The application of Bayesian networks in natural hazard analyses
K. Vogel
2013-10-01
Full Text Available In natural hazards we face several uncertainties due to our lack of knowledge and/or the intrinsic randomness of the underlying natural processes. Nevertheless, deterministic analysis approaches are still widely used in natural hazard assessments, with the pitfall of underestimating the hazard with potentially disastrous consequences. In this paper we show that the Bayesian network approach offers a flexible framework for capturing and expressing a broad range of different uncertainties as those encountered in natural hazard assessments. Although well studied in theory, the application of Bayesian networks on real-world data is often not straightforward and requires specific tailoring and adaption of existing algorithms. We demonstrate by way of three case studies (a ground motion model for a seismic hazard analysis, a flood damage assessment, and a landslide susceptibility study the applicability of Bayesian networks across different domains showcasing various properties and benefits of the Bayesian network framework. We offer suggestions as how to tackle practical problems arising along the way, mainly concentrating on the handling of continuous variables, missing observations, and the interaction of both. We stress that our networks are completely data-driven, although prior domain knowledge can be included if desired.
Using ancient DNA and coalescent-based methods to infer extinction.
Chang, Dan; Shapiro, Beth
2016-02-01
DNA sequences extracted from preserved remains can add considerable resolution to inference of past population dynamics. For example, coalescent-based methods have been used to correlate declines in some arctic megafauna populations with habitat fragmentation during the last ice age. These methods, however, often fail to detect population declines preceding extinction, most likely owing to a combination of sparse sampling, uninformative genetic markers, and models that cannot account for the increasingly structured nature of populations as habitats decline. As ancient DNA research expands to include full-genome analyses, these data will provide greater resolution of the genomic consequences of environmental change and the genetic signatures of extinction. PMID:26864783
A space-time multivariate Bayesian model to analyse road traffic accidents by severity
Boulieri, A; Liverani, S; Hoogh, K. de; Blangiardo, M.
2016-01-01
The paper investigates the dependences between levels of severity of road traffic accidents, accounting at the same time for spatial and temporal correlations. The study analyses road traffic accidents data at ward level in England over the period 2005–2013. We include in our model multivariate spatially structured and unstructured effects to capture the dependences between severities, within a Bayesian hierarchical formulation. We also include a temporal component to capture the time effects...
Mueller, Julie M.; Loomis, John B.
2010-01-01
The choice of weights is a non-nested problem in most applied spatial econometric models. Despite numerous recent advances in spatial econometrics, the choice of spatial weights remains exogenously determined by the researcher in empirical applications. Bayesian techniques provide statistical evidence regarding the simultaneous choice of model specification and spatial weights matrices by using posterior probabilities. This paper demonstrates the Bayesian estimation approach in a spatial hedo...
New insights into the phylogeny of fig pollinators using Bayesian analyses.
Jiang, Zi-Feng; Huang, Da-Wei; Zhu, Chao-Dong; Zhen, Wen-Quan
2006-02-01
The interaction between figs and fig pollinators is one of the most species-specific mutualisms. Recently, phylogenies of both partners based on molecular data provided insights into a wide spectrum of co-evolutionary questions. However, for the phylogeny of fig pollinators, there are some discrepancies between different studies and left some relationships unresolved, especially for deep nodes. The phylogenetic uncertainties of pollinators prohibit our further understanding of the history of the mutualism. Here, we present phylogenetic analyses of a larger COI sequence dataset that includes previously published datasets and our sequences from 20 species using Bayesian method and maximum parsimony. The analyses using different methods share similar topologies. Bayesian analyses provide high level of confidence for most internal nodes in terms of posterior probability. This study also clarifies some discrepancies between previous studies. After rooting with Tetrapus, other pollinators split into two clades. Wiebesia and Blastophaga are at basal positions in respective clade. Ceratosolen is not monophyletic because Kradibia and Liporrhopalum fall inside this group. Three subgenera of Ceratosolen: subgen. Ceratosolen, subgen. Rothropus, and subgen. Strepitus are not supported. Therefore, Ceratosolen is suggested to be re-divided into three groups. Urostigma pollinators (including Dolichoris and Blastophaga psenes) are clustered together. The monophylies of Wiebesia, Blastophaga, Dolichoris are not supported in this analysis. This study also provides a new framework for re-evaluating character evolution and re-inspecting the definition of some genera. PMID:16364663
Velimir Gayevskiy
Full Text Available Bayesian inference methods are extensively used to detect the presence of population structure given genetic data. The primary output of software implementing these methods are ancestry profiles of sampled individuals. While these profiles robustly partition the data into subgroups, currently there is no objective method to determine whether the fixed factor of interest (e.g. geographic origin correlates with inferred subgroups or not, and if so, which populations are driving this correlation. We present ObStruct, a novel tool to objectively analyse the nature of structure revealed in Bayesian ancestry profiles using established statistical methods. ObStruct evaluates the extent of structural similarity between sampled and inferred populations, tests the significance of population differentiation, provides information on the contribution of sampled and inferred populations to the observed structure and crucially determines whether the predetermined factor of interest correlates with inferred population structure. Analyses of simulated and experimental data highlight ObStruct's ability to objectively assess the nature of structure in populations. We show the method is capable of capturing an increase in the level of structure with increasing time since divergence between simulated populations. Further, we applied the method to a highly structured dataset of 1,484 humans from seven continents and a less structured dataset of 179 Saccharomyces cerevisiae from three regions in New Zealand. Our results show that ObStruct provides an objective metric to classify the degree, drivers and significance of inferred structure, as well as providing novel insights into the relationships between sampled populations, and adds a final step to the pipeline for population structure analyses.
An application of the 'Bayesian cohort model' to nuclear power plant cost analyses
We have developed a new method for identifying the effects of calendar year, plant age and commercial operation starting year on the costs and performances of nuclear power plants and also developed an analysis system running on personal computers. The method extends the Bayesian cohort model for time series social survey data proposed by one of the authors. The proposed method was shown to be able to separate the above three effects more properly than traditional methods such as taking simple means by time domain. The analyses of US nuclear plant cost and performance data by using the proposed method suggest that many of the US plants spent relatively long time and much capital cost for modification at their age of about 10 to 20 years, but that, after those ages, they performed fairly well with lower and stabilized O and M and additional capital costs. (author)
Chen, Cong; Zhang, Guohui; Tarefder, Rafiqul; Ma, Jianming; Wei, Heng; Guan, Hongzhi
2015-07-01
Rear-end crash is one of the most common types of traffic crashes in the U.S. A good understanding of its characteristics and contributing factors is of practical importance. Previously, both multinomial Logit models and Bayesian network methods have been used in crash modeling and analysis, respectively, although each of them has its own application restrictions and limitations. In this study, a hybrid approach is developed to combine multinomial logit models and Bayesian network methods for comprehensively analyzing driver injury severities in rear-end crashes based on state-wide crash data collected in New Mexico from 2010 to 2011. A multinomial logit model is developed to investigate and identify significant contributing factors for rear-end crash driver injury severities classified into three categories: no injury, injury, and fatality. Then, the identified significant factors are utilized to establish a Bayesian network to explicitly formulate statistical associations between injury severity outcomes and explanatory attributes, including driver behavior, demographic features, vehicle factors, geometric and environmental characteristics, etc. The test results demonstrate that the proposed hybrid approach performs reasonably well. The Bayesian network reference analyses indicate that the factors including truck-involvement, inferior lighting conditions, windy weather conditions, the number of vehicles involved, etc. could significantly increase driver injury severities in rear-end crashes. The developed methodology and estimation results provide insights for developing effective countermeasures to reduce rear-end crash injury severities and improve traffic system safety performance. PMID:25888994
Bayesian Synthesis: Combining subjective analyses, with an application to ozone data
Yu, Qingzhao; MacEachern, Steven N.; Peruggia, Mario
2011-01-01
Bayesian model averaging enables one to combine the disparate predictions of a number of models in a coherent fashion, leading to superior predictive performance. The improvement in performance arises from averaging models that make different predictions. In this work, we tap into perhaps the biggest driver of different predictions—different analysts—in order to gain the full benefits of model averaging. In a standard implementation of our method, several data analysts work independently on p...
Karacaören Burak
2011-05-01
Full Text Available Abstract Background It has been shown that if genetic relationships among individuals are not taken into account for genome wide association studies, this may lead to false positives. To address this problem, we used Genome-wide Rapid Association using Mixed Model and Regression and principal component stratification analyses. To account for linkage disequilibrium among the significant markers, principal components loadings obtained from top markers can be included as covariates. Estimation of Bayesian networks may also be useful to investigate linkage disequilibrium among SNPs and their relation with environmental variables. For the quantitative trait we first estimated residuals while taking polygenic effects into account. We then used a single SNP approach to detect the most significant SNPs based on the residuals and applied principal component regression to take linkage disequilibrium among these SNPs into account. For the categorical trait we used principal component stratification methodology to account for background effects. For correction of linkage disequilibrium we used principal component logit regression. Bayesian networks were estimated to investigate relationship among SNPs. Results Using the Genome-wide Rapid Association using Mixed Model and Regression and principal component stratification approach we detected around 100 significant SNPs for the quantitative trait (p Conclusions GRAMMAR could efficiently incorporate the information regarding random genetic effects. Principal component stratification should be cautiously used with stringent multiple hypothesis testing correction to correct for ancestral stratification and association analyses for binary traits when there are systematic genetic effects such as half sib family structures. Bayesian networks are useful to investigate relationships among SNPs and environmental variables.
Forecasting neutrino masses from combining KATRIN and the CMB: Frequentist and Bayesian analyses
Host, Ole; Lahav, Ofer; Abdalla, Filipe B.; Eitel, Klaus
2007-01-01
We present a showcase for deriving bounds on the neutrino masses from laboratory experiments and cosmological observations. We compare the frequentist and Bayesian bounds on the effective electron neutrino mass m_beta which the KATRIN neutrino mass experiment is expected to obtain, using both an analytical likelihood function and Monte Carlo simulations of KATRIN. Assuming a uniform prior in m_beta, we find that a null result yields an upper bound of about 0.17 eV at 90% confidence in the Bay...
Predictability of Regional Climate: A Bayesian Approach to Analysing a WRF Model Ensemble
Bruyere, C. L.; Mesquita, M. D. S.; Paimazumder, D.
2013-12-01
This study investigates aspects of climate predictability with a focus on climatic variables and different characteristics of extremes over nine North American climatic regions and two selected Atlantic sectors. An ensemble of state-of-the-art Weather Research and Forecasting Model (WRF) simulations is used for the analysis. The ensemble is comprised of a combination of various physics schemes, initial conditions, domain sizes, boundary conditions and breeding techniques. The main objectives of this research are: 1) to increase our understanding of the ability of WRF to capture regional climate information - both at the individual and collective ensemble members, 2) to investigate the role of different members and their synergy in reproducing regional climate 3) to estimate the associated uncertainty. In this study, we propose a Bayesian framework to study the predictability of extremes and associated uncertainties in order to provide a wealth of knowledge about WRF reliability and provide further clarity and understanding of the sensitivities and optimal combinations. The choice of the Bayesian model, as opposed to standard methods, is made because: a) this method has a mean square error that is less than standard statistics, which makes it a more robust method; b) it allows for the use of small sample sizes, which are typical in high-resolution modeling; c) it provides a probabilistic view of uncertainty, which is useful when making decisions concerning ensemble members.
Jomelli, Vincent; Pavlova, Irina; Eckert, Nicolas; Grancher, Delphine; Brunstein, Daniel
2015-12-01
How can debris flow occurrences be modelled at regional scale and take both environmental and climatic conditions into account? And, of the two, which has the most influence on debris flow activity? In this paper, we try to answer these questions with an innovative Bayesian hierarchical probabilistic model that simultaneously accounts for how debris flows respond to environmental and climatic variables. In it, full decomposition of space and time effects in occurrence probabilities is assumed, revealing an environmental and a climatic trend shared by all years/catchments, respectively, clearly distinguished from residual "random" effects. The resulting regional and annual occurrence probabilities evaluated as functions of the covariates make it possible to weight the respective contribution of the different terms and, more generally, to check the model performances at different spatio-temporal scales. After suitable validation, the model can be used to make predictions at undocumented sites and could be used in further studies for predictions under future climate conditions. Also, the Bayesian paradigm easily copes with missing data, thus making it possible to account for events that may have been missed during surveys. As a case study, we extract 124 debris flow event triggered between 1970 and 2005 in 27 catchments located in the French Alps from the French national natural hazard survey and model their variability of occurrence considering environmental and climatic predictors at the same time. We document the environmental characteristics of each debris flow catchment (morphometry, lithology, land cover, and the presence of permafrost). We also compute 15 climate variables including mean temperature and precipitation between May and October and the number of rainy days with daily cumulative rainfall greater than 10/15/20/25/30/40 mm day- 1. Application of our model shows that the combination of environmental and climatic predictors explained 77% of the overall
Salvidio Sebastiano
2010-02-01
Full Text Available Abstract Background It has been suggested that Plethodontid salamanders are excellent candidates for indicating ecosystem health. However, detailed, long-term data sets of their populations are rare, limiting our understanding of the demographic processes underlying their population fluctuations. Here we present a demographic analysis based on a 1996 - 2008 data set on an underground population of Speleomantes strinatii (Aellen in NW Italy. We utilised a Bayesian state-space approach allowing us to parameterise a stage-structured Lefkovitch model. We used all the available population data from annual temporary removal experiments to provide us with the baseline data on the numbers of juveniles, subadults and adult males and females present at any given time. Results Sampling the posterior chains of the converged state-space model gives us the likelihood distributions of the state-specific demographic rates and the associated uncertainty of these estimates. Analysing the resulting parameterised Lefkovitch matrices shows that the population growth is very close to 1, and that at population equilibrium we expect half of the individuals present to be adults of reproductive age which is what we also observe in the data. Elasticity analysis shows that adult survival is the key determinant for population growth. Conclusion This analysis demonstrates how an understanding of population demography can be gained from structured population data even in a case where following marked individuals over their whole lifespan is not practical.
Hejase, Hussein A; Liu, Kevin J
2016-01-01
Recent studies of eukaryotes including human and Neandertal, mice, and butterflies have highlighted the major role that interspecific introgression has played in adaptive trait evolution. A common question arises in each case: what is the genomic architecture of the introgressed traits? One common approach that can be used to address this question is association mapping, which looks for genotypic markers that have significant statistical association with a trait. It is well understood that sample relatedness can be a confounding factor in association mapping studies if not properly accounted for. Introgression and other evolutionary processes (e.g., incomplete lineage sorting) typically introduce variation among local genealogies, which can also differ from global sample structure measured across all genomic loci. In contrast, state-of-the-art association mapping methods assume fixed sample relatedness across the genome, which can lead to spurious inference. We therefore propose a new association mapping method called Coal-Map, which uses coalescent-based models to capture local genealogical variation alongside global sample structure. Using simulated and empirical data reflecting a range of evolutionary scenarios, we compare the performance of Coal-Map against EIGENSTRAT, a leading association mapping method in terms of its popularity, power, and type I error control. Our empirical data makes use of hundreds of mouse genomes for which adaptive interspecific introgression has recently been described. We found that Coal-Map's performance is comparable or better than EIGENSTRAT in terms of statistical power and false positive rate. Coal-Map's performance advantage was greatest on model conditions that most closely resembled empirically observed scenarios of adaptive introgression. These conditions had: (1) causal SNPs contained in one or a few introgressed genomic loci and (2) varying rates of gene flow - from high rates to very low rates where incomplete lineage
Galbraith, Craig S.; Merrill, Gregory B.; Kline, Doug M.
2012-01-01
In this study we investigate the underlying relational structure between student evaluations of teaching effectiveness (SETEs) and achievement of student learning outcomes in 116 business related courses. Utilizing traditional statistical techniques, a neural network analysis and a Bayesian data reduction and classification algorithm, we find…
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
Draper, D.
2001-01-01
© 2012 Springer Science+Business Media, LLC. All rights reserved. Article Outline: Glossary Definition of the Subject and Introduction The Bayesian Statistical Paradigm Three Examples Comparison with the Frequentist Statistical Paradigm Future Directions Bibliography
Hotaling, Scott; Foley, Mary E; Lawrence, Nicolette M; Bocanegra, Jose; Blanco, Marina B; Rasoloarison, Rodin; Kappeler, Peter M; Barrett, Meredith A; Yoder, Anne D; Weisrock, David W
2016-05-01
Implementation of the coalescent model in a Bayesian framework is an emerging strength in genetically based species delimitation studies. By providing an objective measure of species diagnosis, these methods represent a quantitative enhancement to the analysis of multilocus data, and complement more traditional methods based on phenotypic and ecological characteristics. Recognized as two species 20 years ago, mouse lemurs (genus Microcebus) now comprise more than 20 species, largely diagnosed from mtDNA sequence data. With each new species description, enthusiasm has been tempered with scientific scepticism. Here, we present a statistically justified and unbiased Bayesian approach towards mouse lemur species delimitation. We perform validation tests using multilocus sequence data and two methodologies: (i) reverse-jump Markov chain Monte Carlo sampling to assess the likelihood of different models defined a priori by a guide tree, and (ii) a Bayes factor delimitation test that compares different species-tree models without a guide tree. We assess the sensitivity of these methods using randomized individual assignments, which has been used in bpp studies, but not with Bayes factor delimitation tests. Our results validate previously diagnosed taxa, as well as new species hypotheses, resulting in support for three new mouse lemur species. As the challenge of multiple researchers using differing criteria to describe diversity is not unique to Microcebus, the methods used here have significant potential for clarifying diversity in other taxonomic groups. We echo previous studies in advocating that multiple lines of evidence, including use of the coalescent model, should be trusted to delimit new species. PMID:26946180
Kirstein, Roland
2005-01-01
This paper presents a modification of the inspection game: The ?Bayesian Monitoring? model rests on the assumption that judges are interested in enforcing compliant behavior and making correct decisions. They may base their judgements on an informative but imperfect signal which can be generated costlessly. In the original inspection game, monitoring is costly and generates a perfectly informative signal. While the inspection game has only one mixed strategy equilibrium, three Perfect Bayesia...
