planning of O&M has the potential of reducing these costs. This paper presents how Bayesian graphical models can be used to establish a probabilistic damage model and include data from imperfect...
Non-parametric Bayesian graph models reveal community structure in resting state fMRI
DEFF Research Database (Denmark)
Andersen, Kasper Winther; Madsen, Kristoffer H.; Siebner, Hartwig Roman
2014-01-01
Modeling of resting state functional magnetic resonance imaging (rs-fMRI) data using network models is of increasing interest. It is often desirable to group nodes into clusters to interpret the communication patterns between nodes. In this study we consider three different nonparametric Bayesian...
DEFF Research Database (Denmark)
Dalgaard, Jens; Pena, Jose; Kocka, Tomas
2004-01-01
We propose a method to assist the user in the interpretation of the best Bayesian network model indu- ced from data. The method consists in extracting relevant features from the model (e.g. edges, directed paths and Markov blankets) and, then, assessing the con¯dence in them by studying multiple...
A Bayesian MCMC method for point process models with intractable normalising constants
DEFF Research Database (Denmark)
Berthelsen, Kasper Klitgaard; Møller, Jesper
2004-01-01
to simulate from the "unknown distribution", perfect simulation algorithms become useful. We illustrate the method in cases whre the likelihood is given by a Markov point process model. Particularly, we consider semi-parametric Bayesian inference in connection to both inhomogeneous Markov point process models...
A Bayesian Multi-Level Factor Analytic Model of Consumer Price Sensitivities across Categories
Duvvuri, Sri Devi; Gruca, Thomas S.
2010-01-01
Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to…
Bayesian network models for the management of ventilator-associated pneumonia
Visscher, S.
2008-01-01
The purpose of the research described in this thesis was to develop Bayesian network models for the analysis of patient data, as well as to use such a model as a clinical decision-support system for assisting clinicians in the diagnosis and treatment of ventilator-associated pneumonia (VAP) in mecha
Osei, Frank B.; Duker, Alfred A.; Stein, Alfred
2011-01-01
This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint
Directory of Open Access Journals (Sweden)
Hao Zhang
2016-01-01
Full Text Available Under the increasingly uncertain economic environment, the research on the reliability of urban distribution system has great practical significance for the integration of logistics and supply chain resources. This paper summarizes the factors that affect the city logistics distribution system. Starting from the research of factors that influence the reliability of city distribution system, further construction of city distribution system reliability influence model is built based on Bayesian networks. The complex problem is simplified by using the sub-Bayesian network, and an example is analyzed. In the calculation process, we combined the traditional Bayesian algorithm and the Expectation Maximization (EM algorithm, which made the Bayesian model able to lay a more accurate foundation. The results show that the Bayesian network can accurately reflect the dynamic relationship among the factors affecting the reliability of urban distribution system. Moreover, by changing the prior probability of the node of the cause, the correlation degree between the variables that affect the successful distribution can be calculated. The results have significant practical significance on improving the quality of distribution, the level of distribution, and the efficiency of enterprises.
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Entin Hidayah
2011-02-01
Full Text Available Disaggregation of hourly rainfall data is very important to fulfil the input of continual rainfall-runoff model, when the availability of automatic rainfall records are limited. Continual rainfall-runoff modeling requires rainfall data in form of series of hourly. Such specification can be obtained by temporal disaggregation in single site. The paper attempts to generate single-site rainfall model based upon time series (AR1 model by adjusting and establishing dummy procedure. Estimated with Bayesian Markov Chain Monte Carlo (MCMC the objective variable is hourly rainfall depth. Performance of model has been evaluated by comparison of history data and model prediction. The result shows that the model has a good performance for dry interval periods. The performance of the model good represented by smaller number of MAE by 0.21 respectively.
Forecasting house prices in the 50 states using Dynamic Model Averaging and Dynamic Model Selection
DEFF Research Database (Denmark)
Bork, Lasse; Møller, Stig Vinther
2015-01-01
We examine house price forecastability across the 50 states using Dynamic Model Averaging and Dynamic Model Selection, which allow for model change and parameter shifts. By allowing the entire forecasting model to change over time and across locations, the forecasting accuracy improves...
Model Data Fusion: developing Bayesian inversion to constrain equilibrium and mode structure
Hole, M J; Bertram, J; Svensson, J; Appel, L C; Blackwell, B D; Dewar, R L; Howard, J
2010-01-01
Recently, a new probabilistic "data fusion" framework based on Bayesian principles has been developed on JET and W7-AS. The Bayesian analysis framework folds in uncertainties and inter-dependencies in the diagnostic data and signal forward-models, together with prior knowledge of the state of the plasma, to yield predictions of internal magnetic structure. A feature of the framework, known as MINERVA (J. Svensson, A. Werner, Plasma Physics and Controlled Fusion 50, 085022, 2008), is the inference of magnetic flux surfaces without the use of a force balance model. We discuss results from a new project to develop Bayesian inversion tools that aim to (1) distinguish between competing equilibrium theories, which capture different physics, using the MAST spherical tokamak; and (2) test the predictions of MHD theory, particularly mode structure, using the H-1 Heliac.
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen
2012-01-01
Many successful segmentation algorithms are based on Bayesian models in which prior anatomical knowledge is combined with the available image information. However, these methods typically have many free parameters that are estimated to obtain point estimates only, whereas a faithful Bayesian analysis would also consider all possible alternate values these parameters may take. In this paper, we propose to incorporate the uncertainty of the free parameters in Bayesian segmentation models more accurately by using Monte Carlo sampling. We demonstrate our technique by sampling atlas warps in a recent method for hippocampal subfield segmentation, and show a significant improvement in an Alzheimer's disease classification task. As an additional benefit, the method also yields informative "error bars" on the segmentation results for each of the individual sub-structures.
DEFF Research Database (Denmark)
Iglesias, J. E.; Sabuncu, M. R.; Van Leemput, Koen
2012-01-01
in a recent method for hippocampal subfield segmentation, and show a significant improvement in an Alzheimer’s disease classification task. As an additional benefit, the method also yields informative “error bars” on the segmentation results for each of the individual sub-structures.......Many successful segmentation algorithms are based on Bayesian models in which prior anatomical knowledge is combined with the available image information. However, these methods typically have many free parameters that are estimated to obtain point estimates only, whereas a faithful Bayesian...... analysis would also consider all possible alternate values these parameters may take. In this paper, we propose to incorporate the uncertainty of the free parameters in Bayesian segmentation models more accurately by using Monte Carlo sampling. We demonstrate our technique by sampling atlas warps...
Introduction to Bayesian statistics
Bolstad, William M
2017-01-01
There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...
Wu, J -L; Xiao, H
2015-01-01
Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example, Reynolds-Averaged Navier-Stokes (RANS) simulations are increasingly used in mission-critical systems involving turbulent flows. However, for many practical flows the RANS predictions have large model-form uncertainties originating from the uncertainty in the modeled Reynolds stresses. Recently, a physics-informed Bayesian framework has been proposed to quantify and reduce model-form uncertainties in RANS simulations by utilizing sparse observation data. However, in the design stage of engineering systems, measurement data are usually not available. In the present work we extend the original framework to scenarios where there are no available data on the flow to be predicted. In the proposed method, we first calibrate the model discrepancy on a related flow with available dat...
Pulsar average wave forms and hollow-cone beam models
Backer, D. C.
1976-01-01
Pulsar wave forms have been analyzed from observations conducted over a wide radio-frequency range to assess the wave-form morphologies and to measure wave-form widths. The results of the analysis compare favorably with the predictions of a model with a hollow-cone beam of fixed dimensions and with random orientation of both the observer and the cone axis with respect to the pulsar spin axis. A class of three-component wave forms is included in the model by adding a central pencil beam to the hollow-cone hypothesis. The consequences of a number of discrepancies between observations and quantitative predictions of the model are discussed.
Bayesian artificial intelligence
Korb, Kevin B
2010-01-01
Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente
Goring, S.; Williams, J. W.; Blois, J. L.; Jackson, S. T.; Paciorek, C. J.; Booth, R. K.; Marlon, J. R.; Blaauw, M.; Christen, J. A.
2012-08-01
Bayesian approaches since there is strong variation in the gamma parameters both in the most recent sediments and throughout the Holocene. Time-averaged gamma distributions for lacustrine (α = 1.35, β = 19.64) and palustrine samples (α = 1.40, β = 20.72) show lower overall deposition times, but variability remains. The variation in gamma parameters through time may require the use of multiple gamma distributions during the Holocene to generate accurate age-depth models. We present estimates of gamma parameters for deposition times at 1000 yr intervals. The parameters generated in this study can be used directly within Bacon to act as Bayesian priors for sedimentary age models.
Models and average properties of scale-free directed networks
Bernhardsson, Sebastian; Minnhagen, Petter
2006-08-01
We extend the merging model for undirected networks by Kim [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile merging, give rise to two distinct network types. We uncover that some nontrivial features of these two network types resemble two levels of a certain randomization/nonspecificity in the link reshuffling during network evolution. Furthermore, the same features show up, respectively, in metabolic networks and transcriptional networks. We introduce measures that single out the distinguishing features between the two prototype networks, as well as point out features that are beyond the prototypes.
Elsheikh, Ahmed H.
2014-02-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems. © 2013 Elsevier Inc.
Risk Forecasting of Karachi Stock Exchange: A Comparison of Classical and Bayesian GARCH Models
Directory of Open Access Journals (Sweden)
Farhat Iqbal
2016-09-01
Full Text Available This paper is concerned with the estimation, forecasting and evaluation of Value-at-Risk (VaR of Karachi Stock Exchange before and after the global financial crisis of 2008 using Bayesian method. The generalized autoregressive conditional heteroscedastic (GARCH models under the assumption of normal and heavy-tailed errors are used to forecast one-day-ahead risk estimates. Various measures and backtesting methods are employed to evaluate VaR forecasts. The observed number of VaR violations using Bayesian method is found close to the expected number of violations. The losses are also found smaller than the competing Maximum Likelihood method. The results showed that the Bayesian method produce accurate and reliable VaR forecasts and can be preferred over other methods.
An object-oriented Bayesian network modeling the causes of leg disorders in finisher herds
DEFF Research Database (Denmark)
Jensen, Tina Birk; Kristensen, Anders Ringgaard; Toft, Nils
2009-01-01
The implementation of an effective control strategy against disease in a finisher herd requires knowledge regarding the disease level in the herd. A Bayesian network was constructed that can estimate risk indexes for three cause-categories of leg disorders in a finisher herd. The cause...... pigs (e.g. results from diagnostic tests) were used to estimate the most likely cause of leg disorders at herd level. As information to the model originated from two different levels, we used an object-oriented structure in order to ease the specification of the Bayesian network. Hence, a Herd class...
Prudhomme, Serge
2015-09-17
Parameter estimation for complex models using Bayesian inference is usually a very costly process as it requires a large number of solves of the forward problem. We show here how the construction of adaptive surrogate models using a posteriori error estimates for quantities of interest can significantly reduce the computational cost in problems of statistical inference. As surrogate models provide only approximations of the true solutions of the forward problem, it is nevertheless necessary to control these errors in order to construct an accurate reduced model with respect to the observables utilized in the identification of the model parameters. Effectiveness of the proposed approach is demonstrated on a numerical example dealing with the Spalart–Allmaras model for the simulation of turbulent channel flows. In particular, we illustrate how Bayesian model selection using the adapted surrogate model in place of solving the coupled nonlinear equations leads to the same quality of results while requiring fewer nonlinear PDE solves.
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Gianola Daniel
2007-09-01
Full Text Available Abstract Multivariate linear models are increasingly important in quantitative genetics. In high dimensional specifications, factor analysis (FA may provide an avenue for structuring (covariance matrices, thus reducing the number of parameters needed for describing (codispersion. We describe how FA can be used to model genetic effects in the context of a multivariate linear mixed model. An orthogonal common factor structure is used to model genetic effects under Gaussian assumption, so that the marginal likelihood is multivariate normal with a structured genetic (covariance matrix. Under standard prior assumptions, all fully conditional distributions have closed form, and samples from the joint posterior distribution can be obtained via Gibbs sampling. The model and the algorithm developed for its Bayesian implementation were used to describe five repeated records of milk yield in dairy cattle, and a one common FA model was compared with a standard multiple trait model. The Bayesian Information Criterion favored the FA model.
Energy Technology Data Exchange (ETDEWEB)
Karagiannis, Georgios; Lin, Guang
2014-02-15
Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.
