Actuarial statistics with generalized linear mixed models
Antonio, K.; Beirlant, J.
2007-01-01
Over the last decade the use of generalized linear models (GLMs) in actuarial statistics has received a lot of attention, starting from the actuarial illustrations in the standard text by McCullagh and Nelder [McCullagh, P., Nelder, J.A., 1989. Generalized linear models. In: Monographs on Statistics
Matrix Tricks for Linear Statistical Models
Puntanen, Simo; Styan, George PH
2011-01-01
In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and
Statistical Tests for Mixed Linear Models
Khuri, André I; Sinha, Bimal K
2011-01-01
An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these models a
Linear Mixed Models in Statistical Genetics
R. de Vlaming (Ronald)
2017-01-01
markdownabstractOne of the goals of statistical genetics is to elucidate the genetic architecture of phenotypes (i.e., observable individual characteristics) that are affected by many genetic variants (e.g., single-nucleotide polymorphisms; SNPs). A particular aim is to identify specific SNPs that
Introduction to statistical modelling: linear regression.
Lunt, Mark
2015-07-01
In many studies we wish to assess how a range of variables are associated with a particular outcome and also determine the strength of such relationships so that we can begin to understand how these factors relate to each other at a population level. Ultimately, we may also be interested in predicting the outcome from a series of predictive factors available at, say, a routine clinic visit. In a recent article in Rheumatology, Desai et al. did precisely that when they studied the prediction of hip and spine BMD from hand BMD and various demographic, lifestyle, disease and therapy variables in patients with RA. This article aims to introduce the statistical methodology that can be used in such a situation and explain the meaning of some of the terms employed. It will also outline some common pitfalls encountered when performing such analyses. © The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Linear mixed models a practical guide using statistical software
West, Brady T; Galecki, Andrzej T
2006-01-01
Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementation, model interpretation, and visualization of clustered and longitudinal data. This easy-to-navigate reference details the use of procedures for fitting LMMs in five popular statistical software packages: SAS, SPSS, Stata, R/S-plus, and HLM. The authors introduce basic theoretical concepts, present a heuristic approach to fitting LMMs based on bo
Multivariate statistical modelling based on generalized linear models
Fahrmeir, Ludwig
1994-01-01
This book is concerned with the use of generalized linear models for univariate and multivariate regression analysis. Its emphasis is to provide a detailed introductory survey of the subject based on the analysis of real data drawn from a variety of subjects including the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account to have on their desks. "The basic aim of the authors is to bring together and review a large part of recent advances in statistical modelling of m...
Linear mixed models a practical guide using statistical software
West, Brady T; Galecki, Andrzej T
2014-01-01
Highly recommended by JASA, Technometrics, and other journals, the first edition of this bestseller showed how to easily perform complex linear mixed model (LMM) analyses via a variety of software programs. Linear Mixed Models: A Practical Guide Using Statistical Software, Second Edition continues to lead readers step by step through the process of fitting LMMs. This second edition covers additional topics on the application of LMMs that are valuable for data analysts in all fields. It also updates the case studies using the latest versions of the software procedures and provides up-to-date information on the options and features of the software procedures available for fitting LMMs in SAS, SPSS, Stata, R/S-plus, and HLM.New to the Second Edition A new chapter on models with crossed random effects that uses a case study to illustrate software procedures capable of fitting these models Power analysis methods for longitudinal and clustered study designs, including software options for power analyses and suggest...
Huffman and linear scanning methods with statistical language models.
Roark, Brian; Fried-Oken, Melanie; Gibbons, Chris
2015-03-01
Current scanning access methods for text generation in AAC devices are limited to relatively few options, most notably row/column variations within a matrix. We present Huffman scanning, a new method for applying statistical language models to binary-switch, static-grid typing AAC interfaces, and compare it to other scanning options under a variety of conditions. We present results for 16 adults without disabilities and one 36-year-old man with locked-in syndrome who presents with complex communication needs and uses AAC scanning devices for writing. Huffman scanning with a statistical language model yielded significant typing speedups for the 16 participants without disabilities versus any of the other methods tested, including two row/column scanning methods. A similar pattern of results was found with the individual with locked-in syndrome. Interestingly, faster typing speeds were obtained with Huffman scanning using a more leisurely scan rate than relatively fast individually calibrated scan rates. Overall, the results reported here demonstrate great promise for the usability of Huffman scanning as a faster alternative to row/column scanning.
Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.
Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J
2016-10-03
Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.
Subset Statistics in the linear IV regression model
Kleibergen, F.R.
2005-01-01
We show that the limiting distributions of subset generalizations of the weak instrument robust instrumental variable statistics are boundedly similar when the remaining structural parameters are estimated using maximum likelihood. They are bounded from above by the limiting distributions which
An R2 statistic for fixed effects in the linear mixed model.
Edwards, Lloyd J; Muller, Keith E; Wolfinger, Russell D; Qaqish, Bahjat F; Schabenberger, Oliver
2008-12-20
Statisticians most often use the linear mixed model to analyze Gaussian longitudinal data. The value and familiarity of the R(2) statistic in the linear univariate model naturally creates great interest in extending it to the linear mixed model. We define and describe how to compute a model R(2) statistic for the linear mixed model by using only a single model. The proposed R(2) statistic measures multivariate association between the repeated outcomes and the fixed effects in the linear mixed model. The R(2) statistic arises as a 1-1 function of an appropriate F statistic for testing all fixed effects (except typically the intercept) in a full model. The statistic compares the full model with a null model with all fixed effects deleted (except typically the intercept) while retaining exactly the same covariance structure. Furthermore, the R(2) statistic leads immediately to a natural definition of a partial R(2) statistic. A mixed model in which ethnicity gives a very small p-value as a longitudinal predictor of blood pressure (BP) compellingly illustrates the value of the statistic. In sharp contrast to the extreme p-value, a very small R(2) , a measure of statistical and scientific importance, indicates that ethnicity has an almost negligible association with the repeated BP outcomes for the study.
Searle, Shayle R
2012-01-01
This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.
Hadronic equation of state in the statistical bootstrap model and linear graph theory
Fre, P.; Page, R.
1976-01-01
Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed
Linear mixed-effects models for central statistical monitoring of multicenter clinical trials
Desmet, L.; Venet, D.; Doffagne, E.; Timmermans, C.; BURZYKOWSKI, Tomasz; LEGRAND, Catherine; BUYSE, Marc
2014-01-01
Multicenter studies are widely used to meet accrual targets in clinical trials. Clinical data monitoring is required to ensure the quality and validity of the data gathered across centers. One approach to this end is central statistical monitoring, which aims at detecting atypical patterns in the data by means of statistical methods. In this context, we consider the simple case of a continuous variable, and we propose a detection procedure based on a linear mixed-effects model to detect locat...
Vajargah, Kianoush Fathi; Sadeghi-Bazargani, Homayoun; Mehdizadeh-Esfanjani, Robab; Savadi-Oskouei, Daryoush; Farhoudi, Mehdi
2012-01-01
The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.
Normality of raw data in general linear models: The most widespread myth in statistics
Kery, Marc; Hatfield, Jeff S.
2003-01-01
In years of statistical consulting for ecologists and wildlife biologists, by far the most common misconception we have come across has been the one about normality in general linear models. These comprise a very large part of the statistical models used in ecology and include t tests, simple and multiple linear regression, polynomial regression, and analysis of variance (ANOVA) and covariance (ANCOVA). There is a widely held belief that the normality assumption pertains to the raw data rather than to the model residuals. We suspect that this error may also occur in countless published studies, whenever the normality assumption is tested prior to analysis. This may lead to the use of nonparametric alternatives (if there are any), when parametric tests would indeed be appropriate, or to use of transformations of raw data, which may introduce hidden assumptions such as multiplicative effects on the natural scale in the case of log-transformed data. Our aim here is to dispel this myth. We very briefly describe relevant theory for two cases of general linear models to show that the residuals need to be normally distributed if tests requiring normality are to be used, such as t and F tests. We then give two examples demonstrating that the distribution of the response variable may be nonnormal, and yet the residuals are well behaved. We do not go into the issue of how to test normality; instead we display the distributions of response variables and residuals graphically.
Alfi, V.; Cristelli, M.; Pietronero, L.; Zaccaria, A.
2009-02-01
We present a detailed study of the statistical properties of the Agent Based Model introduced in paper I [Eur. Phys. J. B, DOI: 10.1140/epjb/e2009-00028-4] and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the stylized facts and their self-organization. The key elements are fundamentalist agents, chartist agents, herding dynamics and price behavior. The first two elements correspond to the competition between stability and instability tendencies in the market. The herding behavior governs the possibility of the agents to change strategy and it is a crucial element of this class of models. We consider a linear approximation for the price dynamics which permits a simple interpretation of the model dynamics and, for many properties, it is possible to derive analytical results. The generalized non linear dynamics results to be extremely more sensible to the parameter space and much more difficult to analyze and control. The main results for the nature and self-organization of the stylized facts are, however, very similar in the two cases. The main peculiarity of the non linear dynamics is an enhancement of the fluctuations and a more marked evidence of the stylized facts. We will also discuss some modifications of the model to introduce more realistic elements with respect to the real markets.
Canary, Jana D; Blizzard, Leigh; Barry, Ronald P; Hosmer, David W; Quinn, Stephen J
2016-05-01
Generalized linear models (GLM) with a canonical logit link function are the primary modeling technique used to relate a binary outcome to predictor variables. However, noncanonical links can offer more flexibility, producing convenient analytical quantities (e.g., probit GLMs in toxicology) and desired measures of effect (e.g., relative risk from log GLMs). Many summary goodness-of-fit (GOF) statistics exist for logistic GLM. Their properties make the development of GOF statistics relatively straightforward, but it can be more difficult under noncanonical links. Although GOF tests for logistic GLM with continuous covariates (GLMCC) have been applied to GLMCCs with log links, we know of no GOF tests in the literature specifically developed for GLMCCs that can be applied regardless of link function chosen. We generalize the Tsiatis GOF statistic originally developed for logistic GLMCCs, (TG), so that it can be applied under any link function. Further, we show that the algebraically related Hosmer-Lemeshow (HL) and Pigeon-Heyse (J(2) ) statistics can be applied directly. In a simulation study, TG, HL, and J(2) were used to evaluate the fit of probit, log-log, complementary log-log, and log models, all calculated with a common grouping method. The TG statistic consistently maintained Type I error rates, while those of HL and J(2) were often lower than expected if terms with little influence were included. Generally, the statistics had similar power to detect an incorrect model. An exception occurred when a log GLMCC was incorrectly fit to data generated from a logistic GLMCC. In this case, TG had more power than HL or J(2) . © 2015 John Wiley & Sons Ltd/London School of Economics.
Linear regression models and k-means clustering for statistical analysis of fNIRS data.
Bonomini, Viola; Zucchelli, Lucia; Re, Rebecca; Ieva, Francesca; Spinelli, Lorenzo; Contini, Davide; Paganoni, Anna; Torricelli, Alessandro
2015-02-01
We propose a new algorithm, based on a linear regression model, to statistically estimate the hemodynamic activations in fNIRS data sets. The main concern guiding the algorithm development was the minimization of assumptions and approximations made on the data set for the application of statistical tests. Further, we propose a K-means method to cluster fNIRS data (i.e. channels) as activated or not activated. The methods were validated both on simulated and in vivo fNIRS data. A time domain (TD) fNIRS technique was preferred because of its high performances in discriminating cortical activation and superficial physiological changes. However, the proposed method is also applicable to continuous wave or frequency domain fNIRS data sets.
Role of Statistical Random-Effects Linear Models in Personalized Medicine.
Diaz, Francisco J; Yeh, Hung-Wen; de Leon, Jose
2012-03-01
Some empirical studies and recent developments in pharmacokinetic theory suggest that statistical random-effects linear models are valuable tools that allow describing simultaneously patient populations as a whole and patients as individuals. This remarkable characteristic indicates that these models may be useful in the development of personalized medicine, which aims at finding treatment regimes that are appropriate for particular patients, not just appropriate for the average patient. In fact, published developments show that random-effects linear models may provide a solid theoretical framework for drug dosage individualization in chronic diseases. In particular, individualized dosages computed with these models by means of an empirical Bayesian approach may produce better results than dosages computed with some methods routinely used in therapeutic drug monitoring. This is further supported by published empirical and theoretical findings that show that random effects linear models may provide accurate representations of phase III and IV steady-state pharmacokinetic data, and may be useful for dosage computations. These models have applications in the design of clinical algorithms for drug dosage individualization in chronic diseases; in the computation of dose correction factors; computation of the minimum number of blood samples from a patient that are necessary for calculating an optimal individualized drug dosage in therapeutic drug monitoring; measure of the clinical importance of clinical, demographic, environmental or genetic covariates; study of drug-drug interactions in clinical settings; the implementation of computational tools for web-site-based evidence farming; design of pharmacogenomic studies; and in the development of a pharmacological theory of dosage individualization.
Lunt, Mark
2015-07-01
In the first article in this series we explored the use of linear regression to predict an outcome variable from a number of predictive factors. It assumed that the predictive factors were measured on an interval scale. However, this article shows how categorical variables can also be included in a linear regression model, enabling predictions to be made separately for different groups and allowing for testing the hypothesis that the outcome differs between groups. The use of interaction terms to measure whether the effect of a particular predictor variable differs between groups is also explained. An alternative approach to testing the difference between groups of the effect of a given predictor, which consists of measuring the effect in each group separately and seeing whether the statistical significance differs between the groups, is shown to be misleading. © The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
2017-12-08
STATISTICAL LINEAR TIME-VARYING SYSTEM MODEL OF HIGH GRAZING ANGLE SEA CLUTTER FOR COMPUTING INTERFERENCE POWER 1. INTRODUCTION Statistical linear time...beam. We can approximate one of the sinc factors using the Dirichlet kernel to facilitate computation of the integral in (6) as follows: ∣∣∣∣sinc(WB...plotted in Figure 4. The resultant autocorrelation can then be found by substituting (18) into (28). The Python code used to generate Figures 1-4 is found
Development of statistical linear regression model for metals from transportation land uses.
Maniquiz, Marla C; Lee, Soyoung; Lee, Eunju; Kim, Lee-Hyung
2009-01-01
The transportation landuses possessing impervious surfaces such as highways, parking lots, roads, and bridges were recognized as the highly polluted non-point sources (NPSs) in the urban areas. Lots of pollutants from urban transportation are accumulating on the paved surfaces during dry periods and are washed-off during a storm. In Korea, the identification and monitoring of NPSs still represent a great challenge. Since 2004, the Ministry of Environment (MOE) has been engaged in several researches and monitoring to develop stormwater management policies and treatment systems for future implementation. The data over 131 storm events during May 2004 to September 2008 at eleven sites were analyzed to identify correlation relationships between particulates and metals, and to develop simple linear regression (SLR) model to estimate event mean concentration (EMC). Results indicate that there was no significant relationship between metals and TSS EMC. However, the SLR estimation models although not providing useful results are valuable indicators of high uncertainties that NPS pollution possess. Therefore, long term monitoring employing proper methods and precise statistical analysis of the data should be undertaken to eliminate these uncertainties.
As a fast and effective technique, the multiple linear regression (MLR) method has been widely used in modeling and prediction of beach bacteria concentrations. Among previous works on this subject, however, several issues were insufficiently or inconsistently addressed. Those is...
Statistical properties of the linear σ model used in dynamical simulations of DCC formation
Randrup, J.
1997-01-01
The present work develops a simple approximate framework for initializing and interpreting dynamical simulations with the linear σ model exploring the formation of disoriented chiral condensates in high-energy collisions. By enclosing the system in a rectangular box with periodic boundary conditions, it is possible to decompose uniquely the chiral field into its spatial average (the order parameter) and its fluctuations (the quasiparticles) which can be treated in the Hartree approximation. The quasiparticle modes are then described approximately by Klein-Gordon dispersion relations containing an effective mass depending on both the temperature and the magnitude of the order parameter; their fluctuations are instrumental in shaping the effective potential governing the order parameter, and the emerging statistical description is thermodynamicially consistent. The temperature dependence of the statistical distribution of the order parameter is discussed, as is the behavior of the associated effective masses; as the system is cooled, the field fluctuations subside, causing a smooth change from the high-temperature phase in which chiral symmetry is approximately restored towards the normal phase. Of practical interest is the fact that the equilibrium field configurations can be sampled in a simple manner, thus providing a convenient means for specifying the initial conditions in dynamical simulations of the nonequilibrium relaxation of the chiral field; in particular, the correlation function is much more realistic than those emerging in previous initialization methods. It is illustrated how such samples remain approximately invariant under propagation by the unapproximated equation of motion over times that are long on the scale of interest, thereby suggesting that the treatment is sufficiently accurate to be of practical utility. copyright 1997 The American Physical Society
Valid statistical approaches for analyzing sholl data: Mixed effects versus simple linear models.
Wilson, Machelle D; Sethi, Sunjay; Lein, Pamela J; Keil, Kimberly P
2017-03-01
The Sholl technique is widely used to quantify dendritic morphology. Data from such studies, which typically sample multiple neurons per animal, are often analyzed using simple linear models. However, simple linear models fail to account for intra-class correlation that occurs with clustered data, which can lead to faulty inferences. Mixed effects models account for intra-class correlation that occurs with clustered data; thus, these models more accurately estimate the standard deviation of the parameter estimate, which produces more accurate p-values. While mixed models are not new, their use in neuroscience has lagged behind their use in other disciplines. A review of the published literature illustrates common mistakes in analyses of Sholl data. Analysis of Sholl data collected from Golgi-stained pyramidal neurons in the hippocampus of male and female mice using both simple linear and mixed effects models demonstrates that the p-values and standard deviations obtained using the simple linear models are biased downwards and lead to erroneous rejection of the null hypothesis in some analyses. The mixed effects approach more accurately models the true variability in the data set, which leads to correct inference. Mixed effects models avoid faulty inference in Sholl analysis of data sampled from multiple neurons per animal by accounting for intra-class correlation. Given the widespread practice in neuroscience of obtaining multiple measurements per subject, there is a critical need to apply mixed effects models more widely. Copyright © 2017 Elsevier B.V. All rights reserved.
The mixed linear model (MLM) is currently among the most advanced and flexible statistical modeling techniques and its use in tackling problems in plant pathology has begun surfacing in the literature. The longitudinal MLM is a multivariate extension that handles repeatedly measured data, such as r...
On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model
Unkel, Steffen; Belka, Claus; Lauber, Kirsten
2016-01-01
The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed
Foundations of linear and generalized linear models
Agresti, Alan
2015-01-01
A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,
Bayes linear statistics, theory & methods
Goldstein, Michael
2007-01-01
Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...
Faraway, Julian J
2014-01-01
A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition.New to the Second EditionReorganiz
Huppert, Theodore J
2016-01-01
Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Everson, Howard T.; And Others
This paper explores the feasibility of neural computing methods such as artificial neural networks (ANNs) and abductory induction mechanisms (AIM) for use in educational measurement. ANNs and AIMS methods are contrasted with more traditional statistical techniques, such as multiple regression and discriminant function analyses, for making…
Advanced statistics: linear regression, part II: multiple linear regression.
Marill, Keith A
2004-01-01
The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.
Introducing linear functions: an alternative statistical approach
Nolan, Caroline; Herbert, Sandra
2015-12-01
The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be `threshold concepts'. There is recognition that linear functions can be taught in context through the exploration of linear modelling examples, but this has its limitations. Currently, statistical data is easily attainable, and graphics or computer algebra system (CAS) calculators are common in many classrooms. The use of this technology provides ease of access to different representations of linear functions as well as the ability to fit a least-squares line for real-life data. This means these calculators could support a possible alternative approach to the introduction of linear functions. This study compares the results of an end-of-topic test for two classes of Australian middle secondary students at a regional school to determine if such an alternative approach is feasible. In this study, test questions were grouped by concept and subjected to concept by concept analysis of the means of test results of the two classes. This analysis revealed that the students following the alternative approach demonstrated greater competence with non-standard questions.
MIDAS: Regionally linear multivariate discriminative statistical mapping.
Varol, Erdem; Sotiras, Aristeidis; Davatzikos, Christos
2018-07-01
Statistical parametric maps formed via voxel-wise mass-univariate tests, such as the general linear model, are commonly used to test hypotheses about regionally specific effects in neuroimaging cross-sectional studies where each subject is represented by a single image. Despite being informative, these techniques remain limited as they ignore multivariate relationships in the data. Most importantly, the commonly employed local Gaussian smoothing, which is important for accounting for registration errors and making the data follow Gaussian distributions, is usually chosen in an ad hoc fashion. Thus, it is often suboptimal for the task of detecting group differences and correlations with non-imaging variables. Information mapping techniques, such as searchlight, which use pattern classifiers to exploit multivariate information and obtain more powerful statistical maps, have become increasingly popular in recent years. However, existing methods may lead to important interpretation errors in practice (i.e., misidentifying a cluster as informative, or failing to detect truly informative voxels), while often being computationally expensive. To address these issues, we introduce a novel efficient multivariate statistical framework for cross-sectional studies, termed MIDAS, seeking highly sensitive and specific voxel-wise brain maps, while leveraging the power of regional discriminant analysis. In MIDAS, locally linear discriminative learning is applied to estimate the pattern that best discriminates between two groups, or predicts a variable of interest. This pattern is equivalent to local filtering by an optimal kernel whose coefficients are the weights of the linear discriminant. By composing information from all neighborhoods that contain a given voxel, MIDAS produces a statistic that collectively reflects the contribution of the voxel to the regional classifiers as well as the discriminative power of the classifiers. Critically, MIDAS efficiently assesses the
International Conference on Trends and Perspectives in Linear Statistical Inference
Rosen, Dietrich
2018-01-01
This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference. .
Lloyd-Jones, Luke R; Robinson, Matthew R; Yang, Jian; Visscher, Peter M
2018-04-01
Genome-wide association studies (GWAS) have identified thousands of loci that are robustly associated with complex diseases. The use of linear mixed model (LMM) methodology for GWAS is becoming more prevalent due to its ability to control for population structure and cryptic relatedness and to increase power. The odds ratio (OR) is a common measure of the association of a disease with an exposure ( e.g. , a genetic variant) and is readably available from logistic regression. However, when the LMM is applied to all-or-none traits it provides estimates of genetic effects on the observed 0-1 scale, a different scale to that in logistic regression. This limits the comparability of results across studies, for example in a meta-analysis, and makes the interpretation of the magnitude of an effect from an LMM GWAS difficult. In this study, we derived transformations from the genetic effects estimated under the LMM to the OR that only rely on summary statistics. To test the proposed transformations, we used real genotypes from two large, publicly available data sets to simulate all-or-none phenotypes for a set of scenarios that differ in underlying model, disease prevalence, and heritability. Furthermore, we applied these transformations to GWAS summary statistics for type 2 diabetes generated from 108,042 individuals in the UK Biobank. In both simulation and real-data application, we observed very high concordance between the transformed OR from the LMM and either the simulated truth or estimates from logistic regression. The transformations derived and validated in this study improve the comparability of results from prospective and already performed LMM GWAS on complex diseases by providing a reliable transformation to a common comparative scale for the genetic effects. Copyright © 2018 by the Genetics Society of America.
Alexandrowicz, Rainer W; Jahn, Rebecca; Friedrich, Fabian; Unger, Anne
2016-06-01
Various studies have shown that caregiving relatives of schizophrenic patients are at risk of suffering from depression. These studies differ with respect to the applied statistical methods, which could influence the findings. Therefore, the present study analyzes to which extent different methods may cause differing results. The present study contrasts by means of one data set the results of three different modelling approaches, Rasch Modelling (RM), Structural Equation Modelling (SEM), and Linear Regression Modelling (LRM). The results of the three models varied considerably, reflecting the different assumptions of the respective models. Latent trait models (i. e., RM and SEM) generally provide more convincing results by correcting for measurement error and the RM specifically proves superior for it treats ordered categorical data most adequately.
Introduction to generalized linear models
Dobson, Annette J
2008-01-01
Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions ...
Diffeomorphic Statistical Deformation Models
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...... with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes....
Advanced statistics: linear regression, part I: simple linear regression.
Marill, Keith A
2004-01-01
Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.
Statistical monitoring of linear antenna arrays
Harrou, Fouzi
2016-11-03
The paper concerns the problem of monitoring linear antenna arrays using the generalized likelihood ratio (GLR) test. When an abnormal event (fault) affects an array of antenna elements, the radiation pattern changes and significant deviation from the desired design performance specifications can resulted. In this paper, the detection of faults is addressed from a statistical point of view as a fault detection problem. Specifically, a statistical method rested on the GLR principle is used to detect potential faults in linear arrays. To assess the strength of the GLR-based monitoring scheme, three case studies involving different types of faults were performed. Simulation results clearly shown the effectiveness of the GLR-based fault-detection method to monitor the performance of linear antenna arrays.
Generalized, Linear, and Mixed Models
McCulloch, Charles E; Neuhaus, John M
2011-01-01
An accessible and self-contained introduction to statistical models-now in a modernized new editionGeneralized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects.A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed m
E. Baümler
2014-06-01
Full Text Available In this study the kinetics of oil extraction from partially dehulled safflower seeds under two moisture conditions (7 and 9% dry basis was investigated. The extraction assays were performed using a stirred batch system, thermostated at 50 ºC, using n-hexane as solvent. The data obtained were fitted to a modified diffusion model in order to represent the extraction kinetics. The model took into account a washing and a diffusive step. Fitting parameters were compared statistically for both moisture conditions. The oil yield increased with the extraction time in both cases, although the oil was released at different rates. A comparison of the parameters showed that both the portion extracted in the washing phase and the effective diffusion coefficient were moisture-dependent. The effective diffusivities were 2.81 10-12 and 8.06 10-13 m²s-1 for moisture contents of 7% and 9%, respectively.
Amano, Ken-Ichi; Yoshidome, Takashi; Iwaki, Mitsuhiro; Suzuki, Makoto; Kinoshita, Masahiro
2010-07-28
We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1
Farooq Ahmed Arain
2012-01-01
Full Text Available The aim of this study was to develop a statistical model for the effect of RS (Rotor Speed, YT (Yarn Twist and YLD (Yarn Linear Density on production and quality characteristics of rotor spun yarn. Cotton yarns of 30, 35 and 40 tex were produced on rotor spinning machine at different rotor speeds (i.e. 70000, 80000, 90000 and 100000 rpm and with different twist levels (i.e. 450, 500, 550, 600 and 700 tpm. Yarn production (g/hr and quality characteristics were determined for all the experiments. Based on the results, models were developed using response surface regression on MINITAB�16 statistical tool. The developed models not only characterize the intricate relationships among the factors but may also be used to predict the yarn production and quality characteristics at any level of factors within the range of experimental values.
Høskuldsson, Agnar
1996-01-01
Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four of these cri......Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four...... the basic problems in determining the dimension of linear models. Then each of the eight measures are treated. The results are illustrated by examples....
Introducing Linear Functions: An Alternative Statistical Approach
Nolan, Caroline; Herbert, Sandra
2015-01-01
The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be "threshold concepts". There is recognition that linear functions can be taught in context through the exploration of linear…
Matrix algebra for linear models
Gruber, Marvin H J
2013-01-01
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f
Høskuldsson, Agnar
1996-01-01
Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four...... the basic problems in determining the dimension of linear models. Then each of the eight measures are treated. The results are illustrated by examples....... of these criteria are widely used ones, while the remaining four are ones derived from the H-principle of mathematical modeling. Many examples from practice show that the criteria derived from the H-principle function better than the known and popular criteria for the number of components. We shall briefly review...
Statistical monitoring of linear antenna arrays
Harrou, Fouzi; Sun, Ying
2016-01-01
The paper concerns the problem of monitoring linear antenna arrays using the generalized likelihood ratio (GLR) test. When an abnormal event (fault) affects an array of antenna elements, the radiation pattern changes and significant deviation from
Non linear viscoelastic models
Agerkvist, Finn T.
2011-01-01
Viscoelastic eects are often present in loudspeaker suspensions, this can be seen in the displacement transfer function which often shows a frequency dependent value below the resonance frequency. In this paper nonlinear versions of the standard linear solid model (SLS) are investigated....... The simulations show that the nonlinear version of the Maxwell SLS model can result in a time dependent small signal stiness while the Kelvin Voight version does not....
Composite Linear Models | Division of Cancer Prevention
By Stuart G. Baker The composite linear models software is a matrix approach to compute maximum likelihood estimates and asymptotic standard errors for models for incomplete multinomial data. It implements the method described in Baker SG. Composite linear models for incomplete multinomial data. Statistics in Medicine 1994;13:609-622. The software includes a library of thirty
Sampling, Probability Models and Statistical Reasoning Statistical
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Sampling, Probability Models and Statistical Reasoning Statistical Inference. Mohan Delampady V R Padmawar. General Article Volume 1 Issue 5 May 1996 pp 49-58 ...
H. Apel
2018-04-01
Full Text Available The semi-arid regions of Central Asia crucially depend on the water resources supplied by the mountainous areas of the Tien Shan and Pamir and Altai mountains. During the summer months the snow-melt- and glacier-melt-dominated river discharge originating in the mountains provides the main water resource available for agricultural production, but also for storage in reservoirs for energy generation during the winter months. Thus a reliable seasonal forecast of the water resources is crucial for sustainable management and planning of water resources. In fact, seasonal forecasts are mandatory tasks of all national hydro-meteorological services in the region. In order to support the operational seasonal forecast procedures of hydro-meteorological services, this study aims to develop a generic tool for deriving statistical forecast models of seasonal river discharge based solely on observational records. The generic model structure is kept as simple as possible in order to be driven by meteorological and hydrological data readily available at the hydro-meteorological services, and to be applicable for all catchments in the region. As snow melt dominates summer runoff, the main meteorological predictors for the forecast models are monthly values of winter precipitation and temperature, satellite-based snow cover data, and antecedent discharge. This basic predictor set was further extended by multi-monthly means of the individual predictors, as well as composites of the predictors. Forecast models are derived based on these predictors as linear combinations of up to four predictors. A user-selectable number of the best models is extracted automatically by the developed model fitting algorithm, which includes a test for robustness by a leave-one-out cross-validation. Based on the cross-validation the predictive uncertainty was quantified for every prediction model. Forecasts of the mean seasonal discharge of the period April to September are derived
Apel, Heiko; Abdykerimova, Zharkinay; Agalhanova, Marina; Baimaganbetov, Azamat; Gavrilenko, Nadejda; Gerlitz, Lars; Kalashnikova, Olga; Unger-Shayesteh, Katy; Vorogushyn, Sergiy; Gafurov, Abror
2018-04-01
The semi-arid regions of Central Asia crucially depend on the water resources supplied by the mountainous areas of the Tien Shan and Pamir and Altai mountains. During the summer months the snow-melt- and glacier-melt-dominated river discharge originating in the mountains provides the main water resource available for agricultural production, but also for storage in reservoirs for energy generation during the winter months. Thus a reliable seasonal forecast of the water resources is crucial for sustainable management and planning of water resources. In fact, seasonal forecasts are mandatory tasks of all national hydro-meteorological services in the region. In order to support the operational seasonal forecast procedures of hydro-meteorological services, this study aims to develop a generic tool for deriving statistical forecast models of seasonal river discharge based solely on observational records. The generic model structure is kept as simple as possible in order to be driven by meteorological and hydrological data readily available at the hydro-meteorological services, and to be applicable for all catchments in the region. As snow melt dominates summer runoff, the main meteorological predictors for the forecast models are monthly values of winter precipitation and temperature, satellite-based snow cover data, and antecedent discharge. This basic predictor set was further extended by multi-monthly means of the individual predictors, as well as composites of the predictors. Forecast models are derived based on these predictors as linear combinations of up to four predictors. A user-selectable number of the best models is extracted automatically by the developed model fitting algorithm, which includes a test for robustness by a leave-one-out cross-validation. Based on the cross-validation the predictive uncertainty was quantified for every prediction model. Forecasts of the mean seasonal discharge of the period April to September are derived every month from
Monahan, John F
2008-01-01
Preface Examples of the General Linear Model Introduction One-Sample Problem Simple Linear Regression Multiple Regression One-Way ANOVA First Discussion The Two-Way Nested Model Two-Way Crossed Model Analysis of Covariance Autoregression Discussion The Linear Least Squares Problem The Normal Equations The Geometry of Least Squares Reparameterization Gram-Schmidt Orthonormalization Estimability and Least Squares Estimators Assumptions for the Linear Mean Model Confounding, Identifiability, and Estimability Estimability and Least Squares Estimators F
Faraway, Julian J
2005-01-01
Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway''s critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author''s treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the ...