Kanagi Kanapathy
2014-01-01
Full Text Available The research question is whether the positive relationship found between supplier involvement practices and new product development performances in developed economies also holds in emerging economies. The role of supplier involvement practices in new product development performance is yet to be substantially investigated in the emerging economies (other than China. This premise was examined by distributing a survey instrument (Jayaram’s (2008 published survey instrument that has been utilised in developed economies to Malaysian manufacturing companies. To gauge the relationship between the supplier involvement practices and new product development (NPD project performance of 146 companies, structural equation modelling was adopted. Our findings prove that supplier involvement practices have a significant positive impact on NPD project performance in an emerging economy with respect to quality objectives, design objectives, cost objectives, and “time-to-market” objectives. Further analysis using the Bayesian Markov Chain Monte Carlo algorithm, yielding a more credible and feasible differentiation, confirmed these results (even in the case of an emerging economy and indicated that these practices have a 28% impact on variance of NPD project performance. This considerable effect implies that supplier involvement is a must have, although further research is needed to identify the contingencies for its practices.
Bessiere, Pierre; Ahuactzin, Juan Manuel; Mekhnacha, Kamel
2013-01-01
Probability as an Alternative to Boolean LogicWhile logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain DataEmphasizing probability as an alternative to Boolean
Singh, Garima; Dal Grande, Francesco; Divakar, Pradeep K; Otte, Jürgen; Leavitt, Steven D; Szczepanska, Katarzyna; Crespo, Ana; Rico, Víctor J; Aptroot, André; Cáceres, Marcela Eugenia da Silva; Lumbsch, H Thorsten; Schmitt, Imke
2015-01-01
Species recognition in lichen-forming fungi has been a challenge because of unsettled species concepts, few taxonomically relevant traits, and limitations of traditionally used morphological and chemical characters for identifying closely related species. Here we analyze species diversity in the cosmopolitan genus Protoparmelia s.l. The ~25 described species in this group occur across diverse habitats from the boreal-arctic/alpine to the tropics, but their relationship to each other remains unexplored. In this study, we inferred the phylogeny of 18 species currently assigned to this genus based on 160 specimens and six markers: mtSSU, nuLSU, ITS, RPB1, MCM7, and TSR1. We assessed the circumscription of species-level lineages in Protoparmelia s. str. using two coalescent-based species delimitation methods--BP&P and spedeSTEM. Our results suggest the presence of a tropical and an extra-tropical lineage, and eleven previously unrecognized distinct species-level lineages in Protoparmelia s. str. Several cryptic lineages were discovered as compared to phenotype-based species delimitation. Many of the putative species are supported by geographic evidence. PMID:25932996
Garima Singh
Full Text Available Species recognition in lichen-forming fungi has been a challenge because of unsettled species concepts, few taxonomically relevant traits, and limitations of traditionally used morphological and chemical characters for identifying closely related species. Here we analyze species diversity in the cosmopolitan genus Protoparmelia s.l. The ~25 described species in this group occur across diverse habitats from the boreal-arctic/alpine to the tropics, but their relationship to each other remains unexplored. In this study, we inferred the phylogeny of 18 species currently assigned to this genus based on 160 specimens and six markers: mtSSU, nuLSU, ITS, RPB1, MCM7, and TSR1. We assessed the circumscription of species-level lineages in Protoparmelia s. str. using two coalescent-based species delimitation methods--BP&P and spedeSTEM. Our results suggest the presence of a tropical and an extra-tropical lineage, and eleven previously unrecognized distinct species-level lineages in Protoparmelia s. str. Several cryptic lineages were discovered as compared to phenotype-based species delimitation. Many of the putative species are supported by geographic evidence.
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
Jensen, Finn Verner; Nielsen, Thomas Dyhre
2016-01-01
Mathematically, a Bayesian graphical model is a compact representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks. The structural part of a Bayesian graphical model is a graph consisting of nodes and...... largely due to the availability of efficient inference algorithms for answering probabilistic queries about the states of the variables in the network. Furthermore, to support the construction of Bayesian network models, learning algorithms are also available. We give an overview of the Bayesian network...
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
Yuan, Ying; MacKinnon, David P.
2009-01-01
This article proposes Bayesian analysis of mediation effects. Compared to conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian mediation analysis, inference is straightforward and exact, which makes it appealing for studies with small samples. Third, the Bayesian approach is conceptua...
Bayesian Games with Intentions
Bjorndahl, Adam; Halpern, Joseph Y.; Pass, Rafael
2016-01-01
We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian games with intentions, generalizing both Bayesian games and psychological games, and prove that Nash equilibria in psychological games correspond to a special class of equilibria as defined in our setting.
Konstantinos ANGELIS; Mario DOS REIS
2015-01-01
Although the effects of the coalescent process on sequence divergence and genealogies are well understood, the vir-tual majority of studies that use molecular sequences to estimate times of divergence among species have failed to account for the coalescent process. Here we study the impact of ancestral population size and incomplete lineage sorting on Bayesian estimates of species divergence times under the molecular clock when the inference model ignores the coalescent process. Using a combi-nation of mathematical analysis, computer simulations and analysis of real data, we find that the errors on estimates of times and the molecular rate can be substantial when ancestral populations are large and when there is substantial incomplete lineage sort-ing. For example, in a simple three-species case, we find that if the most precise fossil calibration is placed on the root of the phylogeny, the age of the internal node is overestimated, while if the most precise calibration is placed on the internal node, then the age of the root is underestimated. In both cases, the molecular rate is overestimated. Using simulations on a phylogeny of nine species, we show that substantial errors in time and rate estimates can be obtained even when dating ancient divergence events. We analyse the hominoid phylogeny and show that estimates of the neutral mutation rate obtained while ignoring the coalescent are too high. Using a coalescent-based technique to obtain geological times of divergence, we obtain estimates of the mutation rate that are within experimental estimates and we also obtain substantially older divergence times within the phylogeny [Current Zoology 61 (5): 874–885, 2015].
Bayesian inference of population size history from multiple loci
Drummond Alexei J
2008-10-01
Full Text Available Abstract Background Effective population size (Ne is related to genetic variability and is a basic parameter in many models of population genetics. A number of methods for inferring current and past population sizes from genetic data have been developed since JFC Kingman introduced the n-coalescent in 1982. Here we present the Extended Bayesian Skyline Plot, a non-parametric Bayesian Markov chain Monte Carlo algorithm that extends a previous coalescent-based method in several ways, including the ability to analyze multiple loci. Results Through extensive simulations we show the accuracy and limitations of inferring population size as a function of the amount of data, including recovering information about evolutionary bottlenecks. We also analyzed two real data sets to demonstrate the behavior of the new method; a single gene Hepatitis C virus data set sampled from Egypt and a 10 locus Drosophila ananassae data set representing 16 different populations. Conclusion The results demonstrate the essential role of multiple loci in recovering population size dynamics. Multi-locus data from a small number of individuals can precisely recover past bottlenecks in population size which can not be characterized by analysis of a single locus. We also demonstrate that sequence data quality is important because even moderate levels of sequencing errors result in a considerable decrease in estimation accuracy for realistic levels of population genetic variability.
Ornelas, Juan Francisco; Sosa, Victoria; Soltis, Douglas E; Daza, Juan M; González, Clementina; Soltis, Pamela S; Gutiérrez-Rodríguez, Carla; de los Monteros, Alejandro Espinosa; Castoe, Todd A; Bell, Charles; Ruiz-Sanchez, Eduardo
2013-01-01
Comparative phylogeography can elucidate the influence of historical events on current patterns of biodiversity and can identify patterns of co-vicariance among unrelated taxa that span the same geographic areas. Here we analyze temporal and spatial divergence patterns of cloud forest plant and animal species and relate them to the evolutionary history of naturally fragmented cloud forests--among the most threatened vegetation types in northern Mesoamerica. We used comparative phylogeographic analyses to identify patterns of co-vicariance in taxa that share geographic ranges across cloud forest habitats and to elucidate the influence of historical events on current patterns of biodiversity. We document temporal and spatial genetic divergence of 15 species (including seed plants, birds and rodents), and relate them to the evolutionary history of the naturally fragmented cloud forests. We used fossil-calibrated genealogies, coalescent-based divergence time inference, and estimates of gene flow to assess the permeability of putative barriers to gene flow. We also used the hierarchical Approximate Bayesian Computation (HABC) method implemented in the program msBayes to test simultaneous versus non-simultaneous divergence of the cloud forest lineages. Our results show shared phylogeographic breaks that correspond to the Isthmus of Tehuantepec, Los Tuxtlas, and the Chiapas Central Depression, with the Isthmus representing the most frequently shared break among taxa. However, dating analyses suggest that the phylogeographic breaks corresponding to the Isthmus occurred at different times in different taxa. Current divergence patterns are therefore consistent with the hypothesis of broad vicariance across the Isthmus of Tehuantepec derived from different mechanisms operating at different times. This study, coupled with existing data on divergence cloud forest species, indicates that the evolutionary history of contemporary cloud forest lineages is complex and often lineage
Rubin, Donald B.
1981-01-01
The Bayesian bootstrap is the Bayesian analogue of the bootstrap. Instead of simulating the sampling distribution of a statistic estimating a parameter, the Bayesian bootstrap simulates the posterior distribution of the parameter; operationally and inferentially the methods are quite similar. Because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions, neither method should be applied wit...
Bayesian statistics an introduction
Lee, Peter M
2012-01-01
Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel
Understanding Computational Bayesian Statistics
Bolstad, William M
2011-01-01
A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistic
Frühwirth-Schnatter, Sylvia
1990-01-01
In the paper at hand we apply it to Bayesian statistics to obtain "Fuzzy Bayesian Inference". In the subsequent sections we will discuss a fuzzy valued likelihood function, Bayes' theorem for both fuzzy data and fuzzy priors, a fuzzy Bayes' estimator, fuzzy predictive densities and distributions, and fuzzy H.P.D .-Regions. (author's abstract)
Yuan, Ying; MacKinnon, David P.
2009-01-01
In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…
Space Shuttle RTOS Bayesian Network
Morris, A. Terry; Beling, Peter A.
2001-01-01
With shrinking budgets and the requirements to increase reliability and operational life of the existing orbiter fleet, NASA has proposed various upgrades for the Space Shuttle that are consistent with national space policy. The cockpit avionics upgrade (CAU), a high priority item, has been selected as the next major upgrade. The primary functions of cockpit avionics include flight control, guidance and navigation, communication, and orbiter landing support. Secondary functions include the provision of operational services for non-avionics systems such as data handling for the payloads and caution and warning alerts to the crew. Recently, a process to selection the optimal commercial-off-the-shelf (COTS) real-time operating system (RTOS) for the CAU was conducted by United Space Alliance (USA) Corporation, which is a joint venture between Boeing and Lockheed Martin, the prime contractor for space shuttle operations. In order to independently assess the RTOS selection, NASA has used the Bayesian network-based scoring methodology described in this paper. Our two-stage methodology addresses the issue of RTOS acceptability by incorporating functional, performance and non-functional software measures related to reliability, interoperability, certifiability, efficiency, correctness, business, legal, product history, cost and life cycle. The first stage of the methodology involves obtaining scores for the various measures using a Bayesian network. The Bayesian network incorporates the causal relationships between the various and often competing measures of interest while also assisting the inherently complex decision analysis process with its ability to reason under uncertainty. The structure and selection of prior probabilities for the network is extracted from experts in the field of real-time operating systems. Scores for the various measures are computed using Bayesian probability. In the second stage, multi-criteria trade-off analyses are performed between the scores
An introduction to Gaussian Bayesian networks.
Grzegorczyk, Marco
2010-01-01
The extraction of regulatory networks and pathways from postgenomic data is important for drug -discovery and development, as the extracted pathways reveal how genes or proteins regulate each other. Following up on the seminal paper of Friedman et al. (J Comput Biol 7:601-620, 2000), Bayesian networks have been widely applied as a popular tool to this end in systems biology research. Their popularity stems from the tractability of the marginal likelihood of the network structure, which is a consistent scoring scheme in the Bayesian context. This score is based on an integration over the entire parameter space, for which highly expensive computational procedures have to be applied when using more complex -models based on differential equations; for example, see (Bioinformatics 24:833-839, 2008). This chapter gives an introduction to reverse engineering regulatory networks and pathways with Gaussian Bayesian networks, that is Bayesian networks with the probabilistic BGe scoring metric [see (Geiger and Heckerman 235-243, 1995)]. In the BGe model, the data are assumed to stem from a Gaussian distribution and a normal-Wishart prior is assigned to the unknown parameters. Gaussian Bayesian network methodology for analysing static observational, static interventional as well as dynamic (observational) time series data will be described in detail in this chapter. Finally, we apply these Bayesian network inference methods (1) to observational and interventional flow cytometry (protein) data from the well-known RAF pathway to evaluate the global network reconstruction accuracy of Bayesian network inference and (2) to dynamic gene expression time series data of nine circadian genes in Arabidopsis thaliana to reverse engineer the unknown regulatory network topology for this domain. PMID:20824469
A Bayesian Modelling of Wildfires in Portugal
Silva, Giovani L.; Soares, Paulo; Marques, Susete; Dias, Inês M.; Oliveira, Manuela M.; Borges, Guilherme J.
2015-01-01
In the last decade wildfires became a serious problem in Portugal due to different issues such as climatic characteristics and nature of Portuguese forest. In order to analyse wildfire data, we employ beta regression for modelling the proportion of burned forest area, under a Bayesian perspective. Our main goal is to find out fire risk factors that influence the proportion of area burned and what may make a forest type susceptible or resistant to fire. Then, we analyse wildfire...
Granade, Christopher; Cory, D G
2015-01-01
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of- the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we solve all three problems. First, we use modern statistical methods, as pioneered by Husz\\'ar and Houlsby and by Ferrie, to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first informative priors on quantum states and channels. Finally, we develop a method that allows online tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.
Dynamic Bayesian Combination of Multiple Imperfect Classifiers
Simpson, Edwin; Psorakis, Ioannis; Smith, Arfon
2012-01-01
Classifier combination methods need to make best use of the outputs of multiple, imperfect classifiers to enable higher accuracy classifications. In many situations, such as when human decisions need to be combined, the base decisions can vary enormously in reliability. A Bayesian approach to such uncertain combination allows us to infer the differences in performance between individuals and to incorporate any available prior knowledge about their abilities when training data is sparse. In this paper we explore Bayesian classifier combination, using the computationally efficient framework of variational Bayesian inference. We apply the approach to real data from a large citizen science project, Galaxy Zoo Supernovae, and show that our method far outperforms other established approaches to imperfect decision combination. We go on to analyse the putative community structure of the decision makers, based on their inferred decision making strategies, and show that natural groupings are formed. Finally we present ...
Bayesian exploratory factor analysis
Gabriella Conti; Sylvia Frühwirth-Schnatter; James Heckman; Rémi Piatek
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identifi cation criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study c...
Bayesian Exploratory Factor Analysis
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.; Piatek, Rémi
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study co...
Bayesian Exploratory Factor Analysis
Gabriella Conti; Sylvia Fruehwirth-Schnatter; Heckman, James J.; Remi Piatek
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on \\emph{ad hoc} classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo s...
Bayesian exploratory factor analysis
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.; Piatek, Rémi
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo st...
Bayesian exploratory factor analysis
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James; Piatek, Rémi
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study co...
Carbonetto, Peter; Kisynski, Jacek; De Freitas, Nando; Poole, David L
2012-01-01
The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation. This paper extends BLOG by adopting generative processes over function spaces - known as nonparametrics in the Bayesian literature. We introduce syntax for reasoning about arbitrary collections of objects, and their properties, in an intuitive manner. By expl...
Bayesian default probability models
Andrlíková, Petra
2014-01-01
This paper proposes a methodology for default probability estimation for low default portfolios, where the statistical inference may become troublesome. The author suggests using logistic regression models with the Bayesian estimation of parameters. The piecewise logistic regression model and Box-Cox transformation of credit risk score is used to derive the estimates of probability of default, which extends the work by Neagu et al. (2009). The paper shows that the Bayesian models are more acc...
Bayesian phylogeography finds its roots.