Model Averaging and Dimension Selection for the Singular Value Decomposition
2006-01-10
the analysis of relational data (Harshman et al., 1982), biplots (Gabriel 1971, Gower and Hand 1996) and in reduced-rank interaction models for...numbers of random matrices,” SIAM J. Matrix Anal. Appl., 9, 543–560. Gabriel, K. R. (1971), “The biplot graphic display of matrices with application to...and Hand, D. J. (1996), Biplots , vol. 54 of Monographs on Statistics and Applied Probability, Chapman and Hall Ltd., London. Green, P. J. (2003
A Software Risk Analysis Model Using Bayesian Belief Network
Institute of Scientific and Technical Information of China (English)
Yong Hu; Juhua Chen; Mei Liu; Yang Yun; Junbiao Tang
2006-01-01
The uncertainty during the period of software project development often brings huge risks to contractors and clients. Ifwe can find an effective method to predict the cost and quality of software projects based on facts like the project character and two-side cooperating capability at the beginning of the project, we can reduce the risk.Bayesian Belief Network(BBN) is a good tool for analyzing uncertain consequences, but it is difficult to produce precise network structure and conditional probability table. In this paper, we built up network structure by Delphi method for conditional probability table learning, and learn update probability table and nodes' confidence levels continuously according to the application cases, which made the evaluation network have learning abilities, and evaluate the software development risk of organization more accurately. This paper also introduces EM algorithm, which will enhance the ability to produce hidden nodes caused by variant software projects.
Bayesian state space models for dynamic genetic network construction across multiple tissues.
Liang, Yulan; Kelemen, Arpad
2016-08-01
Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.
Averaging principle for second-order approximation of heterogeneous models with homogeneous models.
Fibich, Gadi; Gavious, Arieh; Solan, Eilon
2012-11-27
Typically, models with a heterogeneous property are considerably harder to analyze than the corresponding homogeneous models, in which the heterogeneous property is replaced by its average value. In this study we show that any outcome of a heterogeneous model that satisfies the two properties of differentiability and symmetry is O(ε(2)) equivalent to the outcome of the corresponding homogeneous model, where ε is the level of heterogeneity. We then use this averaging principle to obtain new results in queuing theory, game theory (auctions), and social networks (marketing).
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Sarah Depaoli
2015-03-01
Full Text Available Background: After traumatic events, such as disaster, war trauma, and injuries including burns (which is the focus here, the risk to develop posttraumatic stress disorder (PTSD is approximately 10% (Breslau & Davis, 1992. Latent Growth Mixture Modeling can be used to classify individuals into distinct groups exhibiting different patterns of PTSD (Galatzer-Levy, 2015. Currently, empirical evidence points to four distinct trajectories of PTSD patterns in those who have experienced burn trauma. These trajectories are labeled as: resilient, recovery, chronic, and delayed onset trajectories (e.g., Bonanno, 2004; Bonanno, Brewin, Kaniasty, & Greca, 2010; Maercker, Gäbler, O'Neil, Schützwohl, & Müller, 2013; Pietrzak et al., 2013. The delayed onset trajectory affects only a small group of individuals, that is, about 4–5% (O'Donnell, Elliott, Lau, & Creamer, 2007. In addition to its low frequency, the later onset of this trajectory may contribute to the fact that these individuals can be easily overlooked by professionals. In this special symposium on Estimating PTSD trajectories (Van de Schoot, 2015a, we illustrate how to properly identify this small group of individuals through the Bayesian estimation framework using previous knowledge through priors (see, e.g., Depaoli & Boyajian, 2014; Van de Schoot, Broere, Perryck, Zondervan-Zwijnenburg, & Van Loey, 2015. Method: We used latent growth mixture modeling (LGMM (Van de Schoot, 2015b to estimate PTSD trajectories across 4 years that followed a traumatic burn. We demonstrate and compare results from traditional (maximum likelihood and Bayesian estimation using priors (see, Depaoli, 2012, 2013. Further, we discuss where priors come from and how to define them in the estimation process. Results: We demonstrate that only the Bayesian approach results in the desired theory-driven solution of PTSD trajectories. Since the priors are chosen subjectively, we also present a sensitivity analysis of the
A continuous-time Bayesian network reliability modeling and analysis framework
Boudali, H.; Dugan, J.B.
2006-01-01
We present a continuous-time Bayesian network (CTBN) framework for dynamic systems reliability modeling and analysis. Dynamic systems exhibit complex behaviors and interactions between their components; where not only the combination of failure events matters, but so does the sequence ordering of th
Generic form of Bayesian Monte Carlo for models with partial monotonicity
Rajabalinejad, M.; Spitas, C.
2012-01-01
This paper presents a generic method for the safety assessments of models with partial monotonicity. For this purpose, a Bayesian interpolation method is developed and implemented in the Monte Carlo process. integrated approach is the generalization of the recently developed techniques used in safet
Bayesian Analysis for Linearized Multi-Stage Models in Quantal Bioassay.
Kuo, Lynn; Cohen, Michael P.
Bayesian methods for estimating dose response curves in quantal bioassay are studied. A linearized multi-stage model is assumed for the shape of the curves. A Gibbs sampling approach with data augmentation is employed to compute the Bayes estimates. In addition, estimation of the "relative additional risk" and the "risk specific…
Generic Form of Bayesian Monte Carlo For Models With Partial Monotonicity
Rajabalinejad, M.
2012-01-01
This paper presents a generic method for the safety assessments of models with partial monotonicity. For this purpose, a Bayesian interpolation method is developed and implemented in the Monte Carlo process. integrated approach is the generalization of the recently developed techniques used in safet
Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data
Lu, Zhenqiu Laura; Zhang, Zhiyong; Lubke, Gitta
2011-01-01
"Growth mixture models" (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class…
A Robust Bayesian Approach for Structural Equation Models with Missing Data
Lee, Sik-Yum; Xia, Ye-Mao
2008-01-01
In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…
Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory
Muthen, Bengt; Asparouhov, Tihomir
2012-01-01
This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…
The Bayesian Evaluation of Categorization Models: Comment on Wills and Pothos (2012)
Vanpaemel, Wolf; Lee, Michael D.
2012-01-01
Wills and Pothos (2012) reviewed approaches to evaluating formal models of categorization, raising a series of worthwhile issues, challenges, and goals. Unfortunately, in discussing these issues and proposing solutions, Wills and Pothos (2012) did not consider Bayesian methods in any detail. This means not only that their review excludes a major…
Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng
2010-01-01
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…
Lin, Lin; Chan, Cliburn; West, Mike
2016-01-01
We discuss the evaluation of subsets of variables for the discriminative evidence they provide in multivariate mixture modeling for classification. The novel development of Bayesian classification analysis presented is partly motivated by problems of design and selection of variables in biomolecular studies, particularly involving widely used assays of large-scale single-cell data generated using flow cytometry technology. For such studies and for mixture modeling generally, we define discriminative analysis that overlays fitted mixture models using a natural measure of concordance between mixture component densities, and define an effective and computationally feasible method for assessing and prioritizing subsets of variables according to their roles in discrimination of one or more mixture components. We relate the new discriminative information measures to Bayesian classification probabilities and error rates, and exemplify their use in Bayesian analysis of Dirichlet process mixture models fitted via Markov chain Monte Carlo methods as well as using a novel Bayesian expectation-maximization algorithm. We present a series of theoretical and simulated data examples to fix concepts and exhibit the utility of the approach, and compare with prior approaches. We demonstrate application in the context of automatic classification and discriminative variable selection in high-throughput systems biology using large flow cytometry datasets.
Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model
Mondal, Anirban
2014-07-03
We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.
Xu, Chengcheng; Wang, Wei; Liu, Pan; Li, Zhibin
2015-12-01
This study aimed to develop a real-time crash risk model with limited data in China by using Bayesian meta-analysis and Bayesian inference approach. A systematic review was first conducted by using three different Bayesian meta-analyses, including the fixed effect meta-analysis, the random effect meta-analysis, and the meta-regression. The meta-analyses provided a numerical summary of the effects of traffic variables on crash risks by quantitatively synthesizing results from previous studies. The random effect meta-analysis and the meta-regression produced a more conservative estimate for the effects of traffic variables compared with the fixed effect meta-analysis. Then, the meta-analyses results were used as informative priors for developing crash risk models with limited data. Three different meta-analyses significantly affect model fit and prediction accuracy. The model based on meta-regression can increase the prediction accuracy by about 15% as compared to the model that was directly developed with limited data. Finally, the Bayesian predictive densities analysis was used to identify the outliers in the limited data. It can further improve the prediction accuracy by 5.0%.
Chen, Chun-Hung; Wu, Ho-Ting; Ke, Kai-Wei
Simulations are often deployed to evaluate proposed mechanisms or algorithms in Mobile Ad Hoc Networks (MANET). In MANET, the impacts of some simulation parameters are noticeable, such as transmission range, data rate etc. However, the effect of mobility model is not clear until recently. Random Waypoint (RWP) is one of the most applied nodal mobility models in many simulations due to its clear procedures and easy employments. However, it exhibits the two major problems: decaying average speed and border effect. Both problems will overestimate the performance of the employed protocols and applications. Although many recently proposed mobility models are able to reduce or eliminate the above-mentioned problems, the concept of Diverse Average Speed (DAS) has not been introduced. DAS aims to provide different average speeds within the same speed range. In most mobility models, the average speed is decided when the minimum and maximum speeds are set. In this paper, we propose a novel mobility model, named General Ripple Mobility Model (GRMM). GRMM targets to provide a uniform nodal spatial distribution and DAS without decaying average speed. The simulations and analytic results have demonstrated the merits of the outstanding properties of the GRMM model.
Bayesian methods for model uncertainty analysis with application to future sea level rise
Energy Technology Data Exchange (ETDEWEB)
Patwardhan, A.; Small, M.J. (Carnegie Mellon Univ., Pittsburgh, PA (United States))
1992-12-01
This paper addresses the use of data for identifying and characterizing uncertainties in model parameters and predictions. The Bayesian Monte Carlo method is formally presented and elaborated, and applied to the analysis of the uncertainty in a predictive model for global mean sea level change. The method uses observations of output variables, made with an assumed error structure, to determine a posterior distribution of model outputs. This is used to derive a posterior distribution for the model parameters. Results demonstrate the resolution of the uncertainty that is obtained as a result of the Bayesian analysis and also indicate the key contributors to the uncertainty in the sea level rise model. While the technique is illustrated with a simple, preliminary model, the analysis provides an iterative framework for model refinement. The methodology developed in this paper provides a mechanism for the incorporation of ongoing data collection and research in decision-making for problems involving uncertain environmental change.
Directory of Open Access Journals (Sweden)
X. Chen
2013-09-01
Full Text Available A Hierarchal Bayesian model for forecasting regional summer rainfall and streamflow season-ahead using exogenous climate variables for East Central China is presented. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multilevel structure with regression coefficients modeled from a common multivariate normal distribution results in partial-pooling of information across multiple stations and better representation of parameter and posterior distribution uncertainty. Covariance structure of the residuals across stations is explicitly modeled. Model performance is tested under leave-10-out cross-validation. Frequentist and Bayesian performance metrics used include Receiver Operating Characteristic, Reduction of Error, Coefficient of Efficiency, Rank Probability Skill Scores, and coverage by posterior credible intervals. The ability of the model to reliably forecast regional summer rainfall and streamflow season-ahead offers potential for developing adaptive water risk management strategies.
An Application of Bayesian Approach in Modeling Risk of Death in an Intensive Care Unit.
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Rowena Syn Yin Wong
Full Text Available There are not many studies that attempt to model intensive care unit (ICU risk of death in developing countries, especially in South East Asia. The aim of this study was to propose and describe application of a Bayesian approach in modeling in-ICU deaths in a Malaysian ICU.This was a prospective study in a mixed medical-surgery ICU in a multidisciplinary tertiary referral hospital in Malaysia. Data collection included variables that were defined in Acute Physiology and Chronic Health Evaluation IV (APACHE IV model. Bayesian Markov Chain Monte Carlo (MCMC simulation approach was applied in the development of four multivariate logistic regression predictive models for the ICU, where the main outcome measure was in-ICU mortality risk. The performance of the models were assessed through overall model fit, discrimination and calibration measures. Results from the Bayesian models were also compared against results obtained using frequentist maximum likelihood method.The study involved 1,286 consecutive ICU admissions between January 1, 2009 and June 30, 2010, of which 1,111 met the inclusion criteria. Patients who were admitted to the ICU were generally younger, predominantly male, with low co-morbidity load and mostly under mechanical ventilation. The overall in-ICU mortality rate was 18.5% and the overall mean Acute Physiology Score (APS was 68.5. All four models exhibited good discrimination, with area under receiver operating characteristic curve (AUC values approximately 0.8. Calibration was acceptable (Hosmer-Lemeshow p-values > 0.05 for all models, except for model M3. Model M1 was identified as the model with the best overall performance in this study.Four prediction models were proposed, where the best model was chosen based on its overall performance in this study. This study has also demonstrated the promising potential of the Bayesian MCMC approach as an alternative in the analysis and modeling of in-ICU mortality outcomes.