Campagnoli, Patrizia; Petris, Giovanni
2009-01-01
State space models have gained tremendous popularity in as disparate fields as engineering, economics, genetics and ecology. Introducing general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. It illustrates the fundamental steps needed to use dynamic linear models in practice, using R package.
(Non) linear regression modelling
Cizek, P.; Gentle, J.E.; Hardle, W.K.; Mori, Y.
2012-01-01
We will study causal relationships of a known form between random variables. Given a model, we distinguish one or more dependent (endogenous) variables Y = (Y1,…,Yl), l ∈ N, which are explained by a model, and independent (exogenous, explanatory) variables X = (X1,…,Xp),p ∈ N, which explain or
Distributed Monitoring of the R2 Statistic for Linear Regression
National Aeronautics and Space Administration — The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and...
Testing Parametric versus Semiparametric Modelling in Generalized Linear Models
Härdle, W.K.; Mammen, E.; Müller, M.D.
1996-01-01
We consider a generalized partially linear model E(Y|X,T) = G{X'b + m(T)} where G is a known function, b is an unknown parameter vector, and m is an unknown function.The paper introduces a test statistic which allows to decide between a parametric and a semiparametric model: (i) m is linear, i.e.
Correlations and Non-Linear Probability Models
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Explorative methods in linear models
Høskuldsson, Agnar
2004-01-01
The author has developed the H-method of mathematical modeling that builds up the model by parts, where each part is optimized with respect to prediction. Besides providing with better predictions than traditional methods, these methods provide with graphic procedures for analyzing different feat...... features in data. These graphic methods extend the well-known methods and results of Principal Component Analysis to any linear model. Here the graphic procedures are applied to linear regression and Ridge Regression....
Takada, Akitsugu; Katashima, Masataka; Kaibara, Atsunori; Sawamoto, Taiji; Zhang, Wenhui; Keirns, James
2014-09-01
Amenamevir is the international non-proprietary name for ASP2151 synthesized by Astellas Pharma, Inc. It is a structurally novel class of helicase-primase inhibitor and demonstrated more potency in vitro anti-viral activity with low cytotoxicity against varicella-zoster virus (VZV), herpes simplex virus type 1 (HSV-1), and herpes simplex virus type 2 (HSV-2) than acyclovir (ACV). Phase II randomized trial assessed the safety and efficacy of ASP2151 for episodic therapy of recurrent genital herpes was conducted. Participants self-initiated with ASP2151 (100, 200, or 400 mg daily for 3 days), ASP2151 (1,200 mg as a single dose), placebo for 3 days, or Valacyclovir (500 mg twice daily for 3 days). We present a first population pharmacokinetic (PPK) modeling analysis of Amenamevir for genital herpes patients. The final model retained the effect of Weight and Albumin on CL. Statistical analysis between pharmacokinetics and clinical efficacies was done by using the time above 200 ng/mL (T200 ). T200 derived from the final PPK model to consider the correlation with Time to lesion healing and viral shedding. This finding suggested that it could be necessary to maintain the Amenamevir concentration above the threshold level to prevent the virus replication. © 2014, The American College of Clinical Pharmacology.
Sparse Linear Identifiable Multivariate Modeling
Henao, Ricardo; Winther, Ole
2011-01-01
and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable......In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully...
Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul
2011-08-22
We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.
Parameterized Linear Longitudinal Airship Model
Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph
2010-01-01
A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics
Exclusion statistics and integrable models
Mashkevich, S.
1998-01-01
The definition of exclusion statistics, as given by Haldane, allows for a statistical interaction between distinguishable particles (multi-species statistics). The thermodynamic quantities for such statistics ca be evaluated exactly. The explicit expressions for the cluster coefficients are presented. Furthermore, single-species exclusion statistics is realized in one-dimensional integrable models. The interesting questions of generalizing this correspondence onto the higher-dimensional and the multi-species cases remain essentially open
Statistical Model-Based Face Pose Estimation
GE Xinliang; YANG Jie; LI Feng; WANG Huahua
2007-01-01
A robust face pose estimation approach is proposed by using face shape statistical model approach and pose parameters are represented by trigonometric functions. The face shape statistical model is firstly built by analyzing the face shapes from different people under varying poses. The shape alignment is vital in the process of building the statistical model. Then, six trigonometric functions are employed to represent the face pose parameters. Lastly, the mapping function is constructed between face image and face pose by linearly relating different parameters. The proposed approach is able to estimate different face poses using a few face training samples. Experimental results are provided to demonstrate its efficiency and accuracy.
Exclusion statistics and integrable models
Mashkevich, S.
1998-01-01
The definition of exclusion statistics that was given by Haldane admits a 'statistical interaction' between distinguishable particles (multispecies statistics). For such statistics, thermodynamic quantities can be evaluated exactly; explicit expressions are presented here for cluster coefficients. Furthermore, single-species exclusion statistics is realized in one-dimensional integrable models of the Calogero-Sutherland type. The interesting questions of generalizing this correspondence to the higher-dimensional and the multispecies cases remain essentially open; however, our results provide some hints as to searches for the models in question
Decomposable log-linear models
Eriksen, Poul Svante
can be characterized by a structured set of conditional independencies between some variables given some other variables. We term the new model class decomposable log-linear models, which is illustrated to be a much richer class than decomposable graphical models.It covers a wide range of non...... The present paper considers discrete probability models with exact computational properties. In relation to contingency tables this means closed form expressions of the maksimum likelihood estimate and its distribution. The model class includes what is known as decomposable graphicalmodels, which......-hierarchical models, models with structural zeroes, models described by quasi independence and models for level merging. Also, they have a very natural interpretation as they may be formulated by a structured set of conditional independencies between two events given some other event. In relation to contingency...
Linear and Generalized Linear Mixed Models and Their Applications
Jiang, Jiming
2007-01-01
This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested
(ajst) statistical mechanics model for orientational
Science and Engineering Series Vol. 6, No. 2, pp. 94 - 101. STATISTICAL MECHANICS MODEL FOR ORIENTATIONAL. MOTION OF TWO-DIMENSIONAL RIGID ROTATOR. Malo, J.O. ... there is no translational motion and that they are well separated so .... constant and I is the moment of inertia of a linear rotator. Thus, the ...
Statistical Model Checking for Biological Systems
David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel
2014-01-01
Statistical Model Checking (SMC) is a highly scalable simulation-based verification approach for testing and estimating the probability that a stochastic system satisfies a given linear temporal property. The technique has been applied to (discrete and continuous time) Markov chains, stochastic...
Statistical Model of Extreme Shear
Larsen, Gunner Chr.; Hansen, Kurt Schaldemose
2004-01-01
In order to continue cost-optimisation of modern large wind turbines, it is important to continously increase the knowledge on wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... by a model that, on a statistically consistent basis, describe the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of high-sampled full-scale time series measurements...... are consistent, given the inevitabel uncertainties associated with model as well as with the extreme value data analysis. Keywords: Statistical model, extreme wind conditions, statistical analysis, turbulence, wind loading, statistical analysis, turbulence, wind loading, wind shear, wind turbines....
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael
2017-07-01
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
A comparison of linear and nonlinear statistical techniques in performance attribution.
Chan, N H; Genovese, C R
2001-01-01
Performance attribution is usually conducted under the linear framework of multifactor models. Although commonly used by practitioners in finance, linear multifactor models are known to be less than satisfactory in many situations. After a brief survey of nonlinear methods, nonlinear statistical techniques are applied to performance attribution of a portfolio constructed from a fixed universe of stocks using factors derived from some commonly used cross sectional linear multifactor models. By rebalancing this portfolio monthly, the cumulative returns for procedures based on standard linear multifactor model and three nonlinear techniques-model selection, additive models, and neural networks-are calculated and compared. It is found that the first two nonlinear techniques, especially in combination, outperform the standard linear model. The results in the neural-network case are inconclusive because of the great variety of possible models. Although these methods are more complicated and may require some tuning, toolboxes are developed and suggestions on calibration are proposed. This paper demonstrates the usefulness of modern nonlinear statistical techniques in performance attribution.
Statistical modeling for degradation data
Lio, Yuhlong; Ng, Hon; Tsai, Tzong-Ru
2017-01-01
This book focuses on the statistical aspects of the analysis of degradation data. In recent years, degradation data analysis has come to play an increasingly important role in different disciplines such as reliability, public health sciences, and finance. For example, information on products’ reliability can be obtained by analyzing degradation data. In addition, statistical modeling and inference techniques have been developed on the basis of different degradation measures. The book brings together experts engaged in statistical modeling and inference, presenting and discussing important recent advances in degradation data analysis and related applications. The topics covered are timely and have considerable potential to impact both statistics and reliability engineering.
Multicollinearity in hierarchical linear models.
Yu, Han; Jiang, Shanhe; Land, Kenneth C
2015-09-01
This study investigates an ill-posed problem (multicollinearity) in Hierarchical Linear Models from both the data and the model perspectives. We propose an intuitive, effective approach to diagnosing the presence of multicollinearity and its remedies in this class of models. A simulation study demonstrates the impacts of multicollinearity on coefficient estimates, associated standard errors, and variance components at various levels of multicollinearity for finite sample sizes typical in social science studies. We further investigate the role multicollinearity plays at each level for estimation of coefficient parameters in terms of shrinkage. Based on these analyses, we recommend a top-down method for assessing multicollinearity in HLMs that first examines the contextual predictors (Level-2 in a two-level model) and then the individual predictors (Level-1) and uses the results for data collection, research problem redefinition, model re-specification, variable selection and estimation of a final model. Copyright © 2015 Elsevier Inc. All rights reserved.
Statistical modelling with quantile functions
Gilchrist, Warren
2000-01-01
Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics.Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data.Statistical Modelling with Quantile Functions adds a new dimension to the practice of stati...
Modelling Loudspeaker Non-Linearities
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
A Statistical Programme Assignment Model
Rosholm, Michael; Staghøj, Jonas; Svarer, Michael
When treatment effects of active labour market programmes are heterogeneous in an observable way across the population, the allocation of the unemployed into different programmes becomes a particularly important issue. In this paper, we present a statistical model designed to improve the present...... duration of unemployment spells may result if a statistical programme assignment model is introduced. We discuss several issues regarding the plementation of such a system, especially the interplay between the statistical model and case workers....
Multivariate covariance generalized linear models
Bonat, W. H.; Jørgensen, Bent
2016-01-01
are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions......We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...
Bearing Fault Diagnosis Based on Statistical Locally Linear Embedding.
Wang, Xiang; Zheng, Yuan; Zhao, Zhenzhou; Wang, Jinping
2015-07-06
Fault diagnosis is essentially a kind of pattern recognition. The measured signal samples usually distribute on nonlinear low-dimensional manifolds embedded in the high-dimensional signal space, so how to implement feature extraction, dimensionality reduction and improve recognition performance is a crucial task. In this paper a novel machinery fault diagnosis approach based on a statistical locally linear embedding (S-LLE) algorithm which is an extension of LLE by exploiting the fault class label information is proposed. The fault diagnosis approach first extracts the intrinsic manifold features from the high-dimensional feature vectors which are obtained from vibration signals that feature extraction by time-domain, frequency-domain and empirical mode decomposition (EMD), and then translates the complex mode space into a salient low-dimensional feature space by the manifold learning algorithm S-LLE, which outperforms other feature reduction methods such as PCA, LDA and LLE. Finally in the feature reduction space pattern classification and fault diagnosis by classifier are carried out easily and rapidly. Rolling bearing fault signals are used to validate the proposed fault diagnosis approach. The results indicate that the proposed approach obviously improves the classification performance of fault pattern recognition and outperforms the other traditional approaches.
Identification of Influential Points in a Linear Regression Model
Jan Grosz
2011-03-01
Full Text Available The article deals with the detection and identification of influential points in the linear regression model. Three methods of detection of outliers and leverage points are described. These procedures can also be used for one-sample (independentdatasets. This paper briefly describes theoretical aspects of several robust methods as well. Robust statistics is a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. A simulation model of the simple linear regression is presented.
Foster, Guy M.; Graham, Jennifer L.
2016-04-06
The Kansas River is a primary source of drinking water for about 800,000 people in northeastern Kansas. Source-water supplies are treated by a combination of chemical and physical processes to remove contaminants before distribution. Advanced notification of changing water-quality conditions and cyanobacteria and associated toxin and taste-and-odor compounds provides drinking-water treatment facilities time to develop and implement adequate treatment strategies. The U.S. Geological Survey (USGS), in cooperation with the Kansas Water Office (funded in part through the Kansas State Water Plan Fund), and the City of Lawrence, the City of Topeka, the City of Olathe, and Johnson County Water One, began a study in July 2012 to develop statistical models at two Kansas River sites located upstream from drinking-water intakes. Continuous water-quality monitors have been operated and discrete-water quality samples have been collected on the Kansas River at Wamego (USGS site number 06887500) and De Soto (USGS site number 06892350) since July 2012. Continuous and discrete water-quality data collected during July 2012 through June 2015 were used to develop statistical models for constituents of interest at the Wamego and De Soto sites. Logistic models to continuously estimate the probability of occurrence above selected thresholds were developed for cyanobacteria, microcystin, and geosmin. Linear regression models to continuously estimate constituent concentrations were developed for major ions, dissolved solids, alkalinity, nutrients (nitrogen and phosphorus species), suspended sediment, indicator bacteria (Escherichia coli, fecal coliform, and enterococci), and actinomycetes bacteria. These models will be used to provide real-time estimates of the probability that cyanobacteria and associated compounds exceed thresholds and of the concentrations of other water-quality constituents in the Kansas River. The models documented in this report are useful for characterizing changes
Statistical modeling of Earth's plasmasphere
Veibell, Victoir
The behavior of plasma near Earth's geosynchronous orbit is of vital importance to both satellite operators and magnetosphere modelers because it also has a significant influence on energy transport, ion composition, and induced currents. The system is highly complex in both time and space, making the forecasting of extreme space weather events difficult. This dissertation examines the behavior and statistical properties of plasma mass density near geosynchronous orbit by using both linear and nonlinear models, as well as epoch analyses, in an attempt to better understand the physical processes that precipitates and drives its variations. It is shown that while equatorial mass density does vary significantly on an hourly timescale when a drop in the disturbance time scale index ( Dst) was observed, it does not vary significantly between the day of a Dst event onset and the day immediately following. It is also shown that increases in equatorial mass density were not, on average, preceded or followed by any significant change in the examined solar wind or geomagnetic variables, including Dst, despite prior results that considered a few selected events and found a notable influence. It is verified that equatorial mass density and and solar activity via the F10.7 index have a strong correlation, which is stronger over longer timescales such as 27 days than it is over an hourly timescale. It is then shown that this connection seems to affect the behavior of equatorial mass density most during periods of strong solar activity leading to large mass density reactions to Dst drops for high values of F10.7. It is also shown that equatorial mass density behaves differently before and after events based on the value of F10.7 at the onset of an equatorial mass density event or a Dst event, and that a southward interplanetary magnetic field at onset leads to slowed mass density growth after event onset. These behavioral differences provide insight into how solar and geomagnetic
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
Statistical Model of Extreme Shear
Hansen, Kurt Schaldemose; Larsen, Gunner Chr.
2005-01-01
In order to continue cost-optimisation of modern large wind turbines, it is important to continuously increase the knowledge of wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... by a model that, on a statistically consistent basis, describes the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of full-scale measurements recorded with a high sampling rate...
Statistical Models for Social Networks
Snijders, Tom A. B.; Cook, KS; Massey, DS
2011-01-01
Statistical models for social networks as dependent variables must represent the typical network dependencies between tie variables such as reciprocity, homophily, transitivity, etc. This review first treats models for single (cross-sectionally observed) networks and then for network dynamics. For
Statistical mechanical analysis of the linear vector channel in digital communication
Takeda, Koujin; Hatabu, Atsushi; Kabashima, Yoshiyuki
2007-01-01
A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in Takeda et al (2006 Europhys. Lett. 76 1193) and enables the analysis of the system in which the elements of the channel transfer matrix are statistically correlated with each other. The significance of the proposed scheme is demonstrated by assessing the performance of an existing model of multi-input multi-output communication systems
Sensometrics: Thurstonian and Statistical Models
Christensen, Rune Haubo Bojesen
. sensR is a package for sensory discrimination testing with Thurstonian models and ordinal supports analysis of ordinal data with cumulative link (mixed) models. While sensR is closely connected to the sensometrics field, the ordinal package has developed into a generic statistical package applicable......This thesis is concerned with the development and bridging of Thurstonian and statistical models for sensory discrimination testing as applied in the scientific discipline of sensometrics. In sensory discrimination testing sensory differences between products are detected and quantified by the use...... and sensory discrimination testing in particular in a series of papers by advancing Thurstonian models for a range of sensory discrimination protocols in addition to facilitating their application by providing software for fitting these models. The main focus is on identifying Thurstonian models...
Nonabelian Gauged Linear Sigma Model
Yongbin RUAN
2017-01-01
The gauged linear sigma model (GLSM for short) is a 2d quantum field theory introduced by Witten twenty years ago.Since then,it has been investigated extensively in physics by Hori and others.Recently,an algebro-geometric theory (for both abelian and nonabelian GLSMs) was developed by the author and his collaborators so that he can start to rigorously compute its invariants and check against physical predications.The abelian GLSM was relatively better understood and is the focus of current mathematical investigation.In this article,the author would like to look over the horizon and consider the nonabelian GLSM.The nonabelian case possesses some new features unavailable to the abelian GLSM.To aid the future mathematical development,the author surveys some of the key problems inspired by physics in the nonabelian GLSM.
Jackknife Variance Estimator for Two Sample Linear Rank Statistics
1988-11-01
Accesion For - - ,NTIS GPA&I "TIC TAB Unann c, nc .. [d Keywords: strong consistency; linear rank test’ influence function . i , at L By S- )Distribut...reverse if necessary and identify by block number) FIELD IGROUP SUB-GROUP Strong consistency; linear rank test; influence function . 19. ABSTRACT
Classical model of intermediate statistics
Kaniadakis, G.
1994-01-01
In this work we present a classical kinetic model of intermediate statistics. In the case of Brownian particles we show that the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions can be obtained, just as the Maxwell-Boltzmann (MD) distribution, as steady states of a classical kinetic equation that intrinsically takes into account an exclusion-inclusion principle. In our model the intermediate statistics are obtained as steady states of a system of coupled nonlinear kinetic equations, where the coupling constants are the transmutational potentials η κκ' . We show that, besides the FD-BE intermediate statistics extensively studied from the quantum point of view, we can also study the MB-FD and MB-BE ones. Moreover, our model allows us to treat the three-state mixing FD-MB-BE intermediate statistics. For boson and fermion mixing in a D-dimensional space, we obtain a family of FD-BE intermediate statistics by varying the transmutational potential η BF . This family contains, as a particular case when η BF =0, the quantum statistics recently proposed by L. Wu, Z. Wu, and J. Sun [Phys. Lett. A 170, 280 (1992)]. When we consider the two-dimensional FD-BE statistics, we derive an analytic expression of the fraction of fermions. When the temperature T→∞, the system is composed by an equal number of bosons and fermions, regardless of the value of η BF . On the contrary, when T=0, η BF becomes important and, according to its value, the system can be completely bosonic or fermionic, or composed both by bosons and fermions
Linear mixed models in sensometrics
Kuznetsova, Alexandra
quality of decision making in Danish as well as international food companies and other companies using the same methods. The two open-source R packages lmerTest and SensMixed implement and support the methodological developments in the research papers as well as the ANOVA modelling part of the Consumer...... an open-source software tool ConsumerCheck was developed in this project and now is available for everyone. will represent a major step forward when concerns this important problem in modern consumer driven product development. Standard statistical software packages can be used for some of the purposes......Today’s companies and researchers gather large amounts of data of different kind. In consumer studies the objective is the collection of the data to better understand consumer acceptance of products. In such studies a number of persons (generally not trained) are selected in order to score products...
Textual information access statistical models
Gaussier, Eric
2013-01-01
This book presents statistical models that have recently been developed within several research communities to access information contained in text collections. The problems considered are linked to applications aiming at facilitating information access:- information extraction and retrieval;- text classification and clustering;- opinion mining;- comprehension aids (automatic summarization, machine translation, visualization).In order to give the reader as complete a description as possible, the focus is placed on the probability models used in the applications
Thurstonian models for sensory discrimination tests as generalized linear models
Brockhoff, Per B.; Christensen, Rune Haubo Bojesen
2010-01-01
as a so-called generalized linear model. The underlying sensory difference 6 becomes directly a parameter of the statistical model and the estimate d' and it's standard error becomes the "usual" output of the statistical analysis. The d' for the monadic A-NOT A method is shown to appear as a standard......Sensory discrimination tests such as the triangle, duo-trio, 2-AFC and 3-AFC tests produce binary data and the Thurstonian decision rule links the underlying sensory difference 6 to the observed number of correct responses. In this paper it is shown how each of these four situations can be viewed...
Improved model for statistical alignment
Miklos, I.; Toroczkai, Z. (Zoltan)
2001-01-01
The statistical approach to molecular sequence evolution involves the stochastic modeling of the substitution, insertion and deletion processes. Substitution has been modeled in a reliable way for more than three decades by using finite Markov-processes. Insertion and deletion, however, seem to be more difficult to model, and thc recent approaches cannot acceptably deal with multiple insertions and deletions. A new method based on a generating function approach is introduced to describe the multiple insertion process. The presented algorithm computes the approximate joint probability of two sequences in 0(13) running time where 1 is the geometric mean of the sequence lengths.
Statistical models of petrol engines vehicles dynamics
Ilie, C. O.; Marinescu, M.; Alexa, O.; Vilău, R.; Grosu, D.
2017-10-01
This paper focuses on studying statistical models of vehicles dynamics. It was design and perform a one year testing program. There were used many same type cars with gasoline engines and different mileage. Experimental data were collected of onboard sensors and those on the engine test stand. A database containing data of 64th tests was created. Several mathematical modelling were developed using database and the system identification method. Each modelling is a SISO or a MISO linear predictive ARMAX (AutoRegressive-Moving-Average with eXogenous inputs) model. It represents a differential equation with constant coefficients. It were made 64th equations for each dependency like engine torque as output and engine’s load and intake manifold pressure, as inputs. There were obtained strings with 64 values for each type of model. The final models were obtained using average values of the coefficients. The accuracy of models was assessed.
Cellular automata and statistical mechanical models
Rujan, P.
1987-01-01
The authors elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata. Transient and stationary properties of probabilistic automata are linked to surface and bulk properties, respectively, of restricted statistical mechanical systems. It is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata. Some exact results are derived, including duality transformations, exact mappings, disorder, and linear solutions. Many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties. This approach is considered to be a first step toward the design of fully parallel, probabilistic systems whose computational abilities rely on the cooperative behavior of their components
Common pitfalls in statistical analysis: Linear regression analysis
Rakesh Aggarwal
2017-01-01
Full Text Available In a previous article in this series, we explained correlation analysis which describes the strength of relationship between two continuous variables. In this article, we deal with linear regression analysis which predicts the value of one continuous variable from another. We also discuss the assumptions and pitfalls associated with this analysis.
Aspects of general linear modelling of migration.
Congdon, P
1992-01-01
"This paper investigates the application of general linear modelling principles to analysing migration flows between areas. Particular attention is paid to specifying the form of the regression and error components, and the nature of departures from Poisson randomness. Extensions to take account of spatial and temporal correlation are discussed as well as constrained estimation. The issue of specification bears on the testing of migration theories, and assessing the role migration plays in job and housing markets: the direction and significance of the effects of economic variates on migration depends on the specification of the statistical model. The application is in the context of migration in London and South East England in the 1970s and 1980s." excerpt
Active Learning with Statistical Models.
1995-01-01
Active Learning with Statistical Models ASC-9217041, NSF CDA-9309300 6. AUTHOR(S) David A. Cohn, Zoubin Ghahramani, and Michael I. Jordan 7. PERFORMING...TERMS 15. NUMBER OF PAGES Al, MIT, Artificial Intelligence, active learning , queries, locally weighted 6 regression, LOESS, mixtures of gaussians...COMPUTATIONAL LEARNING DEPARTMENT OF BRAIN AND COGNITIVE SCIENCES A.I. Memo No. 1522 January 9. 1995 C.B.C.L. Paper No. 110 Active Learning with
Multivariate generalized linear mixed models using R
Berridge, Damon Mark
2011-01-01
Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R. A Unified Framework for a Broad Class of Models The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model...
Nonlinear Modeling by Assembling Piecewise Linear Models
Yao, Weigang; Liou, Meng-Sing
2013-01-01
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
Linear Logistic Test Modeling with R
Baghaei, Purya; Kubinger, Klaus D.
2015-01-01
The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The…
application of Hierachical Linear Models
Erna Kinsey
The only drawback of applying. HLMs is ... structure of the data because it dictates the statistical techniques ..... either through visual inspection of histograms or frequency ... Bivariate/multivariate data cleaning procedures can also be impor-.
Optimizing refiner operation with statistical modelling
Broderick, G [Noranda Research Centre, Pointe Claire, PQ (Canada)
1997-02-01
The impact of refining conditions on the energy efficiency of the process and on the handsheet quality of a chemi-mechanical pulp was studied as part of a series of pilot scale refining trials. Statistical models of refiner performance were constructed from these results and non-linear optimization of process conditions were conducted. Optimization results indicated that increasing the ratio of specific energy applied in the first stage led to a reduction of some 15 per cent in the total energy requirement. The strategy can also be used to obtain significant increases in pulp quality for a given energy input. 20 refs., 6 tabs.
Core seismic behaviour: linear and non-linear models
Bernard, M.; Van Dorsselaere, M.; Gauvain, M.; Jenapierre-Gantenbein, M.
1981-08-01
The usual methodology for the core seismic behaviour analysis leads to a double complementary approach: to define a core model to be included in the reactor-block seismic response analysis, simple enough but representative of basic movements (diagrid or slab), to define a finer core model, with basic data issued from the first model. This paper presents the history of the different models of both kinds. The inert mass model (IMM) yielded a first rough diagrid movement. The direct linear model (DLM), without shocks and with sodium as an added mass, let to two different ones: DLM 1 with independent movements of the fuel and radial blanket subassemblies, and DLM 2 with a core combined movement. The non-linear (NLM) ''CORALIE'' uses the same basic modelization (Finite Element Beams) but accounts for shocks. It studies the response of a diameter on flats and takes into account the fluid coupling and the wrapper tube flexibility at the pad level. Damping consists of one modal part of 2% and one part due to shocks. Finally, ''CORALIE'' yields the time-history of the displacements and efforts on the supports, but damping (probably greater than 2%) and fluid-structures interaction are still to be precised. The validation experiments were performed on a RAPSODIE core mock-up on scale 1, in similitude of 1/3 as to SPX 1. The equivalent linear model (ELM) was developed for the SPX 1 reactor-block response analysis and a specified seismic level (SB or SM). It is composed of several oscillators fixed to the diagrid and yields the same maximum displacements and efforts than the NLM. The SPX 1 core seismic analysis with a diagrid input spectrum which corresponds to a 0,1 g group acceleration, has been carried out with these models: some aspects of these calculations are presented here
Linear models in the mathematics of uncertainty
Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A
2013-01-01
The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data is difficult to measure and an assumption of randomness and/or statistical validity is questionable. We apply our methods to real world issues in international relations such as nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...
Generalized Linear Models in Vehicle Insurance
Silvie Kafková
2014-01-01
Full Text Available Actuaries in insurance companies try to find the best model for an estimation of insurance premium. It depends on many risk factors, e.g. the car characteristics and the profile of the driver. In this paper, an analysis of the portfolio of vehicle insurance data using a generalized linear model (GLM is performed. The main advantage of the approach presented in this article is that the GLMs are not limited by inflexible preconditions. Our aim is to predict the relation of annual claim frequency on given risk factors. Based on a large real-world sample of data from 57 410 vehicles, the present study proposed a classification analysis approach that addresses the selection of predictor variables. The models with different predictor variables are compared by analysis of deviance and Akaike information criterion (AIC. Based on this comparison, the model for the best estimate of annual claim frequency is chosen. All statistical calculations are computed in R environment, which contains stats package with the function for the estimation of parameters of GLM and the function for analysis of deviation.
ARSENIC CONTAMINATION IN GROUNDWATER: A STATISTICAL MODELING
Palas Roy
2013-01-01
Full Text Available High arsenic in natural groundwater in most of the tubewells of the Purbasthali- Block II area of Burdwan district (W.B, India has recently been focused as a serious environmental concern. This paper is intending to illustrate the statistical modeling of the arsenic contaminated groundwater to identify the interrelation of that arsenic contain with other participating groundwater parameters so that the arsenic contamination level can easily be predicted by analyzing only such parameters. Multivariate data analysis was done with the collected groundwater samples from the 132 tubewells of this contaminated region shows that three variable parameters are significantly related with the arsenic. Based on these relationships, a multiple linear regression model has been developed that estimated the arsenic contamination by measuring such three predictor parameters of the groundwater variables in the contaminated aquifer. This model could also be a suggestive tool while designing the arsenic removal scheme for any affected groundwater.
Statistical study of the non-linear propagation of a partially coherent laser beam
Ayanides, J.P.
2001-01-01
This research thesis is related to the LMJ project (Laser MegaJoule) and thus to the study and development of thermonuclear fusion. It reports the study of the propagation of a partially-coherent laser beam by using a statistical modelling in order to obtain mean values for the field, and thus bypassing a complex and costly calculation of deterministic quantities. Random fluctuations of the propagated field are supposed to comply with a Gaussian statistics; the laser central wavelength is supposed to be small with respect with fluctuation magnitude; a scale factor is introduced to clearly distinguish the scale of the random and fast variations of the field fluctuations, and the scale of the slow deterministic variations of the field envelopes. The author reports the study of propagation through a purely linear media and through a non-dispersive media, and then through slow non-dispersive and non-linear media (in which the reaction time is large with respect to grain correlation duration, but small with respect to the variation scale of the field macroscopic envelope), and thirdly through an instantaneous dispersive and non linear media (which instantaneously reacts to the field) [fr
Advanced data analysis in neuroscience integrating statistical and computational models
Durstewitz, Daniel
2017-01-01
This book is intended for use in advanced graduate courses in statistics / machine learning, as well as for all experimental neuroscientists seeking to understand statistical methods at a deeper level, and theoretical neuroscientists with a limited background in statistics. It reviews almost all areas of applied statistics, from basic statistical estimation and test theory, linear and nonlinear approaches for regression and classification, to model selection and methods for dimensionality reduction, density estimation and unsupervised clustering. Its focus, however, is linear and nonlinear time series analysis from a dynamical systems perspective, based on which it aims to convey an understanding also of the dynamical mechanisms that could have generated observed time series. Further, it integrates computational modeling of behavioral and neural dynamics with statistical estimation and hypothesis testing. This way computational models in neuroscience are not only explanat ory frameworks, but become powerfu...
GIGMF - A statistical model program
Vladuca, G.; Deberth, C.