Philippe Lemey
2009-09-01
Full Text Available As a key factor in endemic and epidemic dynamics, the geographical distribution of viruses has been frequently interpreted in the light of their genetic histories. Unfortunately, inference of historical dispersal or migration patterns of viruses has mainly been restricted to model-free heuristic approaches that provide little insight into the temporal setting of the spatial dynamics. The introduction of probabilistic models of evolution, however, offers unique opportunities to engage in this statistical endeavor. Here we introduce a Bayesian framework for inference, visualization and hypothesis testing of phylogeographic history. By implementing character mapping in a Bayesian software that samples time-scaled phylogenies, we enable the reconstruction of timed viral dispersal patterns while accommodating phylogenetic uncertainty. Standard Markov model inference is extended with a stochastic search variable selection procedure that identifies the parsimonious descriptions of the diffusion process. In addition, we propose priors that can incorporate geographical sampling distributions or characterize alternative hypotheses about the spatial dynamics. To visualize the spatial and temporal information, we summarize inferences using virtual globe software. We describe how Bayesian phylogeography compares with previous parsimony analysis in the investigation of the influenza A H5N1 origin and H5N1 epidemiological linkage among sampling localities. Analysis of rabies in West African dog populations reveals how virus diffusion may enable endemic maintenance through continuous epidemic cycles. From these analyses, we conclude that our phylogeographic framework will make an important asset in molecular epidemiology that can be easily generalized to infer biogeogeography from genetic data for many organisms.
闫放; 许开立; 姚锡文; 王文菁
2015-01-01
Fussell-Vesely worth of each event is calculated by Bayesian network .Prevention measures are adopted to the reason event with higher worth .The event tree analysis is conducted to determine control measures and calculate the probability of biomass gasification poisoning accidents before and after measures are taken .Finally the biomass gasification poisoning acci-dents after using bow-tie analysis based on Bayesian network are evaluated by risk assessment matrix .As the result ,this method can reduce probability and risk of accidents by adopting safety measures to parts of the whole points of the system .%本文通过贝叶斯网络计算各原因事件的弗塞－维思利重要度，选取重要度较高的原因事件采取预防措施；并通过事件树分析确定控制措施，计算采取措施前后生物质气化中毒事故发生的概率，最后通过危险性评价矩阵对采取基于贝叶斯网络的bow－tie分析后的生物质气化中毒事故风险进行评价。结果表明，采用该方法只需对系统中部分节点采取安全措施即可有效降低事故发生概率，从而降低事故风险。
Bayesian least squares deconvolution
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Bayesian least squares deconvolution
Ramos, A Asensio
2015-01-01
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Loredo, T J
2004-01-01
I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data and predict future data, and Bayesian decision theory to identify which new observations would teach us the most. When the goal of the experiment is simply to make inferences, the framework identifies a computationally efficient iterative ``maximum entropy sampling'' strategy as the optimal strategy in settings where the noise statistics are independent of signal properties. Results of applying the method to two ``toy'' problems with simulated data--measuring the orbit of an extrasolar planet, and locating a hidden one-dimensional object--show the approach can significantly improve observational eff...
Bayesian Analysis of Individual Level Personality Dynamics
Cripps, Edward; Wood, Robert E.; Beckmann, Nadin; Lau, John; Beckmann, Jens F.; Cripps, Sally Ann
2016-01-01
A Bayesian technique with analyses of within-person processes at the level of the individual is presented. The approach is used to examine whether the patterns of within-person responses on a 12-trial simulation task are consistent with the predictions of ITA theory (Dweck, 1999). ITA theory states that the performance of an individual with an entity theory of ability is more likely to spiral down following a failure experience than the performance of an individual with an incremental theory of ability. This is because entity theorists interpret failure experiences as evidence of a lack of ability which they believe is largely innate and therefore relatively fixed; whilst incremental theorists believe in the malleability of abilities and interpret failure experiences as evidence of more controllable factors such as poor strategy or lack of effort. The results of our analyses support ITA theory at both the within- and between-person levels of analyses and demonstrate the benefits of Bayesian techniques for the analysis of within-person processes. These include more formal specification of the theory and the ability to draw inferences about each individual, which allows for more nuanced interpretations of individuals within a personality category, such as differences in the individual probabilities of spiraling. While Bayesian techniques have many potential advantages for the analyses of processes at the level of the individual, ease of use is not one of them for psychologists trained in traditional frequentist statistical techniques. PMID:27486415
Bayesian Analysis of Individual Level Personality Dynamics.
Cripps, Edward; Wood, Robert E; Beckmann, Nadin; Lau, John; Beckmann, Jens F; Cripps, Sally Ann
2016-01-01
A Bayesian technique with analyses of within-person processes at the level of the individual is presented. The approach is used to examine whether the patterns of within-person responses on a 12-trial simulation task are consistent with the predictions of ITA theory (Dweck, 1999). ITA theory states that the performance of an individual with an entity theory of ability is more likely to spiral down following a failure experience than the performance of an individual with an incremental theory of ability. This is because entity theorists interpret failure experiences as evidence of a lack of ability which they believe is largely innate and therefore relatively fixed; whilst incremental theorists believe in the malleability of abilities and interpret failure experiences as evidence of more controllable factors such as poor strategy or lack of effort. The results of our analyses support ITA theory at both the within- and between-person levels of analyses and demonstrate the benefits of Bayesian techniques for the analysis of within-person processes. These include more formal specification of the theory and the ability to draw inferences about each individual, which allows for more nuanced interpretations of individuals within a personality category, such as differences in the individual probabilities of spiraling. While Bayesian techniques have many potential advantages for the analyses of processes at the level of the individual, ease of use is not one of them for psychologists trained in traditional frequentist statistical techniques. PMID:27486415
Bayesian and frequentist inequality tests
David M. Kaplan; Zhuo, Longhao
2016-01-01
Bayesian and frequentist criteria are fundamentally different, but often posterior and sampling distributions are asymptotically equivalent (and normal). We compare Bayesian and frequentist hypothesis tests of inequality restrictions in such cases. For finite-dimensional parameters, if the null hypothesis is that the parameter vector lies in a certain half-space, then the Bayesian test has (frequentist) size $\\alpha$; if the null hypothesis is any other convex subspace, then the Bayesian test...
Bayesian multiple target tracking
Streit, Roy L
2013-01-01
This second edition has undergone substantial revision from the 1999 first edition, recognizing that a lot has changed in the multiple target tracking field. One of the most dramatic changes is in the widespread use of particle filters to implement nonlinear, non-Gaussian Bayesian trackers. This book views multiple target tracking as a Bayesian inference problem. Within this framework it develops the theory of single target tracking, multiple target tracking, and likelihood ratio detection and tracking. In addition to providing a detailed description of a basic particle filter that implements
Bayesian Exploratory Factor Analysis
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.;
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the...... corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates...
A survey of current Bayesian gene mapping method
Molitor John; Marjoram Paul; Conti David; Thomas Duncan
2004-01-01
Abstract Recently, there has been much interest in the use of Bayesian statistical methods for performing genetic analyses. Many of the computational difficulties previously associated with Bayesian analysis, such as multidimensional integration, can now be easily overcome using modern high-speed computers and Markov chain Monte Carlo (MCMC) methods. Much of this new technology has been used to perform gene mapping, especially through the use of multi-locus linkage disequilibrium techniques. ...
Ildikó Ungvári; Gábor Hullám; Péter Antal; Petra Sz Kiszel; András Gézsi; Éva Hadadi; Viktor Virág; Gergely Hajós; András Millinghoffer; Adrienne Nagy; András Kiss; Semsei, Ágnes F.; Gergely Temesi; Béla Melegh; Péter Kisfali
2012-01-01
Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls). The results were evaluated with traditional frequentist methods and we applied a new statistical method, called bayesian network based bayesian multilevel analysis of relevance (BN-BMLA). Th...
Improving Environmental Scanning Systems Using Bayesian Networks
Simon Welter; Jörg H. Mayer; Reiner Quick
2013-01-01
As companies’ environment is becoming increasingly volatile, scanning systems gain in importance. We propose a hybrid process model for such systems' information gathering and interpretation tasks that combines quantitative information derived from regression analyses and qualitative knowledge from expert interviews. For the latter, we apply Bayesian networks. We derive the need for such a hybrid process model from a literature review. We lay out our model to find a suitable set of business e...
Bayesian Geostatistical Design
Diggle, Peter; Lophaven, Søren Nymand
2006-01-01
locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model...
Krejsa, Jiří; Věchet, S.
Bratislava: Slovak University of Technology in Bratislava, 2010, s. 217-222. ISBN 978-80-227-3353-3. [Robotics in Education . Bratislava (SK), 16.09.2010-17.09.2010] Institutional research plan: CEZ:AV0Z20760514 Keywords : mobile robot localization * bearing only beacons * Bayesian filters Subject RIV: JD - Computer Applications, Robotics
Antoniou, Constantinos; Harrison, Glenn W.; Lau, Morten I.;
2015-01-01
A large literature suggests that many individuals do not apply Bayes’ Rule when making decisions that depend on them correctly pooling prior information and sample data. We replicate and extend a classic experimental study of Bayesian updating from psychology, employing the methods of experimenta...
Bayesian Independent Component Analysis
Winther, Ole; Petersen, Kaare Brandt
2007-01-01
In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine...
Noncausal Bayesian Vector Autoregression
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution as a...
Loredo, Thomas J.
2004-04-01
I describe a framework for adaptive scientific exploration based on iterating an Observation-Inference-Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data and predict future data, and Bayesian decision theory to identify which new observations would teach us the most. When the goal of the experiment is simply to make inferences, the framework identifies a computationally efficient iterative ``maximum entropy sampling'' strategy as the optimal strategy in settings where the noise statistics are independent of signal properties. Results of applying the method to two ``toy'' problems with simulated data-measuring the orbit of an extrasolar planet, and locating a hidden one-dimensional object-show the approach can significantly improve observational efficiency in settings that have well-defined nonlinear models. I conclude with a list of open issues that must be addressed to make Bayesian adaptive exploration a practical and reliable tool for optimizing scientific exploration.
Bayesian logistic regression analysis
Van Erp, H.R.N.; Van Gelder, P.H.A.J.M.
2012-01-01
In this paper we present a Bayesian logistic regression analysis. It is found that if one wishes to derive the posterior distribution of the probability of some event, then, together with the traditional Bayes Theorem and the integrating out of nuissance parameters, the Jacobian transformation is an
Bayesian data analysis in population ecology: motivations, methods, and benefits
Dorazio, Robert
2016-01-01
During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.
A tutorial on Bayesian Normal linear regression
Klauenberg, Katy; Wübbeler, Gerd; Mickan, Bodo; Harris, Peter; Elster, Clemens
2015-12-01
Regression is a common task in metrology and often applied to calibrate instruments, evaluate inter-laboratory comparisons or determine fundamental constants, for example. Yet, a regression model cannot be uniquely formulated as a measurement function, and consequently the Guide to the Expression of Uncertainty in Measurement (GUM) and its supplements are not applicable directly. Bayesian inference, however, is well suited to regression tasks, and has the advantage of accounting for additional a priori information, which typically robustifies analyses. Furthermore, it is anticipated that future revisions of the GUM shall also embrace the Bayesian view. Guidance on Bayesian inference for regression tasks is largely lacking in metrology. For linear regression models with Gaussian measurement errors this tutorial gives explicit guidance. Divided into three steps, the tutorial first illustrates how a priori knowledge, which is available from previous experiments, can be translated into prior distributions from a specific class. These prior distributions have the advantage of yielding analytical, closed form results, thus avoiding the need to apply numerical methods such as Markov Chain Monte Carlo. Secondly, formulas for the posterior results are given, explained and illustrated, and software implementations are provided. In the third step, Bayesian tools are used to assess the assumptions behind the suggested approach. These three steps (prior elicitation, posterior calculation, and robustness to prior uncertainty and model adequacy) are critical to Bayesian inference. The general guidance given here for Normal linear regression tasks is accompanied by a simple, but real-world, metrological example. The calibration of a flow device serves as a running example and illustrates the three steps. It is shown that prior knowledge from previous calibrations of the same sonic nozzle enables robust predictions even for extrapolations.
Bayesian classification and regression trees for predicting incidence of cryptosporidiosis.
Wenbiao Hu
Full Text Available BACKGROUND: Classification and regression tree (CART models are tree-based exploratory data analysis methods which have been shown to be very useful in identifying and estimating complex hierarchical relationships in ecological and medical contexts. In this paper, a Bayesian CART model is described and applied to the problem of modelling the cryptosporidiosis infection in Queensland, Australia. METHODOLOGY/PRINCIPAL FINDINGS: We compared the results of a Bayesian CART model with those obtained using a Bayesian spatial conditional autoregressive (CAR model. Overall, the analyses indicated that the nature and magnitude of the effect estimates were similar for the two methods in this study, but the CART model more easily accommodated higher order interaction effects. CONCLUSIONS/SIGNIFICANCE: A Bayesian CART model for identification and estimation of the spatial distribution of disease risk is useful in monitoring and assessment of infectious diseases prevention and control.
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
Bayesian Magic in Asteroseismology
Kallinger, T.
2015-09-01
Only a few years ago asteroseismic observations were so rare that scientists had plenty of time to work on individual data sets. They could tune their algorithms in any possible way to squeeze out the last bit of information. Nowadays this is impossible. With missions like MOST, CoRoT, and Kepler we basically drown in new data every day. To handle this in a sufficient way statistical methods become more and more important. This is why Bayesian techniques started their triumph march across asteroseismology. I will go with you on a journey through Bayesian Magic Land, that brings us to the sea of granulation background, the forest of peakbagging, and the stony alley of model comparison.
Bayesian Nonparametric Graph Clustering
Banerjee, Sayantan; Akbani, Rehan; Baladandayuthapani, Veerabhadran
2015-01-01
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure of the unknown graph using Bayesian neighborhood selection approaches, wherein we account for the uncertainty of graphical structure learning through model-averaged estimates of the suitable parameters. Subsequently, we develop a nonparametric graph cluster...
Approximate Bayesian recursive estimation
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111. ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Bayesian Benchmark Dose Analysis
Fang, Qijun; Piegorsch, Walter W.; Barnes, Katherine Y.
2014-01-01
An important objective in environmental risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs) that induce a pre-specified Benchmark Response (BMR) in a target population. Established inferential approaches for BMD analysis typically involve one-sided, frequentist confidence limits, leading in practice to what are called Benchmark Dose Lower Limits (BMDLs). Appeal to Bayesian modeling and credible limits for building BMDLs is far less developed, however. Indee...
Bayesian Generalized Rating Curves
Helgi Sigurðarson 1985
2014-01-01
A rating curve is a curve or a model that describes the relationship between water elevation, or stage, and discharge in an observation site in a river. The rating curve is fit from paired observations of stage and discharge. The rating curve then predicts discharge given observations of stage and this methodology is applied as stage is substantially easier to directly observe than discharge. In this thesis a statistical rating curve model is proposed working within the framework of Bayesian...
Heteroscedastic Treed Bayesian Optimisation
Assael, John-Alexander M.; Wang, Ziyu; Shahriari, Bobak; De Freitas, Nando
2014-01-01
Optimising black-box functions is important in many disciplines, such as tuning machine learning models, robotics, finance and mining exploration. Bayesian optimisation is a state-of-the-art technique for the global optimisation of black-box functions which are expensive to evaluate. At the core of this approach is a Gaussian process prior that captures our belief about the distribution over functions. However, in many cases a single Gaussian process is not flexible enough to capture non-stat...
Efficient Bayesian Phase Estimation
Wiebe, Nathan; Granade, Chris
2016-07-01
We introduce a new method called rejection filtering that we use to perform adaptive Bayesian phase estimation. Our approach has several advantages: it is classically efficient, easy to implement, achieves Heisenberg limited scaling, resists depolarizing noise, tracks time-dependent eigenstates, recovers from failures, and can be run on a field programmable gate array. It also outperforms existing iterative phase estimation algorithms such as Kitaev's method.
Brody, Samuel; Lapata, Mirella
2009-01-01
Sense induction seeks to automatically identify word senses directly from a corpus. A key assumption underlying previous work is that the context surrounding an ambiguous word is indicative of its meaning. Sense induction is thus typically viewed as an unsupervised clustering problem where the aim is to partition a word’s contexts into different classes, each representing a word sense. Our work places sense induction in a Bayesian context by modeling the contexts of the ambiguous word as samp...
Bayesian Neural Word Embedding
Barkan, Oren
2016-01-01
Recently, several works in the domain of natural language processing presented successful methods for word embedding. Among them, the Skip-gram (SG) with negative sampling, known also as Word2Vec, advanced the state-of-the-art of various linguistics tasks. In this paper, we propose a scalable Bayesian neural word embedding algorithm that can be beneficial to general item similarity tasks as well. The algorithm relies on a Variational Bayes solution for the SG objective and a detailed step by ...
Wiegerinck, Wim; Schoenaker, Christiaan; Duane, Gregory
2016-04-01
Recently, methods for model fusion by dynamically combining model components in an interactive ensemble have been proposed. In these proposals, fusion parameters have to be learned from data. One can view these systems as parametrized dynamical systems. We address the question of learnability of dynamical systems with respect to both short term (vector field) and long term (attractor) behavior. In particular we are interested in learning in the imperfect model class setting, in which the ground truth has a higher complexity than the models, e.g. due to unresolved scales. We take a Bayesian point of view and we define a joint log-likelihood that consists of two terms, one is the vector field error and the other is the attractor error, for which we take the L1 distance between the stationary distributions of the model and the assumed ground truth. In the context of linear models (like so-called weighted supermodels), and assuming a Gaussian error model in the vector fields, vector field learning leads to a tractable Gaussian solution. This solution can then be used as a prior for the next step, Bayesian attractor learning, in which the attractor error is used as a log-likelihood term. Bayesian attractor learning is implemented by elliptical slice sampling, a sampling method for systems with a Gaussian prior and a non Gaussian likelihood. Simulations with a partially observed driven Lorenz 63 system illustrate the approach.