Choy, Samantha Low; O'Leary, Rebecca; Mengersen, Kerrie
2009-01-01
Bayesian statistical modeling has several benefits within an ecological context. In particular, when observed data are limited in sample size or representativeness, then the Bayesian framework provides a mechanism to combine observed data with other "prior" information. Prior information may be obtained from earlier studies, or in their absence, from expert knowledge. This use of the Bayesian framework reflects the scientific "learning cycle," where prior or initial estimates are updated when new data become available. In this paper we outline a framework for statistical design of expert elicitation processes for quantifying such expert knowledge, in a form suitable for input as prior information into Bayesian models. We identify six key elements: determining the purpose and motivation for using prior information; specifying the relevant expert knowledge available; formulating the statistical model; designing effective and efficient numerical encoding; managing uncertainty; and designing a practical elicitation protocol. We demonstrate this framework applies to a variety of situations, with two examples from the ecological literature and three from our experience. Analysis of these examples reveals several recurring important issues affecting practical design of elicitation in ecological problems.
Equifinality of formal (DREAM) and informal (GLUE) bayesian approaches in hydrologic modeling?
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Robinson, Bruce A [Los Alamos National Laboratory; Ter Braak, Cajo J F [NON LANL; Gupta, Hoshin V [NON LANL
2008-01-01
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.
A Bayesian analysis of kaon photoproduction with the Regge-plus-resonance model
De Cruz, Lesley; Vrancx, Tom; Vancraeyveld, Pieter
2012-01-01
We address the issue of unbiased model selection and propose a methodology based on Bayesian inference to extract physical information from kaon photoproduction $p(\\gamma,K^+)\\Lambda$ data. We use the single-channel Regge-plus-resonance (RPR) framework for $p(\\gamma,K^+)\\Lambda$ to illustrate the proposed strategy. The Bayesian evidence Z is a quantitative measure for the model's fitness given the world's data. We present a numerical method for performing the multidimensional integrals in the expression for the Bayesian evidence. We use the $p(\\gamma,K^+)\\Lambda$ data with an invariant energy W > 2.6 GeV in order to constrain the background contributions in the RPR framework with Bayesian inference. Next, the resonance information is extracted from the analysis of differential cross sections, single and double polarization observables. This background and resonance content constitutes the basis of a model which is coined RPR-2011. It is shown that RPR-2011 yields a comprehensive account of the kaon photoprodu...
Bayesian Network Model with Application to Smart Power Semiconductor Lifetime Data.
Plankensteiner, Kathrin; Bluder, Olivia; Pilz, Jürgen
2015-09-01
In this article, Bayesian networks are used to model semiconductor lifetime data obtained from a cyclic stress test system. The data of interest are a mixture of log-normal distributions, representing two dominant physical failure mechanisms. Moreover, the data can be censored due to limited test resources. For a better understanding of the complex lifetime behavior, interactions between test settings, geometric designs, material properties, and physical parameters of the semiconductor device are modeled by a Bayesian network. Statistical toolboxes in MATLAB® have been extended and applied to find the best structure of the Bayesian network and to perform parameter learning. Due to censored observations Markov chain Monte Carlo (MCMC) simulations are employed to determine the posterior distributions. For model selection the automatic relevance determination (ARD) algorithm and goodness-of-fit criteria such as marginal likelihoods, Bayes factors, posterior predictive density distributions, and sum of squared errors of prediction (SSEP) are applied and evaluated. The results indicate that the application of Bayesian networks to semiconductor reliability provides useful information about the interactions between the significant covariates and serves as a reliable alternative to currently applied methods.
Comparison of a Bayesian Network with a Logistic Regression Model to Forecast IgA Nephropathy
Directory of Open Access Journals (Sweden)
Michel Ducher
2013-01-01
Full Text Available Models are increasingly used in clinical practice to improve the accuracy of diagnosis. The aim of our work was to compare a Bayesian network to logistic regression to forecast IgA nephropathy (IgAN from simple clinical and biological criteria. Retrospectively, we pooled the results of all biopsies (n=155 performed by nephrologists in a specialist clinical facility between 2002 and 2009. Two groups were constituted at random. The first subgroup was used to determine the parameters of the models adjusted to data by logistic regression or Bayesian network, and the second was used to compare the performances of the models using receiver operating characteristics (ROC curves. IgAN was found (on pathology in 44 patients. Areas under the ROC curves provided by both methods were highly significant but not different from each other. Based on the highest Youden indices, sensitivity reached (100% versus 67% and specificity (73% versus 95% using the Bayesian network and logistic regression, respectively. A Bayesian network is at least as efficient as logistic regression to estimate the probability of a patient suffering IgAN, using simple clinical and biological data obtained during consultation.
Comparison of a Bayesian network with a logistic regression model to forecast IgA nephropathy.
Ducher, Michel; Kalbacher, Emilie; Combarnous, François; Finaz de Vilaine, Jérome; McGregor, Brigitte; Fouque, Denis; Fauvel, Jean Pierre
2013-01-01
Models are increasingly used in clinical practice to improve the accuracy of diagnosis. The aim of our work was to compare a Bayesian network to logistic regression to forecast IgA nephropathy (IgAN) from simple clinical and biological criteria. Retrospectively, we pooled the results of all biopsies (n = 155) performed by nephrologists in a specialist clinical facility between 2002 and 2009. Two groups were constituted at random. The first subgroup was used to determine the parameters of the models adjusted to data by logistic regression or Bayesian network, and the second was used to compare the performances of the models using receiver operating characteristics (ROC) curves. IgAN was found (on pathology) in 44 patients. Areas under the ROC curves provided by both methods were highly significant but not different from each other. Based on the highest Youden indices, sensitivity reached (100% versus 67%) and specificity (73% versus 95%) using the Bayesian network and logistic regression, respectively. A Bayesian network is at least as efficient as logistic regression to estimate the probability of a patient suffering IgAN, using simple clinical and biological data obtained during consultation.
Bayesian model selection in complex linear systems, as illustrated in genetic association studies.
Wen, Xiaoquan
2014-03-01
Motivated by examples from genetic association studies, this article considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating context-dependent a priori information through different levels of prior specifications. We also derive analytic Bayes factors and their approximations to facilitate model selection and discuss their theoretical and computational properties. We demonstrate our Bayesian approach based on an implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real data application of mapping tissue-specific eQTLs. Our novel results on Bayes factors provide a general framework to perform efficient model comparisons in complex linear model systems.
Directory of Open Access Journals (Sweden)
Abdelkrim Moussaoui
2006-01-01
Full Text Available The authors discuss the combination of an Artificial Neural Network (ANN with analytical models to improve the performance of the prediction model of finishing rolling force in hot strip rolling mill process. The suggested model was implemented using Bayesian Evidence based training algorithm. It was found that the Bayesian Evidence based approach provided a superior and smoother fit to the real rolling mill data. Completely independent set of real rolling data were used to evaluate the capacity of the fitted ANN model to predict the unseen regions of data. As a result, test rolls obtained by the suggested hybrid model have shown high prediction quality comparatively to the usual empirical prediction models.
A Bayesian Mixture Model for PoS Induction Using Multiple Features
Christodoulopoulos, Christos; Goldwater, Sharon; Steedman, Mark
2011-01-01
In this paper we present a fully unsupervised syntactic class induction system formulated as a Bayesian multinomial mixture model, where each word type is constrained to belong to a single class. By using a mixture model rather than a sequence model (e.g., HMM), we are able to easily add multiple kinds of features, including those at both the type level (morphology features) and token level (context and alignment features, the latter from parallel corpora). Using only context features, our sy...
A Bayesian Approach for Parameter Estimation and Prediction using a Computationally Intensive Model
Higdon, Dave; Schunck, Nicolas; Sarich, Jason; Wild, Stefan M
2014-01-01
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model $\\eta(\\theta)$ where $\\theta$ denotes the uncertain, best input setting. Hence the statistical model is of the form $y = \\eta(\\theta) + \\epsilon$, where $\\epsilon$ accounts for measurement, and possibly other error sources. When non-linearity is present in $\\eta(\\cdot)$, the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and non-standard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. While quite generally applicable, MCMC requires thousands, or even millions of evaluations of the physics model $\\eta(\\cdot)$. This is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we pr...
Bayesian inference for kinetic models of biotransformation using a generalized rate equation.
Ying, Shanshan; Zhang, Jiangjiang; Zeng, Lingzao; Shi, Jiachun; Wu, Laosheng
2017-03-06
Selecting proper rate equations for the kinetic models is essential to quantify biotransformation processes in the environment. Bayesian model selection method can be used to evaluate the candidate models. However, comparisons of all plausible models can result in high computational cost, while limiting the number of candidate models may lead to biased results. In this work, we developed an integrated Bayesian method to simultaneously perform model selection and parameter estimation by using a generalized rate equation. In the approach, the model hypotheses were represented by discrete parameters and the rate constants were represented by continuous parameters. Then Bayesian inference of the kinetic models was solved by implementing Markov Chain Monte Carlo simulation for parameter estimation with the mixed (i.e., discrete and continuous) priors. The validity of this approach was illustrated through a synthetic case and a nitrogen transformation experimental study. It showed that our method can successfully identify the plausible models and parameters, as well as uncertainties therein. Thus this method can provide a powerful tool to reveal more insightful information for the complex biotransformation processes.
bspmma: An R Package for Bayesian Semiparametric Models for Meta-Analysis
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Deborah Burr
2012-07-01
Full Text Available We introduce an R package, bspmma, which implements a Dirichlet-based random effects model specific to meta-analysis. In meta-analysis, when combining effect estimates from several heterogeneous studies, it is common to use a random-effects model. The usual frequentist or Bayesian models specify a normal distribution for the true effects. However, in many situations, the effect distribution is not normal, e.g., it can have thick tails, be skewed, or be multi-modal. A Bayesian nonparametric model based on mixtures of Dirichlet process priors has been proposed in the literature, for the purpose of accommodating the non-normality. We review this model and then describe a competitor, a semiparametric version which has the feature that it allows for a well-defined centrality parameter convenient for determining whether the overall effect is significant. This second Bayesian model is based on a different version of the Dirichlet process prior, and we call it the "conditional Dirichlet model". The package contains functions to carry out analyses based on either the ordinary or the conditional Dirichlet model, functions for calculating certain Bayes factors that provide a check on the appropriateness of the conditional Dirichlet model, and functions that enable an empirical Bayes selection of the precision parameter of the Dirichlet process. We illustrate the use of the package on two examples, and give an interpretation of the results in these two different scenarios.
Dynamic causal modelling of electrographic seizure activity using Bayesian belief updating.
Cooray, Gerald K; Sengupta, Biswa; Douglas, Pamela K; Friston, Karl
2016-01-15
Seizure activity in EEG recordings can persist for hours with seizure dynamics changing rapidly over time and space. To characterise the spatiotemporal evolution of seizure activity, large data sets often need to be analysed. Dynamic causal modelling (DCM) can be used to estimate the synaptic drivers of cortical dynamics during a seizure; however, the requisite (Bayesian) inversion procedure is computationally expensive. In this note, we describe a straightforward procedure, within the DCM framework, that provides efficient inversion of seizure activity measured with non-invasive and invasive physiological recordings; namely, EEG/ECoG. We describe the theoretical background behind a Bayesian belief updating scheme for DCM. The scheme is tested on simulated and empirical seizure activity (recorded both invasively and non-invasively) and compared with standard Bayesian inversion. We show that the Bayesian belief updating scheme provides similar estimates of time-varying synaptic parameters, compared to standard schemes, indicating no significant qualitative change in accuracy. The difference in variance explained was small (less than 5%). The updating method was substantially more efficient, taking approximately 5-10min compared to approximately 1-2h. Moreover, the setup of the model under the updating scheme allows for a clear specification of how neuronal variables fluctuate over separable timescales. This method now allows us to investigate the effect of fast (neuronal) activity on slow fluctuations in (synaptic) parameters, paving a way forward to understand how seizure activity is generated.