1978-01-01
The program GIGMF computes the differential and integrated statistical model cross sections for the reactions proceeding through a compound nuclear stage. The computational method is based on the Hauser-Feshbach-Wolfenstein theory, modified to include the modern version of Tepel et al. Although the program was written for a PDP-15 computer, with 16K high speed memory, many reaction channels can be taken into account with the following restrictions: the pro ectile spin must be less than 2, the maximum spin momenta of the compound nucleus can not be greater than 10. These restrictions are due solely to the storage allotments and may be easily relaxed. The energy of the impinging particle, the target and projectile masses, the spin and paritjes of the projectile, target, emergent and residual nuclei the maximum orbital momentum and transmission coefficients for each reaction channel are the input parameters of the program. (author)
Online Statistical Modeling (Regression Analysis) for Independent Responses
Made Tirta, I.; Anggraeni, Dian; Pandutama, Martinus
2017-06-01
Regression analysis (statistical analmodelling) are among statistical methods which are frequently needed in analyzing quantitative data, especially to model relationship between response and explanatory variables. Nowadays, statistical models have been developed into various directions to model various type and complex relationship of data. Rich varieties of advanced and recent statistical modelling are mostly available on open source software (one of them is R). However, these advanced statistical modelling, are not very friendly to novice R users, since they are based on programming script or command line interface. Our research aims to developed web interface (based on R and shiny), so that most recent and advanced statistical modelling are readily available, accessible and applicable on web. We have previously made interface in the form of e-tutorial for several modern and advanced statistical modelling on R especially for independent responses (including linear models/LM, generalized linier models/GLM, generalized additive model/GAM and generalized additive model for location scale and shape/GAMLSS). In this research we unified them in the form of data analysis, including model using Computer Intensive Statistics (Bootstrap and Markov Chain Monte Carlo/ MCMC). All are readily accessible on our online Virtual Statistics Laboratory. The web (interface) make the statistical modeling becomes easier to apply and easier to compare them in order to find the most appropriate model for the data.
Comparing linear probability model coefficients across groups
Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt
2015-01-01
of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate......This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more...... these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons....
Distributed Monitoring of the R(sup 2) Statistic for Linear Regression
Bhaduri, Kanishka; Das, Kamalika; Giannella, Chris R.
2011-01-01
The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and one or more dependent target variables. This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings. Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the updated model is broadcast back to all nodes. We show empirically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness.
Non-linearity consideration when analyzing reactor noise statistical characteristics. [BWR
Kebadze, B V; Adamovski, L A
1975-06-01
Statistical characteristics of boiling water reactor noise in the vicinity of stability threshold are studied. The reactor is considered as a non-linear system affected by random perturbations. To solve a non-linear problem the principle of statistical linearization is used. It is shown that the halfwidth of resonance peak in neutron power noise spectrum density as well as the reciprocal of noise dispersion, which are used in predicting a stable operation theshold, are different from zero both within and beyond the stability boundary the determination of which was based on linear criteria.
Spaghetti Bridges: Modeling Linear Relationships
Kroon, Cindy D.
2016-01-01
Mathematics and science are natural partners. One of many examples of this partnership occurs when scientific observations are made, thus providing data that can be used for mathematical modeling. Developing mathematical relationships elucidates such scientific principles. This activity describes a data-collection activity in which students employ…
Non-linear statistical downscaling of present and LGM precipitation and temperatures over Europe
M. Vrac
2007-12-01
Full Text Available Local-scale climate information is increasingly needed for the study of past, present and future climate changes. In this study we develop a non-linear statistical downscaling method to generate local temperatures and precipitation values from large-scale variables of a Earth System Model of Intermediate Complexity (here CLIMBER. Our statistical downscaling scheme is based on the concept of Generalized Additive Models (GAMs, capturing non-linearities via non-parametric techniques. Our GAMs are calibrated on the present Western Europe climate. For this region, annual GAMs (i.e. models based on 12 monthly values per location are fitted by combining two types of large-scale explanatory variables: geographical (e.g. topographical information and physical (i.e. entirely simulated by the CLIMBER model.
To evaluate the adequacy of the non-linear transfer functions fitted on the present Western European climate, they are applied to different spatial and temporal large-scale conditions. Local projections for present North America and Northern Europe climates are obtained and compared to local observations. This partially addresses the issue of spatial robustness of our transfer functions by answering the question "does our statistical model remain valid when applied to large-scale climate conditions from a region different from the one used for calibration?". To asses their temporal performances, local projections for the Last Glacial Maximum period are derived and compared to local reconstructions and General Circulation Model outputs.
Our downscaling methodology performs adequately for the Western Europe climate. Concerning the spatial and temporal evaluations, it does not behave as well for Northern America and Northern Europe climates because the calibration domain may be too different from the targeted regions. The physical explanatory variables alone are not capable of downscaling realistic values. However, the inclusion of
Non-linear finite element modeling
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
Extended Linear Models with Gaussian Priors
Quinonero, Joaquin
2002-01-01
In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....
Linear mixed models for longitudinal data
Molenberghs, Geert
2000-01-01
This paperback edition is a reprint of the 2000 edition. This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place. Several variations to the conventional linear mixed model are discussed (a heterogeity model, conditional linear mixed models). This book will be of interest to applied statisticians and biomedical researchers in industry, public health organizations, contract research organizations, and academia. The book is explanatory rather than mathematically rigorous. Most analyses were done with the MIXED procedure of the SAS software package, and many of its features are clearly elucidated. However, some other commerc...
Linear causal modeling with structural equations
Mulaik, Stanley A
2009-01-01
Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal
Estimation and variable selection for generalized additive partial linear models
Wang, Li
2011-08-01
We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration. © Institute of Mathematical Statistics, 2011.
Right-sizing statistical models for longitudinal data.
Wood, Phillip K; Steinley, Douglas; Jackson, Kristina M
2015-12-01
Arguments are proposed that researchers using longitudinal data should consider more and less complex statistical model alternatives to their initially chosen techniques in an effort to "right-size" the model to the data at hand. Such model comparisons may alert researchers who use poorly fitting, overly parsimonious models to more complex, better-fitting alternatives and, alternatively, may identify more parsimonious alternatives to overly complex (and perhaps empirically underidentified and/or less powerful) statistical models. A general framework is proposed for considering (often nested) relationships between a variety of psychometric and growth curve models. A 3-step approach is proposed in which models are evaluated based on the number and patterning of variance components prior to selection of better-fitting growth models that explain both mean and variation-covariation patterns. The orthogonal free curve slope intercept (FCSI) growth model is considered a general model that includes, as special cases, many models, including the factor mean (FM) model (McArdle & Epstein, 1987), McDonald's (1967) linearly constrained factor model, hierarchical linear models (HLMs), repeated-measures multivariate analysis of variance (MANOVA), and the linear slope intercept (linearSI) growth model. The FCSI model, in turn, is nested within the Tuckerized factor model. The approach is illustrated by comparing alternative models in a longitudinal study of children's vocabulary and by comparing several candidate parametric growth and chronometric models in a Monte Carlo study. (c) 2015 APA, all rights reserved).
Aniela Balacescu; Marian Zaharia
2011-01-01
This paper aims to examine the causal relationship between GDP and final consumption. The authors used linear regression model in which GDP is considered variable results, and final consumption variable factor. In drafting article we used Excel software application that is a modern computing and statistical data analysis.
Probing NWP model deficiencies by statistical postprocessing
Rosgaard, Martin Haubjerg; Nielsen, Henrik Aalborg; Nielsen, Torben S.
2016-01-01
The objective in this article is twofold. On one hand, a Model Output Statistics (MOS) framework for improved wind speed forecast accuracy is described and evaluated. On the other hand, the approach explored identifies unintuitive explanatory value from a diagnostic variable in an operational....... Based on the statistical model candidates inferred from the data, the lifted index NWP model diagnostic is consistently found among the NWP model predictors of the best performing statistical models across sites....
Modeling digital switching circuits with linear algebra
Thornton, Mitchell A
2014-01-01
Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transf
Modelling diversity in building occupant behaviour: a novel statistical approach
Haldi, Frédéric; Calì, Davide; Andersen, Rune Korsholm
2016-01-01
We propose an advanced modelling framework to predict the scope and effects of behavioural diversity regarding building occupant actions on window openings, shading devices and lighting. We develop a statistical approach based on generalised linear mixed models to account for the longitudinal nat...
Updating Linear Schedules with Lowest Cost: a Linear Programming Model
Biruk, Sławomir; Jaśkowski, Piotr; Czarnigowska, Agata
2017-10-01
Many civil engineering projects involve sets of tasks repeated in a predefined sequence in a number of work areas along a particular route. A useful graphical representation of schedules of such projects is time-distance diagrams that clearly show what process is conducted at a particular point of time and in particular location. With repetitive tasks, the quality of project performance is conditioned by the ability of the planner to optimize workflow by synchronizing the works and resources, which usually means that resources are planned to be continuously utilized. However, construction processes are prone to risks, and a fully synchronized schedule may expire if a disturbance (bad weather, machine failure etc.) affects even one task. In such cases, works need to be rescheduled, and another optimal schedule should be built for the changed circumstances. This typically means that, to meet the fixed completion date, durations of operations have to be reduced. A number of measures are possible to achieve such reduction: working overtime, employing more resources or relocating resources from less to more critical tasks, but they all come at a considerable cost and affect the whole project. The paper investigates the problem of selecting the measures that reduce durations of tasks of a linear project so that the cost of these measures is kept to the minimum and proposes an algorithm that could be applied to find optimal solutions as the need to reschedule arises. Considering that civil engineering projects, such as road building, usually involve less process types than construction projects, the complexity of scheduling problems is lower, and precise optimization algorithms can be applied. Therefore, the authors put forward a linear programming model of the problem and illustrate its principle of operation with an example.
A linear model of ductile plastic damage
Lemaitre, J.
1983-01-01
A three-dimensional model of isotropic ductile plastic damage based on a continuum damage variable on the effective stress concept and on thermodynamics is derived. As shown by experiments on several metals and alloys, the model, integrated in the case of proportional loading, is linear with respect to the accumulated plastic strain and shows a large influence of stress triaxiality [fr
Takabe, Satoshi; Hukushima, Koji
2016-05-01
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.
Takabe, Satoshi; Hukushima, Koji
2016-05-01
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.
Ker, H. W.
2014-01-01
Multilevel data are very common in educational research. Hierarchical linear models/linear mixed-effects models (HLMs/LMEs) are often utilized to analyze multilevel data nowadays. This paper discusses the problems of utilizing ordinary regressions for modeling multilevel educational data, compare the data analytic results from three regression…
Ground Motion Models for Future Linear Colliders
Seryi, Andrei
2000-01-01
Optimization of the parameters of a future linear collider requires comprehensive models of ground motion. Both general models of ground motion and specific models of the particular site and local conditions are essential. Existing models are not completely adequate, either because they are too general, or because they omit important peculiarities of ground motion. The model considered in this paper is based on recent ground motion measurements performed at SLAC and at other accelerator laboratories, as well as on historical data. The issues to be studied for the models to become more predictive are also discussed
Statistical modelling in biostatistics and bioinformatics selected papers
Peng, Defen
2014-01-01
This book presents selected papers on statistical model development related mainly to the fields of Biostatistics and Bioinformatics. The coverage of the material falls squarely into the following categories: (a) Survival analysis and multivariate survival analysis, (b) Time series and longitudinal data analysis, (c) Statistical model development and (d) Applied statistical modelling. Innovations in statistical modelling are presented throughout each of the four areas, with some intriguing new ideas on hierarchical generalized non-linear models and on frailty models with structural dispersion, just to mention two examples. The contributors include distinguished international statisticians such as Philip Hougaard, John Hinde, Il Do Ha, Roger Payne and Alessandra Durio, among others, as well as promising newcomers. Some of the contributions have come from researchers working in the BIO-SI research programme on Biostatistics and Bioinformatics, centred on the Universities of Limerick and Galway in Ireland and fu...
Interpretation of commonly used statistical regression models.
Kasza, Jessica; Wolfe, Rory
2014-01-01
A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.
Modelling female fertility traits in beef cattle using linear and non-linear models.
Naya, H; Peñagaricano, F; Urioste, J I
2017-06-01
Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2 linear models; h 2 > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.
Statistical modelling of fish stocks
Kvist, Trine
1999-01-01
for modelling the dynamics of a fish population is suggested. A new approach is introduced to analyse the sources of variation in age composition data, which is one of the most important sources of information in the cohort based models for estimation of stock abundancies and mortalities. The approach combines...... and it is argued that an approach utilising stochastic differential equations might be advantagous in fish stoch assessments....
Modelling point patterns with linear structures
Møller, Jesper; Rasmussen, Jakob Gulddahl
2009-01-01
processes whose realizations contain such linear structures. Such a point process is constructed sequentially by placing one point at a time. The points are placed in such a way that new points are often placed close to previously placed points, and the points form roughly line shaped structures. We...... consider simulations of this model and compare with real data....
Modelling point patterns with linear structures
Møller, Jesper; Rasmussen, Jakob Gulddahl
processes whose realizations contain such linear structures. Such a point process is constructed sequentially by placing one point at a time. The points are placed in such a way that new points are often placed close to previously placed points, and the points form roughly line shaped structures. We...... consider simulations of this model and compare with real data....
Optimal designs for linear mixture models
Mendieta, E.J.; Linssen, H.N.; Doornbos, R.
1975-01-01
In a recent paper Snee and Marquardt [8] considered designs for linear mixture models, where the components are subject to individual lower and/or upper bounds. When the number of components is large their algorithm XVERT yields designs far too extensive for practical purposes. The purpose of this
Optimal designs for linear mixture models
Mendieta, E.J.; Linssen, H.N.; Doornbos, R.
1975-01-01
In a recent paper Snee and Marquardt (1974) considered designs for linear mixture models, where the components are subject to individual lower and/or upper bounds. When the number of components is large their algorithm XVERT yields designs far too extensive for practical purposes. The purpose of
Statistical lung model for microdosimetry
Fisher, D.R.; Hadley, R.T.
1984-03-01
To calculate the microdosimetry of plutonium in the lung, a mathematical description is needed of lung tissue microstructure that defines source-site parameters. Beagle lungs were expanded using a glutaraldehyde fixative at 30 cm water pressure. Tissue specimens, five microns thick, were stained with hematoxylin and eosin then studied using an image analyzer. Measurements were made along horizontal lines through the magnified tissue image. The distribution of air space and tissue chord lengths and locations of epithelial cell nuclei were recorded from about 10,000 line scans. The distribution parameters constituted a model of lung microstructure for predicting the paths of random alpha particle tracks in the lung and the probability of traversing biologically sensitive sites. This lung model may be used in conjunction with established deposition and retention models for determining the microdosimetry in the pulmonary lung for a wide variety of inhaled radioactive materials
Linear factor copula models and their properties
Krupskii, Pavel; Genton, Marc G.
2018-01-01
We consider a special case of factor copula models with additive common factors and independent components. These models are flexible and parsimonious with O(d) parameters where d is the dimension. The linear structure allows one to obtain closed form expressions for some copulas and their extreme‐value limits. These copulas can be used to model data with strong tail dependencies, such as extreme data. We study the dependence properties of these linear factor copula models and derive the corresponding limiting extreme‐value copulas with a factor structure. We show how parameter estimates can be obtained for these copulas and apply one of these copulas to analyse a financial data set.
Linear factor copula models and their properties
Krupskii, Pavel
2018-04-25
We consider a special case of factor copula models with additive common factors and independent components. These models are flexible and parsimonious with O(d) parameters where d is the dimension. The linear structure allows one to obtain closed form expressions for some copulas and their extreme‐value limits. These copulas can be used to model data with strong tail dependencies, such as extreme data. We study the dependence properties of these linear factor copula models and derive the corresponding limiting extreme‐value copulas with a factor structure. We show how parameter estimates can be obtained for these copulas and apply one of these copulas to analyse a financial data set.
Diagnostics for Linear Models With Functional Responses
Xu, Hongquan; Shen, Qing
2005-01-01
Linear models where the response is a function and the predictors are vectors are useful in analyzing data from designed experiments and other situations with functional observations. Residual analysis and diagnostics are considered for such models. Studentized residuals are defined and their properties are studied. Chi-square quantile-quantile plots are proposed to check the assumption of Gaussian error process and outliers. Jackknife residuals and an associated test are proposed to det...
Non-linear Loudspeaker Unit Modelling
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Statistical modelling for ship propulsion efficiency
Petersen, Jóan Petur; Jacobsen, Daniel J.; Winther, Ole
2012-01-01
This paper presents a state-of-the-art systems approach to statistical modelling of fuel efficiency in ship propulsion, and also a novel and publicly available data set of high quality sensory data. Two statistical model approaches are investigated and compared: artificial neural networks...
Spherical Process Models for Global Spatial Statistics
Jeong, Jaehong; Jun, Mikyoung; Genton, Marc G.
2017-01-01
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture
Statistical Models and Methods for Lifetime Data
Lawless, Jerald F
2011-01-01
Praise for the First Edition"An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . ."-Choice"This is an important book, which will appeal to statisticians working on survival analysis problems."-Biometrics"A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook."-Statistics in MedicineThe statistical analysis of lifetime or response time data is a key tool in engineering,
Manning, Robert M.
1991-01-01
The dynamic and composite nature of propagation impairments that are incurred on Earth-space communications links at frequencies in and above 30/20 GHz Ka band, i.e., rain attenuation, cloud and/or clear air scintillation, etc., combined with the need to counter such degradations after the small link margins have been exceeded, necessitate the use of dynamic statistical identification and prediction processing of the fading signal in order to optimally estimate and predict the levels of each of the deleterious attenuation components. Such requirements are being met in NASA's Advanced Communications Technology Satellite (ACTS) Project by the implementation of optimal processing schemes derived through the use of the Rain Attenuation Prediction Model and nonlinear Markov filtering theory.
Statistics and the shell model
Weidenmueller, H.A.
1985-01-01
Starting with N. Bohr's paper on compound-nucleus reactions, we confront regular dynamical features and chaotic motion in nuclei. The shell-model and, more generally, mean-field theories describe average nuclear properties which are thus identified as regular features. The fluctuations about the average show chaotic behaviour of the same type as found in classical chaotic systems upon quantisation. These features are therefore generic and quite independent of the specific dynamics of the nucleus. A novel method to calculate fluctuations is discussed, and the results of this method are described. (orig.)
Variability aware compact model characterization for statistical circuit design optimization
Qiao, Ying; Qian, Kun; Spanos, Costas J.
2012-03-01
Variability modeling at the compact transistor model level can enable statistically optimized designs in view of limitations imposed by the fabrication technology. In this work we propose an efficient variabilityaware compact model characterization methodology based on the linear propagation of variance. Hierarchical spatial variability patterns of selected compact model parameters are directly calculated from transistor array test structures. This methodology has been implemented and tested using transistor I-V measurements and the EKV-EPFL compact model. Calculation results compare well to full-wafer direct model parameter extractions. Further studies are done on the proper selection of both compact model parameters and electrical measurement metrics used in the method.
Statistical distributions of earthquakes and related non-linear features in seismic waves
Apostol, B.-F.
2006-01-01
A few basic facts in the science of the earthquakes are briefly reviewed. An accumulation, or growth, model is put forward for the focal mechanisms and the critical focal zone of the earthquakes, which relates the earthquake average recurrence time to the released seismic energy. The temporal statistical distribution for average recurrence time is introduced for earthquakes, and, on this basis, the Omori-type distribution in energy is derived, as well as the distribution in magnitude, by making use of the semi-empirical Gutenberg-Richter law relating seismic energy to earthquake magnitude. On geometric grounds, the accumulation model suggests the value r = 1/3 for the Omori parameter in the power-law of energy distribution, which leads to β = 1,17 for the coefficient in the Gutenberg-Richter recurrence law, in fair agreement with the statistical analysis of the empirical data. Making use of this value, the empirical Bath's law is discussed for the average magnitude of the aftershocks (which is 1.2 less than the magnitude of the main seismic shock), by assuming that the aftershocks are relaxation events of the seismic zone. The time distribution of the earthquakes with a fixed average recurrence time is also derived, the earthquake occurrence prediction is discussed by means of the average recurrence time and the seismicity rate, and application of this discussion to the seismic region Vrancea, Romania, is outlined. Finally, a special effect of non-linear behaviour of the seismic waves is discussed, by describing an exact solution derived recently for the elastic waves equation with cubic anharmonicities, its relevance, and its connection to the approximate quasi-plane waves picture. The properties of the seismic activity accompanying a main seismic shock, both like foreshocks and aftershocks, are relegated to forthcoming publications. (author)
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
[From clinical judgment to linear regression model.
Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O
2013-01-01
When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.
Modeling of Volatility with Non-linear Time Series Model
Kim Song Yon; Kim Mun Chol
2013-01-01
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.
Bayesian models: A statistical primer for ecologists
Hobbs, N. Thompson; Hooten, Mevin B.
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 probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models
Thresholding projection estimators in functional linear models
Cardot, Hervé; Johannes, Jan
2010-01-01
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squ...
Decomposed Implicit Models of Piecewise - Linear Networks
J. Brzobohaty
1992-05-01
Full Text Available The general matrix form of the implicit description of a piecewise-linear (PWL network and the symbolic block diagram of the corresponding circuit model are proposed. Their decomposed forms enable us to determine quite separately the existence of the individual breakpoints of the resultant PWL characteristic and their coordinates using independent network parameters. For the two-diode and three-diode cases all the attainable types of the PWL characteristic are introduced.
Uncertainty the soul of modeling, probability & statistics
Briggs, William
2016-01-01
This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance". The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, suc...
A Graphical User Interface to Generalized Linear Models in MATLAB
Peter Dunn
1999-07-01
Full Text Available Generalized linear models unite a wide variety of statistical models in a common theoretical framework. This paper discusses GLMLAB-software that enables such models to be fitted in the popular mathematical package MATLAB. It provides a graphical user interface to the powerful MATLAB computational engine to produce a program that is easy to use but with many features, including offsets, prior weights and user-defined distributions and link functions. MATLAB's graphical capacities are also utilized in providing a number of simple residual diagnostic plots.
Automated statistical modeling of analytical measurement systems
Jacobson, J.J.
1992-01-01
The statistical modeling of analytical measurement systems at the Idaho Chemical Processing Plant (ICPP) has been completely automated through computer software. The statistical modeling of analytical measurement systems is one part of a complete quality control program used by the Remote Analytical Laboratory (RAL) at the ICPP. The quality control program is an integration of automated data input, measurement system calibration, database management, and statistical process control. The quality control program and statistical modeling program meet the guidelines set forth by the American Society for Testing Materials and American National Standards Institute. A statistical model is a set of mathematical equations describing any systematic bias inherent in a measurement system and the precision of a measurement system. A statistical model is developed from data generated from the analysis of control standards. Control standards are samples which are made up at precise known levels by an independent laboratory and submitted to the RAL. The RAL analysts who process control standards do not know the values of those control standards. The object behind statistical modeling is to describe real process samples in terms of their bias and precision and, to verify that a measurement system is operating satisfactorily. The processing of control standards gives us this ability
Uhlemann, C.; Feix, M.; Codis, S.; Pichon, C.; Bernardeau, F.; L'Huillier, B.; Kim, J.; Hong, S. E.; Laigle, C.; Park, C.; Shin, J.; Pogosyan, D.
2018-02-01
Starting from a very accurate model for density-in-cells statistics of dark matter based on large deviation theory, a bias model for the tracer density in spheres is formulated. It adopts a mean bias relation based on a quadratic bias model to relate the log-densities of dark matter to those of mass-weighted dark haloes in real and redshift space. The validity of the parametrized bias model is established using a parametrization-independent extraction of the bias function. This average bias model is then combined with the dark matter PDF, neglecting any scatter around it: it nevertheless yields an excellent model for densities-in-cells statistics of mass tracers that is parametrized in terms of the underlying dark matter variance and three bias parameters. The procedure is validated on measurements of both the one- and two-point statistics of subhalo densities in the state-of-the-art Horizon Run 4 simulation showing excellent agreement for measured dark matter variance and bias parameters. Finally, it is demonstrated that this formalism allows for a joint estimation of the non-linear dark matter variance and the bias parameters using solely the statistics of subhaloes. Having verified that galaxy counts in hydrodynamical simulations sampled on a scale of 10 Mpc h-1 closely resemble those of subhaloes, this work provides important steps towards making theoretical predictions for density-in-cells statistics applicable to upcoming galaxy surveys like Euclid or WFIRST.
Models for probability and statistical inference theory and applications
Stapleton, James H
2007-01-01
This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readersModels for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses mo...
From spiking neuron models to linear-nonlinear models.
Ostojic, Srdjan; Brunel, Nicolas
2011-01-20
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
Topology for statistical modeling of petascale data.
Pascucci, Valerio (University of Utah, Salt Lake City, UT); Mascarenhas, Ajith Arthur; Rusek, Korben (Texas A& M University, College Station, TX); Bennett, Janine Camille; Levine, Joshua (University of Utah, Salt Lake City, UT); Pebay, Philippe Pierre; Gyulassy, Attila (University of Utah, Salt Lake City, UT); Thompson, David C.; Rojas, Joseph Maurice (Texas A& M University, College Station, TX)
2011-07-01
This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled 'Topology for Statistical Modeling of Petascale Data', funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program. Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is thus to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, our approach is based on the complementary techniques of combinatorial topology and statistical modeling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modeling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. This document summarizes the technical advances we have made to date that were made possible in whole or in part by MAPD funding. These technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modeling, and (3) new integrated topological and statistical methods.
Statistical modelling of citation exchange between statistics journals.
Varin, Cristiano; Cattelan, Manuela; Firth, David
2016-01-01
Rankings of scholarly journals based on citation data are often met with scepticism by the scientific community. Part of the scepticism is due to disparity between the common perception of journals' prestige and their ranking based on citation counts. A more serious concern is the inappropriate use of journal rankings to evaluate the scientific influence of researchers. The paper focuses on analysis of the table of cross-citations among a selection of statistics journals. Data are collected from the Web of Science database published by Thomson Reuters. Our results suggest that modelling the exchange of citations between journals is useful to highlight the most prestigious journals, but also that journal citation data are characterized by considerable heterogeneity, which needs to be properly summarized. Inferential conclusions require care to avoid potential overinterpretation of insignificant differences between journal ratings. Comparison with published ratings of institutions from the UK's research assessment exercise shows strong correlation at aggregate level between assessed research quality and journal citation 'export scores' within the discipline of statistics.
Stochastic linear programming models, theory, and computation
Kall, Peter
2011-01-01
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...
Downlink Linear Precoders Based on Statistical CSI for Multicell MIMO-OFDM
Ebrahim Baktash
2017-01-01
Full Text Available With 5G communication systems on the horizon, efficient interference management in heterogeneous multicell networks is more vital than ever. This paper investigates the linear precoder design for downlink multicell multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM systems, where base stations (BSs coordinate to reduce the interference across space and frequency. In order to minimize the overall feedback overhead in next-generation systems, we consider precoding schemes that require statistical channel state information (CSI only. We apply the random matrix theory to approximate the ergodic weighted sum rate of the system with a closed form expression. After formulating the approximation for general channels, we reduce the results to a more compact form using the Kronecker channel model for which several multicarrier concepts such as frequency selectivity, channel tap correlations, and intercarrier interference (ICI are rigorously represented. We find the local optimal solution for the maximization of the approximate rate using a gradient method that requires only the covariance structure of the MIMO-OFDM channels. Within this covariance structure are the channel tap correlations and ICI information, both of which are taken into consideration in the precoder design. Simulation results show that the rate approximation is very accurate even for very small MIMO-OFDM systems and the proposed method converges rapidly to a near-optimal solution that competes with networked MIMO and precoders based on instantaneous full CSI.
Daily precipitation statistics in regional climate models
Frei, Christoph; Christensen, Jens Hesselbjerg; Déqué, Michel
2003-01-01
An evaluation is undertaken of the statistics of daily precipitation as simulated by five regional climate models using comprehensive observations in the region of the European Alps. Four limited area models and one variable-resolution global model are considered, all with a grid spacing of 50 km...
Infinite Random Graphs as Statistical Mechanical Models
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...
Statistical Validation of Engineering and Scientific Models: Background
Hills, Richard G.; Trucano, Timothy G.
1999-01-01
A tutorial is presented discussing the basic issues associated with propagation of uncertainty analysis and statistical validation of engineering and scientific models. The propagation of uncertainty tutorial illustrates the use of the sensitivity method and the Monte Carlo method to evaluate the uncertainty in predictions for linear and nonlinear models. Four example applications are presented; a linear model, a model for the behavior of a damped spring-mass system, a transient thermal conduction model, and a nonlinear transient convective-diffusive model based on Burger's equation. Correlated and uncorrelated model input parameters are considered. The model validation tutorial builds on the material presented in the propagation of uncertainty tutoriaI and uses the damp spring-mass system as the example application. The validation tutorial illustrates several concepts associated with the application of statistical inference to test model predictions against experimental observations. Several validation methods are presented including error band based, multivariate, sum of squares of residuals, and optimization methods. After completion of the tutorial, a survey of statistical model validation literature is presented and recommendations for future work are made
Crucifix, Michel; Wilkinson, Richard; Carson, Jake; Preston, Simon; Alemeida, Carlos; Rougier, Jonathan
2013-04-01
The existence of an action of astronomical forcing on the Pleistocene climate is almost undisputed. However, quantifying this action is not straightforward. In particular, the phenomenon of deglaciation is generally interpreted as a manifestation of instability, which is typical of non-linear systems. As a consequence, explaining the Pleistocene climate record as the addition of an astronomical contribution and noise-as often done using harmonic analysis tools-is potentially deceptive. Rather, we advocate a methodology in which non-linear stochastic dynamical systems are calibrated on the Pleistocene climate record. The exercise, though, requires careful statistical reasoning and state-of-the-art techniques. In fact, the problem has been judged to be mathematically 'intractable and unsolved' and some pragmatism is justified. In order to illustrate the methodology we consider one dynamical system that potentially captures four dynamical features of the Pleistocene climate : the existence of a saddle-node bifurcation in at least one of its slow components, a time-scale separation between a slow and a fast component, the action of astronomical forcing, and the existence a stochastic contribution to the system dynamics. This model is obviously not the only possible representation of Pleistocene dynamics, but it encapsulates well enough both our theoretical and empirical knowledge into a very simple form to constitute a valid starting point. The purpose of this poster is to outline the practical challenges in calibrating such a model on paleoclimate observations. Just as in time series analysis, there is no one single and universal test or criteria that would demonstrate the validity of an approach. Several methods exist to calibrate the model and judgement develops by the confrontation of the results of the different methods. In particular, we consider here the Kalman filter variants, the Particle Monte-Carlo Markov Chain, and two other variants of Sequential Monte
Linear theory for filtering nonlinear multiscale systems with model error.
Berry, Tyrus; Harlim, John
2014-07-08
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering
Robust Linear Models for Cis-eQTL Analysis.
Rantalainen, Mattias; Lindgren, Cecilia M; Holmes, Christopher C
2015-01-01
Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.
Statistical physics of pairwise probability models
Roudi, Yasser; Aurell, Erik; Hertz, John
2009-01-01
(dansk abstrakt findes ikke) Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data......: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying...
Budgor, A.B.; West, B.J.
1978-01-01
We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation
Distributions with given marginals and statistical modelling
Fortiana, Josep; Rodriguez-Lallena, José
2002-01-01
This book contains a selection of the papers presented at the meeting `Distributions with given marginals and statistical modelling', held in Barcelona (Spain), July 17-20, 2000. In 24 chapters, this book covers topics such as the theory of copulas and quasi-copulas, the theory and compatibility of distributions, models for survival distributions and other well-known distributions, time series, categorical models, definition and estimation of measures of dependence, monotonicity and stochastic ordering, shape and separability of distributions, hidden truncation models, diagonal families, orthogonal expansions, tests of independence, and goodness of fit assessment. These topics share the use and properties of distributions with given marginals, this being the fourth specialised text on this theme. The innovative aspect of the book is the inclusion of statistical aspects such as modelling, Bayesian statistics, estimation, and tests.