Bayesian theory and applications
Dellaportas, Petros; Polson, Nicholas G; Stephens, David A
2013-01-01
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and devel...
Unbounded Bayesian Optimization via Regularization
Shahriari, Bobak; Bouchard-Côté, Alexandre; De Freitas, Nando
2015-01-01
Bayesian optimization has recently emerged as a popular and efficient tool for global optimization and hyperparameter tuning. Currently, the established Bayesian optimization practice requires a user-defined bounding box which is assumed to contain the optimizer. However, when little is known about the probed objective function, it can be difficult to prescribe such bounds. In this work we modify the standard Bayesian optimization framework in a principled way to allow automatic resizing of t...
Bayesian optimization for materials design
Frazier, Peter I.; Wang, Jialei
2015-01-01
We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian pro...
Bayesian nonparametric data analysis
Müller, Peter; Jara, Alejandro; Hanson, Tim
2015-01-01
This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages.
Decentralized Distributed Bayesian Estimation
Dedecius, Kamil; Sečkárová, Vladimíra
Praha: ÚTIA AVČR, v.v.i, 2011 - (Janžura, M.; Ivánek, J.). s. 16-16 [7th International Workshop on Data–Algorithms–Decision Making. 27.11.2011-29.11.2011, Mariánská] R&D Projects: GA ČR 102/08/0567; GA ČR GA102/08/0567 Institutional research plan: CEZ:AV0Z10750506 Keywords : estimation * distributed estimation * model Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2011/AS/dedecius-decentralized distributed bayesian estimation.pdf
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
Computationally efficient Bayesian tracking
Aughenbaugh, Jason; La Cour, Brian
2012-06-01
In this paper, we describe the progress we have achieved in developing a computationally efficient, grid-based Bayesian fusion tracking system. In our approach, the probability surface is represented by a collection of multidimensional polynomials, each computed adaptively on a grid of cells representing state space. Time evolution is performed using a hybrid particle/grid approach and knowledge of the grid structure, while sensor updates use a measurement-based sampling method with a Delaunay triangulation. We present an application of this system to the problem of tracking a submarine target using a field of active and passive sonar buoys.
Improved iterative Bayesian unfolding
D'Agostini, G
2010-01-01
This paper reviews the basic ideas behind a Bayesian unfolding published some years ago and improves their implementation. In particular, uncertainties are now treated at all levels by probability density functions and their propagation is performed by Monte Carlo integration. Thus, small numbers are better handled and the final uncertainty does not rely on the assumption of normality. Theoretical and practical issues concerning the iterative use of the algorithm are also discussed. The new program, implemented in the R language, is freely available, together with sample scripts to play with toy models.
Bayesian Inference on Gravitational Waves
Asad Ali
2015-12-01
Full Text Available The Bayesian approach is increasingly becoming popular among the astrophysics data analysis communities. However, the Pakistan statistics communities are unaware of this fertile interaction between the two disciplines. Bayesian methods have been in use to address astronomical problems since the very birth of the Bayes probability in eighteenth century. Today the Bayesian methods for the detection and parameter estimation of gravitational waves have solid theoretical grounds with a strong promise for the realistic applications. This article aims to introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.
Adaptive Dynamic Bayesian Networks
Ng, B M
2007-10-26
A discrete-time Markov process can be compactly modeled as a dynamic Bayesian network (DBN)--a graphical model with nodes representing random variables and directed edges indicating causality between variables. Each node has a probability distribution, conditional on the variables represented by the parent nodes. A DBN's graphical structure encodes fixed conditional dependencies between variables. But in real-world systems, conditional dependencies between variables may be unknown a priori or may vary over time. Model errors can result if the DBN fails to capture all possible interactions between variables. Thus, we explore the representational framework of adaptive DBNs, whose structure and parameters can change from one time step to the next: a distribution's parameters and its set of conditional variables are dynamic. This work builds on recent work in nonparametric Bayesian modeling, such as hierarchical Dirichlet processes, infinite-state hidden Markov networks and structured priors for Bayes net learning. In this paper, we will explain the motivation for our interest in adaptive DBNs, show how popular nonparametric methods are combined to formulate the foundations for adaptive DBNs, and present preliminary results.
Bayesian analysis toolkit - BAT
Statistical treatment of data is an essential part of any data analysis and interpretation. Different statistical methods and approaches can be used, however the implementation of these approaches is complicated and at times inefficient. The Bayesian analysis toolkit (BAT) is a software package developed in C++ framework that facilitates the statistical analysis of the data using Bayesian theorem. The tool evaluates the posterior probability distributions for models and their parameters using Markov Chain Monte Carlo which in turn provide straightforward parameter estimation, limit setting and uncertainty propagation. Additional algorithms, such as simulated annealing, allow extraction of the global mode of the posterior. BAT sets a well-tested environment for flexible model definition and also includes a set of predefined models for standard statistical problems. The package is interfaced to other software packages commonly used in high energy physics, such as ROOT, Minuit, RooStats and CUBA. We present a general overview of BAT and its algorithms. A few physics examples are shown to introduce the spectrum of its applications. In addition, new developments and features are summarized.
Bayesian analysis of cosmic structures
Kitaura, Francisco-Shu
2011-01-01
We revise the Bayesian inference steps required to analyse the cosmological large-scale structure. Here we make special emphasis in the complications which arise due to the non-Gaussian character of the galaxy and matter distribution. In particular we investigate the advantages and limitations of the Poisson-lognormal model and discuss how to extend this work. With the lognormal prior using the Hamiltonian sampling technique and on scales of about 4 h^{-1} Mpc we find that the over-dense regions are excellent reconstructed, however, under-dense regions (void statistics) are quantitatively poorly recovered. Contrary to the maximum a posteriori (MAP) solution which was shown to over-estimate the density in the under-dense regions we obtain lower densities than in N-body simulations. This is due to the fact that the MAP solution is conservative whereas the full posterior yields samples which are consistent with the prior statistics. The lognormal prior is not able to capture the full non-linear regime at scales ...
Bayesian Analysis of Type Ia Supernova Data
王晓峰; 周旭; 李宗伟; 陈黎
2003-01-01
Recently, the distances to type Ia supernova (SN Ia) at z ～ 0.5 have been measured with the motivation of estimating cosmological parameters. However, different sleuthing techniques tend to give inconsistent measurements for SN Ia distances (～0.3 mag), which significantly affects the determination of cosmological parameters.A Bayesian "hyper-parameter" procedure is used to analyse jointly the current SN Ia data, which considers the relative weights of different datasets. For a flat Universe, the combining analysis yields ΩM = 0.20 ± 0.07.
Book review: Bayesian analysis for population ecology
Link, William A.
2011-01-01
Brian Dennis described the field of ecology as “fertile, uncolonized ground for Bayesian ideas.” He continued: “The Bayesian propagule has arrived at the shore. Ecologists need to think long and hard about the consequences of a Bayesian ecology. The Bayesian outlook is a successful competitor, but is it a weed? I think so.” (Dennis 2004)
Hartelius, Karsten; Carstensen, Jens Michael
2003-01-01
A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which...... represents the spatial coordinates of the grid nodes. Knowledge of how grid nodes are depicted in the observed image is described through the observation model. The prior consists of a node prior and an arc (edge) prior, both modeled as Gaussian MRFs. The node prior models variations in the positions of grid...... nodes and the arc prior models variations in row and column spacing across the grid. Grid matching is done by placing an initial rough grid over the image and applying an ensemble annealing scheme to maximize the posterior distribution of the grid. The method can be applied to noisy images with missing...
Bayesian model discrimination for glucose-insulin homeostasis
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......In this paper we analyse a set of experimental data on a number of healthy and diabetic patients and discuss a variety of models for describing the physiological processes involved in glucose absorption and insulin secretion within the human body. We adopt a Bayesian approach which facilitates...
Current trends in Bayesian methodology with applications
Upadhyay, Satyanshu K; Dey, Dipak K; Loganathan, Appaia
2015-01-01
Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics.Each chapter is self-contained and focuses on
Bayesian Methods and Universal Darwinism
Campbell, John
2010-01-01
Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a 'copy with selective retention' algorithm abstracted from Darwin's theory of...
Portfolio Allocation for Bayesian Optimization
Brochu, Eric; Hoffman, Matthew W.; De Freitas, Nando
2010-01-01
Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several differen...
Neuronanatomy, neurology and Bayesian networks
Bielza Lozoya, Maria Concepcion
2014-01-01
Bayesian networks are data mining models with clear semantics and a sound theoretical foundation. In this keynote talk we will pinpoint a number of neuroscience problems that can be addressed using Bayesian networks. In neuroanatomy, we will show computer simulation models of dendritic trees and classification of neuron types, both based on morphological features. In neurology, we will present the search for genetic biomarkers in Alzheimer's disease and the prediction of health-related qualit...
Bayesian Networks and Influence Diagrams
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Probabilistic networks, also known as Bayesian networks and influence diagrams, have become one of the most promising technologies in the area of applied artificial intelligence, offering intuitive, efficient, and reliable methods for diagnosis, prediction, decision making, classification......, troubleshooting, and data mining under uncertainty. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. Intended...
Dale Poirier
2008-01-01
This paper provides Bayesian rationalizations for White’s heteroskedastic consistent (HC) covariance estimator and various modifications of it. An informed Bayesian bootstrap provides the statistical framework.
Nonparametric Bayesian Classification
Coram, M A
2002-01-01
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if they are present in the unknown regression function $f_0$. An idealized one-dimensional problem is considered in detail. The proposed nonparametric prior uses random split points to partition the unit interval into a random number of pieces. This prior is found to provide a consistent estimate of the regression function in the $\\L^p$ topology, for any $1 \\leq p < \\infty$, and for arbitrary measurable $f_0:[0,1] \\rightarrow [0,1]$. A Markov chain Monte Carlo (MCMC) implementation is outlined and analyzed. Simulation experiments are conducted to show that the proposed estimate compares favorably with a variety of conventional estimators. A striking resemblance between the posterior mean estimate and the bagged CART estimate is noted and discussed. For higher dimensions, a ...
BAT - Bayesian Analysis Toolkit
One of the most vital steps in any data analysis is the statistical analysis and comparison with the prediction of a theoretical model. The many uncertainties associated with the theoretical model and the observed data require a robust statistical analysis tool. The Bayesian Analysis Toolkit (BAT) is a powerful statistical analysis software package based on Bayes' Theorem, developed to evaluate the posterior probability distribution for models and their parameters. It implements Markov Chain Monte Carlo to get the full posterior probability distribution that in turn provides a straightforward parameter estimation, limit setting and uncertainty propagation. Additional algorithms, such as Simulated Annealing, allow to evaluate the global mode of the posterior. BAT is developed in C++ and allows for a flexible definition of models. A set of predefined models covering standard statistical cases are also included in BAT. It has been interfaced to other commonly used software packages such as ROOT, Minuit, RooStats and CUBA. An overview of the software and its algorithms is provided along with several physics examples to cover a range of applications of this statistical tool. Future plans, new features and recent developments are briefly discussed.
Bayesian seismic AVO inversion
Buland, Arild
2002-07-01
A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S
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 ...
Phycas: software for Bayesian phylogenetic analysis.
Lewis, Paul O; Holder, Mark T; Swofford, David L
2015-05-01
Phycas is open source, freely available Bayesian phylogenetics software written primarily in C++ but with a Python interface. Phycas specializes in Bayesian model selection for nucleotide sequence data, particularly the estimation of marginal likelihoods, central to computing Bayes Factors. Marginal likelihoods can be estimated using newer methods (Thermodynamic Integration and Generalized Steppingstone) that are more accurate than the widely used Harmonic Mean estimator. In addition, Phycas supports two posterior predictive approaches to model selection: Gelfand-Ghosh and Conditional Predictive Ordinates. The General Time Reversible family of substitution models, as well as a codon model, are available, and data can be partitioned with all parameters unlinked except tree topology and edge lengths. Phycas provides for analyses in which the prior on tree topologies allows polytomous trees as well as fully resolved trees, and provides for several choices for edge length priors, including a hierarchical model as well as the recently described compound Dirichlet prior, which helps avoid overly informative induced priors on tree length. PMID:25577605
Case studies in Bayesian microbial risk assessments
Turner Joanne
2009-12-01
case study the effective number of inputs was reduced from 30 to 7 in the screening stage, and just 2 inputs were found to explain 82.8% of the output variance. A combined total of 500 runs of the computer code were used. Conclusion These case studies illustrate the use of Bayesian statistics to perform detailed uncertainty and sensitivity analyses, integrating multiple information sources in a way that is both rigorous and efficient.
Probability biases as Bayesian inference
Andre; C. R. Martins
2006-11-01
Full Text Available In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions. %XX In that sense, it should be no surprise that humans reason with % probability as it has been observed.
Bayesian Methods and Universal Darwinism
Campbell, John
2010-01-01
Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a 'copy with selective retention' algorithm abstracted from Darwin's theory of Natural Selection. Arguments are presented for an isomorphism between Bayesian Methods and Darwinian processes. Universal Darwinism, as the term has been developed by Richard Dawkins, Daniel Dennett and Susan Blackmore, is the collection of scientific theories which explain the creation and evolution of their subject matter as due to the operation of Darwinian processes. These subject matters span the fields of atomic physics, chemistry, biology and the social sciences. The principle of Maximum Entropy states that system...
Bayesian methods for proteomic biomarker development
Belinda Hernández
2015-12-01
In this review we provide an introduction to Bayesian inference and demonstrate some of the advantages of using a Bayesian framework. We summarize how Bayesian methods have been used previously in proteomics and other areas of bioinformatics. Finally, we describe some popular and emerging Bayesian models from the statistical literature and provide a worked tutorial including code snippets to show how these methods may be applied for the evaluation of proteomic biomarkers.
Bayesian test and Kuhn's paradigm
Chen Xiaoping
2006-01-01
Kuhn's theory of paradigm reveals a pattern of scientific progress,in which normal science alternates with scientific revolution.But Kuhn underrated too much the function of scientific test in his pattern,because he focuses all his attention on the hypothetico-deductive schema instead of Bayesian schema.This paper employs Bayesian schema to re-examine Kuhn's theory of paradigm,to uncover its logical and rational components,and to illustrate the tensional structure of logic and belief,rationality and irrationality,in the process of scientific revolution.
3D Bayesian contextual classifiers
Larsen, Rasmus
2000-01-01
We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours.......We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours....
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…
Bayesian networks and food security - An introduction
Stein, A.
2004-01-01
This paper gives an introduction to Bayesian networks. Networks are defined and put into a Bayesian context. Directed acyclical graphs play a crucial role here. Two simple examples from food security are addressed. Possible uses of Bayesian networks for implementation and further use in decision sup
Bayesian variable order Markov models: Towards Bayesian predictive state representations
C. Dimitrakakis
2009-01-01
We present a Bayesian variable order Markov model that shares many similarities with predictive state representations. The resulting models are compact and much easier to specify and learn than classical predictive state representations. Moreover, we show that they significantly outperform a more st
Non-stationarity in GARCH models: A Bayesian analysis
Kleibergen, Frank; Dijk, Herman
1993-01-01
textabstractFirst, the non-stationarity properties of the conditional variances in the GARCH(1,1) model are analysed using the concept of infinite persistence of shocks. Given a time sequence of probabilities for increasing/decreasing conditional variances, a theoretical formula for quasi-strict non-stationarity is defined. The resulting conditions for the GARCH(1,1) model are shown to differ from the weak stationarity conditions mainly used in the literature. Bayesian statistical analysis us...
Regional fertility data analysis: A small area Bayesian approach
Eduardo A. Castro; Zhen Zhang; Arnab Bhattacharjee; Martins, José M.; Taps Maiti
2013-01-01
Accurate estimation of demographic variables such as mortality, fertility and migrations, by age groups and regions, is important for analyses and policy. However, traditional estimates based on within cohort counts are often inaccurate, particularly when the sub-populations considered are small. We use small area Bayesian statistics to develop a model for age-specific fertility rates. In turn, such small area estimation requires accurate descriptions of spatial and cross-section dependence. ...
Bayesian Fusion Algorithm for Inferring Trust in Wireless Sensor Networks
Mohammad Momani; Subhash Challa; Rami Alhmouz
2010-01-01
This paper introduces a new Bayesian fusion algorithm to combine more than one trust component (data trust and communication trust) to infer the overall trust between nodes. This research work proposes that one trust component is not enough when deciding on whether or not to trust a specific node in a wireless sensor network. This paper discusses and analyses the results from the communication trust component (binary) and the data trust component (continuous) and proves that either component ...
Bayesian Analysis of Experimental Data
Lalmohan Bhar
2013-10-01
Full Text Available Analysis of experimental data from Bayesian point of view has been considered. Appropriate methodology has been developed for application into designed experiments. Normal-Gamma distribution has been considered for prior distribution. Developed methodology has been applied to real experimental data taken from long term fertilizer experiments.