Diedrichs, Phillippa C; Lee, Christina
2010-06-01
Increasing body size and shape diversity in media imagery may promote positive body image. While research has largely focused on female models and women's body image, men may also be affected by unrealistic images. We examined the impact of average-size and muscular male fashion models on men's and women's body image and perceived advertisement effectiveness. A sample of 330 men and 289 women viewed one of four advertisement conditions: no models, muscular, average-slim or average-large models. Men and women rated average-size models as equally effective in advertisements as muscular models. For men, exposure to average-size models was associated with more positive body image in comparison to viewing no models, but no difference was found in comparison to muscular models. Similar results were found for women. Internalisation of beauty ideals did not moderate these effects. These findings suggest that average-size male models can promote positive body image and appeal to consumers.
Strauss, Jillian; Miranda-Moreno, Luis F; Morency, Patrick
2013-10-01
This study proposes a two-equation Bayesian modelling approach to simultaneously study cyclist injury occurrence and bicycle activity at signalized intersections as joint outcomes. This approach deals with the potential presence of endogeneity and unobserved heterogeneities and is used to identify factors associated with both cyclist injuries and volumes. Its application to identify high-risk corridors is also illustrated. Montreal, Quebec, Canada is the application environment, using an extensive inventory of a large sample of signalized intersections containing disaggregate motor-vehicle traffic volumes and bicycle flows, geometric design, traffic control and built environment characteristics in the vicinity of the intersections. Cyclist injury data for the period of 2003-2008 is used in this study. Also, manual bicycle counts were standardized using temporal and weather adjustment factors to obtain average annual daily volumes. Results confirm and quantify the effects of both bicycle and motor-vehicle flows on cyclist injury occurrence. Accordingly, more cyclists at an intersection translate into more cyclist injuries but lower injury rates due to the non-linear association between bicycle volume and injury occurrence. Furthermore, the results emphasize the importance of turning motor-vehicle movements. The presence of bus stops and total crosswalk length increase cyclist injury occurrence whereas the presence of a raised median has the opposite effect. Bicycle activity through intersections was found to increase as employment, number of metro stations, land use mix, area of commercial land use type, length of bicycle facilities and the presence of schools within 50-800 m of the intersection increase. Intersections with three approaches are expected to have fewer cyclists than those with four. Using Bayesian analysis, expected injury frequency and injury rates were estimated for each intersection and used to rank corridors. Corridors with high bicycle volumes
Precise Network Modeling of Systems Genetics Data Using the Bayesian Network Webserver.
Ziebarth, Jesse D; Cui, Yan
2017-01-01
The Bayesian Network Webserver (BNW, http://compbio.uthsc.edu/BNW ) is an integrated platform for Bayesian network modeling of biological datasets. It provides a web-based network modeling environment that seamlessly integrates advanced algorithms for probabilistic causal modeling and reasoning with Bayesian networks. BNW is designed for precise modeling of relatively small networks that contain less than 20 nodes. The structure learning algorithms used by BNW guarantee the discovery of the best (most probable) network structure given the data. To facilitate network modeling across multiple biological levels, BNW provides a very flexible interface that allows users to assign network nodes into different tiers and define the relationships between and within the tiers. This function is particularly useful for modeling systems genetics datasets that often consist of multiscalar heterogeneous genotype-to-phenotype data. BNW enables users to, within seconds or minutes, go from having a simply formatted input file containing a dataset to using a network model to make predictions about the interactions between variables and the potential effects of experimental interventions. In this chapter, we will introduce the functions of BNW and show how to model systems genetics datasets with BNW.
Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.
Patri, Jean-François; Diard, Julien; Perrier, Pascal
2015-12-01
The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.
Villalba, Jesús
2015-01-01
In this document we are going to derive the equations needed to implement a Variational Bayes estimation of the parameters of the simplified probabilistic linear discriminant analysis (SPLDA) model. This can be used to adapt SPLDA from one database to another with few development data or to implement the fully Bayesian recipe. Our approach is similar to Bishop's VB PPCA.
Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models
Plant, Nathaniel G.; Holland, K. Todd
2011-01-01
A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.
Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models
Plant, Nathaniel G.; Holland, K. Todd
2011-01-01
Prediction of coastal processes, including waves, currents, and sediment transport, can be obtained from a variety of detailed geophysical-process models with many simulations showing significant skill. This capability supports a wide range of research and applied efforts that can benefit from accurate numerical predictions. However, the predictions are only as accurate as the data used to drive the models and, given the large temporal and spatial variability of the surf zone, inaccuracies in data are unavoidable such that useful predictions require corresponding estimates of uncertainty. We demonstrate how a Bayesian-network model can be used to provide accurate predictions of wave-height evolution in the surf zone given very sparse and/or inaccurate boundary-condition data. The approach is based on a formal treatment of a data-assimilation problem that takes advantage of significant reduction of the dimensionality of the model system. We demonstrate that predictions of a detailed geophysical model of the wave evolution are reproduced accurately using a Bayesian approach. In this surf-zone application, forward prediction skill was 83%, and uncertainties in the model inputs were accurately transferred to uncertainty in output variables. We also demonstrate that if modeling uncertainties were not conveyed to the Bayesian network (i.e., perfect data or model were assumed), then overly optimistic prediction uncertainties were computed. More consistent predictions and uncertainties were obtained by including model-parameter errors as a source of input uncertainty. Improved predictions (skill of 90%) were achieved because the Bayesian network simultaneously estimated optimal parameters while predicting wave heights.
SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events
Sekara, Vedran; Jonsson, Håkan; Larsen, Jakob Eg; Lehmann, Sune
2017-01-01
We propose a Bayesian model for extracting sleep patterns from smartphone events. Our method is able to identify individuals’ daily sleep periods and their evolution over time, and provides an estimation of the probability of sleep and wake transitions. The model is fitted to more than 400 participants from two different datasets, and we verify the results against ground truth from dedicated armband sleep trackers. We show that the model is able to produce reliable sleep estimates with an accuracy of 0.89, both at the individual and at the collective level. Moreover the Bayesian model is able to quantify uncertainty and encode prior knowledge about sleep patterns. Compared with existing smartphone-based systems, our method requires only screen on/off events, and is therefore much less intrusive in terms of privacy and more battery-efficient. PMID:28076375
Bayesian inference for a wavefront model of the Neolithisation of Europe
Baggaley, Andrew W; Shukurov, Anvar; Boys, Richard J; Golightly, Andrew
2012-01-01
We consider a wavefront model for the spread of Neolithic culture across Europe, and use Bayesian inference techniques to provide estimates for the parameters within this model, as constrained by radiocarbon data from Southern and Western Europe. Our wavefront model allows for both an isotropic background spread (incorporating the effects of local geography), and a localized anisotropic spread associated with major waterways. We introduce an innovative numerical scheme to track the wavefront, allowing us to simulate the times of the first arrival at any site orders of magnitude more efficiently than traditional PDE approaches. We adopt a Bayesian approach to inference and use Gaussian process emulators to facilitate further increases in efficiency in the inference scheme, thereby making Markov chain Monte Carlo methods practical. We allow for uncertainty in the fit of our model, and also infer a parameter specifying the magnitude of this uncertainty. We obtain a magnitude for the background spread of order 1 ...
Calibration of complex models through Bayesian evidence synthesis: a demonstration and tutorial.
Jackson, Christopher H; Jit, Mark; Sharples, Linda D; De Angelis, Daniela
2015-02-01
Decision-analytic models must often be informed using data that are only indirectly related to the main model parameters. The authors outline how to implement a Bayesian synthesis of diverse sources of evidence to calibrate the parameters of a complex model. A graphical model is built to represent how observed data are generated from statistical models with unknown parameters and how those parameters are related to quantities of interest for decision making. This forms the basis of an algorithm to estimate a posterior probability distribution, which represents the updated state of evidence for all unknowns given all data and prior beliefs. This process calibrates the quantities of interest against data and, at the same time, propagates all parameter uncertainties to the results used for decision making. To illustrate these methods, the authors demonstrate how a previously developed Markov model for the progression of human papillomavirus (HPV-16) infection was rebuilt in a Bayesian framework. Transition probabilities between states of disease severity are inferred indirectly from cross-sectional observations of prevalence of HPV-16 and HPV-16-related disease by age, cervical cancer incidence, and other published information. Previously, a discrete collection of plausible scenarios was identified but with no further indication of which of these are more plausible. Instead, the authors derive a Bayesian posterior distribution, in which scenarios are implicitly weighted according to how well they are supported by the data. In particular, we emphasize the appropriate choice of prior distributions and checking and comparison of fitted models.
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Pengpeng Jiao
2014-01-01
Full Text Available Time-dependent turning movement flows are very important input data for intelligent transportation systems but are impossible to be detected directly through current traffic surveillance systems. Existing estimation models have proved to be not accurate and reliable enough during all intervals. An improved way to address this problem is to develop a combined model framework that can integrate multiple submodels running simultaneously. This paper first presents a back propagation neural network model to estimate dynamic turning movements, as well as the self-adaptive learning rate approach and the gradient descent with momentum method for solving. Second, this paper develops an efficient Kalman filtering model and designs a revised sequential Kalman filtering algorithm. Based on the Bayesian method using both historical data and currently estimated results for error calibration, this paper further integrates above two submodels into a Bayesian combined model framework and proposes a corresponding algorithm. A field survey is implemented at an intersection in Beijing city to collect both time series of link counts and actual time-dependent turning movement flows, including historical and present data. The reported estimation results show that the Bayesian combined model is much more accurate and stable than other models.
A Genomic Bayesian Multi-trait and Multi-environment Model.
Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Toledo, Fernando H; Pérez-Hernández, Oscar; Eskridge, Kent M; Rutkoski, Jessica
2016-09-08
When information on multiple genotypes evaluated in multiple environments is recorded, a multi-environment single trait model for assessing genotype × environment interaction (G × E) is usually employed. Comprehensive models that simultaneously take into account the correlated traits and trait × genotype × environment interaction (T × G × E) are lacking. In this research, we propose a Bayesian model for analyzing multiple traits and multiple environments for whole-genome prediction (WGP) model. For this model, we used Half-[Formula: see text] priors on each standard deviation term and uniform priors on each correlation of the covariance matrix. These priors were not informative and led to posterior inferences that were insensitive to the choice of hyper-parameters. We also developed a computationally efficient Markov Chain Monte Carlo (MCMC) under the above priors, which allowed us to obtain all required full conditional distributions of the parameters leading to an exact Gibbs sampling for the posterior distribution. We used two real data sets to implement and evaluate the proposed Bayesian method and found that when the correlation between traits was high (>0.5), the proposed model (with unstructured variance-covariance) improved prediction accuracy compared to the model with diagonal and standard variance-covariance structures. The R-software package Bayesian Multi-Trait and Multi-Environment (BMTME) offers optimized C++ routines to efficiently perform the analyses.
Reconstructing constructivism: Causal models, Bayesian learning mechanisms and the theory theory
Gopnik, Alison; Wellman, Henry M.
2012-01-01
We propose a new version of the “theory theory” grounded in the computational framework of probabilistic causal models and Bayesian learning. Probabilistic models allow a constructivist but rigorous and detailed approach to cognitive development. They also explain the learning of both more specific causal hypotheses and more abstract framework theories. We outline the new theoretical ideas, explain the computational framework in an intuitive and non-technical way, and review an extensive but ...
Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction.
Epstein, Michael; Calderhead, Ben; Girolami, Mark A; Sivilotti, Lucia G
2016-07-26
The stochastic behavior of single ion channels is most often described as an aggregated continuous-time Markov process with discrete states. For ligand-gated channels each state can represent a different conformation of the channel protein or a different number of bound ligands. Single-channel recordings show only whether the channel is open or shut: states of equal conductance are aggregated, so transitions between them have to be inferred indirectly. The requirement to filter noise from the raw signal further complicates the modeling process, as it limits the time resolution of the data. The consequence of the reduced bandwidth is that openings or shuttings that are shorter than the resolution cannot be observed; these are known as missed events. Postulated models fitted using filtered data must therefore explicitly account for missed events to avoid bias in the estimation of rate parameters and therefore assess parameter identifiability accurately. In this article, we present the first, to our knowledge, Bayesian modeling of ion-channels with exact missed events correction. Bayesian analysis represents uncertain knowledge of the true value of model parameters by considering these parameters as random variables. This allows us to gain a full appreciation of parameter identifiability and uncertainty when estimating values for model parameters. However, Bayesian inference is particularly challenging in this context as the correction for missed events increases the computational complexity of the model likelihood. Nonetheless, we successfully implemented a two-step Markov chain Monte Carlo method that we called "BICME", which performs Bayesian inference in models of realistic complexity. The method is demonstrated on synthetic and real single-channel data from muscle nicotinic acetylcholine channels. We show that parameter uncertainty can be characterized more accurately than with maximum-likelihood methods. Our code for performing inference in these ion channel
Bayesian prediction of spatial count data using generalized linear mixed models
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Christensen, Ole Fredslund; Waagepetersen, Rasmus Plenge
2002-01-01
Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, we...... demonstrate that so-called Langevin-Hastings updates are useful for efficient simulation of the posterior distributions, and we discuss computational issues concerning prediction....