Aspects of statistical model for multifragmentation
Bhattacharyya, P.; Das Gupta, S.; Mekjian, A. Z.
1999-01-01
We deal with two different aspects of an exactly soluble statistical model of fragmentation. First we show, using zero range force and finite temperature Thomas-Fermi theory, that a common link can be found between finite temperature mean field theory and the statistical fragmentation model. We show the latter naturally arises in the spinodal region. Next we show that although the exact statistical model is a canonical model and uses temperature, microcanonical results which use constant energy rather than constant temperature can also be obtained from the canonical model using saddle-point approximation. The methodology is extremely simple to implement and at least in all the examples studied in this work is very accurate. (c) 1999 The American Physical Society
Statistical modeling and extrapolation of carcinogenesis data
Krewski, D.; Murdoch, D.; Dewanji, A.
1986-01-01
Mathematical models of carcinogenesis are reviewed, including pharmacokinetic models for metabolic activation of carcinogenic substances. Maximum likelihood procedures for fitting these models to epidemiological data are discussed, including situations where the time to tumor occurrence is unobservable. The plausibility of different possible shapes of the dose response curve at low doses is examined, and a robust method for linear extrapolation to low doses is proposed and applied to epidemiological data on radiation carcinogenesis
Linear accelerator modeling: development and application
Jameson, R.A.; Jule, W.D.
1977-01-01
Most of the parameters of a modern linear accelerator can be selected by simulating the desired machine characteristics in a computer code and observing how the parameters affect the beam dynamics. The code PARMILA is used at LAMPF for the low-energy portion of linacs. Collections of particles can be traced with a free choice of input distributions in six-dimensional phase space. Random errors are often included in order to study the tolerances which should be imposed during manufacture or in operation. An outline is given of the modifications made to the model, the results of experiments which indicate the validity of the model, and the use of the model to optimize the longitudinal tuning of the Alvarez linac
Running vacuum cosmological models: linear scalar perturbations
Perico, E.L.D. [Instituto de Física, Universidade de São Paulo, Rua do Matão 1371, CEP 05508-090, São Paulo, SP (Brazil); Tamayo, D.A., E-mail: elduartep@usp.br, E-mail: tamayo@if.usp.br [Departamento de Astronomia, Universidade de São Paulo, Rua do Matão 1226, CEP 05508-900, São Paulo, SP (Brazil)
2017-08-01
In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ( H {sup 2}) or Λ( R ). Such models assume an equation of state for the vacuum given by P-bar {sub Λ} = - ρ-bar {sub Λ}, relating its background pressure P-bar {sub Λ} with its mean energy density ρ-bar {sub Λ} ≡ Λ/8π G . This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely ρ-bar {sub Λ} = Σ {sub i} ρ-bar {sub Λ} {sub i} . Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ( H {sup 2}) scenario the vacuum is coupled with every matter component, whereas the Λ( R ) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.
Linear Parametric Model Checking of Timed Automata
Hune, Tohmas Seidelin; Romijn, Judi; Stoelinga, Mariëlle
2001-01-01
We present an extension of the model checker Uppaal capable of synthesize linear parameter constraints for the correctness of parametric timed automata. The symbolic representation of the (parametric) state-space is shown to be correct. A second contribution of this paper is the identication...... of a subclass of parametric timed automata (L/U automata), for which the emptiness problem is decidable, contrary to the full class where it is know to be undecidable. Also we present a number of lemmas enabling the verication eort to be reduced for L/U automata in some cases. We illustrate our approach...
Statistical Compression for Climate Model Output
Hammerling, D.; Guinness, J.; Soh, Y. J.
2017-12-01
Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus is it important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. We decompress the data by computing conditional expectations and conditional simulations from the model given the summary statistics. Conditional expectations represent our best estimate of the original data but are subject to oversmoothing in space and time. Conditional simulations introduce realistic small-scale noise so that the decompressed fields are neither too smooth nor too rough compared with the original data. Considerable attention is paid to accurately modeling the original dataset-one year of daily mean temperature data-particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers.
Performance modeling, loss networks, and statistical multiplexing
Mazumdar, Ravi
2009-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of understanding the phenomenon of statistical multiplexing. The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the important ideas of Palm distributions associated with traffic models and their role in performance measures. Also presented are recent ideas of large buffer, and many sources asymptotics that play an important role in understanding statistical multiplexing. I
Simple statistical model for branched aggregates
Lemarchand, Claire; Hansen, Jesper Schmidt
2015-01-01
, given that it already has bonds with others. The model is applied here to asphaltene nanoaggregates observed in molecular dynamics simulations of Cooee bitumen. The variation with temperature of the probabilities deduced from this model is discussed in terms of statistical mechanics arguments....... The relevance of the statistical model in the case of asphaltene nanoaggregates is checked by comparing the predicted value of the probability for one molecule to have exactly i bonds with the same probability directly measured in the molecular dynamics simulations. The agreement is satisfactory......We propose a statistical model that can reproduce the size distribution of any branched aggregate, including amylopectin, dendrimers, molecular clusters of monoalcohols, and asphaltene nanoaggregates. It is based on the conditional probability for one molecule to form a new bond with a molecule...
Advances in statistical models for data analysis
Minerva, Tommaso; Vichi, Maurizio
2015-01-01
This edited volume focuses on recent research results in classification, multivariate statistics and machine learning and highlights advances in statistical models for data analysis. The volume provides both methodological developments and contributions to a wide range of application areas such as economics, marketing, education, social sciences and environment. The papers in this volume were first presented at the 9th biannual meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, held in September 2013 at the University of Modena and Reggio Emilia, Italy.
Structured statistical models of inductive reasoning.
Kemp, Charles; Tenenbaum, Joshua B
2009-01-01
Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet both goals and describes [corrected] 4 applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the 4 models are defined over different kinds of structures that capture different relationships between the categories in a domain. The framework therefore shows how statistical inference can operate over structured background knowledge, and the authors argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning.
Model for neural signaling leap statistics
Chevrollier, Martine; Oria, Marcos
2011-01-01
We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T 37.5 0 C, awaken regime) and Levy statistics (T = 35.5 0 C, sleeping period), characterized by rare events of long range connections.
Statistical models based on conditional probability distributions
Narayanan, R.S.
1991-10-01
We present a formulation of statistical mechanics models based on conditional probability distribution rather than a Hamiltonian. We show that it is possible to realize critical phenomena through this procedure. Closely linked with this formulation is a Monte Carlo algorithm, in which a configuration generated is guaranteed to be statistically independent from any other configuration for all values of the parameters, in particular near the critical point. (orig.)
Model for neural signaling leap statistics
Chevrollier, Martine; Oriá, Marcos
2011-03-01
We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T = 37.5°C, awaken regime) and Lévy statistics (T = 35.5°C, sleeping period), characterized by rare events of long range connections.
Model for neural signaling leap statistics
Chevrollier, Martine; Oria, Marcos, E-mail: oria@otica.ufpb.br [Laboratorio de Fisica Atomica e Lasers Departamento de Fisica, Universidade Federal da ParaIba Caixa Postal 5086 58051-900 Joao Pessoa, Paraiba (Brazil)
2011-03-01
We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T 37.5{sup 0}C, awaken regime) and Levy statistics (T = 35.5{sup 0}C, sleeping period), characterized by rare events of long range connections.
Statistical modelling of transcript profiles of differentially regulated genes
Sergeant Martin J
2008-07-01
Full Text Available Abstract Background The vast quantities of gene expression profiling data produced in microarray studies, and the more precise quantitative PCR, are often not statistically analysed to their full potential. Previous studies have summarised gene expression profiles using simple descriptive statistics, basic analysis of variance (ANOVA and the clustering of genes based on simple models fitted to their expression profiles over time. We report the novel application of statistical non-linear regression modelling techniques to describe the shapes of expression profiles for the fungus Agaricus bisporus, quantified by PCR, and for E. coli and Rattus norvegicus, using microarray technology. The use of parametric non-linear regression models provides a more precise description of expression profiles, reducing the "noise" of the raw data to produce a clear "signal" given by the fitted curve, and describing each profile with a small number of biologically interpretable parameters. This approach then allows the direct comparison and clustering of the shapes of response patterns between genes and potentially enables a greater exploration and interpretation of the biological processes driving gene expression. Results Quantitative reverse transcriptase PCR-derived time-course data of genes were modelled. "Split-line" or "broken-stick" regression identified the initial time of gene up-regulation, enabling the classification of genes into those with primary and secondary responses. Five-day profiles were modelled using the biologically-oriented, critical exponential curve, y(t = A + (B + CtRt + ε. This non-linear regression approach allowed the expression patterns for different genes to be compared in terms of curve shape, time of maximal transcript level and the decline and asymptotic response levels. Three distinct regulatory patterns were identified for the five genes studied. Applying the regression modelling approach to microarray-derived time course data
Statistical model of a gas diffusion electrode. III. Photomicrograph study
Winsel, A W
1965-12-01
A linear section through a gas diffusion electrode produces a certain distribution function of sinews with the pores. From this distribution function some qualities of the pore structure are derived, and an automatic device to determine the distribution function is described. With a statistical model of a gas diffusion electrode the behavior of a DSK electrode is discussed and compared with earlier measurements of the flow resistance of this material.
Hamid, Ka; Yusoff, An; Rahman, Mza; Mohamad, M; Hamid, Aia
2012-04-01
This fMRI study is about modelling the effective connectivity between Heschl's gyrus (HG) and the superior temporal gyrus (STG) in human primary auditory cortices. MATERIALS #ENTITYSTARTX00026; Ten healthy male participants were required to listen to white noise stimuli during functional magnetic resonance imaging (fMRI) scans. Statistical parametric mapping (SPM) was used to generate individual and group brain activation maps. For input region determination, two intrinsic connectivity models comprising bilateral HG and STG were constructed using dynamic causal modelling (DCM). The models were estimated and inferred using DCM while Bayesian Model Selection (BMS) for group studies was used for model comparison and selection. Based on the winning model, six linear and six non-linear causal models were derived and were again estimated, inferred, and compared to obtain a model that best represents the effective connectivity between HG and the STG, balancing accuracy and complexity. Group results indicated significant asymmetrical activation (p(uncorr) Model comparison results showed strong evidence of STG as the input centre. The winning model is preferred by 6 out of 10 participants. The results were supported by BMS results for group studies with the expected posterior probability, r = 0.7830 and exceedance probability, ϕ = 0.9823. One-sample t-tests performed on connection values obtained from the winning model indicated that the valid connections for the winning model are the unidirectional parallel connections from STG to bilateral HG (p model comparison between linear and non-linear models using BMS prefers non-linear connection (r = 0.9160, ϕ = 1.000) from which the connectivity between STG and the ipsi- and contralateral HG is gated by the activity in STG itself. We are able to demonstrate that the effective connectivity between HG and STG while listening to white noise for the respective participants can be explained by a non-linear dynamic causal model with
Model Selection with the Linear Mixed Model for Longitudinal Data
Ryoo, Ji Hoon
2011-01-01
Model building or model selection with linear mixed models (LMMs) is complicated by the presence of both fixed effects and random effects. The fixed effects structure and random effects structure are codependent, so selection of one influences the other. Most presentations of LMM in psychology and education are based on a multilevel or…
Explicit estimating equations for semiparametric generalized linear latent variable models
Ma, Yanyuan
2010-07-05
We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.
Modelling and Predicting Backstroke Start Performance Using Non-Linear and Linear Models.
de Jesus, Karla; Ayala, Helon V H; de Jesus, Kelly; Coelho, Leandro Dos S; Medeiros, Alexandre I A; Abraldes, José A; Vaz, Mário A P; Fernandes, Ricardo J; Vilas-Boas, João Paulo
2018-03-01
Our aim was to compare non-linear and linear mathematical model responses for backstroke start performance prediction. Ten swimmers randomly completed eight 15 m backstroke starts with feet over the wedge, four with hands on the highest horizontal and four on the vertical handgrip. Swimmers were videotaped using a dual media camera set-up, with the starts being performed over an instrumented block with four force plates. Artificial neural networks were applied to predict 5 m start time using kinematic and kinetic variables and to determine the accuracy of the mean absolute percentage error. Artificial neural networks predicted start time more robustly than the linear model with respect to changing training to the validation dataset for the vertical handgrip (3.95 ± 1.67 vs. 5.92 ± 3.27%). Artificial neural networks obtained a smaller mean absolute percentage error than the linear model in the horizontal (0.43 ± 0.19 vs. 0.98 ± 0.19%) and vertical handgrip (0.45 ± 0.19 vs. 1.38 ± 0.30%) using all input data. The best artificial neural network validation revealed a smaller mean absolute error than the linear model for the horizontal (0.007 vs. 0.04 s) and vertical handgrip (0.01 vs. 0.03 s). Artificial neural networks should be used for backstroke 5 m start time prediction due to the quite small differences among the elite level performances.
Growth curve models and statistical diagnostics
Pan, Jian-Xin
2002-01-01
Growth-curve models are generalized multivariate analysis-of-variance models. These models are especially useful for investigating growth problems on short times in economics, biology, medical research, and epidemiology. This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. The authors provide complete proofs of theorems as well as practical data sets and MATLAB code.
Topology for Statistical Modeling of Petascale Data
Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Bremer, P. -T. [Univ. of Utah, Salt Lake City, UT (United States)
2013-10-31
Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, the approach of the entire team involving all three institutions is based on the complementary techniques of combinatorial topology and statistical modelling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modelling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. The overall technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modelling, and (3) new integrated topological and statistical methods. Roughly speaking, the division of labor between our 3 groups (Sandia Labs in Livermore, Texas A&M in College Station, and U Utah in Salt Lake City) is as follows: the Sandia group focuses on statistical methods and their formulation in algebraic terms, and finds the application problems (and data sets) most relevant to this project, the Texas A&M Group develops new algebraic geometry algorithms, in particular with fewnomial theory, and the Utah group develops new algorithms in computational topology via Discrete Morse Theory. However, we hasten to point out that our three groups stay in tight contact via videconference every 2 weeks, so there is much synergy of ideas between the groups. The following of this document is focused on the contributions that had grater direct involvement from the team at the University of Utah in Salt Lake City.
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
Applied systems ecology: models, data, and statistical methods
Eberhardt, L L
1976-01-01
In this report, systems ecology is largely equated to mathematical or computer simulation modelling. The need for models in ecology stems from the necessity to have an integrative device for the diversity of ecological data, much of which is observational, rather than experimental, as well as from the present lack of a theoretical structure for ecology. Different objectives in applied studies require specialized methods. The best predictive devices may be regression equations, often non-linear in form, extracted from much more detailed models. A variety of statistical aspects of modelling, including sampling, are discussed. Several aspects of population dynamics and food-chain kinetics are described, and it is suggested that the two presently separated approaches should be combined into a single theoretical framework. It is concluded that future efforts in systems ecology should emphasize actual data and statistical methods, as well as modelling.
Modeling patterns in data using linear and related models
Engelhardt, M.E.
1996-06-01
This report considers the use of linear models for analyzing data related to reliability and safety issues of the type usually associated with nuclear power plants. The report discusses some of the general results of linear regression analysis, such as the model assumptions and properties of the estimators of the parameters. The results are motivated with examples of operational data. Results about the important case of a linear regression model with one covariate are covered in detail. This case includes analysis of time trends. The analysis is applied with two different sets of time trend data. Diagnostic procedures and tests for the adequacy of the model are discussed. Some related methods such as weighted regression and nonlinear models are also considered. A discussion of the general linear model is also included. Appendix A gives some basic SAS programs and outputs for some of the analyses discussed in the body of the report. Appendix B is a review of some of the matrix theoretic results which are useful in the development of linear models
Electron Model of Linear-Field FFAG
Koscielniak, Shane R
2005-01-01
A fixed-field alternating-gradient accelerator (FFAG) that employs only linear-field elements ushers in a new regime in accelerator design and dynamics. The linear-field machine has the ability to compact an unprecedented range in momenta within a small component aperture. With a tune variation which results from the natural chromaticity, the beam crosses many strong, uncorrec-table, betatron resonances during acceleration. Further, relativistic particles in this machine exhibit a quasi-parabolic time-of-flight that cannot be addressed with a fixed-frequency rf system. This leads to a new concept of bucketless acceleration within a rotation manifold. With a large energy jump per cell, there is possibly strong synchro-betatron coupling. A few-MeV electron model has been proposed to demonstrate the feasibility of these untested acceleration features and to investigate them at length under a wide range of operating conditions. This paper presents a lattice optimized for a 1.3 GHz rf, initial technology choices f...
Siddiqi, Ariba; Arjunan, Sridhar P; Kumar, Dinesh K
2016-08-01
Age-associated changes in the surface electromyogram (sEMG) of Tibialis Anterior (TA) muscle can be attributable to neuromuscular alterations that precede strength loss. We have used our sEMG model of the Tibialis Anterior to interpret the age-related changes and compared with the experimental sEMG. Eighteen young (20-30 years) and 18 older (60-85 years) performed isometric dorsiflexion at 6 different percentage levels of maximum voluntary contractions (MVC), and their sEMG from the TA muscle was recorded. Six different age-related changes in the neuromuscular system were simulated using the sEMG model at the same MVCs as the experiment. The maximal power of the spectrum, Gaussianity and Linearity Test Statistics were computed from the simulated and experimental sEMG. A correlation analysis at α=0.05 was performed between the simulated and experimental age-related change in the sEMG features. The results show the loss in motor units was distinguished by the Gaussianity and Linearity test statistics; while the maximal power of the PSD distinguished between the muscular factors. The simulated condition of 40% loss of motor units with halved the number of fast fibers best correlated with the age-related change observed in the experimental sEMG higher order statistical features. The simulated aging condition found by this study corresponds with the moderate motor unit remodelling and negligible strength loss reported in literature for the cohorts aged 60-70 years.
Chattopadhyay, Anirban; Khondekar, Mofazzal Hossain; Bhattacharjee, Anup Kumar
2017-09-01
In this paper initiative has been taken to search the periodicities of linear speed of Coronal Mass Ejection in solar cycle 23. Double exponential smoothing and Discrete Wavelet Transform are being used for detrending and filtering of the CME linear speed time series. To choose the appropriate statistical methodology for the said purpose, Smoothed Pseudo Wigner-Ville distribution (SPWVD) has been used beforehand to confirm the non-stationarity of the time series. The Time-Frequency representation tool like Hilbert Huang Transform and Empirical Mode decomposition has been implemented to unearth the underneath periodicities in the non-stationary time series of the linear speed of CME. Of all the periodicities having more than 95% Confidence Level, the relevant periodicities have been segregated out using Integral peak detection algorithm. The periodicities observed are of low scale ranging from 2-159 days with some relevant periods like 4 days, 10 days, 11 days, 12 days, 13.7 days, 14.5 and 21.6 days. These short range periodicities indicate the probable origin of the CME is the active longitude and the magnetic flux network of the sun. The results also insinuate about the probable mutual influence and causality with other solar activities (like solar radio emission, Ap index, solar wind speed, etc.) owing to the similitude between their periods and CME linear speed periods. The periodicities of 4 days and 10 days indicate the possible existence of the Rossby-type waves or planetary waves in Sun.
On the Use of Rank Tests and Estimates in the Linear Model.
1982-06-01
models," Journal of the Royal Statistical Society , Series B, 42, 366-371. Neter, J. and Wasserman, W. (1974), Applied Linear Statistical Models...University Park, PA. Schuster, E. (1974), "On the rate of convergence of an estimate of a functional of a probability density," Scandinavian Acturial
New robust statistical procedures for the polytomous logistic regression models.
Castilla, Elena; Ghosh, Abhik; Martin, Nirian; Pardo, Leandro
2018-05-17
This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications. © 2018, The International Biometric Society.
Statistical transmutation in doped quantum dimer models.
Lamas, C A; Ralko, A; Cabra, D C; Poilblanc, D; Pujol, P
2012-07-06
We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.
STATISTICAL MODELS OF REPRESENTING INTELLECTUAL CAPITAL
Andreea Feraru
2016-06-01
Full Text Available This article entitled Statistical Models of Representing Intellectual Capital approaches and analyses the concept of intellectual capital, as well as the main models which can support enterprisers/managers in evaluating and quantifying the advantages of intellectual capital. Most authors examine intellectual capital from a static perspective and focus on the development of its various evaluation models. In this chapter we surveyed the classical static models: Sveiby, Edvisson, Balanced Scorecard, as well as the canonical model of intellectual capital. Among the group of static models for evaluating organisational intellectual capital the canonical model stands out. This model enables the structuring of organisational intellectual capital in: human capital, structural capital and relational capital. Although the model is widely spread, it is a static one and can thus create a series of errors in the process of evaluation, because all the three entities mentioned above are not independent from the viewpoint of their contents, as any logic of structuring complex entities requires.
Role of statistical linearization in the solution of nonlinear stochastic equations
Budgor, A.B.
1977-01-01
The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables
Topology for Statistical Modeling of Petascale Data
Bennett, Janine Camille [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pebay, Philippe Pierre [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Rojas, Maurice [Texas A & M Univ., College Station, TX (United States)
2014-07-01
This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled "Topology for Statistical Modeling of Petascale Data", funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program.
Establishing statistical models of manufacturing parameters
Senevat, J.; Pape, J.L.; Deshayes, J.F.
1991-01-01
This paper reports on the effect of pilgering and cold-work parameters on contractile strain ratio and mechanical properties that were investigated using a large population of Zircaloy tubes. Statistical models were established between: contractile strain ratio and tooling parameters, mechanical properties (tensile test, creep test) and cold-work parameters, and mechanical properties and stress-relieving temperature
Nonlinear price impact from linear models
Patzelt, Felix; Bouchaud, Jean-Philippe
2017-12-01
The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators, and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales (Patzelt and Bouchaud 2017 arXiv:1706.04163). Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear ‘propagator’ models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.
Statistical models for optimizing mineral exploration
Wignall, T.K.; DeGeoffroy, J.
1987-01-01
The primary purpose of mineral exploration is to discover ore deposits. The emphasis of this volume is on the mathematical and computational aspects of optimizing mineral exploration. The seven chapters that make up the main body of the book are devoted to the description and application of various types of computerized geomathematical models. These chapters include: (1) the optimal selection of ore deposit types and regions of search, as well as prospecting selected areas, (2) designing airborne and ground field programs for the optimal coverage of prospecting areas, and (3) delineating and evaluating exploration targets within prospecting areas by means of statistical modeling. Many of these statistical programs are innovative and are designed to be useful for mineral exploration modeling. Examples of geomathematical models are applied to exploring for six main types of base and precious metal deposits, as well as other mineral resources (such as bauxite and uranium)
A statistical model for mapping morphological shape
Li Jiahan
2010-07-01
Full Text Available Abstract Background Living things come in all shapes and sizes, from bacteria, plants, and animals to humans. Knowledge about the genetic mechanisms for biological shape has far-reaching implications for a range spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine. Results We derived a statistical model for mapping specific genes or quantitative trait loci (QTLs that control morphological shape. The model was formulated within the mixture framework, in which different types of shape are thought to result from genotypic discrepancies at a QTL. The EM algorithm was implemented to estimate QTL genotype-specific shapes based on a shape correspondence analysis. Computer simulation was used to investigate the statistical property of the model. Conclusion By identifying specific QTLs for morphological shape, the model developed will help to ask, disseminate and address many major integrative biological and genetic questions and challenges in the genetic control of biological shape and function.
Understanding and forecasting polar stratospheric variability with statistical models
C. Blume
2012-07-01
Full Text Available The variability of the north-polar stratospheric vortex is a prominent aspect of the middle atmosphere. This work investigates a wide class of statistical models with respect to their ability to model geopotential and temperature anomalies, representing variability in the polar stratosphere. Four partly nonstationary, nonlinear models are assessed: linear discriminant analysis (LDA; a cluster method based on finite elements (FEM-VARX; a neural network, namely the multi-layer perceptron (MLP; and support vector regression (SVR. These methods model time series by incorporating all significant external factors simultaneously, including ENSO, QBO, the solar cycle, volcanoes, to then quantify their statistical importance. We show that variability in reanalysis data from 1980 to 2005 is successfully modeled. The period from 2005 to 2011 can be hindcasted to a certain extent, where MLP performs significantly better than the remaining models. However, variability remains that cannot be statistically hindcasted within the current framework, such as the unexpected major warming in January 2009. Finally, the statistical model with the best generalization performance is used to predict a winter 2011/12 with warm and weak vortex conditions. A vortex breakdown is predicted for late January, early February 2012.
Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.
2009-01-01
This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…
Performance modeling, stochastic networks, and statistical multiplexing
Mazumdar, Ravi R
2013-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the importan
Statistical models for competing risk analysis
Sather, H.N.
1976-08-01
Research results on three new models for potential applications in competing risks problems. One section covers the basic statistical relationships underlying the subsequent competing risks model development. Another discusses the problem of comparing cause-specific risk structure by competing risks theory in two homogeneous populations, P1 and P2. Weibull models which allow more generality than the Berkson and Elveback models are studied for the effect of time on the hazard function. The use of concomitant information for modeling single-risk survival is extended to the multiple failure mode domain of competing risks. The model used to illustrate the use of this methodology is a life table model which has constant hazards within pre-designated intervals of the time scale. Two parametric models for bivariate dependent competing risks, which provide interesting alternatives, are proposed and examined
Statistical physics of pairwise probability models
Yasser Roudi
2009-11-01
Full Text Available Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying and using pairwise models. We build on our previous work on the subject and study the relation between different methods for fitting these models and evaluating their quality. In particular, using data from simulated cortical networks we study how the quality of various approximate methods for inferring the parameters in a pairwise model depends on the time bin chosen for binning the data. We also study the effect of the size of the time bin on the model quality itself, again using simulated data. We show that using finer time bins increases the quality of the pairwise model. We offer new ways of deriving the expressions reported in our previous work for assessing the quality of pairwise models.
Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots
Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.
2013-01-01
Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…
From linear to generalized linear mixed models: A case study in repeated measures
Compared to traditional linear mixed models, generalized linear mixed models (GLMMs) can offer better correspondence between response variables and explanatory models, yielding more efficient estimates and tests in the analysis of data from designed experiments. Using proportion data from a designed...
Montoye, Alexander H K; Begum, Munni; Henning, Zachary; Pfeiffer, Karin A
2017-02-01
This study had three purposes, all related to evaluating energy expenditure (EE) prediction accuracy from body-worn accelerometers: (1) compare linear regression to linear mixed models, (2) compare linear models to artificial neural network models, and (3) compare accuracy of accelerometers placed on the hip, thigh, and wrists. Forty individuals performed 13 activities in a 90 min semi-structured, laboratory-based protocol. Participants wore accelerometers on the right hip, right thigh, and both wrists and a portable metabolic analyzer (EE criterion). Four EE prediction models were developed for each accelerometer: linear regression, linear mixed, and two ANN models. EE prediction accuracy was assessed using correlations, root mean square error (RMSE), and bias and was compared across models and accelerometers using repeated-measures analysis of variance. For all accelerometer placements, there were no significant differences for correlations or RMSE between linear regression and linear mixed models (correlations: r = 0.71-0.88, RMSE: 1.11-1.61 METs; p > 0.05). For the thigh-worn accelerometer, there were no differences in correlations or RMSE between linear and ANN models (ANN-correlations: r = 0.89, RMSE: 1.07-1.08 METs. Linear models-correlations: r = 0.88, RMSE: 1.10-1.11 METs; p > 0.05). Conversely, one ANN had higher correlations and lower RMSE than both linear models for the hip (ANN-correlation: r = 0.88, RMSE: 1.12 METs. Linear models-correlations: r = 0.86, RMSE: 1.18-1.19 METs; p linear models for the wrist-worn accelerometers (ANN-correlations: r = 0.82-0.84, RMSE: 1.26-1.32 METs. Linear models-correlations: r = 0.71-0.73, RMSE: 1.55-1.61 METs; p models offer a significant improvement in EE prediction accuracy over linear models. Conversely, linear models showed similar EE prediction accuracy to machine learning models for hip- and thigh
Equilibrium statistical mechanics of lattice models
Lavis, David A
2015-01-01
Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg—Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi—Hijmans—De Boer hierarchy of approximations. In Part III the use of alge...
Statistical shape and appearance models of bones.
Sarkalkan, Nazli; Weinans, Harrie; Zadpoor, Amir A
2014-03-01
When applied to bones, statistical shape models (SSM) and statistical appearance models (SAM) respectively describe the mean shape and mean density distribution of bones within a certain population as well as the main modes of variations of shape and density distribution from their mean values. The availability of this quantitative information regarding the detailed anatomy of bones provides new opportunities for diagnosis, evaluation, and treatment of skeletal diseases. The potential of SSM and SAM has been recently recognized within the bone research community. For example, these models have been applied for studying the effects of bone shape on the etiology of osteoarthritis, improving the accuracy of clinical osteoporotic fracture prediction techniques, design of orthopedic implants, and surgery planning. This paper reviews the main concepts, methods, and applications of SSM and SAM as applied to bone. Copyright © 2013 Elsevier Inc. All rights reserved.
Statistical Models of Adaptive Immune populations
Sethna, Zachary; Callan, Curtis; Walczak, Aleksandra; Mora, Thierry
The availability of large (104-106 sequences) datasets of B or T cell populations from a single individual allows reliable fitting of complex statistical models for naïve generation, somatic selection, and hypermutation. It is crucial to utilize a probabilistic/informational approach when modeling these populations. The inferred probability distributions allow for population characterization, calculation of probability distributions of various hidden variables (e.g. number of insertions), as well as statistical properties of the distribution itself (e.g. entropy). In particular, the differences between the T cell populations of embryonic and mature mice will be examined as a case study. Comparing these populations, as well as proposed mixed populations, provides a concrete exercise in model creation, comparison, choice, and validation.
Evaluating the double Poisson generalized linear model.
Zou, Yaotian; Geedipally, Srinivas Reddy; Lord, Dominique
2013-10-01
The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle for applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one observed under-dispersed dataset. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. Considering the fact that the DP GLM can be easily estimated with inexpensive computation and that it is simpler to interpret coefficients, it offers a flexible and efficient alternative for researchers to model count data. Copyright © 2013 Elsevier Ltd. All rights reserved.
Statistical Modelling of Wind Proles - Data Analysis and Modelling
Jónsson, Tryggvi; Pinson, Pierre
The aim of the analysis presented in this document is to investigate whether statistical models can be used to make very short-term predictions of wind profiles.......The aim of the analysis presented in this document is to investigate whether statistical models can be used to make very short-term predictions of wind profiles....
Petri Nets as Models of Linear Logic
Engberg, Uffe Henrik; Winskel, Glynn
1990-01-01
The chief purpose of this paper is to appraise the feasibility of Girad's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic...
Statistical modeling of geopressured geothermal reservoirs
Ansari, Esmail; Hughes, Richard; White, Christopher D.
2017-06-01
Identifying attractive candidate reservoirs for producing geothermal energy requires predictive models. In this work, inspectional analysis and statistical modeling are used to create simple predictive models for a line drive design. Inspectional analysis on the partial differential equations governing this design yields a minimum number of fifteen dimensionless groups required to describe the physics of the system. These dimensionless groups are explained and confirmed using models with similar dimensionless groups but different dimensional parameters. This study models dimensionless production temperature and thermal recovery factor as the responses of a numerical model. These responses are obtained by a Box-Behnken experimental design. An uncertainty plot is used to segment the dimensionless time and develop a model for each segment. The important dimensionless numbers for each segment of the dimensionless time are identified using the Boosting method. These selected numbers are used in the regression models. The developed models are reduced to have a minimum number of predictors and interactions. The reduced final models are then presented and assessed using testing runs. Finally, applications of these models are offered. The presented workflow is generic and can be used to translate the output of a numerical simulator into simple predictive models in other research areas involving numerical simulation.