Bayesian image restoration, using configurations
Thorarinsdottir, Thordis Linda
2006-01-01
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for the salt and pepper noise. The inference in the model is discussed...
Bayesian image restoration, using configurations
Thorarinsdottir, Thordis
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in...
ANALYSIS OF BAYESIAN CLASSIFIER ACCURACY
Felipe Schneider Costa
2013-01-01
Full Text Available The naÃ¯ve Bayes classifier is considered one of the most effective classification algorithms today, competing with more modern and sophisticated classifiers. Despite being based on unrealistic (naÃ¯ve assumption that all variables are independent, given the output class, the classifier provides proper results. However, depending on the scenario utilized (network structure, number of samples or training cases, number of variables, the network may not provide appropriate results. This study uses a process variable selection, using the chi-squared test to verify the existence of dependence between variables in the data model in order to identify the reasons which prevent a Bayesian network to provide good performance. A detailed analysis of the data is also proposed, unlike other existing work, as well as adjustments in case of limit values between two adjacent classes. Furthermore, variable weights are used in the calculation of a posteriori probabilities, calculated with mutual information function. Tests were applied in both a naÃ¯ve Bayesian network and a hierarchical Bayesian network. After testing, a significant reduction in error rate has been observed. The naÃ¯ve Bayesian network presented a drop in error rates from twenty five percent to five percent, considering the initial results of the classification process. In the hierarchical network, there was not only a drop in fifteen percent error rate, but also the final result came to zero.
Bayesian Agglomerative Clustering with Coalescents
Teh, Yee Whye; Daumé III, Hal; Roy, Daniel
2009-01-01
We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over others, and demonstrate our approach in document clustering and phylolinguistics.
Bayesian Networks and Influence Diagrams
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Topics in Bayesian statistics and maximum entropy
Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)
Bayesian analysis of rare events
Straub, Daniel; Papaioannou, Iason; Betz, Wolfgang
2016-06-01
In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into the probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.
Bayesian methods for measures of agreement
Broemeling, Lyle D
2009-01-01
Using WinBUGS to implement Bayesian inferences of estimation and testing hypotheses, Bayesian Methods for Measures of Agreement presents useful methods for the design and analysis of agreement studies. It focuses on agreement among the various players in the diagnostic process.The author employs a Bayesian approach to provide statistical inferences based on various models of intra- and interrater agreement. He presents many examples that illustrate the Bayesian mode of reasoning and explains elements of a Bayesian application, including prior information, experimental information, the likelihood function, posterior distribution, and predictive distribution. The appendices provide the necessary theoretical foundation to understand Bayesian methods as well as introduce the fundamentals of programming and executing the WinBUGS software.Taking a Bayesian approach to inference, this hands-on book explores numerous measures of agreement, including the Kappa coefficient, the G coefficient, and intraclass correlation...
Plug & Play object oriented Bayesian networks
Bangsø, Olav; Flores, J.; Jensen, Finn Verner
2003-01-01
Object oriented Bayesian networks have proven themselves useful in recent years. The idea of applying an object oriented approach to Bayesian networks has extended their scope to larger domains that can be divided into autonomous but interrelated entities. Object oriented Bayesian networks have...... been shown to be quite suitable for dynamic domains as well. However, processing object oriented Bayesian networks in practice does not take advantage of their modular structure. Normally the object oriented Bayesian network is transformed into a Bayesian network and, inference is performed...... by constructing a junction tree from this network. In this paper we propose a method for translating directly from object oriented Bayesian networks to junction trees, avoiding the intermediate translation. We pursue two main purposes: firstly, to maintain the original structure organized in an instance tree...
Flexible Bayesian Nonparametric Priors and Bayesian Computational Methods
Zhu, Weixuan
2016-01-01
The definition of vectors of dependent random probability measures is a topic of interest in Bayesian nonparametrics. They represent dependent nonparametric prior distributions that are useful for modelling observables for which specific covariate values are known. Our first contribution is the introduction of novel multivariate vectors of two-parameter Poisson-Dirichlet process. The dependence is induced by applying a L´evy copula to the marginal L´evy intensities. Our attenti...
Complexity analysis of accelerated MCMC methods for Bayesian inversion
Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M.
2013-08-01
The Bayesian approach to inverse problems, in which the posterior probability distribution on an unknown field is sampled for the purposes of computing posterior expectations of quantities of interest, is starting to become computationally feasible for partial differential equation (PDE) inverse problems. Balancing the sources of error arising from finite-dimensional approximation of the unknown field, the PDE forward solution map and the sampling of the probability space under the posterior distribution are essential for the design of efficient computational Bayesian methods for PDE inverse problems. We study Bayesian inversion for a model elliptic PDE with an unknown diffusion coefficient. We provide complexity analyses of several Markov chain Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data δ. Particular attention is given to bounds on the overall work required to achieve a prescribed error level ε. Specifically, we first bound the computational complexity of ‘plain’ MCMC, based on combining MCMC sampling with linear complexity multi-level solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) ‘surrogate’ representation of the forward response map of the PDE over the entire parameter space, and, second, a novel multi-level Markov chain Monte Carlo strategy which utilizes sampling from a multi-level discretization of the posterior and the forward PDE. For both of these strategies, we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular, we provide sufficient conditions on the regularity of the unknown coefficients of the PDE and on the
Bayesian network as a modelling tool for risk management in agriculture
Rasmussen, Svend; Madsen, Anders L.; Lund, Mogens
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, and that......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...
Bayesian approach to rough set
Marwala, Tshilidzi
2007-01-01
This paper proposes an approach to training rough set models using Bayesian framework trained using Markov Chain Monte Carlo (MCMC) method. The prior probabilities are constructed from the prior knowledge that good rough set models have fewer rules. Markov Chain Monte Carlo sampling is conducted through sampling in the rough set granule space and Metropolis algorithm is used as an acceptance criteria. The proposed method is tested to estimate the risk of HIV given demographic data. The results obtained shows that the proposed approach is able to achieve an average accuracy of 58% with the accuracy varying up to 66%. In addition the Bayesian rough set give the probabilities of the estimated HIV status as well as the linguistic rules describing how the demographic parameters drive the risk of HIV.
Attention in a bayesian framework
Whiteley, Louise Emma; Sahani, Maneesh
2012-01-01
include both selective phenomena, where attention is invoked by cues that point to particular stimuli, and integrative phenomena, where attention is invoked dynamically by endogenous processing. However, most previous Bayesian accounts of attention have focused on describing relatively simple experimental...... settings, where cues shape expectations about a small number of upcoming stimuli and thus convey "prior" information about clearly defined objects. While operationally consistent with the experiments it seeks to describe, this view of attention as prior seems to miss many essential elements of both its......The behavioral phenomena of sensory attention are thought to reflect the allocation of a limited processing resource, but there is little consensus on the nature of the resource or why it should be limited. Here we argue that a fundamental bottleneck emerges naturally within Bayesian models of...
Bayesian Sampling using Condition Indicators
Faber, Michael H.; Sørensen, John Dalsgaard
2002-01-01
allows for a Bayesian formulation of the indicators whereby the experience and expertise of the inspection personnel may be fully utilized and consistently updated as frequentistic information is collected. The approach is illustrated on an example considering a concrete structure subject to corrosion......The problem of control quality of components is considered for the special case where the acceptable failure rate is low, the test costs are high and where it may be difficult or impossible to test the condition of interest directly. Based on the classical control theory and the concept of...... condition indicators introduced by Benjamin and Cornell (1970) a Bayesian approach to quality control is formulated. The formulation is then extended to the case where the quality control is based on sampling of indirect information about the condition of the components, i.e. condition indicators. This...
BAYESIAN IMAGE RESTORATION, USING CONFIGURATIONS
Thordis Linda Thorarinsdottir
2011-05-01
Full Text Available In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given.
Bayesian Seismology of the Sun
Gruberbauer, Michael
2013-01-01
We perform a Bayesian grid-based analysis of the solar l=0,1,2 and 3 p modes obtained via BiSON in order to deliver the first Bayesian asteroseismic analysis of the solar composition problem. We do not find decisive evidence to prefer either of the contending chemical compositions, although the revised solar abundances (AGSS09) are more probable in general. We do find indications for systematic problems in standard stellar evolution models, unrelated to the consequences of inadequate modelling of the outer layers on the higher-order modes. The seismic observables are best fit by solar models that are several hundred million years older than the meteoritic age of the Sun. Similarly, meteoritic age calibrated models do not adequately reproduce the observed seismic observables. Our results suggest that these problems will affect any asteroseismic inference that relies on a calibration to the Sun.
Bayesian priors for transiting planets
Kipping, David M
2016-01-01
As astronomers push towards discovering ever-smaller transiting planets, it is increasingly common to deal with low signal-to-noise ratio (SNR) events, where the choice of priors plays an influential role in Bayesian inference. In the analysis of exoplanet data, the selection of priors is often treated as a nuisance, with observers typically defaulting to uninformative distributions. Such treatments miss a key strength of the Bayesian framework, especially in the low SNR regime, where even weak a priori information is valuable. When estimating the parameters of a low-SNR transit, two key pieces of information are known: (i) the planet has the correct geometric alignment to transit and (ii) the transit event exhibits sufficient signal-to-noise to have been detected. These represent two forms of observational bias. Accordingly, when fitting transits, the model parameter priors should not follow the intrinsic distributions of said terms, but rather those of both the intrinsic distributions and the observational ...
Bayesian Inference for Radio Observations
Lochner, Michelle; Zwart, Jonathan T L; Smirnov, Oleg; Bassett, Bruce A; Oozeer, Nadeem; Kunz, Martin
2015-01-01
(Abridged) New telescopes like the Square Kilometre Array (SKA) will push into a new sensitivity regime and expose systematics, such as direction-dependent effects, that could previously be ignored. Current methods for handling such systematics rely on alternating best estimates of instrumental calibration and models of the underlying sky, which can lead to inaccurate uncertainty estimates and biased results because such methods ignore any correlations between parameters. These deconvolution algorithms produce a single image that is assumed to be a true representation of the sky, when in fact it is just one realisation of an infinite ensemble of images compatible with the noise in the data. In contrast, here we report a Bayesian formalism that simultaneously infers both systematics and science. Our technique, Bayesian Inference for Radio Observations (BIRO), determines all parameters directly from the raw data, bypassing image-making entirely, by sampling from the joint posterior probability distribution. Thi...
Bayesian inference on proportional elections.
Brunello, Gabriel Hideki Vatanabe; Nakano, Eduardo Yoshio
2015-01-01
Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software. PMID:25786259
A Bayesian Nonparametric IRT Model
Karabatsos, George
2015-01-01
This paper introduces a flexible Bayesian nonparametric Item Response Theory (IRT) model, which applies to dichotomous or polytomous item responses, and which can apply to either unidimensional or multidimensional scaling. This is an infinite-mixture IRT model, with person ability and item difficulty parameters, and with a random intercept parameter that is assigned a mixing distribution, with mixing weights a probit function of other person and item parameters. As a result of its flexibility...
Bayesian segmentation of hyperspectral images
Mohammadpour, Adel; Mohammad-Djafari, Ali
2007-01-01
In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results.
Bayesian segmentation of hyperspectral images
Mohammadpour, Adel; Féron, Olivier; Mohammad-Djafari, Ali
2004-11-01
In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results.
Bayesian Stable Isotope Mixing Models
Parnell, Andrew C.; Phillips, Donald L.; Bearhop, Stuart; Semmens, Brice X.; Ward, Eric J.; Moore, Jonathan W.; Andrew L Jackson; Inger, Richard
2012-01-01
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 mixture. The most widely used application is quantifying the diet of organisms based on the food sources they have been observed to consume. At the centre of the multivariate statistical model we propose is a compositional m...
Bayesian Network--Response Regression
WANG, LU; Durante, Daniele; Dunson, David B.
2016-01-01
There is an increasing interest in learning how human brain networks vary with continuous traits (e.g., personality, cognitive abilities, neurological disorders), but flexible procedures to accomplish this goal are limited. We develop a Bayesian semiparametric model, which combines low-rank factorizations and Gaussian process priors to allow flexible shifts of the conditional expectation for a network-valued random variable across the feature space, while including subject-specific random eff...
Bayesian estimation of turbulent motion
Héas, P.; Herzet, C.; Mémin, E.; Heitz, D.; P. D. Mininni
2013-01-01
International audience Based on physical laws describing the multi-scale structure of turbulent flows, this article proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian perspective, an algorithm is proposed to jointly estimate motion, regularization hyper-parameters, and to select the ...
Elements of Bayesian experimental design
Sivia, D.S. [Rutherford Appleton Lab., Oxon (United Kingdom)
1997-09-01
We consider some elements of the Bayesian approach that are important for optimal experimental design. While the underlying principles used are very general, and are explained in detail in a recent tutorial text, they are applied here to the specific case of characterising the inferential value of different resolution peakshapes. This particular issue was considered earlier by Silver, Sivia and Pynn (1989, 1990a, 1990b), and the following presentation confirms and extends the conclusions of their analysis.
Skill Rating by Bayesian Inference
Di Fatta, Giuseppe; Haworth, Guy McCrossan; Regan, Kenneth W.
2009-01-01
Systems Engineering often involves computer modelling the behaviour of proposed systems and their components. Where a component is human, fallibility must be modelled by a stochastic agent. The identification of a model of decision-making over quantifiable options is investigated using the game-domain of Chess. Bayesian methods are used to infer the distribution of players’ skill levels from the moves they play rather than from their competitive results. The approach is used on large sets of ...
Topics in Nonparametric Bayesian Statistics
2003-01-01
The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now seems to be growing at a healthy rate. This chapter gives an overview of various theoretical and applied research themes inside this field, partly complementing and extending recent reviews of Dey, Müller and Sinha (1998) and Walker, Damien, Laud and Smith (1999). The intention is not to be complete or exhaustive, but rather to touch on research areas of interest, partly by example.
Cover Tree Bayesian Reinforcement Learning
Tziortziotis, Nikolaos; Dimitrakakis, Christos; Blekas, Konstantinos
2013-01-01
This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tree method, which remains efficient in high dimensional spaces. We combine the model with Thompson sampling and approximate dynamic programming to obtain effective exploration po...
Bayesian kinematic earthquake source models
Minson, S. E.; Simons, M.; Beck, J. L.; Genrich, J. F.; Galetzka, J. E.; Chowdhury, F.; Owen, S. E.; Webb, F.; Comte, D.; Glass, B.; Leiva, C.; Ortega, F. H.
2009-12-01
Most coseismic, postseismic, and interseismic slip models are based on highly regularized optimizations which yield one solution which satisfies the data given a particular set of regularizing constraints. This regularization hampers our ability to answer basic questions such as whether seismic and aseismic slip overlap or instead rupture separate portions of the fault zone. We present a Bayesian methodology for generating kinematic earthquake source models with a focus on large subduction zone earthquakes. Unlike classical optimization approaches, Bayesian techniques sample the ensemble of all acceptable models presented as an a posteriori probability density function (PDF), and thus we can explore the entire solution space to determine, for example, which model parameters are well determined and which are not, or what is the likelihood that two slip distributions overlap in space. Bayesian sampling also has the advantage that all a priori knowledge of the source process can be used to mold the a posteriori ensemble of models. Although very powerful, Bayesian methods have up to now been of limited use in geophysical modeling because they are only computationally feasible for problems with a small number of free parameters due to what is called the "curse of dimensionality." However, our methodology can successfully sample solution spaces of many hundreds of parameters, which is sufficient to produce finite fault kinematic earthquake models. Our algorithm is a modification of the tempered Markov chain Monte Carlo (tempered MCMC or TMCMC) method. In our algorithm, we sample a "tempered" a posteriori PDF using many MCMC simulations running in parallel and evolutionary computation in which models which fit the data poorly are preferentially eliminated in favor of models which better predict the data. We present results for both synthetic test problems as well as for the 2007 Mw 7.8 Tocopilla, Chile earthquake, the latter of which is constrained by InSAR, local high
Bayesian Kernel Mixtures for Counts
Canale, Antonio; David B Dunson
2011-01-01
Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow smooth deviatio...
Bayesian Optimization for Adaptive MCMC
Mahendran, Nimalan; Wang, Ziyu; Hamze, Firas; De Freitas, Nando
2011-01-01
This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially costly objective function evaluations. We demonstrate the strategy in the complex setting of sampling from constrained, discrete and densely connected probabilistic graphical models where, for each variation of the problem, one needs to adjust the parameters o...
Inference in hybrid Bayesian networks
Lanseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael;
2009-01-01
and reliability block diagrams). However, limitations in the BNs' calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last...... decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability....
Quantile pyramids for Bayesian nonparametrics
2009-01-01
P\\'{o}lya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a prior which supports piecewise linear quantile functions, based on the need to work with a finite set of partitions, yet we show that the limiting version of the prior exists. We also discuss and investigate an alternative model based on the so-called substitut...
Bayesian analysis of contingency tables
Gómez Villegas, Miguel A.; González Pérez, Beatriz
2005-01-01
The display of the data by means of contingency tables is used in different approaches to statistical inference, for example, to broach the test of homogeneity of independent multinomial distributions. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. Given independent samples of two binomial distributions and taking a mixed prior distribution, we calculate the posterior probability that the proportion of successes in the first...