Bayesian Model on Fatigue Crack Growth Rate of Type 304 Stainless Steel
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Choi, Sanhae; Yoon, Jae Young; Hwang, Il Soon [Nuclear Materials Laboratory, Seoul National University, Seoul (Korea, Republic of)
2015-10-15
The fatigue crack growth rate curve is typically estimated by deterministic methods in accordance with the ASME Boiler and Pressure Vessel Code Sec. XI. The reliability of nuclear materials must also consider the environmental effect. This can be overcome by probabilistic methods that estimate the degradation of materials. In this study, fatigue tests were carried out on Type 304 stainless steel (STS 304) to obtain a fatigue crack growth rate curve and Paris' law constants. Tests were conducted on a constant load and a constant delta K, respectively. The unknown constants of Paris' law were updated probabilistically by Bayesian inference and the method can be used for the probabilistic structural integrity assessment of other nuclear materials. In this paper, Paris' law constants including C and m for Type 304 stainless steel were determined by probabilistic approach with Bayesian Inference. The Bayesian update process is limited in accuracy, because this method should assume initial data distribution. If we select an appropriate distribution, this updating method is powerful enough to get data results considering the environment and materials. Until now, remaining lives of NPPs are estimated by deterministic methods using a priori model to finally assess structural integrity. Bayesian approach can utilize in-service inspection data derived from aged properties.
Bayat, Sahar; Cuggia, Marc; Kessler, Michel; Briançon, Serge; Le Beux, Pierre; Frimat, Luc
2008-01-01
Evaluation of adult candidates for kidney transplantation diverges from one centre to another. Our purpose was to assess the suitability of Bayesian method for describing the factors associated to registration on the waiting list in a French healthcare network. We have found no published paper using Bayesian method in this domain. Eight hundred and nine patients starting renal replacement therapy were included in the analysis. The data were extracted from the information system of the healthcare network. We performed conventional statistical analysis and data mining analysis using mainly Bayesian networks. The Bayesian model showed that the probability of registration on the waiting list is associated to age, cardiovascular disease, diabetes, serum albumin level, respiratory disease, physical impairment, follow-up in the department performing transplantation and past history of malignancy. These results are similar to conventional statistical method. The comparison between conventional analysis and data mining analysis showed us the contribution of the data mining method for sorting variables and having a global view of the variables' associations. Moreover theses approaches constitute an essential step toward a decisional information system for healthcare networks.
A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China.
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Xiongqing Zhang
Full Text Available Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.Hook. plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF. Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc. on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.
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M. Sadegh
2013-04-01
Full Text Available In recent years, a strong debate has emerged in the hydrologic literature how to properly treat non-traditional error residual distributions and quantify parameter and predictive uncertainty. Particularly, there is strong disagreement whether such uncertainty framework should have its roots within a proper statistical (Bayesian context using Markov chain Monte Carlo (MCMC simulation techniques, or whether such a framework should be based on a quite different philosophy and implement informal likelihood functions and simplistic search methods to summarize parameter and predictive distributions. In this paper we introduce an alternative framework, called Approximate Bayesian Computation (ABC that summarizes the differing viewpoints of formal and informal Bayesian approaches. This methodology has recently emerged in the fields of biology and population genetics and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics that measure the distance of each model simulation to the data. This paper is a follow up of the recent publication of Nott et al. (2012 and further studies the theoretical and numerical equivalence of formal (DREAM and informal (GLUE Bayesian approaches using data from different watersheds in the United States. We demonstrate that the limits of acceptability approach of GLUE is a special variant of ABC in which each discharge observation of the calibration data set is used as a summary diagnostic.
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C Elizabeth McCarron
Full Text Available BACKGROUND: Bayesian hierarchical models have been proposed to combine evidence from different types of study designs. However, when combining evidence from randomised and non-randomised controlled studies, imbalances in patient characteristics between study arms may bias the results. The objective of this study was to assess the performance of a proposed Bayesian approach to adjust for imbalances in patient level covariates when combining evidence from both types of study designs. METHODOLOGY/PRINCIPAL FINDINGS: Simulation techniques, in which the truth is known, were used to generate sets of data for randomised and non-randomised studies. Covariate imbalances between study arms were introduced in the non-randomised studies. The performance of the Bayesian hierarchical model adjusted for imbalances was assessed in terms of bias. The data were also modelled using three other Bayesian approaches for synthesising evidence from randomised and non-randomised studies. The simulations considered six scenarios aimed at assessing the sensitivity of the results to changes in the impact of the imbalances and the relative number and size of studies of each type. For all six scenarios considered, the Bayesian hierarchical model adjusted for differences within studies gave results that were unbiased and closest to the true value compared to the other models. CONCLUSIONS/SIGNIFICANCE: Where informed health care decision making requires the synthesis of evidence from randomised and non-randomised study designs, the proposed hierarchical Bayesian method adjusted for differences in patient characteristics between study arms may facilitate the optimal use of all available evidence leading to unbiased results compared to unadjusted analyses.
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Stephen W Hartley
2012-09-01
Full Text Available Genome-wide association studies (GWAS have identified numerous associations between genetic loci and individual phenotypes; however, relatively few GWAS have attempted to detect pleiotropic associations, in which loci are simultaneously associated with multiple distinct phenotypes. We show that pleiotropic associations can be directly modeled via the construction of simple Bayesian networks, and that these models can be applied to produce single or ensembles of Bayesian classifiers that leverage pleiotropy to improve genetic risk prediction.The proposed method includes two phases: (1 Bayesian model comparison, to identify SNPs associated with one or more traits; and (2 cross validation feature selection, in which a final set of SNPs is selected to optimize prediction.To demonstrate the capabilities and limitations of the method, a total of 1600 case-control GWAS datasets with 2 dichotomous phenotypes were simulated under 16 scenarios, varying the association strengths of causal SNPs, the size of the discovery sets, the balance between cases and controls, and the number of pleiotropic causal SNPs.Across the 16 scenarios, prediction accuracy varied from 90% to 50%. In the 14 scenarios that included pleiotropically-associated SNPs, the pleiotropic model search and prediction methods consistently outperformed the naive model search and prediction. In the 2 scenarios in which there were no true pleiotropic SNPs, the differences between the pleiotropic and naive model searches were minimal.
Varvia, Petri; Rautiainen, Miina; Seppänen, Aku
2017-04-01
Hyperspectral remote sensing data carry information on the leaf area index (LAI) of forests, and thus in principle, LAI can be estimated based on the data by inverting a forest reflectance model. However, LAI is usually not the only unknown in a reflectance model; especially, the leaf spectral albedo and understory reflectance are also not known. If the uncertainties of these parameters are not accounted for, the inversion of a forest reflectance model can lead to biased estimates for LAI. In this paper, we study the effects of reflectance model uncertainties on LAI estimates, and further, investigate whether the LAI estimates could recover from these uncertainties with the aid of Bayesian inference. In the proposed approach, the unknown leaf albedo and understory reflectance are estimated simultaneously with LAI from hyperspectral remote sensing data. The feasibility of the approach is tested with numerical simulation studies. The results show that in the presence of unknown parameters, the Bayesian LAI estimates which account for the model uncertainties outperform the conventional estimates that are based on biased model parameters. Moreover, the results demonstrate that the Bayesian inference can also provide feasible measures for the uncertainty of the estimated LAI.
Yu, Hwa-Lung; Wang, Chih-Hsin
2013-02-05
Understanding the daily changes in ambient air quality concentrations is important to the assessing human exposure and environmental health. However, the fine temporal scales (e.g., hourly) involved in this assessment often lead to high variability in air quality concentrations. This is because of the complex short-term physical and chemical mechanisms among the pollutants. Consequently, high heterogeneity is usually present in not only the averaged pollution levels, but also the intraday variance levels of the daily observations of ambient concentration across space and time. This characteristic decreases the estimation performance of common techniques. This study proposes a novel quantile-based Bayesian maximum entropy (QBME) method to account for the nonstationary and nonhomogeneous characteristics of ambient air pollution dynamics. The QBME method characterizes the spatiotemporal dependence among the ambient air quality levels based on their location-specific quantiles and accounts for spatiotemporal variations using a local weighted smoothing technique. The epistemic framework of the QBME method can allow researchers to further consider the uncertainty of space-time observations. This study presents the spatiotemporal modeling of daily CO and PM10 concentrations across Taiwan from 1998 to 2009 using the QBME method. Results show that the QBME method can effectively improve estimation accuracy in terms of lower mean absolute errors and standard deviations over space and time, especially for pollutants with strong nonhomogeneous variances across space. In addition, the epistemic framework can allow researchers to assimilate the site-specific secondary information where the observations are absent because of the common preferential sampling issues of environmental data. The proposed QBME method provides a practical and powerful framework for the spatiotemporal modeling of ambient pollutants.
Brochu, Eric; de Freitas, Nando
2010-01-01
We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences.
Improving Bayesian population dynamics inference: a coalescent-based model for multiple loci.
Gill, Mandev S; Lemey, Philippe; Faria, Nuno R; Rambaut, Andrew; Shapiro, Beth; Suchard, Marc A
2013-03-01
Effective population size is fundamental in population genetics and characterizes genetic diversity. To infer past population dynamics from molecular sequence data, coalescent-based models have been developed for Bayesian nonparametric estimation of effective population size over time. Among the most successful is a Gaussian Markov random field (GMRF) model for a single gene locus. Here, we present a generalization of the GMRF model that allows for the analysis of multilocus sequence data. Using simulated data, we demonstrate the improved performance of our method to recover true population trajectories and the time to the most recent common ancestor (TMRCA). We analyze a multilocus alignment of HIV-1 CRF02_AG gene sequences sampled from Cameroon. Our results are consistent with HIV prevalence data and uncover some aspects of the population history that go undetected in Bayesian parametric estimation. Finally, we recover an older and more reconcilable TMRCA for a classic ancient DNA data set.
A Bayesian Hierarchical Model for Relating Multiple SNPs within Multiple Genes to Disease Risk
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Lewei Duan
2013-01-01
Full Text Available A variety of methods have been proposed for studying the association of multiple genes thought to be involved in a common pathway for a particular disease. Here, we present an extension of a Bayesian hierarchical modeling strategy that allows for multiple SNPs within each gene, with external prior information at either the SNP or gene level. The model involves variable selection at the SNP level through latent indicator variables and Bayesian shrinkage at the gene level towards a prior mean vector and covariance matrix that depend on external information. The entire model is fitted using Markov chain Monte Carlo methods. Simulation studies show that the approach is capable of recovering many of the truly causal SNPs and genes, depending upon their frequency and size of their effects. The method is applied to data on 504 SNPs in 38 candidate genes involved in DNA damage response in the WECARE study of second breast cancers in relation to radiotherapy exposure.
BAYESIAN INFERENCE OF HIDDEN GAMMA WEAR PROCESS MODEL FOR SURVIVAL DATA WITH TIES.
Sinha, Arijit; Chi, Zhiyi; Chen, Ming-Hui
2015-10-01
Survival data often contain tied event times. Inference without careful treatment of the ties can lead to biased estimates. This paper develops the Bayesian analysis of a stochastic wear process model to fit survival data that might have a large number of ties. Under a general wear process model, we derive the likelihood of parameters. When the wear process is a Gamma process, the likelihood has a semi-closed form that allows posterior sampling to be carried out for the parameters, hence achieving model selection using Bayesian deviance information criterion. An innovative simulation algorithm via direct forward sampling and Gibbs sampling is developed to sample event times that may have ties in the presence of arbitrary covariates; this provides a tool to assess the precision of inference. An extensive simulation study is reported and a data set is used to further illustrate the proposed methodology.
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Fidel Ernesto Castro Morales
2016-03-01
Full Text Available Abstract Objectives: to propose the use of a Bayesian hierarchical model to study the allometric scaling of the fetoplacental weight ratio, including possible confounders. Methods: data from 26 singleton pregnancies with gestational age at birth between 37 and 42 weeks were analyzed. The placentas were collected immediately after delivery and stored under refrigeration until the time of analysis, which occurred within up to 12 hours. Maternal data were collected from medical records. A Bayesian hierarchical model was proposed and Markov chain Monte Carlo simulation methods were used to obtain samples from distribution a posteriori. Results: the model developed showed a reasonable fit, even allowing for the incorporation of variables and a priori information on the parameters used. Conclusions: new variables can be added to the modelfrom the available code, allowing many possibilities for data analysis and indicating the potential for use in research on the subject.