A statistical model for instable thermodynamical systems
Sommer, Jens-Uwe
2003-01-01
A generic model is presented for statistical systems which display thermodynamic features in contrast to our everyday experience, such as infinite and negative heat capacities. Such system are instable in terms of classical equilibrium thermodynamics. Using our statistical model, we are able to investigate states of instable systems which are undefined in the framework of equilibrium thermodynamics. We show that a region of negative heat capacity in the adiabatic environment, leads to a first order like phase transition when the system is coupled to a heat reservoir. This phase transition takes place without a phase coexistence. Nevertheless, all intermediate states are stable due to fluctuations. When two instable system are brought in thermal contact, the temperature of the composed system is lower than the minimum temperature of the individual systems. Generally, the equilibrium states of instable system cannot be simply decomposed into equilibrium states of the individual systems. The properties of instable system depend on the environment, ensemble equivalence is broken
Logarithmic transformed statistical models in calibration
Zeis, C.D.
1975-01-01
A general type of statistical model used for calibration of instruments having the property that the standard deviations of the observed values increase as a function of the mean value is described. The application to the Helix Counter at the Rocky Flats Plant is primarily from a theoretical point of view. The Helix Counter measures the amount of plutonium in certain types of chemicals. The method described can be used also for other calibrations. (U.S.)
ARSENIC CONTAMINATION IN GROUNDWATER: A STATISTICAL MODELING
Palas Roy; Naba Kumar Mondal; Biswajit Das; Kousik Das
2013-01-01
High arsenic in natural groundwater in most of the tubewells of the Purbasthali- Block II area of Burdwan district (W.B, India) has recently been focused as a serious environmental concern. This paper is intending to illustrate the statistical modeling of the arsenic contaminated groundwater to identify the interrelation of that arsenic contain with other participating groundwater parameters so that the arsenic contamination level can easily be predicted by analyzing only such parameters. Mul...
Analyzing longitudinal data with the linear mixed models procedure in SPSS.
West, Brady T
2009-09-01
Many applied researchers analyzing longitudinal data share a common misconception: that specialized statistical software is necessary to fit hierarchical linear models (also known as linear mixed models [LMMs], or multilevel models) to longitudinal data sets. Although several specialized statistical software programs of high quality are available that allow researchers to fit these models to longitudinal data sets (e.g., HLM), rapid advances in general purpose statistical software packages have recently enabled analysts to fit these same models when using preferred packages that also enable other more common analyses. One of these general purpose statistical packages is SPSS, which includes a very flexible and powerful procedure for fitting LMMs to longitudinal data sets with continuous outcomes. This article aims to present readers with a practical discussion of how to analyze longitudinal data using the LMMs procedure in the SPSS statistical software package.
Connection between weighted LPC and higher-order statistics for AR model estimation
Kamp, Y.; Ma, C.
1993-01-01
This paper establishes the relationship between a weighted linear prediction method used for robust analysis of voiced speech and the autoregressive modelling based on higher-order statistics, known as cumulants
A simple statistical model for geomagnetic reversals
Constable, Catherine
1990-01-01
The diversity of paleomagnetic records of geomagnetic reversals now available indicate that the field configuration during transitions cannot be adequately described by simple zonal or standing field models. A new model described here is based on statistical properties inferred from the present field and is capable of simulating field transitions like those observed. Some insight is obtained into what one can hope to learn from paleomagnetic records. In particular, it is crucial that the effects of smoothing in the remanence acquisition process be separated from true geomagnetic field behavior. This might enable us to determine the time constants associated with the dominant field configuration during a reversal.
Linear approximation model network and its formation via ...
To overcome the deficiency of `local model network' (LMN) techniques, an alternative `linear approximation model' (LAM) network approach is proposed. Such a network models a nonlinear or practical system with multiple linear models fitted along operating trajectories, where individual models are simply networked ...
Probabilistic model of ligaments and tendons: Quasistatic linear stretching
Bontempi, M.
2009-03-01
Ligaments and tendons have a significant role in the musculoskeletal system and are frequently subjected to injury. This study presents a model of collagen fibers, based on the study of a statistical distribution of fibers when they are subjected to quasistatic linear stretching. With respect to other methodologies, this model is able to describe the behavior of the bundle using less ad hoc hypotheses and is able to describe all the quasistatic stretch-load responses of the bundle, including the yield and failure regions described in the literature. It has two other important results: the first is that it is able to correlate the mechanical behavior of the bundle with its internal structure, and it suggests a methodology to deduce the fibers population distribution directly from the tensile-test data. The second is that it can follow fibers’ structure evolution during the stretching and it is possible to study the internal adaptation of fibers in physiological and pathological conditions.
Linear regression crash prediction models : issues and proposed solutions.
2010-05-01
The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...
Game Theory and its Relationship with Linear Programming Models ...
Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.
Statistical Modelling of the Soil Dielectric Constant
Usowicz, Boguslaw; Marczewski, Wojciech; Bogdan Usowicz, Jerzy; Lipiec, Jerzy
2010-05-01
The dielectric constant of soil is the physical property being very sensitive on water content. It funds several electrical measurement techniques for determining the water content by means of direct (TDR, FDR, and others related to effects of electrical conductance and/or capacitance) and indirect RS (Remote Sensing) methods. The work is devoted to a particular statistical manner of modelling the dielectric constant as the property accounting a wide range of specific soil composition, porosity, and mass density, within the unsaturated water content. Usually, similar models are determined for few particular soil types, and changing the soil type one needs switching the model on another type or to adjust it by parametrization of soil compounds. Therefore, it is difficult comparing and referring results between models. The presented model was developed for a generic representation of soil being a hypothetical mixture of spheres, each representing a soil fraction, in its proper phase state. The model generates a serial-parallel mesh of conductive and capacitive paths, which is analysed for a total conductive or capacitive property. The model was firstly developed to determine the thermal conductivity property, and now it is extended on the dielectric constant by analysing the capacitive mesh. The analysis is provided by statistical means obeying physical laws related to the serial-parallel branching of the representative electrical mesh. Physical relevance of the analysis is established electrically, but the definition of the electrical mesh is controlled statistically by parametrization of compound fractions, by determining the number of representative spheres per unitary volume per fraction, and by determining the number of fractions. That way the model is capable covering properties of nearly all possible soil types, all phase states within recognition of the Lorenz and Knudsen conditions. In effect the model allows on generating a hypothetical representative of
Casellas, J; Bach, R
2012-06-01
Lambing interval is a relevant reproductive indicator for sheep populations under continuous mating systems, although there is a shortage of selection programs accounting for this trait in the sheep industry. Both the historical assumption of small genetic background and its unorthodox distribution pattern have limited its implementation as a breeding objective. In this manuscript, statistical performances of 3 alternative parametrizations [i.e., symmetric Gaussian mixed linear (GML) model, skew-Gaussian mixed linear (SGML) model, and piecewise Weibull proportional hazard (PWPH) model] have been compared to elucidate the preferred methodology to handle lambing interval data. More specifically, flock-by-flock analyses were performed on 31,986 lambing interval records (257.3 ± 0.2 d) from 6 purebred Ripollesa flocks. Model performances were compared in terms of deviance information criterion (DIC) and Bayes factor (BF). For all flocks, PWPH models were clearly preferred; they generated a reduction of 1,900 or more DIC units and provided BF estimates larger than 100 (i.e., PWPH models against linear models). These differences were reduced when comparing PWPH models with different number of change points for the baseline hazard function. In 4 flocks, only 2 change points were required to minimize the DIC, whereas 4 and 6 change points were needed for the 2 remaining flocks. These differences demonstrated a remarkable degree of heterogeneity across sheep flocks that must be properly accounted for in genetic evaluation models to avoid statistical biases and suboptimal genetic trends. Within this context, all 6 Ripollesa flocks revealed substantial genetic background for lambing interval with heritabilities ranging between 0.13 and 0.19. This study provides the first evidence of the suitability of PWPH models for lambing interval analysis, clearly discarding previous parametrizations focused on mixed linear models.
A statistical theory of cell killing by radiation of varying linear energy transfer
Hawkins, R.B.
1994-01-01
A theory is presented that provides an explanation for the observed features of the survival of cultured cells after exposure to densely ionizing high-linear energy transfer (LET) radiation. It starts from a phenomenological postulate based on the linear-quadratic form of cell survival observed for low-LET radiation and uses principles of statistics and fluctuation theory to demonstrate that the effect of varying LET on cell survival can be attributed to random variation of dose to small volumes contained within the nucleus. A simple relation is presented for surviving fraction of cells after exposure to radiation of varying LET that depends on the α and β parameters for the same cells in the limit of low-LET radiation. This relation implies that the value of β is independent of LET. Agreement of the theory with selected observations of cell survival from the literature is demonstrated. A relation is presented that gives relative biological effectiveness (RBE) as a function of the α and β parameters for low-LET radiation. Measurements from microdosimetry are used to estimate the size of the subnuclear volume to which the fluctuation pertains. 11 refs., 4 figs., 2 tabs
Encoding Dissimilarity Data for Statistical Model Building.
Wahba, Grace
2010-12-01
We summarize, review and comment upon three papers which discuss the use of discrete, noisy, incomplete, scattered pairwise dissimilarity data in statistical model building. Convex cone optimization codes are used to embed the objects into a Euclidean space which respects the dissimilarity information while controlling the dimension of the space. A "newbie" algorithm is provided for embedding new objects into this space. This allows the dissimilarity information to be incorporated into a Smoothing Spline ANOVA penalized likelihood model, a Support Vector Machine, or any model that will admit Reproducing Kernel Hilbert Space components, for nonparametric regression, supervised learning, or semi-supervised learning. Future work and open questions are discussed. The papers are: F. Lu, S. Keles, S. Wright and G. Wahba 2005. A framework for kernel regularization with application to protein clustering. Proceedings of the National Academy of Sciences 102, 12332-1233.G. Corrada Bravo, G. Wahba, K. Lee, B. Klein, R. Klein and S. Iyengar 2009. Examining the relative influence of familial, genetic and environmental covariate information in flexible risk models. Proceedings of the National Academy of Sciences 106, 8128-8133F. Lu, Y. Lin and G. Wahba. Robust manifold unfolding with kernel regularization. TR 1008, Department of Statistics, University of Wisconsin-Madison.
A Note on the Identifiability of Generalized Linear Mixed Models
Labouriau, Rodrigo
2014-01-01
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first and second order moments and some general mild regularity...... conditions, and, therefore, is extensible to quasi-likelihood based generalized linear models. In particular, binomial and Poisson mixed models with dispersion parameter are identifiable when equipped with the standard parametrization...
Linear control theory for gene network modeling.
Shin, Yong-Jun; Bleris, Leonidas
2010-09-16
Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.
LINEAR MODEL FOR NON ISOSCELES ABSORBERS.
BERG,J.S.
2003-05-12
Previous analyses have assumed that wedge absorbers are triangularly shaped with equal angles for the two faces. In this case, to linear order, the energy loss depends only on the position in the direction of the face tilt, and is independent of the incoming angle. One can instead construct an absorber with entrance and exit faces facing rather general directions. In this case, the energy loss can depend on both the position and the angle of the particle in question. This paper demonstrates that and computes the effect to linear order.
Average Nuclear properties based on statistical model
El-Jaick, L.J.
1974-01-01
The rough properties of nuclei were investigated by statistical model, in systems with the same and different number of protons and neutrons, separately, considering the Coulomb energy in the last system. Some average nuclear properties were calculated based on the energy density of nuclear matter, from Weizsscker-Beth mass semiempiric formulae, generalized for compressible nuclei. In the study of a s surface energy coefficient, the great influence exercised by Coulomb energy and nuclear compressibility was verified. For a good adjust of beta stability lines and mass excess, the surface symmetry energy were established. (M.C.K.) [pt
Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer
2013-01-01
Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…
Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.
Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad
2016-02-01
In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.
A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation
Rajeswaran, Jeevanantham; Blackstone, Eugene H.
2014-01-01
In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830
An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...
Statistical approach for selection of regression model during validation of bioanalytical method
Natalija Nakov
2014-06-01
Full Text Available The selection of an adequate regression model is the basis for obtaining accurate and reproducible results during the bionalytical method validation. Given the wide concentration range, frequently present in bioanalytical assays, heteroscedasticity of the data may be expected. Several weighted linear and quadratic regression models were evaluated during the selection of the adequate curve fit using nonparametric statistical tests: One sample rank test and Wilcoxon signed rank test for two independent groups of samples. The results obtained with One sample rank test could not give statistical justification for the selection of linear vs. quadratic regression models because slight differences between the error (presented through the relative residuals were obtained. Estimation of the significance of the differences in the RR was achieved using Wilcoxon signed rank test, where linear and quadratic regression models were treated as two independent groups. The application of this simple non-parametric statistical test provides statistical confirmation of the choice of an adequate regression model.
Statistical pairwise interaction model of stock market
Bury, Thomas
2013-03-01
Financial markets are a classical example of complex systems as they are compound by many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or they are agent-based models with rules designed in order to recover some empirical behaviors. Here we show that the pairwise model is actually a statistically consistent model with the observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach only based on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviors, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.
Tried and True: Springing into Linear Models
Darling, Gerald
2012-01-01
In eighth grade, students usually learn about forces in science class and linear relationships in math class, crucial topics that form the foundation for further study in science and engineering. An activity that links these two fundamental concepts involves measuring the distance a spring stretches as a function of how much weight is suspended…
Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems
Bambang Riyanto
2005-11-01
Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.
Ordinal Log-Linear Models for Contingency Tables
Brzezińska Justyna
2016-12-01
Full Text Available A log-linear analysis is a method providing a comprehensive scheme to describe the association for categorical variables in a contingency table. The log-linear model specifies how the expected counts depend on the levels of the categorical variables for these cells and provide detailed information on the associations. The aim of this paper is to present theoretical, as well as empirical, aspects of ordinal log-linear models used for contingency tables with ordinal variables. We introduce log-linear models for ordinal variables: linear-by-linear association, row effect model, column effect model and RC Goodman’s model. Algorithm, advantages and disadvantages will be discussed in the paper. An empirical analysis will be conducted with the use of R.
Recent Updates to the GEOS-5 Linear Model
Holdaway, Dan; Kim, Jong G.; Errico, Ron; Gelaro, Ronald; Mahajan, Rahul
2014-01-01
Global Modeling and Assimilation Office (GMAO) is close to having a working 4DVAR system and has developed a linearized version of GEOS-5.This talk outlines a series of improvements made to the linearized dynamics, physics and trajectory.Of particular interest is the development of linearized cloud microphysics, which provides the framework for 'all-sky' data assimilation.
Statistical modeling to support power system planning
Staid, Andrea
This dissertation focuses on data-analytic approaches that improve our understanding of power system applications to promote better decision-making. It tackles issues of risk analysis, uncertainty management, resource estimation, and the impacts of climate change. Tools of data mining and statistical modeling are used to bring new insight to a variety of complex problems facing today's power system. The overarching goal of this research is to improve the understanding of the power system risk environment for improved operation, investment, and planning decisions. The first chapter introduces some challenges faced in planning for a sustainable power system. Chapter 2 analyzes the driving factors behind the disparity in wind energy investments among states with a goal of determining the impact that state-level policies have on incentivizing wind energy. Findings show that policy differences do not explain the disparities; physical and geographical factors are more important. Chapter 3 extends conventional wind forecasting to a risk-based focus of predicting maximum wind speeds, which are dangerous for offshore operations. Statistical models are presented that issue probabilistic predictions for the highest wind speed expected in a three-hour interval. These models achieve a high degree of accuracy and their use can improve safety and reliability in practice. Chapter 4 examines the challenges of wind power estimation for onshore wind farms. Several methods for wind power resource assessment are compared, and the weaknesses of the Jensen model are demonstrated. For two onshore farms, statistical models outperform other methods, even when very little information is known about the wind farm. Lastly, chapter 5 focuses on the power system more broadly in the context of the risks expected from tropical cyclones in a changing climate. Risks to U.S. power system infrastructure are simulated under different scenarios of tropical cyclone behavior that may result from climate
Acceleration transforms and statistical kinetic models
LuValle, M.J.; Welsher, T.L.; Svoboda, K.
1988-01-01
For a restricted class of problems a mathematical model of microscopic degradation processes, statistical kinetics, is developed and linked through acceleration transforms to the information which can be obtained from a system in which the only observable sign of degradation is sudden and catastrophic failure. The acceleration transforms were developed in accelerated life testing applications as a tool for extrapolating from the observable results of an accelerated life test to the dynamics of the underlying degradation processes. A particular concern of a physicist attempting to interpreted the results of an analysis based on acceleration transforms is determining the physical species involved in the degradation process. These species may be (a) relatively abundant or (b) relatively rare. The main results of this paper are a theorem showing that for an important subclass of statistical kinetic models, acceleration transforms cannot be used to distinguish between cases a and b, and an example showing that in some cases falling outside the restrictions of the theorem, cases a and b can be distinguished by their acceleration transforms
Solar radiation data - statistical analysis and simulation models
Mustacchi, C; Cena, V; Rocchi, M; Haghigat, F
1984-01-01
The activities consisted in collecting meteorological data on magnetic tape for ten european locations (with latitudes ranging from 42/sup 0/ to 56/sup 0/ N), analysing the multi-year sequences, developing mathematical models to generate synthetic sequences having the same statistical properties of the original data sets, and producing one or more Short Reference Years (SRY's) for each location. The meteorological parameters examinated were (for all the locations) global + diffuse radiation on horizontal surface, dry bulb temperature, sunshine duration. For some of the locations additional parameters were available, namely, global, beam and diffuse radiation on surfaces other than horizontal, wet bulb temperature, wind velocity, cloud type, cloud cover. The statistical properties investigated were mean, variance, autocorrelation, crosscorrelation with selected parameters, probability density function. For all the meteorological parameters, various mathematical models were built: linear regression, stochastic models of the AR and the DAR type. In each case, the model with the best statistical behaviour was selected for the production of a SRY for the relevant parameter/location.
Distributing Correlation Coefficients of Linear Structure-Activity/Property Models
Sorana D. BOLBOACA
2011-12-01
Full Text Available Quantitative structure-activity/property relationships are mathematical relationships linking chemical structure and activity/property in a quantitative manner. These in silico approaches are frequently used to reduce animal testing and risk-assessment, as well as to increase time- and cost-effectiveness in characterization and identification of active compounds. The aim of our study was to investigate the pattern of correlation coefficients distribution associated to simple linear relationships linking the compounds structure with their activities. A set of the most common ordnance compounds found at naval facilities with a limited data set with a range of toxicities on aquatic ecosystem and a set of seven properties was studied. Statistically significant models were selected and investigated. The probability density function of the correlation coefficients was investigated using a series of possible continuous distribution laws. Almost 48% of the correlation coefficients proved fit Beta distribution, 40% fit Generalized Pareto distribution, and 12% fit Pert distribution.
A Dynamic Linear Modeling Approach to Public Policy Change
Loftis, Matthew; Mortensen, Peter Bjerre
2017-01-01
Theories of public policy change, despite their differences, converge on one point of strong agreement. The relationship between policy and its causes can and does change over time. This consensus yields numerous empirical implications, but our standard analytical tools are inadequate for testing...... them. As a result, the dynamic and transformative relationships predicted by policy theories have been left largely unexplored in time-series analysis of public policy. This paper introduces dynamic linear modeling (DLM) as a useful statistical tool for exploring time-varying relationships in public...... policy. The paper offers a detailed exposition of the DLM approach and illustrates its usefulness with a time series analysis of U.S. defense policy from 1957-2010. The results point the way for a new attention to dynamics in the policy process and the paper concludes with a discussion of how...
Atmospheric corrosion: statistical validation of models
Diaz, V.; Martinez-Luaces, V.; Guineo-Cobs, G.
2003-01-01
In this paper we discuss two different methods for validation of regression models, applied to corrosion data. One of them is based on the correlation coefficient and the other one is the statistical test of lack of fit. Both methods are used here to analyse fitting of bi logarithmic model in order to predict corrosion for very low carbon steel substrates in rural and urban-industrial atmospheres in Uruguay. Results for parameters A and n of the bi logarithmic model are reported here. For this purpose, all repeated values were used instead of using average values as usual. Modelling is carried out using experimental data corresponding to steel substrates under the same initial meteorological conditions ( in fact, they are put in the rack at the same time). Results of correlation coefficient are compared with the lack of it tested at two different signification levels (α=0.01 and α=0.05). Unexpected differences between them are explained and finally, it is possible to conclude, at least in the studied atmospheres, that the bi logarithmic model does not fit properly the experimental data. (Author) 18 refs
Inventory model using bayesian dynamic linear model for demand forecasting
Marisol Valencia-Cárdenas
2014-12-01
Full Text Available An important factor of manufacturing process is the inventory management of terminated product. Constantly, industry is looking for better alternatives to establish an adequate plan of production and stored quantities, with optimal cost, getting quantities in a time horizon, which permits to define resources and logistics with anticipation, needed to distribute products on time. Total absence of historical data, required by many statistical models to forecast, demands the search for other kind of accurate techniques. This work presents an alternative that not only permits to forecast, in an adjusted way, but also, to provide optimal quantities to produce and store with an optimal cost, using Bayesian statistics. The proposal is illustrated with real data. Palabras clave: estadística bayesiana, optimización, modelo de inventarios, modelo lineal dinámico bayesiano. Keywords: Bayesian statistics, opti
Double generalized linear compound poisson models to insurance claims data
Andersen, Daniel Arnfeldt; Bonat, Wagner Hugo
2017-01-01
This paper describes the specification, estimation and comparison of double generalized linear compound Poisson models based on the likelihood paradigm. The models are motivated by insurance applications, where the distribution of the response variable is composed by a degenerate distribution...... implementation and illustrate the application of double generalized linear compound Poisson models using a data set about car insurances....
Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis
Luo, Wen; Azen, Razia
2013-01-01
Dominance analysis (DA) is a method used to evaluate the relative importance of predictors that was originally proposed for linear regression models. This article proposes an extension of DA that allows researchers to determine the relative importance of predictors in hierarchical linear models (HLM). Commonly used measures of model adequacy in…
Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William
2016-01-01
Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19
Linear control theory for gene network modeling.
Yong-Jun Shin
Full Text Available Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain and linear state-space (time domain can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.
A comparison of linear interpolation models for iterative CT reconstruction.
Hahn, Katharina; Schöndube, Harald; Stierstorfer, Karl; Hornegger, Joachim; Noo, Frédéric
2016-12-01
Recent reports indicate that model-based iterative reconstruction methods may improve image quality in computed tomography (CT). One difficulty with these methods is the number of options available to implement them, including the selection of the forward projection model and the penalty term. Currently, the literature is fairly scarce in terms of guidance regarding this selection step, whereas these options impact image quality. Here, the authors investigate the merits of three forward projection models that rely on linear interpolation: the distance-driven method, Joseph's method, and the bilinear method. The authors' selection is motivated by three factors: (1) in CT, linear interpolation is often seen as a suitable trade-off between discretization errors and computational cost, (2) the first two methods are popular with manufacturers, and (3) the third method enables assessing the importance of a key assumption in the other methods. One approach to evaluate forward projection models is to inspect their effect on discretized images, as well as the effect of their transpose on data sets, but significance of such studies is unclear since the matrix and its transpose are always jointly used in iterative reconstruction. Another approach is to investigate the models in the context they are used, i.e., together with statistical weights and a penalty term. Unfortunately, this approach requires the selection of a preferred objective function and does not provide clear information on features that are intrinsic to the model. The authors adopted the following two-stage methodology. First, the authors analyze images that progressively include components of the singular value decomposition of the model in a reconstructed image without statistical weights and penalty term. Next, the authors examine the impact of weights and penalty on observed differences. Image quality metrics were investigated for 16 different fan-beam imaging scenarios that enabled probing various aspects
Yoneoka, Daisuke; Henmi, Masayuki
2017-06-01
Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Forecasting Volatility of Dhaka Stock Exchange: Linear Vs Non-linear models
Masudul Islam
2012-10-01
Full Text Available Prior information about a financial market is very essential for investor to invest money on parches share from the stock market which can strengthen the economy. The study examines the relative ability of various models to forecast daily stock indexes future volatility. The forecasting models that employed from simple to relatively complex ARCH-class models. It is found that among linear models of stock indexes volatility, the moving average model ranks first using root mean square error, mean absolute percent error, Theil-U and Linex loss function criteria. We also examine five nonlinear models. These models are ARCH, GARCH, EGARCH, TGARCH and restricted GARCH models. We find that nonlinear models failed to dominate linear models utilizing different error measurement criteria and moving average model appears to be the best. Then we forecast the next two months future stock index price volatility by the best (moving average model.
Some computer simulations based on the linear relative risk model
Gilbert, E.S.
1991-10-01
This report presents the results of computer simulations designed to evaluate and compare the performance of the likelihood ratio statistic and the score statistic for making inferences about the linear relative risk mode. The work was motivated by data on workers exposed to low doses of radiation, and the report includes illustration of several procedures for obtaining confidence limits for the excess relative risk coefficient based on data from three studies of nuclear workers. The computer simulations indicate that with small sample sizes and highly skewed dose distributions, asymptotic approximations to the score statistic or to the likelihood ratio statistic may not be adequate. For testing the null hypothesis that the excess relative risk is equal to zero, the asymptotic approximation to the likelihood ratio statistic was adequate, but use of the asymptotic approximation to the score statistic rejected the null hypothesis too often. Frequently the likelihood was maximized at the lower constraint, and when this occurred, the asymptotic approximations for the likelihood ratio and score statistics did not perform well in obtaining upper confidence limits. The score statistic and likelihood ratio statistics were found to perform comparably in terms of power and width of the confidence limits. It is recommended that with modest sample sizes, confidence limits be obtained using computer simulations based on the score statistic. Although nuclear worker studies are emphasized in this report, its results are relevant for any study investigating linear dose-response functions with highly skewed exposure distributions. 22 refs., 14 tabs
Andersen, Per Kragh; Klein, John P.; Rosthøj, Susanne
2003-01-01
Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model......Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model...
Linear and non-linear autoregressive models for short-term wind speed forecasting
Lydia, M.; Suresh Kumar, S.; Immanuel Selvakumar, A.; Edwin Prem Kumar, G.
2016-01-01
Highlights: • Models for wind speed prediction at 10-min intervals up to 1 h built on time-series wind speed data. • Four different multivariate models for wind speed built based on exogenous variables. • Non-linear models built using three data mining algorithms outperform the linear models. • Autoregressive models based on wind direction perform better than other models. - Abstract: Wind speed forecasting aids in estimating the energy produced from wind farms. The soaring energy demands of the world and minimal availability of conventional energy sources have significantly increased the role of non-conventional sources of energy like solar, wind, etc. Development of models for wind speed forecasting with higher reliability and greater accuracy is the need of the hour. In this paper, models for predicting wind speed at 10-min intervals up to 1 h have been built based on linear and non-linear autoregressive moving average models with and without external variables. The autoregressive moving average models based on wind direction and annual trends have been built using data obtained from Sotavento Galicia Plc. and autoregressive moving average models based on wind direction, wind shear and temperature have been built on data obtained from Centre for Wind Energy Technology, Chennai, India. While the parameters of the linear models are obtained using the Gauss–Newton algorithm, the non-linear autoregressive models are developed using three different data mining algorithms. The accuracy of the models has been measured using three performance metrics namely, the Mean Absolute Error, Root Mean Squared Error and Mean Absolute Percentage Error.
Spherical Process Models for Global Spatial Statistics
Jeong, Jaehong
2017-11-28
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.
A statistical mechanical model of economics
Lubbers, Nicholas Edward Williams
Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth vi condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex
Applicability of linear and non-linear potential flow models on a Wavestar float
Bozonnet, Pauline; Dupin, Victor; Tona, Paolino
2017-01-01
as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...
A linear model of population dynamics
Lushnikov, A. A.; Kagan, A. I.
2016-08-01
The Malthus process of population growth is reformulated in terms of the probability w(n,t) to find exactly n individuals at time t assuming that both the birth and the death rates are linear functions of the population size. The master equation for w(n,t) is solved exactly. It is shown that w(n,t) strongly deviates from the Poisson distribution and is expressed in terms either of Laguerre’s polynomials or a modified Bessel function. The latter expression allows for considerable simplifications of the asymptotic analysis of w(n,t).
Current algebra, statistical mechanics and quantum models
Vilela Mendes, R.
2017-11-01
Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.
Statistical model for OCT image denoising
Li, Muxingzi
2017-08-01
Optical coherence tomography (OCT) is a non-invasive technique with a large array of applications in clinical imaging and biological tissue visualization. However, the presence of speckle noise affects the analysis of OCT images and their diagnostic utility. In this article, we introduce a new OCT denoising algorithm. The proposed method is founded on a numerical optimization framework based on maximum-a-posteriori estimate of the noise-free OCT image. It combines a novel speckle noise model, derived from local statistics of empirical spectral domain OCT (SD-OCT) data, with a Huber variant of total variation regularization for edge preservation. The proposed approach exhibits satisfying results in terms of speckle noise reduction as well as edge preservation, at reduced computational cost.
Direction of Effects in Multiple Linear Regression Models.
Wiedermann, Wolfgang; von Eye, Alexander
2015-01-01
Previous studies analyzed asymmetric properties of the Pearson correlation coefficient using higher than second order moments. These asymmetric properties can be used to determine the direction of dependence in a linear regression setting (i.e., establish which of two variables is more likely to be on the outcome side) within the framework of cross-sectional observational data. Extant approaches are restricted to the bivariate regression case. The present contribution extends the direction of dependence methodology to a multiple linear regression setting by analyzing distributional properties of residuals of competing multiple regression models. It is shown that, under certain conditions, the third central moments of estimated regression residuals can be used to decide upon direction of effects. In addition, three different approaches for statistical inference are discussed: a combined D'Agostino normality test, a skewness difference test, and a bootstrap difference test. Type I error and power of the procedures are assessed using Monte Carlo simulations, and an empirical example is provided for illustrative purposes. In the discussion, issues concerning the quality of psychological data, possible extensions of the proposed methods to the fourth central moment of regression residuals, and potential applications are addressed.
Due to the complexity of the processes contributing to beach bacteria concentrations, many researchers rely on statistical modeling, among which multiple linear regression (MLR) modeling is most widely used. Despite its ease of use and interpretation, there may be time dependence...
Dijkstra, T.K.; Henseler, J.
2011-01-01
The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with
New advances in statistical modeling and applications
Santos, Rui; Oliveira, Maria; Paulino, Carlos
2014-01-01
This volume presents selected papers from the XIXth Congress of the Portuguese Statistical Society, held in the town of Nazaré, Portugal, from September 28 to October 1, 2011. All contributions were selected after a thorough peer-review process. It covers a broad range of papers in the areas of statistical science, probability and stochastic processes, extremes and statistical applications.
A test for the parameters of multiple linear regression models ...
A test for the parameters of multiple linear regression models is developed for conducting tests simultaneously on all the parameters of multiple linear regression models. The test is robust relative to the assumptions of homogeneity of variances and absence of serial correlation of the classical F-test. Under certain null and ...
Modeling Non-Linear Material Properties in Composite Materials
2016-06-28
Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions
A statistical model for predicting muscle performance
Byerly, Diane Leslie De Caix
The objective of these studies was to develop a capability for predicting muscle performance and fatigue to be utilized for both space- and ground-based applications. To develop this predictive model, healthy test subjects performed a defined, repetitive dynamic exercise to failure using a Lordex spinal machine. Throughout the exercise, surface electromyography (SEMG) data were collected from the erector spinae using a Mega Electronics ME3000 muscle tester and surface electrodes placed on both sides of the back muscle. These data were analyzed using a 5th order Autoregressive (AR) model and statistical regression analysis. It was determined that an AR derived parameter, the mean average magnitude of AR poles, significantly correlated with the maximum number of repetitions (designated Rmax) that a test subject was able to perform. Using the mean average magnitude of AR poles, a test subject's performance to failure could be predicted as early as the sixth repetition of the exercise. This predictive model has the potential to provide a basis for improving post-space flight recovery, monitoring muscle atrophy in astronauts and assessing the effectiveness of countermeasures, monitoring astronaut performance and fatigue during Extravehicular Activity (EVA) operations, providing pre-flight assessment of the ability of an EVA crewmember to perform a given task, improving the design of training protocols and simulations for strenuous International Space Station assembly EVA, and enabling EVA work task sequences to be planned enhancing astronaut performance and safety. Potential ground-based, medical applications of the predictive model include monitoring muscle deterioration and performance resulting from illness, establishing safety guidelines in the industry for repetitive tasks, monitoring the stages of rehabilitation for muscle-related injuries sustained in sports and accidents, and enhancing athletic performance through improved training protocols while reducing
Mixed models, linear dependency, and identification in age-period-cohort models.