Bayesian Credit Ratings (new version)
Paola Cerchiello; Paolo Giudici
2013-01-01
In this contribution we aim at improving ordinal variable selection in the context of causal models. In this regard, we propose an approach that provides a formal inferential tool to compare the explanatory power of each covariate, and, therefore, to select an effective model for classification purposes. Our proposed model is Bayesian nonparametric, and, thus, keeps the amount of model specification to a minimum. We consider the case in which information from the covariates is at the ordinal ...
Embracing Uncertainty: The Interface of Bayesian Statistics and Cognitive Psychology
Judith L. Anderson
1998-06-01
Full Text Available Ecologists working in conservation and resource management are discovering the importance of using Bayesian analytic methods to deal explicitly with uncertainty in data analyses and decision making. However, Bayesian procedures require, as inputs and outputs, an idea that is problematic for the human brain: the probability of a hypothesis ("single-event probability". I describe several cognitive concepts closely related to single-event probabilities, and discuss how their interchangeability in the human mind results in "cognitive illusions," apparent deficits in reasoning about uncertainty. Each cognitive illusion implies specific possible pitfalls for the use of single-event probabilities in ecology and resource management. I then discuss recent research in cognitive psychology showing that simple tactics of communication, suggested by an evolutionary perspective on human cognition, help people to process uncertain information more effectively as they read and talk about probabilities. In addition, I suggest that carefully considered standards for methodology and conventions for presentation may also make Bayesian analyses easier to understand.
Bayesian second law of thermodynamics
Bartolotta, Anthony; Carroll, Sean M.; Leichenauer, Stefan; Pollack, Jason
2016-08-01
We derive a generalization of the second law of thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically evolving system degrades over time. The Bayesian second law can be written as Δ H (ρm,ρ ) + F |m≥0 , where Δ H (ρm,ρ ) is the change in the cross entropy between the original phase-space probability distribution ρ and the measurement-updated distribution ρm and F |m is the expectation value of a generalized heat flow out of the system. We also derive refined versions of the second law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of integral fluctuation theorems. We demonstrate the formalism using simple analytical and numerical examples.
Quantum Inference on Bayesian Networks
Yoder, Theodore; Low, Guang Hao; Chuang, Isaac
2014-03-01
Because quantum physics is naturally probabilistic, it seems reasonable to expect physical systems to describe probabilities and their evolution in a natural fashion. Here, we use quantum computation to speedup sampling from a graphical probability model, the Bayesian network. A specialization of this sampling problem is approximate Bayesian inference, where the distribution on query variables is sampled given the values e of evidence variables. Inference is a key part of modern machine learning and artificial intelligence tasks, but is known to be NP-hard. Classically, a single unbiased sample is obtained from a Bayesian network on n variables with at most m parents per node in time (nmP(e) - 1 / 2) , depending critically on P(e) , the probability the evidence might occur in the first place. However, by implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking (n2m P(e) -1/2) time per sample. The speedup is the result of amplitude amplification, which is proving to be broadly applicable in sampling and machine learning tasks. In particular, we provide an explicit and efficient circuit construction that implements the algorithm without the need for oracle access.
12th Brazilian Meeting on Bayesian Statistics
Louzada, Francisco; Rifo, Laura; Stern, Julio; Lauretto, Marcelo
2015-01-01
Through refereed papers, this volume focuses on the foundations of the Bayesian paradigm; their comparison to objectivistic or frequentist Statistics counterparts; and the appropriate application of Bayesian foundations. This research in Bayesian Statistics is applicable to data analysis in biostatistics, clinical trials, law, engineering, and the social sciences. EBEB, the Brazilian Meeting on Bayesian Statistics, is held every two years by the ISBrA, the International Society for Bayesian Analysis, one of the most active chapters of the ISBA. The 12th meeting took place March 10-14, 2014 in Atibaia. Interest in foundations of inductive Statistics has grown recently in accordance with the increasing availability of Bayesian methodological alternatives. Scientists need to deal with the ever more difficult choice of the optimal method to apply to their problem. This volume shows how Bayes can be the answer. The examination and discussion on the foundations work towards the goal of proper application of Bayesia...
Bayesian Posterior Distributions Without Markov Chains
Cole, Stephen R.; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B.
2012-01-01
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976–1983) assessing the relation between residential ex...
Bayesian networks with applications in reliability analysis
Langseth, Helge
2002-01-01
A common goal of the papers in this thesis is to propose, formalize and exemplify the use of Bayesian networks as a modelling tool in reliability analysis. The papers span work in which Bayesian networks are merely used as a modelling tool (Paper I), work where models are specially designed to utilize the inference algorithms of Bayesian networks (Paper II and Paper III), and work where the focus has been on extending the applicability of Bayesian networks to very large domains (Paper IV and ...
Ildikó Ungvári
Full Text Available Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls. The results were evaluated with traditional frequentist methods and we applied a new statistical method, called bayesian network based bayesian multilevel analysis of relevance (BN-BMLA. This method uses bayesian network representation to provide detailed characterization of the relevance of factors, such as joint significance, the type of dependency, and multi-target aspects. We estimated posteriors for these relations within the bayesian statistical framework, in order to estimate the posteriors whether a variable is directly relevant or its association is only mediated.With frequentist methods one SNP (rs3751464 in the FRMD6 gene provided evidence for an association with asthma (OR = 1.43(1.2-1.8; p = 3×10(-4. The possible role of the FRMD6 gene in asthma was also confirmed in an animal model and human asthmatics.In the BN-BMLA analysis altogether 5 SNPs in 4 genes were found relevant in connection with asthma phenotype: PRPF19 on chromosome 11, and FRMD6, PTGER2 and PTGDR on chromosome 14. In a subsequent step a partial dataset containing rhinitis and further clinical parameters was used, which allowed the analysis of relevance of SNPs for asthma and multiple targets. These analyses suggested that SNPs in the AHNAK and MS4A2 genes were indirectly associated with asthma. This paper indicates that BN-BMLA explores the relevant factors more comprehensively than traditional statistical methods and extends the scope of strong relevance based methods to include partial relevance, global characterization of relevance and multi-target relevance.
parallelMCMCcombine: an R package for bayesian methods for big data and analytics.
Alexey Miroshnikov
Full Text Available Recent advances in big data and analytics research have provided a wealth of large data sets that are too big to be analyzed in their entirety, due to restrictions on computer memory or storage size. New Bayesian methods have been developed for data sets that are large only due to large sample sizes. These methods partition big data sets into subsets and perform independent Bayesian Markov chain Monte Carlo analyses on the subsets. The methods then combine the independent subset posterior samples to estimate a posterior density given the full data set. These approaches were shown to be effective for Bayesian models including logistic regression models, Gaussian mixture models and hierarchical models. Here, we introduce the R package parallelMCMCcombine which carries out four of these techniques for combining independent subset posterior samples. We illustrate each of the methods using a Bayesian logistic regression model for simulation data and a Bayesian Gamma model for real data; we also demonstrate features and capabilities of the R package. The package assumes the user has carried out the Bayesian analysis and has produced the independent subposterior samples outside of the package. The methods are primarily suited to models with unknown parameters of fixed dimension that exist in continuous parameter spaces. We envision this tool will allow researchers to explore the various methods for their specific applications and will assist future progress in this rapidly developing field.
Bayesian Methods and Universal Darwinism
Campbell, John
2009-12-01
Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent Champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a `copy with selective retention' algorithm abstracted from Darwin's theory of Natural Selection. Arguments are presented for an isomorphism between Bayesian Methods and Darwinian processes. Universal Darwinism, as the term has been developed by Richard Dawkins, Daniel Dennett and Susan Blackmore, is the collection of scientific theories which explain the creation and evolution of their subject matter as due to the Operation of Darwinian processes. These subject matters span the fields of atomic physics, chemistry, biology and the social sciences. The principle of Maximum Entropy states that Systems will evolve to states of highest entropy subject to the constraints of scientific law. This principle may be inverted to provide illumination as to the nature of scientific law. Our best cosmological theories suggest the universe contained much less complexity during the period shortly after the Big Bang than it does at present. The scientific subject matter of atomic physics, chemistry, biology and the social sciences has been created since that time. An explanation is proposed for the existence of this subject matter as due to the evolution of constraints in the form of adaptations imposed on Maximum Entropy. It is argued these adaptations were discovered and instantiated through the Operations of a succession of Darwinian processes.
Bayesian Query-Focused Summarization
Daumé, Hal
2009-01-01
We present BayeSum (for ``Bayesian summarization''), a model for sentence extraction in query-focused summarization. BayeSum leverages the common case in which multiple documents are relevant to a single query. Using these documents as reinforcement for query terms, BayeSum is not afflicted by the paucity of information in short queries. We show that approximate inference in BayeSum is possible on large data sets and results in a state-of-the-art summarization system. Furthermore, we show how BayeSum can be understood as a justified query expansion technique in the language modeling for IR framework.
Numeracy, frequency, and Bayesian reasoning
Gretchen B. Chapman
2009-02-01
Full Text Available Previous research has demonstrated that Bayesian reasoning performance is improved if uncertainty information is presented as natural frequencies rather than single-event probabilities. A questionnaire study of 342 college students replicated this effect but also found that the performance-boosting benefits of the natural frequency presentation occurred primarily for participants who scored high in numeracy. This finding suggests that even comprehension and manipulation of natural frequencies requires a certain threshold of numeracy abilities, and that the beneficial effects of natural frequency presentation may not be as general as previously believed.
Bayesian inference for Hawkes processes
Rasmussen, Jakob Gulddahl
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Bayesian inference for Hawkes processes
Rasmussen, Jakob Gulddahl
2013-01-01
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Collaborative Kalman Filtration: Bayesian Perspective
Dedecius, Kamil
Lisabon, Portugalsko: Institute for Systems and Technologies of Information, Control and Communication (INSTICC), 2014, s. 468-474. ISBN 978-989-758-039-0. [11th International Conference on Informatics in Control, Automation and Robotics - ICINCO 2014. Vien (AT), 01.09.2014-03.09.2014] R&D Projects: GA ČR(CZ) GP14-06678P Institutional support: RVO:67985556 Keywords : Bayesian analysis * Kalman filter * distributed estimation Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2014/AS/dedecius-0431324.pdf
Pooled Bayesian meta-analysis of two Polish studies on radiation-induced cancers
The robust Bayesian regression method was applied to perform meta-analysis of two independent studies on influence of low ionising radiation doses on the occurrence of fatal cancers. The re-analysed data come from occupational exposure analysis of nuclear workers in Swierk (Poland) and from ecological study of cancer risk from natural background radiation in Poland. Such two different types of data were analysed, and three popular models were tested: constant, linear and quadratic dose-response dependencies. The Bayesian model selection algorithm was used for all models. The Bayesian statistics clearly indicates that the popular linear no-threshold (LNT) assumption is not valid for presented cancer risks in the range of low doses of ionising radiation. The subject of LNT hypothesis use in radiation risk prediction and assessment is also discussed. (authors)
Bayesian credible interval construction for Poisson statistics
ZHU Yong-Sheng
2008-01-01
The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented.Introducing the conditional probability satisfying the requirement of the background not larger than the observed events to construct the Bayesian credible interval is also discussed.A Fortran routine,BPOCI,has been developed to implement the calculation.
Bayesian Decision Theoretical Framework for Clustering
Chen, Mo
2011-01-01
In this thesis, we establish a novel probabilistic framework for the data clustering problem from the perspective of Bayesian decision theory. The Bayesian decision theory view justifies the important questions: what is a cluster and what a clustering algorithm should optimize. We prove that the spectral clustering (to be specific, the…
Bayesian Statistics for Biological Data: Pedigree Analysis
Stanfield, William D.; Carlton, Matthew A.
2004-01-01
The use of Bayes' formula is applied to the biological problem of pedigree analysis to show that the Bayes' formula and non-Bayesian or "classical" methods of probability calculation give different answers. First year college students of biology can be introduced to the Bayesian statistics.
Using Bayesian Networks to Improve Knowledge Assessment
Millan, Eva; Descalco, Luis; Castillo, Gladys; Oliveira, Paula; Diogo, Sandra
2013-01-01
In this paper, we describe the integration and evaluation of an existing generic Bayesian student model (GBSM) into an existing computerized testing system within the Mathematics Education Project (PmatE--Projecto Matematica Ensino) of the University of Aveiro. This generic Bayesian student model had been previously evaluated with simulated…
Nonparametric Bayesian Modeling of Complex Networks
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....
Compiling Relational Bayesian Networks for Exact Inference
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating and ...
Compiling Relational Bayesian Networks for Exact Inference
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by eva...
Bayesian analysis of exoplanet and binary orbits
Schulze-Hartung, Tim; Henning, Thomas
2012-01-01
We introduce BASE (Bayesian astrometric and spectroscopic exoplanet detection and characterisation tool), a novel program for the combined or separate Bayesian analysis of astrometric and radial-velocity measurements of potential exoplanet hosts and binary stars. The capabilities of BASE are demonstrated using all publicly available data of the binary Mizar A.
Computational methods for Bayesian model choice
Robert, Christian P.; Wraith, Darren
2009-01-01
In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and nested sampling from a unified perspective.
Fracture prediction of cardiac lead medical devices using Bayesian networks
A novel Bayesian network methodology has been developed to enable the prediction of fatigue fracture of cardiac lead medical devices. The methodology integrates in-vivo device loading measurements, patient demographics, patient activity level, in-vitro fatigue strength measurements, and cumulative damage modeling techniques. Many plausible combinations of these variables can be simulated within a Bayesian network framework to generate a family of fatigue fracture survival curves, enabling sensitivity analyses and the construction of confidence bounds on reliability predictions. The method was applied to the prediction of conductor fatigue fracture near the shoulder for two market-released cardiac defibrillation leads which had different product performance histories. The case study used recently published data describing the in-vivo curvature conditions and the in-vitro fatigue strength. The prediction results from the methodology aligned well with the observed qualitative ranking of field performance, as well as the quantitative field survival from fracture. This initial success suggests that study of further extension of this method to other medical device applications is warranted. - Highlights: • A new method to simulate the fatigue experience of an implanted cardiac lead. • Fatigue strength and use conditions are incorporated within a Bayesian network. • Confidence bounds reflect the uncertainty in all input parameters. • A case study is presented using market released cardiac leads
Halo detection via large-scale Bayesian inference
Merson, Alexander I.; Jasche, Jens; Abdalla, Filipe B.; Lahav, Ofer; Wandelt, Benjamin; Jones, D. Heath; Colless, Matthew
2016-08-01
We present a proof-of-concept of a novel and fully Bayesian methodology designed to detect haloes of different masses in cosmological observations subject to noise and systematic uncertainties. Our methodology combines the previously published Bayesian large-scale structure inference algorithm, HAmiltonian Density Estimation and Sampling algorithm (HADES), and a Bayesian chain rule (the Blackwell-Rao estimator), which we use to connect the inferred density field to the properties of dark matter haloes. To demonstrate the capability of our approach, we construct a realistic galaxy mock catalogue emulating the wide-area 6-degree Field Galaxy Survey, which has a median redshift of approximately 0.05. Application of HADES to the catalogue provides us with accurately inferred three-dimensional density fields and corresponding quantification of uncertainties inherent to any cosmological observation. We then use a cosmological simulation to relate the amplitude of the density field to the probability of detecting a halo with mass above a specified threshold. With this information, we can sum over the HADES density field realisations to construct maps of detection probabilities and demonstrate the validity of this approach within our mock scenario. We find that the probability of successful detection of haloes in the mock catalogue increases as a function of the signal to noise of the local galaxy observations. Our proposed methodology can easily be extended to account for more complex scientific questions and is a promising novel tool to analyse the cosmic large-scale structure in observations.
2nd Bayesian Young Statisticians Meeting
Bitto, Angela; Kastner, Gregor; Posekany, Alexandra
2015-01-01
The Second Bayesian Young Statisticians Meeting (BAYSM 2014) and the research presented here facilitate connections among researchers using Bayesian Statistics by providing a forum for the development and exchange of ideas. WU Vienna University of Business and Economics hosted BAYSM 2014 from September 18th to 19th. The guidance of renowned plenary lecturers and senior discussants is a critical part of the meeting and this volume, which follows publication of contributions from BAYSM 2013. The meeting's scientific program reflected the variety of fields in which Bayesian methods are currently employed or could be introduced in the future. Three brilliant keynote lectures by Chris Holmes (University of Oxford), Christian Robert (Université Paris-Dauphine), and Mike West (Duke University), were complemented by 24 plenary talks covering the major topics Dynamic Models, Applications, Bayesian Nonparametrics, Biostatistics, Bayesian Methods in Economics, and Models and Methods, as well as a lively poster session ...
BAYESIAN BICLUSTERING FOR PATIENT STRATIFICATION.
Khakabimamaghani, Sahand; Ester, Martin
2016-01-01
The move from Empirical Medicine towards Personalized Medicine has attracted attention to Stratified Medicine (SM). Some methods are provided in the literature for patient stratification, which is the central task of SM, however, there are still significant open issues. First, it is still unclear if integrating different datatypes will help in detecting disease subtypes more accurately, and, if not, which datatype(s) are most useful for this task. Second, it is not clear how we can compare different methods of patient stratification. Third, as most of the proposed stratification methods are deterministic, there is a need for investigating the potential benefits of applying probabilistic methods. To address these issues, we introduce a novel integrative Bayesian biclustering method, called B2PS, for patient stratification and propose methods for evaluating the results. Our experimental results demonstrate the superiority of B2PS over a popular state-of-the-art method and the benefits of Bayesian approaches. Our results agree with the intuition that transcriptomic data forms a better basis for patient stratification than genomic data. PMID:26776199
Bayesian Estimation of Small Effects in Exercise and Sports Science.