Bayesian approaches to spatial inference: Modelling and computational challenges and solutions
Moores, Matthew; Mengersen, Kerrie
2014-12-01
We discuss a range of Bayesian modelling approaches for spatial data and investigate some of the associated computational challenges. This paper commences with a brief review of Bayesian mixture models and Markov random fields, with enabling computational algorithms including Markov chain Monte Carlo (MCMC) and integrated nested Laplace approximation (INLA). Following this, we focus on the Potts model as a canonical approach, and discuss the challenge of estimating the inverse temperature parameter that controls the degree of spatial smoothing. We compare three approaches to addressing the doubly intractable nature of the likelihood, namely pseudo-likelihood, path sampling and the exchange algorithm. These techniques are applied to satellite data used to analyse water quality in the Great Barrier Reef.
Xu, Lei; Johnson, Timothy D.; Nichols, Thomas E.; Nee, Derek E.
2010-01-01
Summary The aim of this work is to develop a spatial model for multi-subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi-subject data, some work on spatial modeling of single-subject data, and some recent work on spatial modeling of multi-subject data. However, there has been no work on spatial models that explicitly account for inter-subject variability in activation locations. In this work, we use the idea of activation centers and model the inter-subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical frame work which allows us to draw inferences at all levels: the population level, the individual level and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question which is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov Chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data. PMID:19210732
Freni, Gabriele; Mannina, Giorgio
In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box-Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box-Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the
Bayesian latent variable models for the analysis of experimental psychology data.
Merkle, Edgar C; Wang, Ting
2016-03-18
In this paper, we address the use of Bayesian factor analysis and structural equation models to draw inferences from experimental psychology data. While such application is non-standard, the models are generally useful for the unified analysis of multivariate data that stem from, e.g., subjects' responses to multiple experimental stimuli. We first review the models and the parameter identification issues inherent in the models. We then provide details on model estimation via JAGS and on Bayes factor estimation. Finally, we use the models to re-analyze experimental data on risky choice, comparing the approach to simpler, alternative methods.
Kuczera, George; Kavetski, Dmitri; Franks, Stewart; Thyer, Mark
2006-11-01
SummaryCalibration and prediction in conceptual rainfall-runoff (CRR) modelling is affected by the uncertainty in the observed forcing/response data and the structural error in the model. This study works towards the goal of developing a robust framework for dealing with these sources of error and focuses on model error. The characterisation of model error in CRR modelling has been thwarted by the convenient but indefensible treatment of CRR models as deterministic descriptions of catchment dynamics. This paper argues that the fluxes in CRR models should be treated as stochastic quantities because their estimation involves spatial and temporal averaging. Acceptance that CRR models are intrinsically stochastic paves the way for a more rational characterisation of model error. The hypothesis advanced in this paper is that CRR model error can be characterised by storm-dependent random variation of one or more CRR model parameters. A simple sensitivity analysis is used to identify the parameters most likely to behave stochastically, with variation in these parameters yielding the largest changes in model predictions as measured by the Nash-Sutcliffe criterion. A Bayesian hierarchical model is then formulated to explicitly differentiate between forcing, response and model error. It provides a very general framework for calibration and prediction, as well as for testing hypotheses regarding model structure and data uncertainty. A case study calibrating a six-parameter CRR model to daily data from the Abercrombie catchment (Australia) demonstrates the considerable potential of this approach. Allowing storm-dependent variation in just two model parameters (with one of the parameters characterising model error and the other reflecting input uncertainty) yields a substantially improved model fit raising the Nash-Sutcliffe statistic from 0.74 to 0.94. Of particular significance is the use of posterior diagnostics to test the key assumptions about the data and model errors
On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization
Energy Technology Data Exchange (ETDEWEB)
Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang
2015-02-01
The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesian inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.
Institute of Scientific and Technical Information of China (English)
Jongbin Im; Jungsun Park
2013-01-01
This paper focuses on a method to solve structural optimization problems using particle swarm optimization (PSO),surrogate models and Bayesian statistics.PSO is a random/stochastic search algorithm designed to find the global optimum.However,PSO needs many evaluations compared to gradient-based optimization.This means PSO increases the analysis costs of structural optimization.One of the methods to reduce computing costs in stochastic optimization is to use approximation techniques.In this work,surrogate models are used,including the response surface method (RSM) and Kriging.When surrogate models are used,there are some errors between exact values and approximated values.These errors decrease the reliability of the optimum values and discard the realistic approximation of using surrogate models.In this paper,Bayesian statistics is used to obtain more reliable results.To verify and confirm the efficiency of the proposed method using surrogate models and Bayesian statistics for stochastic structural optimization,two numerical examples are optimized,and the optimization of a hub sleeve is demonstrated as a practical problem.
Directory of Open Access Journals (Sweden)
Brodjol Sutijo Supri Ulama
2012-01-01
Full Text Available Problem statement: Household expenditure analysis was highly demanding for government in order to formulate its policy. Since household data was viewed as hierarchical structure with household nested in its regional residence which varies inter region, the contextual welfare analysis was needed. This study proposed to develop a hierarchical model for estimating household expenditure in an attempt to measure the effect of regional diversity by taking into account district characteristics and household attributes using a Bayesian approach. Approach: Due to the variation of household expenditure data which was captured by the three parameters of Log-Normal (LN3 distribution, the model was developed based on LN3 distribution. Data used in this study was household expenditure data in Central Java, Indonesia. Since, data were unbalanced and hierarchical models using a classical approach work well for balanced data, thus the estimation process was done by using Bayesian method with MCMC and Gibbs sampling. Results: The hierarchical Bayesian model based on LN3 distribution could be implemented to explain the variation of household expenditure using district characteristics and household attributes. Conclusion: The model shows that districts characteristics which include demographic and economic conditions of districts and the availability of public facilities which are strongly associated with a dimension of human development index, i.e., economic, education and health, do affect to household expenditure through its household attributes."
Xu, T.; Valocchi, A. J.
2014-12-01
Effective water resource management typically relies on numerical models to analyse groundwater flow and solute transport processes. These models are usually subject to model structure error due to simplification and/or misrepresentation of the real system. As a result, the model outputs may systematically deviate from measurements, thus violating a key assumption for traditional regression-based calibration and uncertainty analysis. On the other hand, model structure error induced bias can be described statistically in an inductive, data-driven way based on historical model-to-measurement misfit. We adopt a fully Bayesian approach that integrates a Gaussian process error model to account for model structure error to the calibration, prediction and uncertainty analysis of groundwater models. The posterior distributions of parameters of the groundwater model and the Gaussian process error model are jointly inferred using DREAM, an efficient Markov chain Monte Carlo sampler. We test the usefulness of the fully Bayesian approach towards a synthetic case study of surface-ground water interaction under changing pumping conditions. We first illustrate through this example that traditional least squares regression without accounting for model structure error yields biased parameter estimates due to parameter compensation as well as biased predictions. In contrast, the Bayesian approach gives less biased parameter estimates. Moreover, the integration of a Gaussian process error model significantly reduces predictive bias and leads to prediction intervals that are more consistent with observations. The results highlight the importance of explicit treatment of model structure error especially in circumstances where subsequent decision-making and risk analysis require accurate prediction and uncertainty quantification. In addition, the data-driven error modelling approach is capable of extracting more information from observation data than using a groundwater model alone.
Grzegorczyk, Marco; Husmeier, Dirk
2013-01-01
To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori inde
Bayes统计模型在出山月均径流极小值研究中的应用%A Bayesian Analysis of Monthly Average Runoff Minima in Mountain Areas
Institute of Scientific and Technical Information of China (English)
刘友存; 霍雪丽; 郝永红; 崔玉环; 韩添丁; 沈永平; 王建
2015-01-01
Global warming has intensified hydrological extreme events and resulted in disasters around the world. For disaster management and adaption of extreme events,it is essential to improve the accuracy of extreme value statistical models. In this study,Bayes’Theorem is introduced to estimate parameters in the Generalized Pareto Distribution( GPD)model which is applied to simulate the distribution of monthly average runoff minima during dry periods in mountain areas of Ürümqi River. Bayes’Theorem treats parameters as random variables and provides machinery way to convert the prior distribution of parameters into a posterior distribution. Statistical inferences based on posterior distribution can provide a more comprehensive representation of the parameters. An improved Markov Chain Monte Carlo( MCMC)method,which can solve high-dimensional integral computation in the Bayes equation,is used to generate parameter simulations from the posterior distribution. Model diagnosis plots are made to guarantee the fitted GPD model is appropriate. Then based on the GPD model with Bayesian parameter esti-mates,monthly average minima corresponding to different return periods can be calculated. The results show that the improved MCMC method is able to make Markov chains converge at a high speed. Compared with the GPD model based on maximum likelihood parameter estimates,the GPD model based on Bayesian parameter estimates obtain more accurate estimations of minimum monthly average runoff. Moreover,the monthly average runoff minima in dry periods corresponding to 10 a,25 a,50 a and 100 a return periods are 0. 60 m3/s,0. 44 m3/s,0. 32 m3/s and 0. 20 m3/s respectively. The lower boundary of 95% confidence interval of 100a return level is -0. 238 m3/s,which implies that Ürümqi River is likely to cease when 100 a return level occurs in dry periods.%数理统计方法在解决全球气候变化引起的洪水、干旱等极端水文事件中获得了越来越广泛的
Bayesian model comparison in nonlinear BOLD fMRI hemodynamics
DEFF Research Database (Denmark)
Jacobsen, Danjal Jakup; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
2008-01-01
Nonlinear hemodynamic models express the BOLD (blood oxygenation level dependent) signal as a nonlinear, parametric functional of the temporal sequence of local neural activity. Several models have been proposed for both the neural activity and the hemodynamics. We compare two such combined model...... different visual stimulation paradigms. The results show that the simple model is the better one for these data....
Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models
DEFF Research Database (Denmark)
Rombouts, Jeroen V.K.; Stentoft, Lars Peter
While stochastic volatility models improve on the option pricing error when compared to the Black-Scholes-Merton model, mispricings remain. This paper uses mixed normal heteroskedasticity models to price options. Our model allows for significant negative skewness and time varying higher order...
Nonidentical twins: Comparison of frequentist and Bayesian lasso for Cox models.
Zucknick, Manuela; Saadati, Maral; Benner, Axel
2015-11-01
One important task in translational cancer research is the search for new prognostic biomarkers to improve survival prognosis for patients. The use of high-throughput technologies allows simultaneous measurement of genome-wide gene expression or other genomic data for all patients in a clinical trial. Penalized likelihood methods such as lasso regression can be applied to such high-dimensional data, where the number of (genomic) covariables is usually much larger than the sample size. There is a connection between the lasso and the Bayesian regression model with independent Laplace priors on the regression parameters, and understanding this connection has been useful for understanding the properties of lasso estimates in linear models (e.g. Park and Casella, 2008). In this paper, we study the lasso in the frequentist and Bayesian frameworks in the context of Cox models. For the Bayesian lasso we extend the approach by Lee et al. (2011). In particular, we impose the lasso penalty only on the genome features, but not on relevant clinical covariates, to allow the mandatory inclusion of important established factors. We investigate the models in high- and low-dimensional simulation settings and in an application to chronic lymphocytic leukemia.
A Bayesian Hierarchical Model for Reconstructing Sea Levels: From Raw Data to Rates of Change
Cahill, Niamh; Horton, Benjamin P; Parnell, Andrew C
2015-01-01
We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical ({\\delta}13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment {\\delta}13C values); (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, U.S.A. We develop a new Bayesian transfer function (B-TF), with and without the {\\delta}13C proxy and compare our results to those from a widely...
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Dario Cuevas Rivera
2015-10-01
Full Text Available The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an 'intelligent coincidence detector', which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena.
Cuevas Rivera, Dario; Bitzer, Sebastian; Kiebel, Stefan J.