O'Brien, Robert M
2017-07-20
This paper examines the identification problem in age-period-cohort models that use either linear or categorically coded ages, periods, and cohorts or combinations of these parameterizations. These models are not identified using the traditional fixed effect regression model approach because of a linear dependency between the ages, periods, and cohorts. However, these models can be identified if the researcher introduces a single just identifying constraint on the model coefficients. The problem with such constraints is that the results can differ substantially depending on the constraint chosen. Somewhat surprisingly, age-period-cohort models that specify one or more of ages and/or periods and/or cohorts as random effects are identified. This is the case without introducing an additional constraint. I label this identification as statistical model identification and show how statistical model identification comes about in mixed models and why which effects are treated as fixed and which are treated as random can substantially change the estimates of the age, period, and cohort effects. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
Reliability modelling and simulation of switched linear system ...
Reliability modelling and simulation of switched linear system control using temporal databases. ... design of fault-tolerant real-time switching systems control and modelling embedded micro-schedulers for complex systems maintenance.
Approximating chiral quark models with linear σ-models
Broniowski, Wojciech; Golli, Bojan
2003-01-01
We study the approximation of chiral quark models with simpler models, obtained via gradient expansion. The resulting Lagrangian of the type of the linear σ-model contains, at the lowest level of the gradient-expanded meson action, an additional term of the form ((1)/(2))A(σ∂ μ σ+π∂ μ π) 2 . We investigate the dynamical consequences of this term and its relevance to the phenomenology of the soliton models of the nucleon. It is found that the inclusion of the new term allows for a more efficient approximation of the underlying quark theory, especially in those cases where dynamics allows for a large deviation of the chiral fields from the chiral circle, such as in quark models with non-local regulators. This is of practical importance, since the σ-models with valence quarks only are technically much easier to treat and simpler to solve than the quark models with the full-fledged Dirac sea
Statistical Model Checking of Rich Models and Properties
Poulsen, Danny Bøgsted
in undecidability issues for the traditional model checking approaches. Statistical model checking has proven itself a valuable supplement to model checking and this thesis is concerned with extending this software validation technique to stochastic hybrid systems. The thesis consists of two parts: the first part...... motivates why existing model checking technology should be supplemented by new techniques. It also contains a brief introduction to probability theory and concepts covered by the six papers making up the second part. The first two papers are concerned with developing online monitoring techniques...... systems. The fifth paper shows how stochastic hybrid automata are useful for modelling biological systems and the final paper is concerned with showing how statistical model checking is efficiently distributed. In parallel with developing the theory contained in the papers, a substantial part of this work...
Statistical Downscaling of Temperature with the Random Forest Model
Bo Pang
2017-01-01
Full Text Available The issues with downscaling the outputs of a global climate model (GCM to a regional scale that are appropriate to hydrological impact studies are investigated using the random forest (RF model, which has been shown to be superior for large dataset analysis and variable importance evaluation. The RF is proposed for downscaling daily mean temperature in the Pearl River basin in southern China. Four downscaling models were developed and validated by using the observed temperature series from 61 national stations and large-scale predictor variables derived from the National Center for Environmental Prediction–National Center for Atmospheric Research reanalysis dataset. The proposed RF downscaling model was compared to multiple linear regression, artificial neural network, and support vector machine models. Principal component analysis (PCA and partial correlation analysis (PAR were used in the predictor selection for the other models for a comprehensive study. It was shown that the model efficiency of the RF model was higher than that of the other models according to five selected criteria. By evaluating the predictor importance, the RF could choose the best predictor combination without using PCA and PAR. The results indicate that the RF is a feasible tool for the statistical downscaling of temperature.
R. Barbiero
2007-05-01
Full Text Available Model Output Statistics (MOS refers to a method of post-processing the direct outputs of numerical weather prediction (NWP models in order to reduce the biases introduced by a coarse horizontal resolution. This technique is especially useful in orographically complex regions, where large differences can be found between the NWP elevation model and the true orography. This study carries out a comparison of linear and non-linear MOS methods, aimed at the prediction of minimum temperatures in a fruit-growing region of the Italian Alps, based on the output of two different NWPs (ECMWF T511–L60 and LAMI-3. Temperature, of course, is a particularly important NWP output; among other roles it drives the local frost forecast, which is of great interest to agriculture. The mechanisms of cold air drainage, a distinctive aspect of mountain environments, are often unsatisfactorily captured by global circulation models. The simplest post-processing technique applied in this work was a correction for the mean bias, assessed at individual model grid points. We also implemented a multivariate linear regression on the output at the grid points surrounding the target area, and two non-linear models based on machine learning techniques: Neural Networks and Random Forest. We compare the performance of all these techniques on four different NWP data sets. Downscaling the temperatures clearly improved the temperature forecasts with respect to the raw NWP output, and also with respect to the basic mean bias correction. Multivariate methods generally yielded better results, but the advantage of using non-linear algorithms was small if not negligible. RF, the best performing method, was implemented on ECMWF prognostic output at 06:00 UTC over the 9 grid points surrounding the target area. Mean absolute errors in the prediction of 2 m temperature at 06:00 UTC were approximately 1.2°C, close to the natural variability inside the area itself.
Latent log-linear models for handwritten digit classification.
Deselaers, Thomas; Gass, Tobias; Heigold, Georg; Ney, Hermann
2012-06-01
We present latent log-linear models, an extension of log-linear models incorporating latent variables, and we propose two applications thereof: log-linear mixture models and image deformation-aware log-linear models. The resulting models are fully discriminative, can be trained efficiently, and the model complexity can be controlled. Log-linear mixture models offer additional flexibility within the log-linear modeling framework. Unlike previous approaches, the image deformation-aware model directly considers image deformations and allows for a discriminative training of the deformation parameters. Both are trained using alternating optimization. For certain variants, convergence to a stationary point is guaranteed and, in practice, even variants without this guarantee converge and find models that perform well. We tune the methods on the USPS data set and evaluate on the MNIST data set, demonstrating the generalization capabilities of our proposed models. Our models, although using significantly fewer parameters, are able to obtain competitive results with models proposed in the literature.
Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne
2012-12-01
In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.
Linear Regression Models for Estimating True Subsurface ...
47
The objective is to minimize the processing time and computer memory required. 10 to carry out inversion .... to the mainland by two long bridges. .... term. In this approach, the model converges when the squared sum of the differences. 143.
Numerical modelling in non linear fracture mechanics
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
Network Data: Statistical Theory and New Models
2016-02-17
and with environmental scientists at JPL and Emory University to retrieval from NASA MISR remote sensing images aerosol index AOD for air pollution ...Beijing, May, 2013 Beijing Statistics Forum, Beijing, May, 2013 Statistics Seminar, CREST-ENSAE, Paris , March, 2013 Statistics Seminar, University...to retrieval from NASA MISR remote sensing images aerosol index AOD for air pollution monitoring and management. Satellite- retrieved Aerosol Optical
Zafar, I.; Edirisinghe, E. A.; Acar, S.; Bez, H. E.
2007-02-01
Automatic vehicle Make and Model Recognition (MMR) systems provide useful performance enhancements to vehicle recognitions systems that are solely based on Automatic License Plate Recognition (ALPR) systems. Several car MMR systems have been proposed in literature. However these approaches are based on feature detection algorithms that can perform sub-optimally under adverse lighting and/or occlusion conditions. In this paper we propose a real time, appearance based, car MMR approach using Two Dimensional Linear Discriminant Analysis that is capable of addressing this limitation. We provide experimental results to analyse the proposed algorithm's robustness under varying illumination and occlusions conditions. We have shown that the best performance with the proposed 2D-LDA based car MMR approach is obtained when the eigenvectors of lower significance are ignored. For the given database of 200 car images of 25 different make-model classifications, a best accuracy of 91% was obtained with the 2D-LDA approach. We use a direct Principle Component Analysis (PCA) based approach as a benchmark to compare and contrast the performance of the proposed 2D-LDA approach to car MMR. We conclude that in general the 2D-LDA based algorithm supersedes the performance of the PCA based approach.
Log-normal frailty models fitted as Poisson generalized linear mixed models.
Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver
2016-12-01
The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Quantum statistical model for hot dense matter
Rukhsana Kouser; Tasneem, G.; Saleem Shahzad, M.; Shafiq-ur-Rehman; Nasim, M.H.; Amjad Ali
2015-01-01
In solving numerous applied problems, one needs to know the equation of state, photon absorption coefficient and opacity of substances employed. We present a code for absorption coefficient and opacity calculation based on quantum statistical model. A self-consistent method for the calculation of potential is used. By solving Schrödinger equation with self-consistent potential we find energy spectrum of quantum mechanical system and corresponding wave functions. In addition we find mean occupation numbers of electron states and average charge state of the substance studied. The main processes of interaction of radiation with matter included in our opacity calculation are photon absorption in spectral lines (Bound-bound), photoionization (Bound-free), inverse bremsstrahlung (Free-free), Compton and Thomson scattering. Bound-bound line shape function has contribution from natural, Doppler, fine structure, collisional and stark broadening. To illustrate the main features of the code and its capabilities, calculation of average charge state, absorption coefficient, Rosseland and Planck mean and group opacities of aluminum and iron are presented. Results are satisfactorily compared with the published data. (authors)
Weighted A-statistical convergence for sequences of positive linear operators.
Mohiuddine, S A; Alotaibi, Abdullah; Hazarika, Bipan
2014-01-01
We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a rate of weighted A-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our result.
Random effect selection in generalised linear models
Denwood, Matt; Houe, Hans; Forkman, Björn
We analysed abattoir recordings of meat inspection codes with possible relevance to onfarm animal welfare in cattle. Random effects logistic regression models were used to describe individual-level data obtained from 461,406 cattle slaughtered in Denmark. Our results demonstrate that the largest...
Model Order Reduction for Non Linear Mechanics
Pinillo, Rubén
2017-01-01
Context: Automotive industry is moving towards a new generation of cars. Main idea: Cars are furnished with radars, cameras, sensors, etc… providing useful information about the environment surrounding the car. Goals: Provide an efficient model for the radar input/output. Reducing computational costs by means of big data techniques.
Heterotic sigma models and non-linear strings
Hull, C.M.
1986-01-01
The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)
Linear latent variable models: the lava-package
Holst, Klaus Kähler; Budtz-Jørgensen, Esben
2013-01-01
are implemented including robust standard errors for clustered correlated data, multigroup analyses, non-linear parameter constraints, inference with incomplete data, maximum likelihood estimation with censored and binary observations, and instrumental variable estimators. In addition an extensive simulation......An R package for specifying and estimating linear latent variable models is presented. The philosophy of the implementation is to separate the model specification from the actual data, which leads to a dynamic and easy way of modeling complex hierarchical structures. Several advanced features...
On-line control models for the Stanford Linear Collider
Sheppard, J.C.; Helm, R.H.; Lee, M.J.; Woodley, M.D.
1983-03-01
Models for computer control of the SLAC three-kilometer linear accelerator and damping rings have been developed as part of the control system for the Stanford Linear Collider. Some of these models have been tested experimentally and implemented in the control program for routine linac operations. This paper will describe the development and implementation of these models, as well as some of the operational results
A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.
Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S
2017-06-01
The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were
Frank, Laurence Emmanuelle
2006-01-01
Feature Network Models (FNM) are graphical structures that represent proximity data in a discrete space with the use of features. A statistical inference theory is introduced, based on the additivity properties of networks and the linear regression framework. Considering features as predictor
Generalized Linear Models with Applications in Engineering and the Sciences
Myers, Raymond H; Vining, G Geoffrey; Robinson, Timothy J
2012-01-01
Praise for the First Edition "The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities."-Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Ma
Modelling a linear PM motor including magnetic saturation
Polinder, H.; Slootweg, J.G.; Compter, J.C.; Hoeijmakers, M.J.
2002-01-01
The use of linear permanent-magnet (PM) actuators increases in a wide variety of applications because of the high force density, robustness and accuracy. The paper describes the modelling of a linear PM motor applied in, for example, wafer steppers, including magnetic saturation. This is important
Application of the simplex method of linear programming model to ...
This work discussed how the simplex method of linear programming could be used to maximize the profit of any business firm using Saclux Paint Company as a case study. It equally elucidated the effect variation in the optimal result obtained from linear programming model, will have on any given firm. It was demonstrated ...
On Linear Hulls, Statistical Saturation Attacks, PRESENT and a Cryptanalysis of PUFFIN
Leander, Gregor
2011-01-01
which breaks the cipher for at least a quarter of the keys with a complexity less than 258. In the case of PRESENT we show that the design is sound. The design criteria are sufficient to ensure the resistance against linear attacks, taking into account the notion of linear hulls. Finally, we show...
The Relationship between Economic Growth and Money Laundering – a Linear Regression Model
Daniel Rece
2009-09-01
Full Text Available This study provides an overview of the relationship between economic growth and money laundering modeled by a least squares function. The report analyzes statistically data collected from USA, Russia, Romania and other eleven European countries, rendering a linear regression model. The study illustrates that 23.7% of the total variance in the regressand (level of money laundering is “explained” by the linear regression model. In our opinion, this model will provide critical auxiliary judgment and decision support for anti-money laundering service systems.
Genetic parameters for racing records in trotters using linear and generalized linear models.
Suontama, M; van der Werf, J H J; Juga, J; Ojala, M
2012-09-01
Heritability and repeatability and genetic and phenotypic correlations were estimated for trotting race records with linear and generalized linear models using 510,519 records on 17,792 Finnhorses and 513,161 records on 25,536 Standardbred trotters. Heritability and repeatability were estimated for single racing time and earnings traits with linear models, and logarithmic scale was used for racing time and fourth-root scale for earnings to correct for nonnormality. Generalized linear models with a gamma distribution were applied for single racing time and with a multinomial distribution for single earnings traits. In addition, genetic parameters for annual earnings were estimated with linear models on the observed and fourth-root scales. Racing success traits of single placings, winnings, breaking stride, and disqualifications were analyzed using generalized linear models with a binomial distribution. Estimates of heritability were greatest for racing time, which ranged from 0.32 to 0.34. Estimates of heritability were low for single earnings with all distributions, ranging from 0.01 to 0.09. Annual earnings were closer to normal distribution than single earnings. Heritability estimates were moderate for annual earnings on the fourth-root scale, 0.19 for Finnhorses and 0.27 for Standardbred trotters. Heritability estimates for binomial racing success variables ranged from 0.04 to 0.12, being greatest for winnings and least for breaking stride. Genetic correlations among racing traits were high, whereas phenotypic correlations were mainly low to moderate, except correlations between racing time and earnings were high. On the basis of a moderate heritability and moderate to high repeatability for racing time and annual earnings, selection of horses for these traits is effective when based on a few repeated records. Because of high genetic correlations, direct selection for racing time and annual earnings would also result in good genetic response in racing success.
Modeling exposure–lag–response associations with distributed lag non-linear models
Gasparrini, Antonio
2014-01-01
In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094
A BRDF statistical model applying to space target materials modeling
Liu, Chenghao; Li, Zhi; Xu, Can; Tian, Qichen
2017-10-01
In order to solve the problem of poor effect in modeling the large density BRDF measured data with five-parameter semi-empirical model, a refined statistical model of BRDF which is suitable for multi-class space target material modeling were proposed. The refined model improved the Torrance-Sparrow model while having the modeling advantages of five-parameter model. Compared with the existing empirical model, the model contains six simple parameters, which can approximate the roughness distribution of the material surface, can approximate the intensity of the Fresnel reflectance phenomenon and the attenuation of the reflected light's brightness with the azimuth angle changes. The model is able to achieve parameter inversion quickly with no extra loss of accuracy. The genetic algorithm was used to invert the parameters of 11 different samples in the space target commonly used materials, and the fitting errors of all materials were below 6%, which were much lower than those of five-parameter model. The effect of the refined model is verified by comparing the fitting results of the three samples at different incident zenith angles in 0° azimuth angle. Finally, the three-dimensional modeling visualizations of these samples in the upper hemisphere space was given, in which the strength of the optical scattering of different materials could be clearly shown. It proved the good describing ability of the refined model at the material characterization as well.
Statistical Challenges in Modeling Big Brain Signals
Yu, Zhaoxia
2017-11-01
Brain signal data are inherently big: massive in amount, complex in structure, and high in dimensions. These characteristics impose great challenges for statistical inference and learning. Here we review several key challenges, discuss possible solutions, and highlight future research directions.
Statistical Challenges in Modeling Big Brain Signals
Yu, Zhaoxia; Pluta, Dustin; Shen, Tong; Chen, Chuansheng; Xue, Gui; Ombao, Hernando
2017-01-01
Brain signal data are inherently big: massive in amount, complex in structure, and high in dimensions. These characteristics impose great challenges for statistical inference and learning. Here we review several key challenges, discuss possible
Statistical Learning Theory: Models, Concepts, and Results
von Luxburg, Ulrike; Schoelkopf, Bernhard
2008-01-01
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. This paper can serve as a starting point for people who want to get an overview on the field before diving into technical details.
Weighted A-Statistical Convergence for Sequences of Positive Linear Operators
S. A. Mohiuddine
2014-01-01
Full Text Available We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a rate of weighted A-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our result.
Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren
2010-01-01
, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations...... and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...
Linear approximation model network and its formation via ...
niques, an alternative `linear approximation model' (LAM) network approach is .... network is LPV, existing LTI theory is difficult to apply (Kailath 1980). ..... Beck J V, Arnold K J 1977 Parameter estimation in engineering and science (New York: ...
Sphaleron in a non-linear sigma model
Sogo, Kiyoshi; Fujimoto, Yasushi.
1989-08-01
We present an exact classical saddle point solution in a non-linear sigma model. It has a topological charge 1/2 and mediates the vacuum transition. The quantum fluctuations and the transition rate are also examined. (author)
On D-branes from gauged linear sigma models
Govindarajan, S.; Jayaraman, T.; Sarkar, T.
2001-01-01
We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields are first considered in the large-volume phase/non-linear sigma model limit of the corresponding Calabi-Yau manifold, where we find that we need to add a contact term on the boundary. These considerations enable to us to derive the boundary conditions in the full gauged linear sigma model, including the addition of the appropriate boundary contact terms, such that these boundary conditions have the correct non-linear sigma model limit. Most of the analysis is for the case of Calabi-Yau manifolds with one Kaehler modulus (including those corresponding to hypersurfaces in weighted projective space), though we comment on possible generalisations
Optimization for decision making linear and quadratic models
Murty, Katta G
2010-01-01
While maintaining the rigorous linear programming instruction required, Murty's new book is unique in its focus on developing modeling skills to support valid decision-making for complex real world problems, and includes solutions to brand new algorithms.
Study of linear induction motor characteristics : the Mosebach model
1976-05-31
This report covers the Mosebach theory of the double-sided linear induction motor, starting with the ideallized model and accompanying assumptions, and ending with relations for thrust, airgap power, and motor efficiency. Solutions of the magnetic in...
Study of linear induction motor characteristics : the Oberretl model
1975-05-30
The Oberretl theory of the double-sided linear induction motor (LIM) is examined, starting with the idealized model and accompanying assumptions, and ending with relations for predicted thrust, airgap power, and motor efficiency. The effect of varyin...
Optimization Research of Generation Investment Based on Linear Programming Model
Wu, Juan; Ge, Xueqian
Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.
Ntaka, L
2013-08-01
Full Text Available . In this work, statistical inference approach specifically the non-parametric bootstrapping and linear model were applied. Data used to develop the model were sourced from the literature. 104 data points with information on aggregation, natural organic matter...
Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs
Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.
2018-04-01
Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.
Integer Set Compression and Statistical Modeling
Larsson, N. Jesper
2014-01-01
enumeration of elements may be arbitrary or random, but where statistics is kept in order to estimate probabilities of elements. We present a recursive subset-size encoding method that is able to benefit from statistics, explore the effects of permuting the enumeration order based on element probabilities......Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher compression performance. In this work, we address the case where...
Generalized linear mixed models modern concepts, methods and applications
Stroup, Walter W
2012-01-01
PART I The Big PictureModeling BasicsWhat Is a Model?Two Model Forms: Model Equation and Probability DistributionTypes of Model EffectsWriting Models in Matrix FormSummary: Essential Elements for a Complete Statement of the ModelDesign MattersIntroductory Ideas for Translating Design and Objectives into ModelsDescribing ""Data Architecture"" to Facilitate Model SpecificationFrom Plot Plan to Linear PredictorDistribution MattersMore Complex Example: Multiple Factors with Different Units of ReplicationSetting the StageGoals for Inference with Models: OverviewBasic Tools of InferenceIssue I: Data
A comparison of linear tyre models for analysing shimmy
Besselink, I.J.M.; Maas, J.W.L.H.; Nijmeijer, H.
2011-01-01
A comparison is made between three linear, dynamic tyre models using low speed step responses and yaw oscillation tests. The match with the measurements improves with increasing complexity of the tyre model. Application of the different tyre models to a two degree of freedom trailing arm suspension
Unification of three linear models for the transient visual system
Brinker, den A.C.
1989-01-01
Three different linear filters are considered as a model describing the experimentally determined triphasic impulse responses of discs. These impulse responses arc associated with the transient visual system. Each model reveals a different feature of the system. Unification of the models is
A BEHAVIORAL-APPROACH TO LINEAR EXACT MODELING
ANTOULAS, AC; WILLEMS, JC
1993-01-01
The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The main contribution of this paper is the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both
Statistical modelling for social researchers principles and practice
Tarling, Roger
2008-01-01
This book explains the principles and theory of statistical modelling in an intelligible way for the non-mathematical social scientist looking to apply statistical modelling techniques in research. The book also serves as an introduction for those wishing to develop more detailed knowledge and skills in statistical modelling. Rather than present a limited number of statistical models in great depth, the aim is to provide a comprehensive overview of the statistical models currently adopted in social research, in order that the researcher can make appropriate choices and select the most suitable model for the research question to be addressed. To facilitate application, the book also offers practical guidance and instruction in fitting models using SPSS and Stata, the most popular statistical computer software which is available to most social researchers. Instruction in using MLwiN is also given. Models covered in the book include; multiple regression, binary, multinomial and ordered logistic regression, log-l...
Linearized models for a new magnetic control in MAST
Artaserse, G., E-mail: giovanni.artaserse@enea.it [Associazione Euratom-ENEA sulla Fusione, Via Enrico Fermi 45, I-00044 Frascati (RM) (Italy); Maviglia, F.; Albanese, R. [Associazione Euratom-ENEA-CREATE sulla Fusione, Via Claudio 21, I-80125 Napoli (Italy); McArdle, G.J.; Pangione, L. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxon, OX14 3DB (United Kingdom)
2013-10-15
Highlights: ► We applied linearized models for a new magnetic control on MAST tokamak. ► A suite of procedures, conceived to be machine independent, have been used. ► We carried out model-based simulations, taking into account eddy currents effects. ► Comparison with the EFIT flux maps and the experimental magnetic signals are shown. ► A current driven model for the dynamic simulations of the experimental data have been performed. -- Abstract: The aim of this work is to provide reliable linearized models for the design and assessment of a new magnetic control system for MAST (Mega Ampère Spherical Tokamak) using rtEFIT, which can easily be exported to MAST Upgrade. Linearized models for magnetic control have been obtained using the 2D axisymmetric finite element code CREATE L. MAST linearized models include equivalent 2D axisymmetric schematization of poloidal field (PF) coils, vacuum vessel, and other conducting structures. A plasmaless and a double null configuration have been chosen as benchmark cases for the comparison with experimental data and EFIT reconstructions. Good agreement has been found with the EFIT flux map and the experimental signals coming from magnetic probes with only few mismatches probably due to broken sensors. A suite of procedures (equipped with a user friendly interface to be run even remotely) to provide linearized models for magnetic control is now available on the MAST linux machines. A new current driven model has been used to obtain a state space model having the PF coil currents as inputs. Dynamic simulations of experimental data have been carried out using linearized models, including modelling of the effects of the passive structures, showing a fair agreement. The modelling activity has been useful also to reproduce accurately the interaction between plasma current and radial position control loops.
Linearized models for a new magnetic control in MAST
Artaserse, G.; Maviglia, F.; Albanese, R.; McArdle, G.J.; Pangione, L.
2013-01-01
Highlights: ► We applied linearized models for a new magnetic control on MAST tokamak. ► A suite of procedures, conceived to be machine independent, have been used. ► We carried out model-based simulations, taking into account eddy currents effects. ► Comparison with the EFIT flux maps and the experimental magnetic signals are shown. ► A current driven model for the dynamic simulations of the experimental data have been performed. -- Abstract: The aim of this work is to provide reliable linearized models for the design and assessment of a new magnetic control system for MAST (Mega Ampère Spherical Tokamak) using rtEFIT, which can easily be exported to MAST Upgrade. Linearized models for magnetic control have been obtained using the 2D axisymmetric finite element code CREATE L. MAST linearized models include equivalent 2D axisymmetric schematization of poloidal field (PF) coils, vacuum vessel, and other conducting structures. A plasmaless and a double null configuration have been chosen as benchmark cases for the comparison with experimental data and EFIT reconstructions. Good agreement has been found with the EFIT flux map and the experimental signals coming from magnetic probes with only few mismatches probably due to broken sensors. A suite of procedures (equipped with a user friendly interface to be run even remotely) to provide linearized models for magnetic control is now available on the MAST linux machines. A new current driven model has been used to obtain a state space model having the PF coil currents as inputs. Dynamic simulations of experimental data have been carried out using linearized models, including modelling of the effects of the passive structures, showing a fair agreement. The modelling activity has been useful also to reproduce accurately the interaction between plasma current and radial position control loops
Statistical models and methods for reliability and survival analysis
Couallier, Vincent; Huber-Carol, Catherine; Mesbah, Mounir; Huber -Carol, Catherine; Limnios, Nikolaos; Gerville-Reache, Leo
2013-01-01
Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical
H∞ /H2 model reduction through dilated linear matrix inequalities
Adegas, Fabiano Daher; Stoustrup, Jakob
2012-01-01
This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field{N}$. Arb......This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field...
Non-linear Growth Models in Mplus and SAS
Grimm, Kevin J.; Ram, Nilam
2013-01-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134
Variance Function Partially Linear Single-Index Models1.
Lian, Heng; Liang, Hua; Carroll, Raymond J
2015-01-01
We consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model. We do not insist that the variance function depend only upon the mean function, as happens in the classical generalized partially linear single index model. We develop efficient and practical estimation methods for the variance function and for the mean function. Asymptotic theory for the parametric and nonparametric parts of the model is developed. Simulations illustrate the results. An empirical example involving ozone levels is used to further illustrate the results, and is shown to be a case where the variance function does not depend upon the mean function.
Reflexion on linear regression trip production modelling method for ensuring good model quality
Suprayitno, Hitapriya; Ratnasari, Vita
2017-11-01
Transport Modelling is important. For certain cases, the conventional model still has to be used, in which having a good trip production model is capital. A good model can only be obtained from a good sample. Two of the basic principles of a good sampling is having a sample capable to represent the population characteristics and capable to produce an acceptable error at a certain confidence level. It seems that this principle is not yet quite understood and used in trip production modeling. Therefore, investigating the Trip Production Modelling practice in Indonesia and try to formulate a better modeling method for ensuring the Model Quality is necessary. This research result is presented as follows. Statistics knows a method to calculate span of prediction value at a certain confidence level for linear regression, which is called Confidence Interval of Predicted Value. The common modeling practice uses R2 as the principal quality measure, the sampling practice varies and not always conform to the sampling principles. An experiment indicates that small sample is already capable to give excellent R2 value and sample composition can significantly change the model. Hence, good R2 value, in fact, does not always mean good model quality. These lead to three basic ideas for ensuring good model quality, i.e. reformulating quality measure, calculation procedure, and sampling method. A quality measure is defined as having a good R2 value and a good Confidence Interval of Predicted Value. Calculation procedure must incorporate statistical calculation method and appropriate statistical tests needed. A good sampling method must incorporate random well distributed stratified sampling with a certain minimum number of samples. These three ideas need to be more developed and tested.
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Challenges in dental statistics: data and modelling
Matranga, D.; Castiglia, P.; Solinas, G.
2013-01-01
The aim of this work is to present the reflections and proposals derived from the first Workshop of the SISMEC STATDENT working group on statistical methods and applications in dentistry, held in Ancona (Italy) on 28th September 2011. STATDENT began as a forum of comparison and discussion for statisticians working in the field of dental research in order to suggest new and improve existing biostatistical and clinical epidemiological methods. During the meeting, we dealt with very important to...
Qi, D.; Majda, A.
2017-12-01
A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with
Comparison between linear quadratic and early time dose models
Chougule, A.A.; Supe, S.J.
1993-01-01
During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs
Phylogenetic mixtures and linear invariants for equal input models.
Casanellas, Marta; Steel, Mike
2017-04-01
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).
Non-linear calibration models for near infrared spectroscopy
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-01-01
by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear...... models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS......-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration...
Vector generalized linear and additive models with an implementation in R
Yee, Thomas W
2015-01-01
This book presents a statistical framework that expands generalized linear models (GLMs) for regression modelling. The framework shared in this book allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. This is possible through the approximately half-a-dozen major classes of statistical models included in the book and the software infrastructure component, which makes the models easily operable. The book’s methodology and accompanying software (the extensive VGAM R package) are directed at these limitations, and this is the first time the methodology and software are covered comprehensively in one volume. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. The demands of practical data analysis, however, require a flexibility that GLMs do not have. Data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. This book ...
A statistical model of future human actions
Woo, G.
1992-02-01
A critical review has been carried out of models of future human actions during the long term post-closure period of a radioactive waste repository. Various Markov models have been considered as alternatives to the standard Poisson model, and the problems of parameterisation have been addressed. Where the simplistic Poisson model unduly exaggerates the intrusion risk, some form of Markov model may have to be introduced. This situation may well arise for shallow repositories, but it is less likely for deep repositories. Recommendations are made for a practical implementation of a computer based model and its associated database. (Author)
Enhanced surrogate models for statistical design exploiting space mapping technology
Koziel, Slawek; Bandler, John W.; Mohamed, Achmed S.
2005-01-01
We present advances in microwave and RF device modeling exploiting Space Mapping (SM) technology. We propose new SM modeling formulations utilizing input mappings, output mappings, frequency scaling and quadratic approximations. Our aim is to enhance circuit models for statistical analysis...
Statistical models of shape optimisation and evaluation
Davies, Rhodri; Taylor, Chris
2014-01-01
Deformable shape models have wide application in computer vision and biomedical image analysis. This book addresses a key issue in shape modelling: establishment of a meaningful correspondence between a set of shapes. Full implementation details are provided.
Matrix model and time-like linear dila ton matter
Takayanagi, Tadashi
2004-01-01
We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)
Vortices, semi-local vortices in gauged linear sigma model
Kim, Namkwon
1998-11-01
We consider the static (2+1)D gauged linear sigma model. By analyzing the governing system of partial differential equations, we investigate various aspects of the model. We show the existence of energy finite vortices under a partially broken symmetry on R 2 with the necessary condition suggested by Y. Yang. We also introduce generalized semi-local vortices and show the existence of energy finite semi-local vortices under a certain condition. The vacuum manifold for the semi-local vortices turns out to be graded. Besides, with a special choice of a representation, we show that the O(3) sigma model of which target space is nonlinear is a singular limit of the gauged linear sigma model of which target space is linear. (author)
TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS
Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.