Mengersen, Kerrie L; Drovandi, Christopher C; Robert, Christian P; Pyne, David B; Gore, Christopher J
2016-01-01
The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a 'magnitude-based inference' approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements. PMID:27073897
A Bayesian foundation for individual learning under uncertainty
Christoph Mathys
2011-05-01
Full Text Available Computational learning models are critical for understanding mechanisms of adaptive behavior. However, the two major current frameworks, reinforcement learning (RL and Bayesian learning, both have certain limitations. For example, many Bayesian models are agnostic of inter-individual variability and involve complicated integrals, making online learning difficult. Here, we introduce a generic hierarchical Bayesian framework for individual learning under multiple forms of uncertainty (e.g., environmental volatility and perceptual uncertainty. The model assumes Gaussian random walks of states at all but the first level, with the step size determined by the next higher level. The coupling between levels is controlled by parameters that shape the influence of uncertainty on learning in a subject-specific fashion. Using variational Bayes under a mean field approximation and a novel approximation to the posterior energy function, we derive trial-by-trial update equations which (i are analytical and extremely efficient, enabling real-time learning, (ii have a natural interpretation in terms of RL, and (iii contain parameters representing processes which play a key role in current theories of learning, e.g., precision-weighting of prediction error. These parameters allow for the expression of individual differences in learning and may relate to specific neuromodulatory mechanisms in the brain. Our model is very general: it can deal with both discrete and continuous states and equally accounts for deterministic and probabilistic relations between environmental events and perceptual states (i.e., situations with and without perceptual uncertainty. These properties are illustrated by simulations and analyses of empirical time series. Overall, our framework provides a novel foundation for understanding normal and pathological learning that contextualizes RL within a generic Bayesian scheme and thus connects it to principles of optimality from probability
Bayesian Estimation of Small Effects in Exercise and Sports Science
Mengersen, Kerrie L.; Drovandi, Christopher C.; Robert, Christian P.; Pyne, David B.; Gore, Christopher J.
2016-01-01
The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a ‘magnitude-based inference’ approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements. PMID:27073897
A Gibbs sampler for Bayesian analysis of site-occupancy data
Dorazio, Robert M.; Rodriguez, Daniel Taylor
2012-01-01
1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.
Analysis of KATRIN data using Bayesian inference
Riis, Anna Sejersen; Weinheimer, Christian
2011-01-01
The KATRIN (KArlsruhe TRItium Neutrino) experiment will be analyzing the tritium beta-spectrum to determine the mass of the neutrino with a sensitivity of 0.2 eV (90% C.L.). This approach to a measurement of the absolute value of the neutrino mass relies only on the principle of energy conservation and can in some sense be called model-independent as compared to cosmology and neutrino-less double beta decay. However by model independent we only mean in case of the minimal extension of the standard model. One should therefore also analyse the data for non-standard couplings to e.g. righthanded or sterile neutrinos. As an alternative to the frequentist minimization methods used in the analysis of the earlier experiments in Mainz and Troitsk we have been investigating Markov Chain Monte Carlo (MCMC) methods which are very well suited for probing multi-parameter spaces. We found that implementing the KATRIN chi squared function in the COSMOMC package - an MCMC code using Bayesian parameter inference - solved the ...
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
Skare, Øivind; Møller, Jesper; Vedel Jensen, Eva B.
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample f...
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
Skare, Øivind; Møller, Jesper; Jensen, Eva B. Vedel
2007-01-01
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample f...
Jelsøe, Erling; Jæger, Birgit
2015-01-01
When analysing the results of a European wide citizen consultation on sustainable consumption it is necessary to take a number of issues into account, such as the question of representativity and tensions between national and European identies and between consumer and Citizen orientations regarding...
Bayesian networks in educational assessment
Almond, Russell G; Steinberg, Linda S; Yan, Duanli; Williamson, David M
2015-01-01
Bayesian inference networks, a synthesis of statistics and expert systems, have advanced reasoning under uncertainty in medicine, business, and social sciences. This innovative volume is the first comprehensive treatment exploring how they can be applied to design and analyze innovative educational assessments. Part I develops Bayes nets’ foundations in assessment, statistics, and graph theory, and works through the real-time updating algorithm. Part II addresses parametric forms for use with assessment, model-checking techniques, and estimation with the EM algorithm and Markov chain Monte Carlo (MCMC). A unique feature is the volume’s grounding in Evidence-Centered Design (ECD) framework for assessment design. This “design forward” approach enables designers to take full advantage of Bayes nets’ modularity and ability to model complex evidentiary relationships that arise from performance in interactive, technology-rich assessments such as simulations. Part III describes ECD, situates Bayes nets as ...
Quantum Bayesianism at the Perimeter
Fuchs, Christopher A
2010-01-01
The author summarizes the Quantum Bayesian viewpoint of quantum mechanics, developed originally by C. M. Caves, R. Schack, and himself. It is a view crucially dependent upon the tools of quantum information theory. Work at the Perimeter Institute for Theoretical Physics continues the development and is focused on the hard technical problem of a finding a good representation of quantum mechanics purely in terms of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves a mysterious entity called a symmetric informationally complete quantum measurement. Contemplation of it gives a way of thinking of the Born Rule as an addition to the rules of probability theory, applicable when one gambles on the consequences of interactions with physical systems. The article ends by outlining some directions for future work.
Bayesian Kernel Mixtures for Counts.
Canale, Antonio; Dunson, David B
2011-12-01
Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow smooth deviations from the Poisson. As a broad class of alternative models, we propose to use nonparametric mixtures of rounded continuous kernels. An efficient Gibbs sampler is developed for posterior computation, and a simulation study is performed to assess performance. Focusing on the rounded Gaussian case, we generalize the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications. The methods are illustrated through applications to a developmental toxicity study and marketing data. This article has supplementary material online. PMID:22523437
Hedging Strategies for Bayesian Optimization
Brochu, Eric; de Freitas, Nando
2010-01-01
Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It is able to do this by sampling the objective using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We describe the method, which we call GP-Hedge, and show that this method almost always outperforms the best individual acquisition function.
Nonparametric Bayesian inference in biostatistics
Müller, Peter
2015-01-01
As chapters in this book demonstrate, BNP has important uses in clinical sciences and inference for issues like unknown partitions in genomics. Nonparametric Bayesian approaches (BNP) play an ever expanding role in biostatistical inference from use in proteomics to clinical trials. Many research problems involve an abundance of data and require flexible and complex probability models beyond the traditional parametric approaches. As this book's expert contributors show, BNP approaches can be the answer. Survival Analysis, in particular survival regression, has traditionally used BNP, but BNP's potential is now very broad. This applies to important tasks like arrangement of patients into clinically meaningful subpopulations and segmenting the genome into functionally distinct regions. This book is designed to both review and introduce application areas for BNP. While existing books provide theoretical foundations, this book connects theory to practice through engaging examples and research questions. Chapters c...
On Bayesian System Reliability Analysis
The view taken in this thesis is that reliability, the probability that a system will perform a required function for a stated period of time, depends on a person's state of knowledge. Reliability changes as this state of knowledge changes, i.e. when new relevant information becomes available. Most existing models for system reliability prediction are developed in a classical framework of probability theory and they overlook some information that is always present. Probability is just an analytical tool to handle uncertainty, based on judgement and subjective opinions. It is argued that the Bayesian approach gives a much more comprehensive understanding of the foundations of probability than the so called frequentistic school. A new model for system reliability prediction is given in two papers. The model encloses the fact that component failures are dependent because of a shared operational environment. The suggested model also naturally permits learning from failure data of similar components in non identical environments. 85 refs
Elvira, Clément; Dobigeon, Nicolas
2015-01-01
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients exhibits relevant properties in various applications such as digital communications. Anti-sparse regularization can be naturally expressed through an $\\ell_{\\infty}$-norm penalty. This paper derives a probabilistic formulation of such representations. A new probability distribution, referred to as the democratic prior, is first introduced. Its main properties as well as three random variate generators for this distribution are derived. Then this probability distribution is used as a prior to promote anti-sparsity in a Gaussian linear inverse problem, yielding a fully Bayesian formulation of anti-sparse coding. Two Markov chain Monte Carlo (MCMC) algorithms are proposed to generate samples according to the posterior distribution. The first one is a standard Gibbs sampler. The seco...
State Information in Bayesian Games
Cuff, Paul
2009-01-01
Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the resulting value of the game has been analyzed under the framework of Bayesian games. This investigation considers the optimal performance in a game when a helper is transmitting state information to one of the players. Encoding information for an adversarial setting (game) requires a different result than rate-distortion theory provides. Game theory has accentuated the importance of randomization (mixed strategy), which does not find a significant role in most communication modems and source coding codecs. Higher rates of communication, used in the right way, allow the message to include the necessary random component useful in games.
Cooperative extensions of the Bayesian game
Ichiishi, Tatsuro
2006-01-01
This is the very first comprehensive monograph in a burgeoning, new research area - the theory of cooperative game with incomplete information with emphasis on the solution concept of Bayesian incentive compatible strong equilibrium that encompasses the concept of the Bayesian incentive compatible core. Built upon the concepts and techniques in the classical static cooperative game theory and in the non-cooperative Bayesian game theory, the theory constructs and analyzes in part the powerful n -person game-theoretical model characterized by coordinated strategy-choice with individualistic ince
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
Supra-Bayesian Combination of Probability Distributions
Sečkárová, Vladimíra
Veszprém : University of Pannonia, 2010, s. 112-117. ISBN 978-615-5044-00-7. [11th International PhD Workshop on Systems and Control. Veszprém (HU), 01.09.2010-03.09.2010] R&D Projects: GA ČR GA102/08/0567 Institutional research plan: CEZ:AV0Z10750506 Keywords : Supra-Bayesian approach * sharing of probabilistic information * Bayesian decision making Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2010/AS/seckarova-supra-bayesian combination of probability distributions.pdf
Bayesian Soft Sensing in Cold Sheet Rolling
Dedecius, Kamil; Jirsa, Ladislav
Praha: ÚTIA AV ČR, v.v.i, 2010. s. 45-45. [6th International Workshop on Data–Algorithms–Decision Making. 2.12.2010-4.12.2010, Jindřichův Hradec] R&D Projects: GA MŠk(CZ) 7D09008 Institutional research plan: CEZ:AV0Z10750506 Keywords : soft sensor * bayesian statistics * bayesian model averaging Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2010/AS/dedecius-bayesian soft sensing in cold sheet rolling.pdf
A population-based Bayesian approach to the minimal model of glucose and insulin homeostasis
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...... to a population-based model. The estimation of the parameters are efficiently implemented in a Bayesian approach where posterior inference is made through the use of Markov chain Monte Carlo techniques. Hereby we obtain a powerful and flexible modelling framework for regularizing the ill-posed estimation problem...
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.
Application of Bayesian networks for risk analysis of MV air insulated switch operation
Electricity distribution companies regard risk-based approaches as a good philosophy to address their asset management challenges, and there is an increasing trend on developing methods to support decisions where different aspects of risks are taken into consideration. This paper describes a methodology for application of Bayesian networks for risk analysis in electricity distribution system maintenance management. The methodology is used on a case analysing safety risk related to operation of MV air insulated switches. The paper summarises some challenges and benefits of using Bayesian networks as a part of distribution system maintenance management.
The Diagnosis of Reciprocating Machinery by Bayesian Networks
无
2003-01-01
A Bayesian Network is a reasoning tool based on probability theory and has many advantages that other reasoning tools do not have. This paper discusses the basic theory of Bayesian networks and studies the problems in constructing Bayesian networks. The paper also constructs a Bayesian diagnosis network of a reciprocating compressor. The example helps us to draw a conclusion that Bayesian diagnosis networks can diagnose reciprocating machinery effectively.
An Intuitive Dashboard for Bayesian Network Inference
Reddy, Vikas; Charisse Farr, Anna; Wu, Paul; Mengersen, Kerrie; Yarlagadda, Prasad K. D. V.
2014-03-01
Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++.
A Bayesian approach to model uncertainty
A Bayesian approach to model uncertainty is taken. For the case of a finite number of alternative models, the model uncertainty is equivalent to parameter uncertainty. A derivation based on Savage's partition problem is given
An Intuitive Dashboard for Bayesian Network Inference
Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++
Bayesian Control for Concentrating Mixed Nuclear Waste
Welch, Robert L.; Smith, Clayton
2013-01-01
A control algorithm for batch processing of mixed waste is proposed based on conditional Gaussian Bayesian networks. The network is compiled during batch staging for real-time response to sensor input.
Learning Bayesian networks for discrete data
Liang, Faming
2009-02-01
Bayesian networks have received much attention in the recent literature. In this article, we propose an approach to learn Bayesian networks using the stochastic approximation Monte Carlo (SAMC) algorithm. Our approach has two nice features. Firstly, it possesses the self-adjusting mechanism and thus avoids essentially the local-trap problem suffered by conventional MCMC simulation-based approaches in learning Bayesian networks. Secondly, it falls into the class of dynamic importance sampling algorithms; the network features can be inferred by dynamically weighted averaging the samples generated in the learning process, and the resulting estimates can have much lower variation than the single model-based estimates. The numerical results indicate that our approach can mix much faster over the space of Bayesian networks than the conventional MCMC simulation-based approaches. © 2008 Elsevier B.V. All rights reserved.
Bayesian Variable Selection in Spatial Autoregressive Models
Jesus Crespo Cuaresma; Philipp Piribauer
2015-01-01
This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. We present two alternative approaches which can be implemented using Gibbs sampling methods in a straightforward way and allow us to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. In a simulation study we show that the variable selection approaches tend to outperform existing Bayesian model averaging tech...
Bayesian Analysis of Multivariate Probit Models
Siddhartha Chib; Edward Greenberg
1996-01-01
This paper provides a unified simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods, and maximum likelihood estimates are obtained by a Markov chain Monte Carlo version of the E-M algorithm. Computation of Bayes factors from the simulation output is also considered. The methods are applied to a bivariate data set, to a 534-subject, four-year longitudinal dat...
Kernel Bayesian Inference with Posterior Regularization
Song, Yang; Jun ZHU; Ren, Yong
2016-01-01
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former th...
Fitness inheritance in the Bayesian optimization algorithm
Pelikan, Martin; Sastry, Kumara
2004-01-01
This paper describes how fitness inheritance can be used to estimate fitness for a proportion of newly sampled candidate solutions in the Bayesian optimization algorithm (BOA). The goal of estimating fitness for some candidate solutions is to reduce the number of fitness evaluations for problems where fitness evaluation is expensive. Bayesian networks used in BOA to model promising solutions and generate the new ones are extended to allow not only for modeling and sampling candidate solutions...
Bayesian Network Models for Adaptive Testing
Plajner, Martin; Vomlel, Jiří
Achen: Sun SITE Central Europe, 2016 - (Agosta, J.; Carvalho, R.), s. 24-33. (CEUR Workshop Proceedings. Vol 1565). ISSN 1613-0073. [The Twelfth UAI Bayesian Modeling Applications Workshop (BMAW 2015). Amsterdam (NL), 16.07.2015] R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : Bayesian networks * Computerized adaptive testing Subject RIV: JD - Computer Applications, Robotics http://library.utia.cas.cz/separaty/2016/MTR/plajner-0458062.pdf
Nomograms for Visualization of Naive Bayesian Classifier
Možina, Martin; Demšar, Janez; Michael W Kattan; Zupan, Blaz
2004-01-01
Besides good predictive performance, the naive Bayesian classifier can also offer a valuable insight into the structure of the training data and effects of the attributes on the class probabilities. This structure may be effectively revealed through visualization of the classifier. We propose a new way to visualize the naive Bayesian model in the form of a nomogram. The advantages of the proposed method are simplicity of presentation, clear display of the effects of individual attribute value...
Subjective Bayesian Analysis: Principles and Practice
Goldstein, Michael
2006-01-01
We address the position of subjectivism within Bayesian statistics. We argue, first, that the subjectivist Bayes approach is the only feasible method for tackling many important practical problems. Second, we describe the essential role of the subjectivist approach in scientific analysis. Third, we consider possible modifications to the Bayesian approach from a subjectivist viewpoint. Finally, we address the issue of pragmatism in implementing the subjectivist approach.
An Entropy Search Portfolio for Bayesian Optimization
Shahriari, Bobak; Wang, Ziyu; Hoffman, Matthew W.; Bouchard-Côté, Alexandre; De Freitas, Nando
2014-01-01
Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and it is not clear a priori which choice will result in superior performance. While portfolio methods provide an effective, principled way of combining a collection of acquisition functions, they are often based on measures of past performance which can be misl...
A Bayesian Framework for Active Artificial Perception
Ferreira, Joao; Lobo, Jorge; Bessiere, Pierre; Castelo-Branco, M; Dias, Jorge
2012-01-01
In this text, we present a Bayesian framework for active multimodal perception of 3D structure and motion. The design of this framework finds its inspiration in the role of the dorsal perceptual pathway of the human brain. Its composing models build upon a common egocentric spatial configuration that is naturally fitting for the integration of readings from multiple sensors using a Bayesian approach. In the process, we will contribute with efficient and robust probabilistic solutions for cycl...