2015-01-01
The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an ‘intelligent coincidence detector’, which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena. PMID:26451888
Schöniger, Anneli; Illman, Walter A.; Wöhling, Thomas; Nowak, Wolfgang
2015-12-01
Groundwater modelers face the challenge of how to assign representative parameter values to the studied aquifer. Several approaches are available to parameterize spatial heterogeneity in aquifer parameters. They differ in their conceptualization and complexity, ranging from homogeneous models to heterogeneous random fields. While it is common practice to invest more effort into data collection for models with a finer resolution of heterogeneities, there is a lack of advice which amount of data is required to justify a certain level of model complexity. In this study, we propose to use concepts related to Bayesian model selection to identify this balance. We demonstrate our approach on the characterization of a heterogeneous aquifer via hydraulic tomography in a sandbox experiment (Illman et al., 2010). We consider four increasingly complex parameterizations of hydraulic conductivity: (1) Effective homogeneous medium, (2) geology-based zonation, (3) interpolation by pilot points, and (4) geostatistical random fields. First, we investigate the shift in justified complexity with increasing amount of available data by constructing a model confusion matrix. This matrix indicates the maximum level of complexity that can be justified given a specific experimental setup. Second, we determine which parameterization is most adequate given the observed drawdown data. Third, we test how the different parameterizations perform in a validation setup. The results of our test case indicate that aquifer characterization via hydraulic tomography does not necessarily require (or justify) a geostatistical description. Instead, a zonation-based model might be a more robust choice, but only if the zonation is geologically adequate.
DEFF Research Database (Denmark)
Strathe, Anders Bjerring; Jørgensen, Henry; Kebreab, E
2012-01-01
developed, reflecting current knowledge about metabolic scaling and partial efficiencies of PD and LD rates, whereas flat non-informative priors were used for the reminder of the parameters. The experimental data analysed originate from a balance and respiration trial with 17 cross-bred pigs of three......ABSTRACT SUMMARY The objective of the current study was to develop Bayesian simultaneous equation models for modelling energy intake and partitioning in growing pigs. A key feature of the Bayesian approach is that parameters are assigned prior distributions, which may reflect the current state...... genders (barrows, boars and gilts) selected on the basis of similar birth weight. The pigs were fed four diets based on barley, wheat and soybean meal supplemented with crystalline amino acids to meet or exceed Danish nutrient requirement standards. Nutrient balances and gas exchanges were measured at c...
DEFF Research Database (Denmark)
Boonstra, Philip S; Mukherjee, Bhramar; Taylor, Jeremy M G
2011-01-01
. In this article, we posit a Bayesian approach to infer genetic anticipation under flexible random effects models for censored data that capture the effect of successive generations on AOO. Primary interest lies in the random effects. Misspecifying the distribution of random effects may result in incorrect...... inferential conclusions. We compare the fit of four-candidate random effects distributions via Bayesian model fit diagnostics. A related statistical issue here is isolating the confounding effect of changes in secular trends, screening, and medical practices that may affect time to disease detection across...... birth cohorts. Using historic cancer registry data, we borrow from relative survival analysis methods to adjust for changes in age-specific incidence across birth cohorts. Our motivating case study comes from a Danish cancer register of 124 families with mutations in mismatch repair (MMR) genes known...
From least squares to multilevel modeling: A graphical introduction to Bayesian inference
Loredo, Thomas J.
2016-01-01
This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.
Wu, Stephen; Angelikopoulos, Panagiotis; Tauriello, Gerardo; Papadimitriou, Costas; Koumoutsakos, Petros
2016-12-28
We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierarchical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.
PARALLEL ADAPTIVE MULTILEVEL SAMPLING ALGORITHMS FOR THE BAYESIAN ANALYSIS OF MATHEMATICAL MODELS
Prudencio, Ernesto
2012-01-01
In recent years, Bayesian model updating techniques based on measured data have been applied to many engineering and applied science problems. At the same time, parallel computational platforms are becoming increasingly more powerful and are being used more frequently by the engineering and scientific communities. Bayesian techniques usually require the evaluation of multi-dimensional integrals related to the posterior probability density function (PDF) of uncertain model parameters. The fact that such integrals cannot be computed analytically motivates the research of stochastic simulation methods for sampling posterior PDFs. One such algorithm is the adaptive multilevel stochastic simulation algorithm (AMSSA). In this paper we discuss the parallelization of AMSSA, formulating the necessary load balancing step as a binary integer programming problem. We present a variety of results showing the effectiveness of load balancing on the overall performance of AMSSA in a parallel computational environment.
Bayesian Computation Methods for Inferring Regulatory Network Models Using Biomedical Data.
Tian, Tianhai
2016-01-01
The rapid advancement of high-throughput technologies provides huge amounts of information for gene expression and protein activity in the genome-wide scale. The availability of genomics, transcriptomics, proteomics, and metabolomics dataset gives an unprecedented opportunity to study detailed molecular regulations that is very important to precision medicine. However, it is still a significant challenge to design effective and efficient method to infer the network structure and dynamic property of regulatory networks. In recent years a number of computing methods have been designed to explore the regulatory mechanisms as well as estimate unknown model parameters. Among them, the Bayesian inference method can combine both prior knowledge and experimental data to generate updated information regarding the regulatory mechanisms. This chapter gives a brief review for Bayesian statistical methods that are used to infer the network structure and estimate model parameters based on experimental data.
Bayesian networks modeling for thermal error of numerical control machine tools
Institute of Scientific and Technical Information of China (English)
Xin-hua YAO; Jian-zhong FU; Zi-chen CHEN
2008-01-01
The interaction between the heat source location,its intensity,thermal expansion coefficient,the machine system configuration and the running environment creates complex thermal behavior of a machine tool,and also makes thermal error prediction difficult.To address this issue,a novel prediction method for machine tool thermal error based on Bayesian networks (BNs) was presented.The method described causal relationships of factors inducing thermal deformation by graph theory and estimated the thermal error by Bayesian statistical techniques.Due to the effective combination of domain knowledge and sampled data,the BN method could adapt to the change of running state of machine,and obtain satisfactory prediction accuracy.Ex-periments on spindle thermal deformation were conducted to evaluate the modeling performance.Experimental results indicate that the BN method performs far better than the least squares(LS)analysis in terms of modeling estimation accuracy.
Bayesian Inference using Neural Net Likelihood Models for Protein Secondary Structure Prediction
Directory of Open Access Journals (Sweden)
Seong-Gon Kim
2011-06-01
Full Text Available Several techniques such as Neural Networks, Genetic Algorithms, Decision Trees and other statistical or heuristic methods have been used to approach the complex non-linear task of predicting Alpha-helicies, Beta-sheets and Turns of a proteins secondary structure in the past. This project introduces a new machine learning method by using an offline trained Multilayered Perceptrons (MLP as the likelihood models within a Bayesian Inference framework to predict secondary structures proteins. Varying window sizes are used to extract neighboring amino acid information and passed back and forth between the Neural Net models and the Bayesian Inference process until there is a convergence of the posterior secondary structure probability.
Predictive data-derived Bayesian statistic-transport model and simulator of sunken oil mass
Echavarria Gregory, Maria Angelica
Sunken oil is difficult to locate because remote sensing techniques cannot as yet provide views of sunken oil over large areas. Moreover, the oil may re-suspend and sink with changes in salinity, sediment load, and temperature, making deterministic fate models difficult to deploy and calibrate when even the presence of sunken oil is difficult to assess. For these reasons, together with the expense of field data collection, there is a need for a statistical technique integrating limited data collection with stochastic transport modeling. Predictive Bayesian modeling techniques have been developed and demonstrated for exploiting limited information for decision support in many other applications. These techniques brought to a multi-modal Lagrangian modeling framework, representing a near-real time approach to locating and tracking sunken oil driven by intrinsic physical properties of field data collected following a spill after oil has begun collecting on a relatively flat bay bottom. Methods include (1) development of the conceptual predictive Bayesian model and multi-modal Gaussian computational approach based on theory and literature review; (2) development of an object-oriented programming and combinatorial structure capable of managing data, integration and computation over an uncertain and highly dimensional parameter space; (3) creating a new bi-dimensional approach of the method of images to account for curved shoreline boundaries; (4) confirmation of model capability for locating sunken oil patches using available (partial) real field data and capability for temporal projections near curved boundaries using simulated field data; and (5) development of a stand-alone open-source computer application with graphical user interface capable of calibrating instantaneous oil spill scenarios, obtaining sets maps of relative probability profiles at different prediction times and user-selected geographic areas and resolution, and capable of performing post
Licquia, Timothy C.; Newman, Jeffrey A.
2016-11-01
The exponential scale length (L d ) of the Milky Way’s (MW’s) disk is a critical parameter for describing the global physical size of our Galaxy, important both for interpreting other Galactic measurements and helping us to understand how our Galaxy fits into extragalactic contexts. Unfortunately, current estimates span a wide range of values and are often statistically incompatible with one another. Here, we perform a Bayesian meta-analysis to determine an improved, aggregate estimate for L d , utilizing a mixture-model approach to account for the possibility that any one measurement has not properly accounted for all statistical or systematic errors. Within this machinery, we explore a variety of ways of modeling the nature of problematic measurements, and then employ a Bayesian model averaging technique to derive net posterior distributions that incorporate any model-selection uncertainty. Our meta-analysis combines 29 different (15 visible and 14 infrared) photometric measurements of L d available in the literature; these involve a broad assortment of observational data sets, MW models and assumptions, and methodologies, all tabulated herein. Analyzing the visible and infrared measurements separately yields estimates for L d of {2.71}-0.20+0.22 kpc and {2.51}-0.13+0.15 kpc, respectively, whereas considering them all combined yields 2.64 ± 0.13 kpc. The ratio between the visible and infrared scale lengths determined here is very similar to that measured in external spiral galaxies. We use these results to update the model of the Galactic disk from our previous work, constraining its stellar mass to be {4.8}-1.1+1.5× {10}10 M ⊙, and the MW’s total stellar mass to be {5.7}-1.1+1.5× {10}10 M ⊙.
MOLLOY, ANNE
2014-01-01
PUBLISHED OBJECTIVE: To determine an optimal population red blood cell (RBC) folate concentration for the prevention of neural tube birth defects. DESIGN: Bayesian model. SETTING: Data from two population based studies in China. PARTICIPANTS: 247,831 participants in a prospective community intervention project in China (1993-95) to prevent neural tube defects with 400 μg/day folic acid supplementation and 1194 participants in a population based randomized trial (20...
Bayesian network as a modelling tool for risk management in agriculture
Svend Rasmussen; Madsen, Anders L.; Mogens Lund
2013-01-01
The importance of risk management increases as farmers become more exposed to risk. But risk management is a difficult topic because income risk is the result of the complex interaction of multiple risk factors combined with the effect of an increasing array of possible risk management tools. In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be e...
Directory of Open Access Journals (Sweden)
Kelemen Arpad
2008-08-01
Full Text Available Abstract Background This paper addresses key biological problems and statistical issues in the analysis of large gene expression data sets that describe systemic temporal response cascades to therapeutic doses in multiple tissues such as liver, skeletal muscle, and kidney from the same animals. Affymetrix time course gene expression data U34A are obtained from three different tissues including kidney, liver and muscle. Our goal is not only to find the concordance of gene in different tissues, identify the common differentially expressed genes over time and also examine the reproducibility of the findings by integrating the results through meta analysis from multiple tissues in order to gain a significant increase in the power of detecting differentially expressed genes over time and to find the differential differences of three tissues responding to the drug. Results and conclusion Bayesian categorical model for estimating the proportion of the 'call' are used for pre-screening genes. Hierarchical Bayesian Mixture Model is further developed for the identifications of differentially expressed genes across time and dynamic clusters. Deviance information criterion is applied to determine the number of components for model comparisons and selections. Bayesian mixture model produces the gene-specific posterior probability of differential/non-differential expression and the 95% credible interval, which is the basis for our further Bayesian meta-inference. Meta-analysis is performed in order to identify commonly expressed genes from multiple tissues that may serve as ideal targets for novel treatment strategies and to integrate the results across separate studies. We have found the common expressed genes in the three tissues. However, the up/down/no regulations of these common genes are different at different time points. Moreover, the most differentially expressed genes were found in the liver, then in kidney, and then in muscle.
Batterbee, D C; Sims, N D; Becker, W; Worden, K; Rowson, J
2011-11-01
Non-accidental head injury in infants, or shaken baby syndrome, is a highly controversial and disputed topic. Biomechanical studies often suggest that shaking alone cannot cause the classical symptoms, yet many medical experts believe the contrary. Researchers have turned to finite element modelling for a more detailed understanding of the interactions between the brain, skull, cerebrospinal fluid (CSF), and surrounding tissues. However, the uncertainties in such models are significant; these can arise from theoretical approximations, lack of information, and inherent variability. Consequently, this study presents an uncertainty analysis of a finite element model of a human head subject to shaking. Although the model geometry was greatly simplified, fluid-structure-interaction techniques were used to model the brain, skull, and CSF using a Eulerian mesh formulation with penalty-based coupling. Uncertainty and sensitivity measurements were obtained using Bayesian sensitivity analysis, which is a technique that is relatively new to the engineering community. Uncertainty in nine different model parameters was investigated for two different shaking excitations: sinusoidal translation only, and sinusoidal translation plus rotation about the base of the head. The level and type of sensitivity in the results was found to be highly dependent on the excitation type.