2017-01-01
Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions. PMID:29332971
Borsboom, D.; Haig, B.D.
2013-01-01
Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science
Statistics Based Models for the Dynamics of Chernivtsi Children Disease
Igor G. Nesteruk
2017-10-01
Full Text Available Background. Simple mathematical models of contamination and SIR-model of spreading an infection were used to simulate the time dynamics of the unknown before children disease, which occurred in Chernivtsi (Ukraine. The cause of many cases of alopecia, which began in this city in August 1988 is still not fully clarified. According to the official report of the governmental commission, the last new cases occurred in the middle of November 1988, and the reason of the illness was reported as chemical exogenous intoxication. Later this illness became the name “Chernivtsi chemical disease”. Nevertheless, the significantly increased number of new cases of the local alopecia was registered almost three years and is still not clarified. Objective. The comparison of two different versions of the disease: chemical exogenous intoxication and infection. Identification of the parameters of mathematical models and prediction of the disease development. Methods. Analytical solutions of the contamination models and SIR-model for an epidemic are obtained. The optimal values of parameters with the use of linear regression were found. Results. The optimal values of the models parameters with the use of statistical approach were identified. The calculations showed that the infectious version of the disease is more reliable in comparison with the popular contamination one. The possible date of the epidemic beginning was estimated. Conclusions. The optimal parameters of SIR-model allow calculating the realistic number of victims and other characteristics of possible epidemic. They also show that increased number of cases of local alopecia could be a part of the same epidemic as “Chernivtsi chemical disease”.
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
Optical linear algebra processors - Noise and error-source modeling
Casasent, D.; Ghosh, A.
1985-01-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Optical linear algebra processors: noise and error-source modeling.
Casasent, D; Ghosh, A
1985-06-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
CONTRIBUTIONS TO THE FINITE ELEMENT MODELING OF LINEAR ULTRASONIC MOTORS
Oana CHIVU
2013-05-01
Full Text Available The present paper is concerned with the main modeling elements as produced by means of thefinite element method of linear ultrasonic motors. Hence, first the model is designed and then a modaland harmonic analysis are carried out in view of outlining the main outcomes
Linear and Nonlinear Career Models: Metaphors, Paradigms, and Ideologies.
Buzzanell, Patrice M.; Goldzwig, Steven R.
1991-01-01
Examines the linear or bureaucratic career models (dominant in career research, metaphors, paradigms, and ideologies) which maintain career myths of flexibility and individualized routes to success in organizations incapable of offering such versatility. Describes nonlinear career models which offer suggestive metaphors for re-visioning careers…
Statistical modelling of traffic safety development
Christens, Peter
2004-01-01
there were 6861 injury trafficc accidents reported by the police, resulting in 4519 minor injuries, 3946 serious injuries, and 431 fatalities. The general purpose of the research was to improve the insight into aggregated road safety methodology in Denmark. The aim was to analyse advanced statistical methods......, that were designed to study developments over time, including effects of interventions. This aim has been achieved by investigating variations in aggregated Danish traffic accident series and by applying state of the art methodologies to specific case studies. The thesis comprises an introduction...
A statistical mechanical model for equilibrium ionization
Macris, N.; Martin, P.A.; Pule, J.
1990-01-01
A quantum electron interacts with a classical gas of hard spheres and is in thermal equilibrium with it. The interaction is attractive and the electron can form a bound state with the classical particles. It is rigorously shown that in a well defined low density and low temperature limit, the ionization probability for the electron tends to the value predicted by the Saha formula for thermal ionization. In this regime, the electron is found to be in a statistical mixture of a bound and a free state. (orig.)
Statistical image processing and multidimensional modeling
Fieguth, Paul
2010-01-01
Images are all around us! The proliferation of low-cost, high-quality imaging devices has led to an explosion in acquired images. When these images are acquired from a microscope, telescope, satellite, or medical imaging device, there is a statistical image processing task: the inference of something - an artery, a road, a DNA marker, an oil spill - from imagery, possibly noisy, blurry, or incomplete. A great many textbooks have been written on image processing. However this book does not so much focus on images, per se, but rather on spatial data sets, with one or more measurements taken over
Stochastic linear hybrid systems: Modeling, estimation, and application
Seah, Chze Eng
Hybrid systems are dynamical systems which have interacting continuous state and discrete state (or mode). Accurate modeling and state estimation of hybrid systems are important in many applications. We propose a hybrid system model, known as the Stochastic Linear Hybrid System (SLHS), to describe hybrid systems with stochastic linear system dynamics in each mode and stochastic continuous-state-dependent mode transitions. We then develop a hybrid estimation algorithm, called the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm, to estimate the continuous state and discrete state of the SLHS from noisy measurements. It is shown that the SDTHE algorithm is more accurate or more computationally efficient than existing hybrid estimation algorithms. Next, we develop a performance analysis algorithm to evaluate the performance of the SDTHE algorithm in a given operating scenario. We also investigate sufficient conditions for the stability of the SDTHE algorithm. The proposed SLHS model and SDTHE algorithm are illustrated to be useful in several applications. In Air Traffic Control (ATC), to facilitate implementations of new efficient operational concepts, accurate modeling and estimation of aircraft trajectories are needed. In ATC, an aircraft's trajectory can be divided into a number of flight modes. Furthermore, as the aircraft is required to follow a given flight plan or clearance, its flight mode transitions are dependent of its continuous state. However, the flight mode transitions are also stochastic due to navigation uncertainties or unknown pilot intents. Thus, we develop an aircraft dynamics model in ATC based on the SLHS. The SDTHE algorithm is then used in aircraft tracking applications to estimate the positions/velocities of aircraft and their flight modes accurately. Next, we develop an aircraft conformance monitoring algorithm to detect any deviations of aircraft trajectories in ATC that might compromise safety. In this application, the SLHS
Fluctuations and correlations in statistical models of hadron production
Gorenstein, M. I.
2012-01-01
An extension of the standard concept of the statistical ensembles is suggested. Namely, the statistical ensembles with extensive quantities fluctuating according to an externally given distribution are introduced. Applications in the statistical models of multiple hadron production in high energy physics are discussed.
Analysis and Evaluation of Statistical Models for Integrated Circuits Design
Sáenz-Noval J.J.
2011-10-01
Full Text Available Statistical models for integrated circuits (IC allow us to estimate the percentage of acceptable devices in the batch before fabrication. Actually, Pelgrom is the statistical model most accepted in the industry; however it was derived from a micrometer technology, which does not guarantee reliability in nanometric manufacturing processes. This work considers three of the most relevant statistical models in the industry and evaluates their limitations and advantages in analog design, so that the designer has a better criterion to make a choice. Moreover, it shows how several statistical models can be used for each one of the stages and design purposes.
Modeling of uncertainties in statistical inverse problems
Kaipio, Jari
2008-01-01
In all real world problems, the models that tie the measurements to the unknowns of interest, are at best only approximations for reality. While moderate modeling and approximation errors can be tolerated with stable problems, inverse problems are a notorious exception. Typical modeling errors include inaccurate geometry, unknown boundary and initial data, properties of noise and other disturbances, and simply the numerical approximations of the physical models. In principle, the Bayesian approach to inverse problems, in which all uncertainties are modeled as random variables, is capable of handling these uncertainties. Depending on the type of uncertainties, however, different strategies may be adopted. In this paper we give an overview of typical modeling errors and related strategies within the Bayesian framework.
Plan Recognition using Statistical Relational Models
2014-08-25
corresponding undirected model can be significantly more complex since there is no closed form solution for the maximum-likelihood set of parameters unlike in...algorithm did not scale to larger training sets, and the overall results are still not competitive with BALPs. 5In directed models, a closed form solution...opinions of ARO, DARPA, NSF or any other government agency. References Albrecht DW, Zukerman I, Nicholson AE. Bayesian models for keyhole plan
Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.
This paper contains an analyses of the error induced by applying the method of the equivalent statistical linearzation (ESL) to randomly-exited multi-degree-of-freedom (MDOF) geometrically nonlinear shear-frame structures as the number of degrees of freedom increases. The quantity that is analyzed...
Statistical Modelling of Extreme Rainfall in Taiwan
L-F. Chu (Lan-Fen); M.J. McAleer (Michael); C-C. Chang (Ching-Chung)
2012-01-01
textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.
Statistical Modelling of Extreme Rainfall in Taiwan
L. Chu (LanFen); M.J. McAleer (Michael); C-H. Chang (Chu-Hsiang)
2013-01-01
textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.
What type of statistical model to choose for the analysis of radioimmunoassays
Huet, S.
1984-01-01
The current techniques used for statistical analysis of radioimmunoassays are not very satisfactory for either the statistician or the biologist. They are based on an attempt to make the response curve linear to avoid complicated computations. The present article shows that this practice has considerable effects (often neglected) on the statistical assumptions which must be formulated. A more strict analysis is proposed by applying the four-parameter logistic model. The advantages of this method are: the statistical assumptions formulated are based on observed data, and the model can be applied to almost all radioimmunoassays [fr
Low-energy limit of the extended Linear Sigma Model
Divotgey, Florian [Johann Wolfgang Goethe-Universitaet, Institut fuer Theoretische Physik, Frankfurt am Main (Germany); Kovacs, Peter [Wigner Research Center for Physics, Hungarian Academy of Sciences, Institute for Particle and Nuclear Physics, Budapest (Hungary); GSI Helmholtzzentrum fuer Schwerionenforschung, ExtreMe Matter Institute, Darmstadt (Germany); Giacosa, Francesco [Johann Wolfgang Goethe-Universitaet, Institut fuer Theoretische Physik, Frankfurt am Main (Germany); Jan-Kochanowski University, Institute of Physics, Kielce (Poland); Rischke, Dirk H. [Johann Wolfgang Goethe-Universitaet, Institut fuer Theoretische Physik, Frankfurt am Main (Germany); University of Science and Technology of China, Interdisciplinary Center for Theoretical Study and Department of Modern Physics, Hefei, Anhui (China)
2018-01-15
The extended Linear Sigma Model is an effective hadronic model based on the linear realization of chiral symmetry SU(N{sub f}){sub L} x SU(N{sub f}){sub R}, with (pseudo)scalar and (axial-)vector mesons as degrees of freedom. In this paper, we study the low-energy limit of the extended Linear Sigma Model (eLSM) for N{sub f} = flavors by integrating out all fields except for the pions, the (pseudo-)Nambu-Goldstone bosons of chiral symmetry breaking. The resulting low-energy effective action is identical to Chiral Perturbation Theory (ChPT) after choosing a representative for the coset space generated by chiral symmetry breaking and expanding it in powers of (derivatives of) the pion fields. The tree-level values of the coupling constants of the effective low-energy action agree remarkably well with those of ChPT. (orig.)
Linear Power-Flow Models in Multiphase Distribution Networks: Preprint
Bernstein, Andrey; Dall' Anese, Emiliano
2017-05-26
This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- from advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.
On the Logical Development of Statistical Models.
1983-12-01
1978). "Modelos con parametros variables en el analisis de series temporales " Questiio, 4, 2, 75-87. [25] Seal, H. L. (1967). "The historical...example, a classical state-space representation of a simple time series model is: yt = it + ut Ut = *It-I + Ct (2.2) ut and et are independent normal...on its past values is displayed in the structural equation. This approach has been particularly useful in time series models. For example, model (2.2
A Noise Robust Statistical Texture Model
Hilger, Klaus Baggesen; Stegmann, Mikkel Bille; Larsen, Rasmus
2002-01-01
Appearance Models segmentation framework. This is accomplished by augmenting the model with an estimate of the covariance of the noise present in the training data. This results in a more compact model maximising the signal-to-noise ratio, thus favouring subspaces rich on signal, but low on noise......This paper presents a novel approach to the problem of obtaining a low dimensional representation of texture (pixel intensity) variation present in a training set after alignment using a Generalised Procrustes analysis.We extend the conventional analysis of training textures in the Active...
Modelling and measurement of a moving magnet linear compressor performance
Liang, Kun; Stone, Richard; Davies, Gareth; Dadd, Mike; Bailey, Paul
2014-01-01
A novel moving magnet linear compressor with clearance seals and flexure bearings has been designed and constructed. It is suitable for a refrigeration system with a compact heat exchanger, such as would be needed for CPU cooling. The performance of the compressor has been experimentally evaluated with nitrogen and a mathematical model has been developed to evaluate the performance of the linear compressor. The results from the compressor model and the measurements have been compared in terms of cylinder pressure, the ‘P–V’ loop, stroke, mass flow rate and shaft power. The cylinder pressure was not measured directly but was derived from the compressor dynamics and the motor magnetic force characteristics. The comparisons indicate that the compressor model is well validated and can be used to study the performance of this type of compressor, to help with design optimization and the identification of key parameters affecting the system transients. The electrical and thermodynamic losses were also investigated, particularly for the design point (stroke of 13 mm and pressure ratio of 3.0), since a full understanding of these can lead to an increase in compressor efficiency. - Highlights: • Model predictions of the performance of a novel moving magnet linear compressor. • Prototype linear compressor performance measurements using nitrogen. • Reconstruction of P–V loops using a model of the dynamics and electromagnetics. • Close agreement between the model and measurements for the P–V loops. • The design point motor efficiency was 74%, with potential improvements identified
The minimal linear σ model for the Goldstone Higgs
Feruglio, F.; Gavela, M.B.; Kanshin, K.; Machado, P.A.N.; Rigolin, S.; Saa, S.
2016-01-01
In the context of the minimal SO(5) linear σ-model, a complete renormalizable Lagrangian -including gauge bosons and fermions- is considered, with the symmetry softly broken to SO(4). The scalar sector describes both the electroweak Higgs doublet and the singlet σ. Varying the σ mass would allow to sweep from the regime of perturbative ultraviolet completion to the non-linear one assumed in models in which the Higgs particle is a low-energy remnant of some strong dynamics. We analyze the phenomenological implications and constraints from precision observables and LHC data. Furthermore, we derive the d≤6 effective Lagrangian in the limit of heavy exotic fermions.
A variational formulation for linear models in coupled dynamic thermoelasticity
Feijoo, R.A.; Moura, C.A. de.
1981-07-01
A variational formulation for linear models in coupled dynamic thermoelasticity which quite naturally motivates the design of a numerical scheme for the problem, is studied. When linked to regularization or penalization techniques, this algorithm may be applied to more general models, namely, the ones that consider non-linear constraints associated to variational inequalities. The basic postulates of Mechanics and Thermodynamics as well as some well-known mathematical techniques are described. A thorough description of the algorithm implementation with the finite-element method is also provided. Proofs for existence and uniqueness of solutions and for convergence of the approximations are presented, and some numerical results are exhibited. (Author) [pt
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...
Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables
Henson, Robert A.; Templin, Jonathan L.; Willse, John T.
2009-01-01
This paper uses log-linear models with latent variables (Hagenaars, in "Loglinear Models with Latent Variables," 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for…
Hayslett, H T
1991-01-01
Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text the
12th Workshop on Stochastic Models, Statistics and Their Applications
Rafajłowicz, Ewaryst; Szajowski, Krzysztof
2015-01-01
This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.
Functional linear models for association analysis of quantitative traits.
Fan, Ruzong; Wang, Yifan; Mills, James L; Wilson, Alexander F; Bailey-Wilson, Joan E; Xiong, Momiao
2013-11-01
Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F-distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT-O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT-O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study. © 2013 WILEY
The Impact of a Flipped Classroom Model of Learning on a Large Undergraduate Statistics Class
Nielson, Perpetua Lynne; Bean, Nathan William Bean; Larsen, Ross Allen Andrew
2018-01-01
We examine the impact of a flipped classroom model of learning on student performance and satisfaction in a large undergraduate introductory statistics class. Two professors each taught a lecture-section and a flipped-class section. Using MANCOVA, a linear combination of final exam scores, average quiz scores, and course ratings was compared for…
Kleijnen, J.P.C.
2006-01-01
Classic linear regression models and their concomitant statistical designs assume a univariate response and white noise.By definition, white noise is normally, independently, and identically distributed with zero mean.This survey tries to answer the following questions: (i) How realistic are these
Materials Informatics: Statistical Modeling in Material Science.
Yosipof, Abraham; Shimanovich, Klimentiy; Senderowitz, Hanoch
2016-12-01
Material informatics is engaged with the application of informatic principles to materials science in order to assist in the discovery and development of new materials. Central to the field is the application of data mining techniques and in particular machine learning approaches, often referred to as Quantitative Structure Activity Relationship (QSAR) modeling, to derive predictive models for a variety of materials-related "activities". Such models can accelerate the development of new materials with favorable properties and provide insight into the factors governing these properties. Here we provide a comparison between medicinal chemistry/drug design and materials-related QSAR modeling and highlight the importance of developing new, materials-specific descriptors. We survey some of the most recent QSAR models developed in materials science with focus on energetic materials and on solar cells. Finally we present new examples of material-informatic analyses of solar cells libraries produced from metal oxides using combinatorial material synthesis. Different analyses lead to interesting physical insights as well as to the design of new cells with potentially improved photovoltaic parameters. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
ANALISIS MODEL REGRESI NONPARAMETRIK SIRKULAR-LINEAR BERGANDA
KOMANG CANDRA IVAN
2016-05-01
Full Text Available Circular data are data which the value in form of vector is circular data. Statistic analysis that is used in analyzing circular data is circular statistics analysis. In regression analysis, if any of predictor or response variables or both are circular then the regression analysis used is called circular regression analysis. Observation data in circular statistic which use direction and time units usually don’t satisfy all of the parametric assumptions, thus making nonparametric regression as a good solution. Nonparametric regression function estimation is using epanechnikov kernel estimator for the linier variables and von Mises kernel estimator for the circular variable. This study showed that the result of circular analysis by using circular descriptive statistic is better than common statistic. Multiple circular-linier nonparametric regressions with Epanechnikov and von Mises kernel estimator didn’t create estimation model explicitly as parametric regression does, but create estimation from its observation knots instead.
Practical likelihood analysis for spatial generalized linear mixed models
Bonat, W. H.; Ribeiro, Paulo Justiniano
2016-01-01
We investigate an algorithm for maximum likelihood estimation of spatial generalized linear mixed models based on the Laplace approximation. We compare our algorithm with a set of alternative approaches for two datasets from the literature. The Rhizoctonia root rot and the Rongelap are......, respectively, examples of binomial and count datasets modeled by spatial generalized linear mixed models. Our results show that the Laplace approximation provides similar estimates to Markov Chain Monte Carlo likelihood, Monte Carlo expectation maximization, and modified Laplace approximation. Some advantages...... of Laplace approximation include the computation of the maximized log-likelihood value, which can be used for model selection and tests, and the possibility to obtain realistic confidence intervals for model parameters based on profile likelihoods. The Laplace approximation also avoids the tuning...
Stochastic modeling of mode interactions via linear parabolized stability equations
Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo
2017-11-01
Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.
Linear and nonlinear methods in modeling the aqueous solubility of organic compounds.
Catana, Cornel; Gao, Hua; Orrenius, Christian; Stouten, Pieter F W
2005-01-01
Solubility data for 930 diverse compounds have been analyzed using linear Partial Least Square (PLS) and nonlinear PLS methods, Continuum Regression (CR), and Neural Networks (NN). 1D and 2D descriptors from MOE package in combination with E-state or ISIS keys have been used. The best model was obtained using linear PLS for a combination between 22 MOE descriptors and 65 ISIS keys. It has a correlation coefficient (r2) of 0.935 and a root-mean-square error (RMSE) of 0.468 log molar solubility (log S(w)). The model validated on a test set of 177 compounds not included in the training set has r2 0.911 and RMSE 0.475 log S(w). The descriptors were ranked according to their importance, and at the top of the list have been found the 22 MOE descriptors. The CR model produced results as good as PLS, and because of the way in which cross-validation has been done it is expected to be a valuable tool in prediction besides PLS model. The statistics obtained using nonlinear methods did not surpass those got with linear ones. The good statistic obtained for linear PLS and CR recommends these models to be used in prediction when it is difficult or impossible to make experimental measurements, for virtual screening, combinatorial library design, and efficient leads optimization.
Latent domain models for statistical machine translation
Hoàng, C.
2017-01-01
A data-driven approach to model translation suffers from the data mismatch problem and demands domain adaptation techniques. Given parallel training data originating from a specific domain, training an MT system on the data would result in a rather suboptimal translation for other domains. But does
Behavioral and statistical models of educational inequality
Holm, Anders; Breen, Richard
2016-01-01
This paper addresses the question of how students and their families make educational decisions. We describe three types of behavioral model that might underlie decision-making and we show that they have consequences for what decisions are made. Our study thus has policy implications if we wish...
Statistical modelling of fine red wine production
María Rosa Castro
2010-01-01
Full Text Available Producing wine is a very important economic activity in the province of San Juan in Argentina; it is therefore most important to predict production regarding the quantity of raw material needed. This work was aimed at obtaining a model relating kilograms of crushed grape to the litres of wine so produced. Such model will be used for predicting precise future values and confidence intervals for determined quantities of crushed grapes. Data from a vineyard in the province of San Juan was thus used in this work. The sampling coefficient of correlation was calculated and a dispersion diagram was then constructed; this indicated a li- neal relationship between the litres of wine obtained and the kilograms of crushed grape. Two lineal models were then adopted and variance analysis was carried out because the data came from normal populations having the same variance. The most appropriate model was obtained from this analysis; it was validated with experimental values, a good approach being obtained.
Statistical models of global Langmuir mixing
Li, Qing; Fox-Kemper, Baylor; Breivik, Øyvind; Webb, Adrean
2017-05-01
The effects of Langmuir mixing on the surface ocean mixing may be parameterized by applying an enhancement factor which depends on wave, wind, and ocean state to the turbulent velocity scale in the K-Profile Parameterization. Diagnosing the appropriate enhancement factor online in global climate simulations is readily achieved by coupling with a prognostic wave model, but with significant computational and code development expenses. In this paper, two alternatives that do not require a prognostic wave model, (i) a monthly mean enhancement factor climatology, and (ii) an approximation to the enhancement factor based on the empirical wave spectra, are explored and tested in a global climate model. Both appear to reproduce the Langmuir mixing effects as estimated using a prognostic wave model, with nearly identical and substantial improvements in the simulated mixed layer depth and intermediate water ventilation over control simulations, but significantly less computational cost. Simpler approaches, such as ignoring Langmuir mixing altogether or setting a globally constant Langmuir number, are found to be deficient. Thus, the consequences of Stokes depth and misaligned wind and waves are important.
Sampling, Probability Models and Statistical Reasoning -RE ...
random sampling allows data to be modelled with the help of probability ... g based on different trials to get an estimate of the experimental error. ... research interests lie in the .... if e is indeed the true value of the proportion of defectives in the.
Statistical Model Checking for Product Lines
ter Beek, Maurice H.; Legay, Axel; Lluch Lafuente, Alberto
2016-01-01
average cost of products (in terms of the attributes of the products’ features) and the probability of features to be (un)installed at runtime. The product lines must be modelled in QFLan, which extends the probabilistic feature-oriented language PFLan with novel quantitative constraints among features...
A Statistical Model for Energy Intensity
Marjaneh Issapour
2012-12-01
Full Text Available A promising approach to improve scientific literacy in regards to global warming and climate change is using a simulation as part of a science education course. The simulation needs to employ scientific analysis of actual data from internationally accepted and reputable databases to demonstrate the reality of the current climate change situation. One of the most important criteria for using a simulation in a science education course is the fidelity of the model. The realism of the events and consequences modeled in the simulation is significant as well. Therefore, all underlying equations and algorithms used in the simulation must have real-world scientific basis. The "Energy Choices" simulation is one such simulation. The focus of this paper is the development of a mathematical model for "Energy Intensity" as a part of the overall system dynamics in "Energy Choices" simulation. This model will define the "Energy Intensity" as a function of other independent variables that can be manipulated by users of the simulation. The relationship discovered by this research will be applied to an algorithm in the "Energy Choices" simulation.
Structured Statistical Models of Inductive Reasoning
Kemp, Charles; Tenenbaum, Joshua B.
2009-01-01
Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet…
Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations
Daniel T. L. Shek
2011-01-01
Full Text Available Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes in Hong Kong are presented.
Shek, Daniel T L; Ma, Cecilia M S
2011-01-05
Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented.
Learning Statistics - in a WEB-based and non-linear way
Rootzen, Helle
2007-01-01
different from one another. They have different prior knowledge and different learning styles so it is a challenging task to teach them all in the same way. Furthermore the world of statistics has become so huge that it is impossible to cover everything. The structure imposed by the Bologna agreement gives...... can design the course – or a part of the course – so that it fits their individual learning style and their prior knowledge. Some prefer to look at examples first and afterwards look at which theories it is based on. Others want to do it the opposite way. Some wants to work with the problem themselves...
Lecarpentier, Yves; Claes, Victor; Hébert, Jean-Louis; Krokidis, Xénophon; Blanc, François-Xavier; Michel, Francine; Timbely, Oumar
2015-01-01
All near-equilibrium systems under linear regime evolve to stationary states in which there is constant entropy production rate. In an open chemical system that exchanges matter and energy with the exterior, we can identify both the energy and entropy flows associated with the exchange of matter and energy. This can be achieved by applying statistical mechanics (SM), which links the microscopic properties of a system to its bulk properties. In the case of contractile tissues such as human placenta, Huxley's equations offer a phenomenological formalism for applying SM. SM was investigated in human placental stem villi (PSV) (n = 40). PSV were stimulated by means of KCl exposure (n = 20) and tetanic electrical stimulation (n = 20). This made it possible to determine statistical entropy (S), internal energy (E), affinity (A), thermodynamic force (A / T) (T: temperature), thermodynamic flow (v) and entropy production rate (A / T x v). We found that PSV operated near equilibrium, i.e., A ≺≺ 2500 J/mol and in a stationary linear regime, i.e., (A / T) varied linearly with v. As v was dramatically low, entropy production rate which quantified irreversibility of chemical processes appeared to be the lowest ever observed in any contractile system.
Burgués, Javier; Jiménez-Soto, Juan Manuel; Marco, Santiago
2018-07-12
The limit of detection (LOD) is a key figure of merit in chemical sensing. However, the estimation of this figure of merit is hindered by the non-linear calibration curve characteristic of semiconductor gas sensor technologies such as, metal oxide (MOX), gasFETs or thermoelectric sensors. Additionally, chemical sensors suffer from cross-sensitivities and temporal stability problems. The application of the International Union of Pure and Applied Chemistry (IUPAC) recommendations for univariate LOD estimation in non-linear semiconductor gas sensors is not straightforward due to the strong statistical requirements of the IUPAC methodology (linearity, homoscedasticity, normality). Here, we propose a methodological approach to LOD estimation through linearized calibration models. As an example, the methodology is applied to the detection of low concentrations of carbon monoxide using MOX gas sensors in a scenario where the main source of error is the presence of uncontrolled levels of humidity. Copyright © 2018 Elsevier B.V. All rights reserved.
Ju, Sang Gyu; Huh, Seung Jae; Han, Young Yih
2005-01-01
To improve the management of a medical linear accelerator, the records of operational failures of a Varian CL2100C over a ten year period were retrospectively analyzed. The failures were classified according to the involved functional subunits, with each class rated into one of three levels depending on the operational conditions. The relationships between the failure rate and working ratio and between the failure rate and outside temperature were investigated. In addition, the average life time of the main part and the operating efficiency over the last 4 years were analyzed. Among the recorded failures (total 587 failures), the most frequent failure was observed in the parts related with the collimation system, including the monitor chamber, which accounted for 20% of all failures. With regard to the operational conditions, 2nd level of failures, which temporally interrupted treatments, were the most frequent. Third level of failures, which interrupted treatment for more than several hours, were mostly caused by the accelerating subunit. The number of failures was increased with number of treatments and operating time. The average life-times of the Klystron and Thyratron became shorter as the working ratio increased, and were 42 and 83% of the expected values, respectively. The operating efficiency was maintained at 95% or higher, but this value slightly decreased. There was no significant correlation between the number of failures and the outside temperature. The maintenance of detailed equipment problems and failures records over a long period of time can provide good knowledge of equipment function as well as the capability of predicting future failure. More rigorous equipment maintenance is required for old medical linear accelerators for the advanced avoidance of serious failure and to improve the quality of patient treatment
Statistical Analysis and Modelling of Olkiluoto Structures
Hellae, P.; Vaittinen, T.; Saksa, P.; Nummela, J.
2004-11-01
Posiva Oy is carrying out investigations for the disposal of the spent nuclear fuel at the Olkiluoto site in SW Finland. The investigations have focused on the central part of the island. The layout design of the entire repository requires characterization of notably larger areas and must rely at least at the current stage on borehole information from a rather sparse network and on the geophysical soundings providing information outside and between the holes. In this work, the structural data according to the current version of the Olkiluoto bedrock model is analyzed. The bedrock model relies much on the borehole data although results of the seismic surveys and, for example, pumping tests are used in determining the orientation and continuation of the structures. Especially in the analysis, questions related to the frequency of structures and size of the structures are discussed. The structures observed in the boreholes are mainly dipping gently to the southeast. About 9 % of the sample length belongs to structures. The proportion is higher in the upper parts of the rock. The number of fracture and crushed zones seems not to depend greatly on the depth, whereas the hydraulic features concentrate on the depth range above -100 m. Below level -300 m, the hydraulic conductivity occurs in connection of fractured zones. Especially the hydraulic features, but also fracture and crushed zones often occur in groups. The frequency of the structure (area of structures per total volume) is estimated to be of the order of 1/100m. The size of the local structures was estimated by calculating the intersection of the zone to the nearest borehole where the zone has not been detected. Stochastic models using the Fracman software by Golder Associates were generated based on the bedrock model data complemented with the magnetic ground survey data. The seismic surveys (from boreholes KR5, KR13, KR14, and KR19) were used as alternative input data. The generated models were tested by
Modeling statistical properties of written text.
M Angeles Serrano
Full Text Available Written text is one of the fundamental manifestations of human language, and the study of its universal regularities can give clues about how our brains process information and how we, as a society, organize and share it. Among these regularities, only Zipf's law has been explored in depth. Other basic properties, such as the existence of bursts of rare words in specific documents, have only been studied independently of each other and mainly by descriptive models. As a consequence, there is a lack of understanding of linguistic processes as complex emergent phenomena. Beyond Zipf's law for word frequencies, here we focus on burstiness, Heaps' law describing the sublinear growth of vocabulary size with the length of a document, and the topicality of document collections, which encode correlations within and across documents absent in random null models. We introduce and validate a generative model that explains the simultaneous emergence of all these patterns from simple rules. As a result, we find a connection between the bursty nature of rare words and the topical organization of texts and identify dynamic word ranking and memory across documents as key mechanisms explaining the non trivial organization of written text. Our research can have broad implications and practical applications in computer science, cognitive science and linguistics.
Linear modeling of possible mechanisms for parkinson tremor generation
Lohnberg, P.
1978-01-01
The power of Parkinson tremor is expressed in terms of possibly changed frequency response functions between relevant variables in the neuromuscular system. The derivation starts out from a linear loopless equivalent model of mechanisms for general tremor generation. Hypothetical changes in this
Current algebra of classical non-linear sigma models
Forger, M.; Laartz, J.; Schaeper, U.
1992-01-01
The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)
Mathematical modelling and linear stability analysis of laser fusion cutting
Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg; Thombansen, Ulrich
2016-01-01
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.
Non Linear signa models probing the string structure
Abdalla, E.
1987-01-01
The introduction of a term depending on the extrinsic curvature to the string action, and related non linear sigma models defined on a symmetric space SO(D)/SO(2) x SO(d-2) is descussed . Coupling to fermions are also treated. (author) [pt
Confidence Intervals for Assessing Heterogeneity in Generalized Linear Mixed Models
Wagler, Amy E.
2014-01-01
Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…
Penalized Estimation in Large-Scale Generalized Linear Array Models
Lund, Adam; Vincent, Martin; Hansen, Niels Richard
2017-01-01
Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free algorithms do not scale well with the dimension...