Bayesian Classification in Medicine: The Transferability Question *
Zagoria, Ronald J.; Reggia, James A.; Price, Thomas R.; Banko, Maryann
1981-01-01
Using probabilities derived from a geographically distant patient population, we applied Bayesian classification to categorize stroke patients by etiology. Performance was assessed both by error rate and with a new linear accuracy coefficient. This approach to patient classification was found to be surprisingly accurate when compared to classification by two neurologists and to classification by the Bayesian method using “low cost” local and subjective probabilities. We conclude that for some...
Fuzzy Functional Dependencies and Bayesian Networks
LIU WeiYi(刘惟一); SONG Ning(宋宁)
2003-01-01
Bayesian networks have become a popular technique for representing and reasoning with probabilistic information. The fuzzy functional dependency is an important kind of data dependencies in relational databases with fuzzy values. The purpose of this paper is to set up a connection between these data dependencies and Bayesian networks. The connection is done through a set of methods that enable people to obtain the most information of independent conditions from fuzzy functional dependencies.
Evaluation System for a Bayesian Optimization Service
Dewancker, Ian; McCourt, Michael; Clark, Scott; Hayes, Patrick; Johnson, Alexandra; Ke, George
2016-01-01
Bayesian optimization is an elegant solution to the hyperparameter optimization problem in machine learning. Building a reliable and robust Bayesian optimization service requires careful testing methodology and sound statistical analysis. In this talk we will outline our development of an evaluation framework to rigorously test and measure the impact of changes to the SigOpt optimization service. We present an overview of our evaluation system and discuss how this framework empowers our resea...
Bayesian target tracking based on particle filter
无
2005-01-01
For being able to deal with the nonlinear or non-Gaussian problems, particle filters have been studied by many researchers. Based on particle filter, the extended Kalman filter (EKF) proposal function is applied to Bayesian target tracking. Markov chain Monte Carlo (MCMC) method, the resampling step, etc novel techniques are also introduced into Bayesian target tracking. And the simulation results confirm the improved particle filter with these techniques outperforms the basic one.
Bayesian Models of Brain and Behaviour
Penny, William
2012-01-01
This paper presents a review of Bayesian models of brain and behaviour. We first review the basic principles of Bayesian inference. This is followed by descriptions of sampling and variational methods for approximate inference, and forward and backward recursions in time for inference in dynamical models. The review of behavioural models covers work in visual processing, sensory integration, sensorimotor integration, and collective decision making. The review of brain models covers a range of...
Bayesian Approach to Handling Informative Sampling
Sikov, Anna
2015-01-01
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this research I investigate the problem of informative sampling from the Bayesian perspective. Application of the Bayesian approach permits solving the problems, which arise due to complexity of the models, being used for handling informative sampling. The main...
Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent.
Wen, Dingqiao; Yu, Yun; Nakhleh, Luay
2016-05-01
The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation. PMID:27144273
Perceptual decision making: Drift-diffusion model is equivalent to a Bayesian model
Sebastian Bitzer
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.
Bayesian demography 250 years after Bayes.
Bijak, Jakub; Bryant, John
2016-01-01
Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889
Inverse problems in the Bayesian framework
The history of Bayesian methods dates back to the original works of Reverend Thomas Bayes and Pierre-Simon Laplace: the former laid down some of the basic principles on inverse probability in his classic article ‘An essay towards solving a problem in the doctrine of chances’ that was read posthumously in the Royal Society in 1763. Laplace, on the other hand, in his ‘Memoirs on inverse probability’ of 1774 developed the idea of updating beliefs and wrote down the celebrated Bayes’ formula in the form we know today. Although not identified yet as a framework for investigating inverse problems, Laplace used the formalism very much in the spirit it is used today in the context of inverse problems, e.g., in his study of the distribution of comets. With the evolution of computational tools, Bayesian methods have become increasingly popular in all fields of human knowledge in which conclusions need to be drawn based on incomplete and noisy data. Needless to say, inverse problems, almost by definition, fall into this category. Systematic work for developing a Bayesian inverse problem framework can arguably be traced back to the 1980s, (the original first edition being published by Elsevier in 1987), although articles on Bayesian methodology applied to inverse problems, in particular in geophysics, had appeared much earlier. Today, as testified by the articles in this special issue, the Bayesian methodology as a framework for considering inverse problems has gained a lot of popularity, and it has integrated very successfully with many traditional inverse problems ideas and techniques, providing novel ways to interpret and implement traditional procedures in numerical analysis, computational statistics, signal analysis and data assimilation. The range of applications where the Bayesian framework has been fundamental goes from geophysics, engineering and imaging to astronomy, life sciences and economy, and continues to grow. There is no question that Bayesian
Bayesian Vision for Shape Recovery
Jalobeanu, Andre
2004-01-01
We present a new Bayesian vision technique that aims at recovering a shape from two or more noisy observations taken under similar lighting conditions. The shape is parametrized by a piecewise linear height field, textured by a piecewise linear irradiance field, and we assume Gaussian Markovian priors for both shape vertices and irradiance variables. The observation process. also known as rendering, is modeled by a non-affine projection (e.g. perspective projection) followed by a convolution with a piecewise linear point spread function. and contamination by additive Gaussian noise. We assume that the observation parameters are calibrated beforehand. The major novelty of the proposed method consists of marginalizing out the irradiances considered as nuisance parameters, which is achieved by Laplace approximations. This reduces the inference to minimizing an energy that only depends on the shape vertices, and therefore allows an efficient Iterated Conditional Mode (ICM) optimization scheme to be implemented. A Gaussian approximation of the posterior shape density is computed, thus providing estimates both the geometry and its uncertainty. We illustrate the effectiveness of the new method by shape reconstruction results in a 2D case. A 3D version is currently under development and aims at recovering a surface from multiple images, reconstructing the topography by marginalizing out both albedo and shading.
BAYESIAN APPROACH OF DECISION PROBLEMS
DRAGOŞ STUPARU
2010-01-01
Full Text Available Management is nowadays a basic vector of economic development, a concept frequently used in our country as well as all over the world. Indifferently of the hierarchical level at which the managerial process is manifested, decision represents its essential moment, the supreme act of managerial activity. Its can be met in all fields of activity, practically having an unlimited degree of coverage, and in all the functions of management. It is common knowledge that the activity of any type of manger, no matter the hierarchical level he occupies, represents a chain of interdependent decisions, their aim being the elimination or limitation of the influence of disturbing factors that may endanger the achievement of predetermined objectives, and the quality of managerial decisions condition the progress and viability of any enterprise. Therefore, one of the principal characteristics of a successful manager is his ability to adopt the most optimal decisions of high quality. The quality of managerial decisions are conditioned by the manager’s general level of education and specialization, the manner in which they are preoccupied to assimilate the latest information and innovations in the domain of management’s theory and practice and the applying of modern managerial methods and techniques in the activity of management. We are presenting below the analysis of decision problems in hazardous conditions in terms of Bayesian theory – a theory that uses the probabilistic calculus.
Bayesian analysis of volcanic eruptions
Ho, Chih-Hsiang
1990-10-01
The simple Poisson model generally gives a good fit to many volcanoes for volcanic eruption forecasting. Nonetheless, empirical evidence suggests that volcanic activity in successive equal time-periods tends to be more variable than a simple Poisson with constant eruptive rate. An alternative model is therefore examined in which eruptive rate(λ) for a given volcano or cluster(s) of volcanoes is described by a gamma distribution (prior) rather than treated as a constant value as in the assumptions of a simple Poisson model. Bayesian analysis is performed to link two distributions together to give the aggregate behavior of the volcanic activity. When the Poisson process is expanded to accomodate a gamma mixing distribution on λ, a consequence of this mixed (or compound) Poisson model is that the frequency distribution of eruptions in any given time-period of equal length follows the negative binomial distribution (NBD). Applications of the proposed model and comparisons between the generalized model and simple Poisson model are discussed based on the historical eruptive count data of volcanoes Mauna Loa (Hawaii) and Etna (Italy). Several relevant facts lead to the conclusion that the generalized model is preferable for practical use both in space and time.
Internal dosimetry of uranium isotopes using bayesian inference methods
A group of personnel at Los Alamos National Laboratory is routinely monitored for the presence of uranium isotopes by urine bioassay. Samples are analysed by alpha spectroscopy, and the results are examined for evidence of an intake of uranium. Because the measurement uncertainties are often comparable to the quantities of material we wish to detect, statistical considerations are crucial for the proper interpretation of the data. The problem is further complicated by the significant, but highly non-uniform, presence of uranium in local drinking water and, in some cases, food supply. Software originally developed for internal dosimetry of plutonium has been adapted to the problem of uranium dosimetry. The software uses an unfolding algorithm to calculate an approximate Bayesian solution to the problem of characterising any intakes which may have occurred, given the history of urine bioassay results for each individual in the monitored population. The program uses biokinetic models from ICRP Publications 68 and later, and a prior probability distribution derived empirically from the body of uranium bioassay data collected at Los Alamos over the operating history of the Laboratory. For each individual, the software creates a posterior probability distribution of intake quantity and solubility type as a function of time. From this distribution, estimates are made of the cumulative committed dose (CEDE) to each individual. Results of the method are compared with those obtained using an earlier classical (non-Bayesian) algorithm for uranium dosimetry. We also discuss the problem of distinguishing occupational intakes from intake of environmental uranium, within a Bayesian framework. (author)
Computationally efficient Bayesian inference for inverse problems.
Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A.
2007-10-01
Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problems - representing indirect estimation of model parameters, inputs, or structural components - can be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field. We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also explore dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties. We also present a Bayesian framework for parameter estimation in stochastic models, where intrinsic stochasticity may be intermingled with observational noise. Evaluation of a likelihood function may not be analytically tractable in these cases, and thus several alternative Markov chain Monte Carlo (MCMC) schemes, operating on the product space of the observations and the parameters, are introduced.
Dimensionality reduction in Bayesian estimation algorithms
G. W. Petty
2013-03-01
Full Text Available An idealized synthetic database loosely resembling 3-channel passive microwave observations of precipitation against a variable background is employed to examine the performance of a conventional Bayesian retrieval algorithm. For this dataset, algorithm performance is found to be poor owing to an irreconcilable conflict between the need to find matches in the dependent database versus the need to exclude inappropriate matches. It is argued that the likelihood of such conflicts increases sharply with the dimensionality of the observation space of real satellite sensors, which may utilize 9 to 13 channels to retrieve precipitation, for example. An objective method is described for distilling the relevant information content from N real channels into a much smaller number (M of pseudochannels while also regularizing the background (geophysical plus instrument noise component. The pseudochannels are linear combinations of the original N channels obtained via a two-stage principal component analysis of the dependent dataset. Bayesian retrievals based on a single pseudochannel applied to the independent dataset yield striking improvements in overall performance. The differences between the conventional Bayesian retrieval and reduced-dimensional Bayesian retrieval suggest that a major potential problem with conventional multichannel retrievals – whether Bayesian or not – lies in the common but often inappropriate assumption of diagonal error covariance. The dimensional reduction technique described herein avoids this problem by, in effect, recasting the retrieval problem in a coordinate system in which the desired covariance is lower-dimensional, diagonal, and unit magnitude.
Tactile length contraction as Bayesian inference.
Tong, Jonathan; Ngo, Vy; Goldreich, Daniel
2016-08-01
To perceive, the brain must interpret stimulus-evoked neural activity. This is challenging: The stochastic nature of the neural response renders its interpretation inherently uncertain. Perception would be optimized if the brain used Bayesian inference to interpret inputs in light of expectations derived from experience. Bayesian inference would improve perception on average but cause illusions when stimuli violate expectation. Intriguingly, tactile, auditory, and visual perception are all prone to length contraction illusions, characterized by the dramatic underestimation of the distance between punctate stimuli delivered in rapid succession; the origin of these illusions has been mysterious. We previously proposed that length contraction illusions occur because the brain interprets punctate stimulus sequences using Bayesian inference with a low-velocity expectation. A novel prediction of our Bayesian observer model is that length contraction should intensify if stimuli are made more difficult to localize. Here we report a tactile psychophysical study that tested this prediction. Twenty humans compared two distances on the forearm: a fixed reference distance defined by two taps with 1-s temporal separation and an adjustable comparison distance defined by two taps with temporal separation t ≤ 1 s. We observed significant length contraction: As t was decreased, participants perceived the two distances as equal only when the comparison distance was made progressively greater than the reference distance. Furthermore, the use of weaker taps significantly enhanced participants' length contraction. These findings confirm the model's predictions, supporting the view that the spatiotemporal percept is a best estimate resulting from a Bayesian inference process. PMID:27121574
Bayesian Methods for Medical Test Accuracy
Lyle D. Broemeling
2011-05-01
Full Text Available Bayesian methods for medical test accuracy are presented, beginning with the basic measures for tests with binary scores: true positive fraction, false positive fraction, positive predictive values, and negative predictive value. The Bayesian approach is taken because of its efficient use of prior information, and the analysis is executed with a Bayesian software package WinBUGS®. The ROC (receiver operating characteristic curve gives the intrinsic accuracy of medical tests that have ordinal or continuous scores, and the Bayesian approach is illustrated with many examples from cancer and other diseases. Medical tests include X-ray, mammography, ultrasound, computed tomography, magnetic resonance imaging, nuclear medicine and tests based on biomarkers, such as blood glucose values for diabetes. The presentation continues with more specialized methods suitable for measuring the accuracies of clinical studies that have verification bias, and medical tests without a gold standard. Lastly, the review is concluded with Bayesian methods for measuring the accuracy of the combination of two or more tests.
Bayesian tomographic reconstruction of microsystems
Salem, Sofia Fekih; Vabre, Alexandre; Mohammad-Djafari, Ali
2007-11-01
The microtomography by X ray transmission plays an increasingly dominating role in the study and the understanding of microsystems. Within this framework, an experimental setup of high resolution X ray microtomography was developed at CEA-List to quantify the physical parameters related to the fluids flow in microsystems. Several difficulties rise from the nature of experimental data collected on this setup: enhanced error measurements due to various physical phenomena occurring during the image formation (diffusion, beam hardening), and specificities of the setup (limited angle, partial view of the object, weak contrast). To reconstruct the object we must solve an inverse problem. This inverse problem is known to be ill-posed. It therefore needs to be regularized by introducing prior information. The main prior information we account for is that the object is composed of a finite known number of different materials distributed in compact regions. This a priori information is introduced via a Gauss-Markov field for the contrast distributions with a hidden Potts-Markov field for the class materials in the Bayesian estimation framework. The computations are done by using an appropriate Markov Chain Monte Carlo (MCMC) technique. In this paper, we present first the basic steps of the proposed algorithms. Then we focus on one of the main steps in any iterative reconstruction method which is the computation of forward and adjoint operators (projection and backprojection). A fast implementation of these two operators is crucial for the real application of the method. We give some details on the fast computation of these steps and show some preliminary results of simulations.
A Large Sample Study of the Bayesian Bootstrap
Lo, Albert Y.
1987-01-01
An asymptotic justification of the Bayesian bootstrap is given. Large-sample Bayesian bootstrap probability intervals for the mean, the variance and bands for the distribution, the smoothed density and smoothed rate function are also provided.
Bayesian statistic methods and theri application in probabilistic simulation models
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.
Bayesian approach in MN low dose of radiation counting
The Micronucleus assay in lymphocytes is a well established technique for the assessment of genetic damage induced by ionizing radiation. Due to the presence of a natural background of MN the net MN is obtained by subtracting this value to the gross value. When very low doses of radiation are given the induced MN is close even lower than the predetermined background value. Furthermore, the damage distribution induced by the radiation follows a Poisson probability distribution. These two facts pose a difficult task to obtain the net counting rate in the exposed situations. It is possible to overcome this problem using a bayesian approach, in which the selection of a priori distributions for the background and net counting rate plays an important role. In the present work we make a detailed analysed using bayesian theory to infer the net counting rate in two different situations: a) when the background is known for an individual sample, using exact value value for the background and Jeffreys prior for the net counting rate, and b) when the background is not known and we make use of a population background distribution as background prior function and constant prior for the net counting rate. (Author)
Bayesian analysis of inflationary features in Planck and SDSS data
Benetti, Micol
2016-01-01
We perform a Bayesian analysis to study possible features in the primordial inflationary power spectrum of scalar perturbations. In particular, we analyse the possibility of detecting the imprint of these primordial features in the anisotropy temperature power spectrum of the Cosmic Microwave Background (CMB) and also in the matter power spectrum P (k). We use the most recent CMB data provided by the Planck Collaboration and P (k) measurements from the eleventh data release of the Sloan Digital Sky Survey. We focus our analysis on a class of potentials whose features are localised at different intervals of angular scales, corresponding to multipoles in the ranges 10 < l < 60 (Oscill-1) and 150 < l < 300 (Oscill-2). Our results show that one of the step-potentials (Oscill-1) provides a better fit to the CMB data than does the featureless LCDM scenario, with a moderate Bayesian evidence in favor of the former. Adding the P (k) data to the analysis weakens the evidence of the Oscill-1 potential relat...
AIC, BIC, Bayesian evidence against the interacting dark energy model
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.)