Waif goodbye! Average-size female models promote positive body image and appeal to consumers.
Diedrichs, Phillippa C; Lee, Christina
2011-10-01
Despite consensus that exposure to media images of thin fashion models is associated with poor body image and disordered eating behaviours, few attempts have been made to enact change in the media. This study sought to investigate an effective alternative to current media imagery, by exploring the advertising effectiveness of average-size female fashion models, and their impact on the body image of both women and men. A sample of 171 women and 120 men were assigned to one of three advertisement conditions: no models, thin models and average-size models. Women and men rated average-size models as equally effective in advertisements as thin and no models. For women with average and high levels of internalisation of cultural beauty ideals, exposure to average-size female models was associated with a significantly more positive body image state in comparison to exposure to thin models and no models. For men reporting high levels of internalisation, exposure to average-size models was also associated with a more positive body image state in comparison to viewing thin models. These findings suggest that average-size female models can promote positive body image and appeal to consumers.
Bayesian Data Assimilation for Improved Modeling of Road Traffic
Van Hinsbergen, C.P.Y.
2010-01-01
This thesis deals with the optimal use of existing models that predict certain phenomena of the road traffic system. Such models are extensively used in Advanced Traffic Information Systems (ATIS), Dynamic Traffic Management (DTM) or Model Predictive Control (MPC) approaches in order to improve the
Gene function classification using Bayesian models with hierarchy-based priors
Directory of Open Access Journals (Sweden)
Neal Radford M
2006-10-01
Full Text Available Abstract Background We investigate whether annotation of gene function can be improved using a classification scheme that is aware that functional classes are organized in a hierarchy. The classifiers look at phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL model, a hierarchical model based on a set of nested MNL models, and an MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs from the E. coli genome. Results The results from all three models show substantial improvement over previous methods, which were based on the C5 decision tree algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining the three sources of information in this dataset, our new approach to combining data sources produces a higher accuracy rate than applying our models to each data source alone. Conclusion Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information.
Estimation of temporal gait parameters using Bayesian models on acceleration signals.
López-Nava, I H; Muñoz-Meléndez, A; Pérez Sanpablo, A I; Alessi Montero, A; Quiñones Urióstegui, I; Núñez Carrera, L
2016-01-01
The purpose of this study is to develop a system capable of performing calculation of temporal gait parameters using two low-cost wireless accelerometers and artificial intelligence-based techniques as part of a larger research project for conducting human gait analysis. Ten healthy subjects of different ages participated in this study and performed controlled walking tests. Two wireless accelerometers were placed on their ankles. Raw acceleration signals were processed in order to obtain gait patterns from characteristic peaks related to steps. A Bayesian model was implemented to classify the characteristic peaks into steps or nonsteps. The acceleration signals were segmented based on gait events, such as heel strike and toe-off, of actual steps. Temporal gait parameters, such as cadence, ambulation time, step time, gait cycle time, stance and swing phase time, simple and double support time, were estimated from segmented acceleration signals. Gait data-sets were divided into two groups of ages to test Bayesian models in order to classify the characteristic peaks. The mean error obtained from calculating the temporal gait parameters was 4.6%. Bayesian models are useful techniques that can be applied to classification of gait data of subjects at different ages with promising results.
Declarative Modeling and Bayesian Inference of Dark Matter Halos
Kronberger, Gabriel
2013-01-01
Probabilistic programming allows specification of probabilistic models in a declarative manner. Recently, several new software systems and languages for probabilistic programming have been developed on the basis of newly developed and improved methods for approximate inference in probabilistic models. In this contribution a probabilistic model for an idealized dark matter localization problem is described. We first derive the probabilistic model for the inference of dark matter locations and masses, and then show how this model can be implemented using BUGS and Infer.NET, two software systems for probabilistic programming. Finally, the different capabilities of both systems are discussed. The presented dark matter model includes mainly non-conjugate factors, thus, it is difficult to implement this model with Infer.NET.
Bayesian latent structure modeling of walking behavior in a physical activity intervention
Lawson, Andrew B; Ellerbe, Caitlyn; Carroll, Rachel; Alia, Kassandra; Coulon, Sandra; Wilson, Dawn K; VanHorn, M Lee; St George, Sara M
2017-01-01
The analysis of walking behavior in a physical activity intervention is considered. A Bayesian latent structure modeling approach is proposed whereby the ability and willingness of participants is modeled via latent effects. The dropout process is jointly modeled via a linked survival model. Computational issues are addressed via posterior sampling and a simulated evaluation of the longitudinal model’s ability to recover latent structure and predictor effects is considered. We evaluate the effect of a variety of socio-psychological and spatial neighborhood predictors on the propensity to walk and the estimation of latent ability and willingness in the full study. PMID:24741000
Dose-Response Modeling Under Simple Order Restrictions Using Bayesian Variable Selection Methods
Otava, Martin; Shkedy, Ziv; Lin, Dan; Goehlmann, Hinrich W. H.; Bijnens, Luc; Talloen, Willem; Kasim, Adetayo
2014-01-01
Bayesian modeling of dose–response data offers the possibility to establish the relationship between a clinical or a genomic response and increasing doses of a therapeutic compound and to determine the nature of the relationship wherever it exists. In this article, we focus on an order-restricted one-way ANOVA model which can be used to test the null hypothesis of no dose effect against an ordered alternative. Within the framework of the dose–response modeling, a model uncertainty can be addr...
A population-based Bayesian approach to the minimal model of glucose and insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Højbjerre, Malene
2005-01-01
for a whole population. Traditionally it has been analysed in a deterministic set-up with only error terms on the measurements. In this work we adopt a Bayesian graphical model to describe the coupled minimal model that accounts for both measurement and process variability, and the model is extended......-posed estimation problem, where the reconstruction most often has been done by non-linear least squares techniques separately for each entity. The minmal model was originally specified for a single individual and does not combine several individuals with the advantage of estimating the metabolic portrait...
A High Performance Bayesian Computing Framework for Spatiotemporal Uncertainty Modeling
Cao, G.
2015-12-01
All types of spatiotemporal measurements are subject to uncertainty. With spatiotemporal data becomes increasingly involved in scientific research and decision making, it is important to appropriately model the impact of uncertainty. Quantitatively modeling spatiotemporal uncertainty, however, is a challenging problem considering the complex dependence and dataheterogeneities.State-space models provide a unifying and intuitive framework for dynamic systems modeling. In this paper, we aim to extend the conventional state-space models for uncertainty modeling in space-time contexts while accounting for spatiotemporal effects and data heterogeneities. Gaussian Markov Random Field (GMRF) models, also known as conditional autoregressive models, are arguably the most commonly used methods for modeling of spatially dependent data. GMRF models basically assume that a geo-referenced variable primarily depends on its neighborhood (Markov property), and the spatial dependence structure is described via a precision matrix. Recent study has shown that GMRFs are efficient approximation to the commonly used Gaussian fields (e.g., Kriging), and compared with Gaussian fields, GMRFs enjoy a series of appealing features, such as fast computation and easily accounting for heterogeneities in spatial data (e.g, point and areal). This paper represents each spatial dataset as a GMRF and integrates them into a state-space form to statistically model the temporal dynamics. Different types of spatial measurements (e.g., categorical, count or continuous), can be accounted for by according link functions. A fast alternative to MCMC framework, so-called Integrated Nested Laplace Approximation (INLA), was adopted for model inference.Preliminary case studies will be conducted to showcase the advantages of the described framework. In the first case, we apply the proposed method for modeling the water table elevation of Ogallala aquifer over the past decades. In the second case, we analyze the
A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models
Energy Technology Data Exchange (ETDEWEB)
Xu, Jin; Yu, Yaming [Department of Statistics, University of California, Irvine, Irvine, CA 92697-1250 (United States); Van Dyk, David A. [Statistics Section, Imperial College London, Huxley Building, South Kensington Campus, London SW7 2AZ (United Kingdom); Kashyap, Vinay L.; Siemiginowska, Aneta; Drake, Jeremy; Ratzlaff, Pete [Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138 (United States); Connors, Alanna; Meng, Xiao-Li, E-mail: jinx@uci.edu, E-mail: yamingy@ics.uci.edu, E-mail: dvandyk@imperial.ac.uk, E-mail: vkashyap@cfa.harvard.edu, E-mail: asiemiginowska@cfa.harvard.edu, E-mail: jdrake@cfa.harvard.edu, E-mail: pratzlaff@cfa.harvard.edu, E-mail: meng@stat.harvard.edu [Department of Statistics, Harvard University, 1 Oxford Street, Cambridge, MA 02138 (United States)
2014-10-20
Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use a principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.
A Fully Bayesian Method for Jointly Fitting Instrumental Calibration and X-Ray Spectral Models
Xu, Jin; van Dyk, David A.; Kashyap, Vinay L.; Siemiginowska, Aneta; Connors, Alanna; Drake, Jeremy; Meng, Xiao-Li; Ratzlaff, Pete; Yu, Yaming
2014-10-01
Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is "pragmatic" in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use a principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.
Combining Bayesian Networks and Agent Based Modeling to develop a decision-support model in Vietnam
Nong, Bao Anh; Ertsen, Maurits; Schoups, Gerrit
2016-04-01
Complexity and uncertainty in natural resources management have been focus themes in recent years. Within these debates, with the aim to define an approach feasible for water management practice, we are developing an integrated conceptual modeling framework for simulating decision-making processes of citizens, in our case in the Day river area, Vietnam. The model combines Bayesian Networks (BNs) and Agent-Based Modeling (ABM). BNs are able to combine both qualitative data from consultants / experts / stakeholders, and quantitative data from observations on different phenomena or outcomes from other models. Further strengths of BNs are that the relationship between variables in the system is presented in a graphical interface, and that components of uncertainty are explicitly related to their probabilistic dependencies. A disadvantage is that BNs cannot easily identify the feedback of agents in the system once changes appear. Hence, ABM was adopted to represent the reaction among stakeholders under changes. The modeling framework is developed as an attempt to gain better understanding about citizen's behavior and factors influencing their decisions in order to reduce uncertainty in the implementation of water management policy.
Critical elements on fitting the Bayesian multivariate Poisson Lognormal model
Zamzuri, Zamira Hasanah binti
2015-10-01
Motivated by a problem on fitting multivariate models to traffic accident data, a detailed discussion of the Multivariate Poisson Lognormal (MPL) model is presented. This paper reveals three critical elements on fitting the MPL model: the setting of initial estimates, hyperparameters and tuning parameters. These issues have not been highlighted in the literature. Based on simulation studies conducted, we have shown that to use the Univariate Poisson Model (UPM) estimates as starting values, at least 20,000 iterations are needed to obtain reliable final estimates. We also illustrated the sensitivity of the specific hyperparameter, which if it is not given extra attention, may affect the final estimates. The last issue is regarding the tuning parameters where they depend on the acceptance rate. Finally, a heuristic algorithm to fit the MPL model is presented. This acts as a guide to ensure that the model works satisfactorily given any data set.
A Bayesian framework for parameter estimation in dynamical models.
Directory of Open Access Journals (Sweden)
Flávio Codeço Coelho
Full Text Available Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.
Molitor, John
2012-03-01
Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.
Modeling the Frequency of Cyclists’ Red-Light Running Behavior Using Bayesian PG Model and PLN Model
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Yao Wu
2016-01-01
Full Text Available Red-light running behaviors of bicycles at signalized intersection lead to a large number of traffic conflicts and high collision potentials. The primary objective of this study is to model the cyclists’ red-light running frequency within the framework of Bayesian statistics. Data was collected at twenty-five approaches at seventeen signalized intersections. The Poisson-gamma (PG and Poisson-lognormal (PLN model were developed and compared. The models were validated using Bayesian p values based on posterior predictive checking indicators. It was found that the two models have a good fit of the observed cyclists’ red-light running frequency. Furthermore, the PLN model outperformed the PG model. The model estimated results showed that the amount of cyclists’ red-light running is significantly influenced by bicycle flow, conflict traffic flow, pedestrian signal type, vehicle speed, and e-bike rate. The validation result demonstrated the reliability of the PLN model. The research results can help transportation professionals to predict the expected amount of the cyclists’ red-light running and develop effective guidelines or policies to reduce red-light running frequency of bicycles at signalized intersections.
Link, William; Sauer, John R.
2016-01-01
The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.
Link, William A; Sauer, John R
2016-07-01
The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.