Expressions for linearized perturbations in ideal-fluid cosmological models
Ratra, B.
1988-01-01
We present closed-form solutions of the relativistic linear perturbation equations (in synchronous gauge) that govern the evolution of inhomogeneities in homogeneous, spatially flat, ideal-fluid, cosmological models. These expressions, which are valid for irregularities on any scale, allow one to analytically interpolate between the known approximate solutions which are valid at early times and at late times
S-AMP for non-linear observation models
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Plane answers to complex questions the theory of linear models
Christensen, Ronald
1987-01-01
This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems freq...
A simulation model of a coordinated decentralized linear supply chain
Ashayeri, Jalal; Cannella, S.; Lopez Campos, M.; Miranda, P.A.
2015-01-01
This paper presents a simulation-based study of a coordinated, decentralized linear supply chain (SC) system. In the proposed model, any supply tier considers its successors as part of its inventory system and generates replenishment orders on the basis of its partners’ operational information. We
Mathematical modelling and linear stability analysis of laser fusion cutting
Hermanns, Torsten; Schulz, Wolfgang [RWTH Aachen University, Chair for Nonlinear Dynamics, Steinbachstr. 15, 52047 Aachen (Germany); Vossen, Georg [Niederrhein University of Applied Sciences, Chair for Applied Mathematics and Numerical Simulations, Reinarzstr.. 49, 47805 Krefeld (Germany); Thombansen, Ulrich [RWTH Aachen University, Chair for Laser Technology, Steinbachstr. 15, 52047 Aachen (Germany)
2016-06-08
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.
Performances Of Estimators Of Linear Models With Autocorrelated ...
The performances of five estimators of linear models with Autocorrelated error terms are compared when the independent variable is autoregressive. The results reveal that the properties of the estimators when the sample size is finite is quite similar to the properties of the estimators when the sample size is infinite although ...
Performances of estimators of linear auto-correlated error model ...
The performances of five estimators of linear models with autocorrelated disturbance terms are compared when the independent variable is exponential. The results reveal that for both small and large samples, the Ordinary Least Squares (OLS) compares favourably with the Generalized least Squares (GLS) estimators in ...
A non-linear dissipative model of magnetism
Durand, P.; Paidarová, Ivana
2010-01-01
Roč. 89, č. 6 (2010), s. 67004 ISSN 1286-4854 R&D Projects: GA AV ČR IAA100400501 Institutional research plan: CEZ:AV0Z40400503 Keywords : non-linear dissipative model of magnetism * thermodynamics * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry http://epljournal.edpsciences.org/
Modeling and verifying non-linearities in heterodyne displacement interferometry
Cosijns, S.J.A.G.; Haitjema, H.; Schellekens, P.H.J.
2002-01-01
The non-linearities in a heterodyne laser interferometer system occurring from the phase measurement system of the interferometer andfrom non-ideal polarization effects of the optics are modeled into one analytical expression which includes the initial polarization state ofthe laser source, the
Holst, René; Jørgensen, Bent
2015-01-01
The paper proposes a versatile class of multiplicative generalized linear longitudinal mixed models (GLLMM) with additive dispersion components, based on explicit modelling of the covariance structure. The class incorporates a longitudinal structure into the random effects models and retains...... a marginal as well as a conditional interpretation. The estimation procedure is based on a computationally efficient quasi-score method for the regression parameters combined with a REML-like bias-corrected Pearson estimating function for the dispersion and correlation parameters. This avoids...... the multidimensional integral of the conventional GLMM likelihood and allows an extension of the robust empirical sandwich estimator for use with both association and regression parameters. The method is applied to a set of otholit data, used for age determination of fish....
Identifiability Results for Several Classes of Linear Compartment Models.
Meshkat, Nicolette; Sullivant, Seth; Eisenberg, Marisa
2015-08-01
Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.
Statistically Based Morphodynamic Modeling of Tracer Slowdown
Borhani, S.; Ghasemi, A.; Hill, K. M.; Viparelli, E.
2017-12-01
Tracer particles are used to study bedload transport in gravel-bed rivers. One of the advantages associated with using of tracer particles is that they allow for direct measures of the entrainment rates and their size distributions. The main issue in large scale studies with tracer particles is the difference between tracer stone short term and long term behavior. This difference is due to the fact that particles undergo vertical mixing or move to less active locations such as bars or even floodplains. For these reasons the average virtual velocity of tracer particle decreases in time, i.e. the tracer slowdown. In summary, tracer slowdown can have a significant impact on the estimation of bedload transport rate or long term dispersal of contaminated sediment. The vast majority of the morphodynamic models that account for the non-uniformity of the bed material (tracer and not tracer, in this case) are based on a discrete description of the alluvial deposit. The deposit is divided in two different regions; the active layer and the substrate. The active layer is a thin layer in the topmost part of the deposit whose particles can interact with the bed material transport. The substrate is the part of the deposit below the active layer. Due to the discrete representation of the alluvial deposit, active layer models are not able to reproduce tracer slowdown. In this study we try to model the slowdown of tracer particles with the continuous Parker-Paola-Leclair morphodynamic framework. This continuous, i.e. not layer-based, framework is based on a stochastic description of the temporal variation of bed surface elevation, and of the elevation specific particle entrainment and deposition. Particle entrainment rates are computed as a function of the flow and sediment characteristics, while particle deposition is estimated with a step length formulation. Here we present one of the first implementation of the continuum framework at laboratory scale, its validation against
Finite element modeling of nanotube structures linear and non-linear models
Awang, Mokhtar; Muhammad, Ibrahim Dauda
2016-01-01
This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.
Gohil, B. S.; Hariharan, T. A.; Sharma, A. K.; Pandey, P. C.
1982-01-01
The 19.35 GHz and 22.235 GHz passive microwave radiometers (SAMIR) on board the Indian satellite Bhaskara have provided very useful data. From these data has been demonstrated the feasibility of deriving atmospheric and ocean surface parameters such as water vapor content, liquid water content, rainfall rate and ocean surface winds. Different approaches have been tried for deriving the atmospheric water content. The statistical and empirical methods have been used by others for the analysis of the Nimbus data. A simulation technique has been attempted for the first time for 19.35 GHz and 22.235 GHz radiometer data. The results obtained from three different methods are compared with radiosonde data. A case study of a tropical depression has been undertaken to demonstrate the capability of Bhaskara SAMIR data to show the variation of total water vapor and liquid water contents.
Jaikuna, Tanwiwat; Khadsiri, Phatchareewan; Chawapun, Nisa; Saekho, Suwit; Tharavichitkul, Ekkasit
2017-02-01
To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL) model. The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR), and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD 2 ) was calculated using biological effective dose (BED) based on the LQL model. The software calculation and the manual calculation were compared for EQD 2 verification with pair t -test statistical analysis using IBM SPSS Statistics version 22 (64-bit). Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS) in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV) determined by D 90% , 0.56% in the bladder, 1.74% in the rectum when determined by D 2cc , and less than 1% in Pinnacle. The difference in the EQD 2 between the software calculation and the manual calculation was not significantly different with 0.00% at p -values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT) and 0.240, 0.320, and 0.849 for brachytherapy (BT) in HR-CTV, bladder, and rectum, respectively. The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Linear Dynamics Model for Steam Cooled Fast Power Reactors
Vollmer, H
1968-04-15
A linear analytical dynamic model is developed for steam cooled fast power reactors. All main components of such a plant are investigated on a general though relatively simple basis. The model is distributed in those parts concerning the core but lumped as to the external plant components. Coolant is considered as compressible and treated by the actual steam law. Combined use of analogue and digital computer seems most attractive.
Deterministic operations research models and methods in linear optimization
Rader, David J
2013-01-01
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations resear
One-loop dimensional reduction of the linear σ model
Malbouisson, A.P.C.; Silva-Neto, M.B.; Svaiter, N.F.
1997-05-01
We perform the dimensional reduction of the linear σ model at one-loop level. The effective of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum instability of the model for large N. (author)
Links to sources of cancer-related statistics, including the Surveillance, Epidemiology and End Results (SEER) Program, SEER-Medicare datasets, cancer survivor prevalence data, and the Cancer Trends Progress Report.
Artificial Neural Network versus Linear Models Forecasting Doha Stock Market
Yousif, Adil; Elfaki, Faiz
2017-12-01
The purpose of this study is to determine the instability of Doha stock market and develop forecasting models. Linear time series models are used and compared with a nonlinear Artificial Neural Network (ANN) namely Multilayer Perceptron (MLP) Technique. It aims to establish the best useful model based on daily and monthly data which are collected from Qatar exchange for the period starting from January 2007 to January 2015. Proposed models are for the general index of Qatar stock exchange and also for the usages in other several sectors. With the help of these models, Doha stock market index and other various sectors were predicted. The study was conducted by using various time series techniques to study and analyze data trend in producing appropriate results. After applying several models, such as: Quadratic trend model, double exponential smoothing model, and ARIMA, it was concluded that ARIMA (2,2) was the most suitable linear model for the daily general index. However, ANN model was found to be more accurate than time series models.
A linearized dispersion relation for orthorhombic pseudo-acoustic modeling
Song, Xiaolei; Alkhalifah, Tariq Ali
2012-01-01
Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen's parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.
Statistical mechanics of the cluster Ising model
Smacchia, Pietro; Amico, Luigi; Facchi, Paolo; Fazio, Rosario; Florio, Giuseppe; Pascazio, Saverio; Vedral, Vlatko
2011-01-01
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
Statistical mechanics of the cluster Ising model
Smacchia, Pietro [SISSA - via Bonomea 265, I-34136, Trieste (Italy); Amico, Luigi [CNR-MATIS-IMM and Dipartimento di Fisica e Astronomia Universita di Catania, C/O ed. 10, viale Andrea Doria 6, I-95125 Catania (Italy); Facchi, Paolo [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Fazio, Rosario [NEST, Scuola Normale Superiore and Istituto Nanoscienze - CNR, 56126 Pisa (Italy); Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Florio, Giuseppe; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Vedral, Vlatko [Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom)
2011-08-15
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
Linear models of income patterns in consumer demand for foods and evaluation of its elasticity
Pavel Syrovátka
2005-01-01
Full Text Available The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:ret* = At + 0.0946 · rmt*,where the values of absolute member are defined as:At = 1773.0973 + 9.3064 · t – 0.3023 · t2; (t = 1, 2, ... 32.The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002 always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:ηt ∈〈+0; +1.Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions.
Non-linear sigma model on the fuzzy supersphere
Kurkcuoglu, Seckin
2004-01-01
In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S (2,2) . In hep-th/0212133 Bott projectors have been used to obtain the fuzzy C P 1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super)-projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model. (author)
Functional summary statistics for the Johnson-Mehl model
Møller, Jesper; Ghorbani, Mohammad
The Johnson-Mehl germination-growth model is a spatio-temporal point process model which among other things have been used for the description of neurotransmitters datasets. However, for such datasets parametric Johnson-Mehl models fitted by maximum likelihood have yet not been evaluated by means...... of functional summary statistics. This paper therefore invents four functional summary statistics adapted to the Johnson-Mehl model, with two of them based on the second-order properties and the other two on the nuclei-boundary distances for the associated Johnson-Mehl tessellation. The functional summary...... statistics theoretical properties are investigated, non-parametric estimators are suggested, and their usefulness for model checking is examined in a simulation study. The functional summary statistics are also used for checking fitted parametric Johnson-Mehl models for a neurotransmitters dataset....
Optimal difference-based estimation for partially linear models
Zhou, Yuejin; Cheng, Yebin; Dai, Wenlin; Tong, Tiejun
2017-01-01
Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.
Modeling and analysis of linear hyperbolic systems of balance laws
Bartecki, Krzysztof
2016-01-01
This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...
Optimal difference-based estimation for partially linear models
Zhou, Yuejin
2017-12-16
Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.
der, R.
1987-01-01
The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transformwidetilde{C}(z)) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z=∞ and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover,widetilde{C}(z) may be expressed by a Laurent series expansion in positive and negative powers of z, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions ofwidetilde{C}(z) as obtained from the application of conventional many-body techniques to the calculation
USE OF THE SIMPLE LINEAR REGRESSION MODEL IN MACRO-ECONOMICAL ANALYSES
Constantin ANGHELACHE
2011-10-01
Full Text Available The article presents the fundamental aspects of the linear regression, as a toolbox which can be used in macroeconomic analyses. The article describes the estimation of the parameters, the statistical tests used, the homoscesasticity and heteroskedasticity. The use of econometrics instrument in macroeconomics is an important factor that guarantees the quality of the models, analyses, results and possible interpretation that can be drawn at this level.
Mayvan, Ali D.; Aghaeinia, Hassan; Kazemi, Mohammad
2017-12-01
This paper focuses on robust transceiver design for throughput enhancement on the interference channel (IC), under imperfect channel state information (CSI). In this paper, two algorithms are proposed to improve the throughput of the multi-input multi-output (MIMO) IC. Each transmitter and receiver has, respectively, M and N antennas and IC operates in a time division duplex mode. In the first proposed algorithm, each transceiver adjusts its filter to maximize the expected value of signal-to-interference-plus-noise ratio (SINR). On the other hand, the second algorithm tries to minimize the variances of the SINRs to hedge against the variability due to CSI error. Taylor expansion is exploited to approximate the effect of CSI imperfection on mean and variance. The proposed robust algorithms utilize the reciprocity of wireless networks to optimize the estimated statistical properties in two different working modes. Monte Carlo simulations are employed to investigate sum rate performance of the proposed algorithms and the advantage of incorporating variation minimization into the transceiver design.
A penalized framework for distributed lag non-linear models.
Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G
2017-09-01
Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.
General mirror pairs for gauged linear sigma models
Aspinwall, Paul S.; Plesser, M. Ronen [Departments of Mathematics and Physics, Duke University,Box 90320, Durham, NC 27708-0320 (United States)
2015-11-05
We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.
General mirror pairs for gauged linear sigma models
Aspinwall, Paul S.; Plesser, M. Ronen
2015-01-01
We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.
Petersson, K M; Nichols, T E; Poline, J B; Holmes, A P
1999-01-01
Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference. PMID:10466149
2005-01-01
For the years 2004 and 2005 the figures shown in the tables of Energy Review are partly preliminary. The annual statistics published in Energy Review are presented in more detail in a publication called Energy Statistics that comes out yearly. Energy Statistics also includes historical time-series over a longer period of time (see e.g. Energy Statistics, Statistics Finland, Helsinki 2004.) The applied energy units and conversion coefficients are shown in the back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supplies and total consumption of electricity GWh, Energy imports by country of origin in January-June 2003, Energy exports by recipient country in January-June 2003, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes, precautionary stock fees and oil pollution fees
Mixed deterministic statistical modelling of regional ozone air pollution
Kalenderski, Stoitchko
2011-03-17
We develop a physically motivated statistical model for regional ozone air pollution by separating the ground-level pollutant concentration field into three components, namely: transport, local production and large-scale mean trend mostly dominated by emission rates. The model is novel in the field of environmental spatial statistics in that it is a combined deterministic-statistical model, which gives a new perspective to the modelling of air pollution. The model is presented in a Bayesian hierarchical formalism, and explicitly accounts for advection of pollutants, using the advection equation. We apply the model to a specific case of regional ozone pollution-the Lower Fraser valley of British Columbia, Canada. As a predictive tool, we demonstrate that the model vastly outperforms existing, simpler modelling approaches. Our study highlights the importance of simultaneously considering different aspects of an air pollution problem as well as taking into account the physical bases that govern the processes of interest. © 2011 John Wiley & Sons, Ltd..
Linear models for joint association and linkage QTL mapping
Fernando Rohan L
2009-09-01
Full Text Available Abstract Background Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure. Results We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission average of the substitution effects of founders' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided. Conclusion The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.
A Model of Statistics Performance Based on Achievement Goal Theory.
Bandalos, Deborah L.; Finney, Sara J.; Geske, Jenenne A.
2003-01-01
Tests a model of statistics performance based on achievement goal theory. Both learning and performance goals affected achievement indirectly through study strategies, self-efficacy, and test anxiety. Implications of these findings for teaching and learning statistics are discussed. (Contains 47 references, 3 tables, 3 figures, and 1 appendix.)…
Kolmogorov complexity, pseudorandom generators and statistical models testing
Šindelář, Jan; Boček, Pavel
2002-01-01
Roč. 38, č. 6 (2002), s. 747-759 ISSN 0023-5954 R&D Projects: GA ČR GA102/99/1564 Institutional research plan: CEZ:AV0Z1075907 Keywords : Kolmogorov complexity * pseudorandom generators * statistical models testing Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.341, year: 2002
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
MAGDM linear-programming models with distinct uncertain preference structures.
Xu, Zeshui S; Chen, Jian
2008-10-01
Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.
Østergaard, Jacob; Kramer, Mark A.; Eden, Uri T.
2018-01-01
current. We then fit these spike train datawith a statistical model (a generalized linear model, GLM, with multiplicative influences of past spiking). For different levels of noise, we show how the GLM captures both the deterministic features of the Izhikevich neuron and the variability driven...... by the noise. We conclude that the GLM captures essential features of the simulated spike trains, but for near-deterministic spike trains, goodness-of-fit analyses reveal that the model does not fit very well in a statistical sense; the essential random part of the GLM is not captured....... are separately applied; understanding the relationships between these modeling approaches remains an area of active research. In this letter, we examine this relationship using simulation. To do so, we first generate spike train data from a well-known dynamical model, the Izhikevich neuron, with a noisy input...
Multiple Linear Regression Model for Estimating the Price of a ...
Ghana Mining Journal ... In the modeling, the Ordinary Least Squares (OLS) normality assumption which could introduce errors in the statistical analyses was dealt with by log transformation of the data, ensuring the data is normally ... The resultant MLRM is: Ŷi MLRM = (X'X)-1X'Y(xi') where X is the sample data matrix.
2001-01-01
For the year 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g. Energiatilastot 1999, Statistics Finland, Helsinki 2000, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions from the use of fossil fuels, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in 2000, Energy exports by recipient country in 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products
2000-01-01
For the year 1999 and 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g., Energiatilastot 1998, Statistics Finland, Helsinki 1999, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-March 2000, Energy exports by recipient country in January-March 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products
1999-01-01
For the year 1998 and the year 1999, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g. Energiatilastot 1998, Statistics Finland, Helsinki 1999, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-June 1999, Energy exports by recipient country in January-June 1999, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products
Kooths, Stefan; Mitze, Timo Friedel; Ringhut, Eric
2004-01-01
This paper compares the predictive power of linear econometric and non-linear computational models for forecasting the inflation rate in the European Monetary Union (EMU). Various models of both types are developed using different monetary and real activity indicators. They are compared according...
Improving statistical reasoning theoretical models and practical implications
Sedlmeier, Peter
1999-01-01
This book focuses on how statistical reasoning works and on training programs that can exploit people''s natural cognitive capabilities to improve their statistical reasoning. Training programs that take into account findings from evolutionary psychology and instructional theory are shown to have substantially larger effects that are more stable over time than previous training regimens. The theoretical implications are traced in a neural network model of human performance on statistical reasoning problems. This book apppeals to judgment and decision making researchers and other cognitive scientists, as well as to teachers of statistics and probabilistic reasoning.
Modelling of Asphalt Concrete Stiffness in the Linear Viscoelastic Region
Mazurek, Grzegorz; Iwański, Marek
2017-10-01
Stiffness modulus is a fundamental parameter used in the modelling of the viscoelastic behaviour of bituminous mixtures. On the basis of the master curve in the linear viscoelasticity range, the mechanical properties of asphalt concrete at different loading times and temperatures can be predicted. This paper discusses the construction of master curves under rheological mathematical models i.e. the sigmoidal function model (MEPDG), the fractional model, and Bahia and co-workers’ model in comparison to the results from mechanistic rheological models i.e. the generalized Huet-Sayegh model, the generalized Maxwell model and the Burgers model. For the purposes of this analysis, the reference asphalt concrete mix (denoted as AC16W) intended for the binder coarse layer and for traffic category KR3 (5×105 controlled strain mode. The fixed strain level was set at 25με to guarantee that the stiffness modulus of the asphalt concrete would be tested in a linear viscoelasticity range. The master curve was formed using the time-temperature superposition principle (TTSP). The stiffness modulus of asphalt concrete was determined at temperatures 10°C, 20°C and 40°C and at loading times (frequency) of 0.1, 0.3, 1, 3, 10, 20 Hz. The model parameters were fitted to the rheological models using the original programs based on the nonlinear least squares sum method. All the rheological models under analysis were found to be capable of predicting changes in the stiffness modulus of the reference asphalt concrete to satisfactory accuracy. In the cases of the fractional model and the generalized Maxwell model, their accuracy depends on a number of elements in series. The best fit was registered for Bahia and co-workers model, generalized Maxwell model and fractional model. As for predicting the phase angle parameter, the largest discrepancies between experimental and modelled results were obtained using the fractional model. Except the Burgers model, the model matching quality was
A Non-Gaussian Spatial Generalized Linear Latent Variable Model
Irincheeva, Irina
2012-08-03
We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.
Linear Model for Optimal Distributed Generation Size Predication
Ahmed Al Ameri
2017-01-01
Full Text Available This article presents a linear model predicting optimal size of Distributed Generation (DG that addresses the minimum power loss. This method is based fundamentally on strong coupling between active power and voltage angle as well as between reactive power and voltage magnitudes. This paper proposes simplified method to calculate the total power losses in electrical grid for different distributed generation sizes and locations. The method has been implemented and tested on several IEEE bus test systems. The results show that the proposed method is capable of predicting approximate optimal size of DG when compared with precision calculations. The method that linearizes a complex model showed a good result, which can actually reduce processing time required. The acceptable accuracy with less time and memory required can help the grid operator to assess power system integrated within large-scale distribution generation.
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
A Non-Gaussian Spatial Generalized Linear Latent Variable Model
Irincheeva, Irina; Cantoni, Eva; Genton, Marc G.
2012-01-01
We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Dynamic generalized linear models for monitoring endemic diseases
Lopes Antunes, Ana Carolina; Jensen, Dan; Hisham Beshara Halasa, Tariq
2016-01-01
The objective was to use a Dynamic Generalized Linear Model (DGLM) based on abinomial distribution with a linear trend, for monitoring the PRRS (Porcine Reproductive and Respiratory Syndrome sero-prevalence in Danish swine herds. The DGLM was described and its performance for monitoring control...... and eradication programmes based on changes in PRRS sero-prevalence was explored. Results showed a declining trend in PRRS sero-prevalence between 2007 and 2014 suggesting that Danish herds are slowly eradicating PRRS. The simulation study demonstrated the flexibility of DGLMs in adapting to changes intrends...... in sero-prevalence. Based on this, it was possible to detect variations in the growth model component. This study is a proof-of-concept, demonstrating the use of DGLMs for monitoring endemic diseases. In addition, the principles stated might be useful in general research on monitoring and surveillance...
Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.
Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine
2010-09-01
Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.
Statistical validation of normal tissue complication probability models
Xu, Cheng-Jian; van der Schaaf, Arjen; van t Veld, Aart; Langendijk, Johannes A.; Schilstra, Cornelis
2012-01-01
PURPOSE: To investigate the applicability and value of double cross-validation and permutation tests as established statistical approaches in the validation of normal tissue complication probability (NTCP) models. METHODS AND MATERIALS: A penalized regression method, LASSO (least absolute shrinkage
Some remarks on the statistical model of heavy ion collisions
Koch, V.
2003-01-01
This contribution is an attempt to assess what can be learned from the remarkable success of this statistical model in describing ratios of particle abundances in ultra-relativistic heavy ion collisions
Eigenfunction statistics for Anderson model with Hölder continuous ...
The Institute of Mathematical Sciences, Taramani, Chennai 600 113, India ... Anderson model; Hölder continuous measure; Poisson statistics. ...... [4] Combes J-M, Hislop P D and Klopp F, An optimal Wegner estimate and its application to.
Estimation and Inference for Very Large Linear Mixed Effects Models
Gao, K.; Owen, A. B.
2016-01-01
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N observations. Such problems arise in any setting where the underlying factors satisfy a many to many relationship (instead of a nested one) and in electronic commerce applications, the N can be quite large. Methods that do not account for the correlation structure can...
Using Quartile-Quartile Lines as Linear Models
Gordon, Sheldon P.
2015-01-01
This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and…
NON-LINEAR MODELING OF THE RHIC INTERACTION REGIONS
TOMAS, R.; FISCHER, W.; JAIN, A.; LUO, Y.; PILAT, F.
2004-01-01
For RHIC's collision lattices the dominant sources of transverse non-linearities are located in the interaction regions. The field quality is available for most of the magnets in the interaction regions from the magnetic measurements, or from extrapolations of these measurements. We discuss the implementation of these measurements in the MADX models of the Blue and the Yellow rings and their impact on beam stability
Electromagnetic axial anomaly in a generalized linear sigma model
Fariborz, Amir H.; Jora, Renata
2017-06-01
We construct the electromagnetic anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four-quark content. We compute in the leading order of this framework the decays into two photons of six pseudoscalars: π0(137 ), π0(1300 ), η (547 ), η (958 ), η (1295 ) and η (1760 ). Our results agree well with the available experimental data.
Comparison of Linear Prediction Models for Audio Signals
2009-03-01
Full Text Available While linear prediction (LP has become immensely popular in speech modeling, it does not seem to provide a good approach for modeling audio signals. This is somewhat surprising, since a tonal signal consisting of a number of sinusoids can be perfectly predicted based on an (all-pole LP model with a model order that is twice the number of sinusoids. We provide an explanation why this result cannot simply be extrapolated to LP of audio signals. If noise is taken into account in the tonal signal model, a low-order all-pole model appears to be only appropriate when the tonal components are uniformly distributed in the Nyquist interval. Based on this observation, different alternatives to the conventional LP model can be suggested. Either the model should be changed to a pole-zero, a high-order all-pole, or a pitch prediction model, or the conventional LP model should be preceded by an appropriate frequency transform, such as a frequency warping or downsampling. By comparing these alternative LP models to the conventional LP model in terms of frequency estimation accuracy, residual spectral flatness, and perceptual frequency resolution, we obtain several new and promising approaches to LP-based audio modeling.
A no extensive statistical model for the nucleon structure function
Trevisan, Luis A.; Mirez, Carlos
2013-01-01
We studied an application of nonextensive thermodynamics to describe the structure function of nucleon, in a model where the usual Fermi-Dirac and Bose-Einstein energy distribution were replaced by the equivalent functions of the q-statistical. The parameters of the model are given by an effective temperature T, the q parameter (from Tsallis statistics), and two chemical potentials given by the corresponding up (u) and down (d) quark normalization in the nucleon.
Yock, Adam D; Rao, Arvind; Dong, Lei; Beadle, Beth M; Garden, Adam S; Kudchadker, Rajat J; Court, Laurence E
2014-05-01
The purpose of this work was to develop and evaluate the accuracy of several predictive models of variation in tumor volume throughout the course of radiation therapy. Nineteen patients with oropharyngeal cancers were imaged daily with CT-on-rails for image-guided alignment per an institutional protocol. The daily volumes of 35 tumors in these 19 patients were determined and used to generate (1) a linear model in which tumor volume changed at a constant rate, (2) a general linear model that utilized the power fit relationship between the daily and initial tumor volumes, and (3) a functional general linear model that identified and exploited the primary modes of variation between time series describing the changing tumor volumes. Primary and nodal tumor volumes were examined separately. The accuracy of these models in predicting daily tumor volumes were compared with those of static and linear reference models using leave-one-out cross-validation. In predicting the daily volume of primary tumors, the general linear model and the functional general linear model were more accurate than the static reference model by 9.9% (range: -11.6%-23.8%) and 14.6% (range: -7.3%-27.5%), respectively, and were more accurate than the linear reference model by 14.2% (range: -6.8%-40.3%) and 13.1% (range: -1.5%-52.5%), respectively. In predicting the daily volume of nodal tumors, only the 14.4% (range: -11.1%-20.5%) improvement in accuracy of the functional general linear model compared to the static reference model was statistically significant. A general linear model and a functional general linear model trained on data from a small population of patients can predict the primary tumor volume throughout the course of radiation therapy with greater accuracy than standard reference models. These more accurate models may increase the prognostic value of information about the tumor garnered from pretreatment computed tomography images and facilitate improved treatment management.
A quasi-linear gyrokinetic transport model for tokamak plasmas
Casati, A.
2009-10-01
After a presentation of some basics around nuclear fusion, this research thesis introduces the framework of the tokamak strategy to deal with confinement, hence the main plasma instabilities which are responsible for turbulent transport of energy and matter in such a system. The author also briefly introduces the two principal plasma representations, the fluid and the kinetic ones. He explains why the gyro-kinetic approach has been preferred. A tokamak relevant case is presented in order to highlight the relevance of a correct accounting of the kinetic wave-particle resonance. He discusses the issue of the quasi-linear response. Firstly, the derivation of the model, called QuaLiKiz, and its underlying hypotheses to get the energy and the particle turbulent flux are presented. Secondly, the validity of the quasi-linear response is verified against the nonlinear gyro-kinetic simulations. The saturation model that is assumed in QuaLiKiz, is presented and discussed. Then, the author qualifies the global outcomes of QuaLiKiz. Both the quasi-linear energy and the particle flux are compared to the expectations from the nonlinear simulations, across a wide scan of tokamak relevant parameters. Therefore, the coupling of QuaLiKiz within the integrated transport solver CRONOS is presented: this procedure allows the time-dependent transport problem to be solved, hence the direct application of the model to the experiment. The first preliminary results regarding the experimental analysis are finally discussed
Doherty, W.
2013-01-01
A nebulizer-centric response function model of the analytical inductively coupled argon plasma ion source was used to investigate the statistical frequency distributions and noise reduction factors of simultaneously measured flicker noise limited isotope ion signals and their ratios. The response function model was extended by assuming i) a single gaussian distributed random noise source (nebulizer gas pressure fluctuations) and ii) the isotope ion signal response is a parabolic function of the nebulizer gas pressure. Model calculations of ion signal and signal ratio histograms were obtained by applying the statistical method of translation to the non-linear response function model of the plasma. Histograms of Ni, Cu, Pr, Tl and Pb isotope ion signals measured using a multi-collector plasma mass spectrometer were, without exception, negative skew. Histograms of the corresponding isotope ratios of Ni, Cu, Tl and Pb were either positive or negative skew. There was a complete agreement between the measured and model calculated histogram skew properties. The nebulizer-centric response function model was also used to investigate the effect of non-linear response functions on the effectiveness of noise cancellation by signal division. An alternative noise correction procedure suitable for parabolic signal response functions was derived and applied to measurements of isotope ratios of Cu, Ni, Pb and Tl. The largest noise reduction factors were always obtained when the non-linearity of the response functions was taken into account by the isotope ratio calculation. Possible applications of the nebulizer-centric response function model to other types of analytical instrumentation, large amplitude signal noise sources (e.g., lasers, pumped nebulizers) and analytical error in isotope ratio measurements by multi-collector plasma mass spectrometry are discussed. - Highlights: ► Isotope ion signal noise is modelled as a parabolic transform of a gaussian variable. ► Flicker
Statistical models and NMR analysis of polymer microstructure
Statistical models can be used in conjunction with NMR spectroscopy to study polymer microstructure and polymerization mechanisms. Thus, Bernoullian, Markovian, and enantiomorphic-site models are well known. Many additional models have been formulated over the years for additional situations. Typica...
2003-01-01
For the year 2002, part of the figures shown in the tables of the Energy Review are partly preliminary. The annual statistics of the Energy Review also includes historical time-series over a longer period (see e.g. Energiatilastot 2001, Statistics Finland, Helsinki 2002). The applied energy units and conversion coefficients are shown in the inside back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supply and total consumption of electricity GWh, Energy imports by country of origin in January-June 2003, Energy exports by recipient country in January-June 2003, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Excise taxes, precautionary stock fees on oil pollution fees on energy products