Download or read book Bayesian Unimodal Density Regression for Causal Inference written by George Karabatsos and published by . This book was released on 2011 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Karabatsos and Walker (2011) introduced a new Bayesian nonparametric (BNP) regression model. Through analyses of real and simulated data, they showed that the BNP regression model outperforms other parametric and nonparametric regression models of common use, in terms of predictive accuracy of the outcome (dependent) variable. The other, outperformed, regression models include random-effects/hierarchical linear and generalized linear models, when the random effects were assumed to be normally-distributed (Laird & Ware, 1982; Breslow & Clayton 1993), and when the random effects were more generally modeled by a nonparametric, Dirichlet process (DP) mixture prior (Kleinman & Ibrahim, 1998a,1998b). The authors argue that the new Bayesian nonparametric (BNP) regression model provides a novel, richer, and more valid approach to causal inference, which allows the researcher to investigate how treatments causally change the entire distribution (density) of (potential) outcomes, including not only the mean, but also other features of the outcome variable, such as quantiles (e.g., median, 10th percentile), and the variance. They illustrate the BNP model through the analysis of observational data, to estimate the causal effect of exposure to excellent high school math education (versus non-exposure, the control), on ACT math achievement. In the data analysis, they also compare the predictive accuracy of the new BNP model against other regression models. These other models assume symmetric distributions for the outcomes, and for the inverse-link function of the propensity score model (when specified), and have been recommended for causal inference from observational data. The other models include the normal linear regression model, having one interaction between (1) subject (pre-treatment) covariates, (2) treatment indicators, and (3) indicators of (greater than or equal) 5 matched groups of subjects, formed either by subclassification (Rosenbaum & Rubin, 1984) or optimal full matching on the estimated propensity score. They also compare with the BART model, which provides a very flexible regression of observed outcomes on the treatment variable and the covariates. Extensive data-based simulation studies have shown that, in terms of bias and mean square error in causal effect estimation, these linear regression models and BART outperform normal linear regression of outcomes using (1) propensity-score-based pair-matching or subclassification alone, (2) treatment indicators and estimated propensity scores as covariates, and (3) observation weights defined by inverse of propensity score estimates, when the only covariate is a treatment indicator (Robins, et al. 2000), and when the linear model also includes subject covariates (Kang & Schafer, 2007; Schafer & Kang, 2008; Hill, 2011). These results seemed to hold true, especially when both the outcome and propensity score models were misspecified for the data, which, arguably, almost always occurs in practice. Through the analysis of an observational data set on math achievement, the authors showed that the new BNP regression model can provide richer causal inferences with higher predictive accuracy, compared to typical causal models which focus inference on the mean outcome, and which make restrictive parametric assumptions about the outcome variable and about the propensity score model. The new BNP model allows one to investigate how treatments causally change any interesting aspect of the distribution (density) of (potential) outcomes, in a flexible manner. (Contains 3 tables and 1 figure.) [This research is supported by the Chicago Teacher Partnership Project.].

Download or read book Bayesian Analysis of Linear Models written by Broemeling and published by Routledge. This book was released on 2017-11-22 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Bayesian statistics rapidly becoming accepted as a way to solve applied statisticalproblems, the need for a comprehensive, up-to-date source on the latest advances in thisfield has arisen.Presenting the basic theory of a large variety of linear models from a Bayesian viewpoint,Bayesian Analysis of Linear Models fills this need. Plus, this definitive volume containssomething traditional-a review of Bayesian techniques and methods of estimation, hypothesis,testing, and forecasting as applied to the standard populations ... somethinginnovative-a new approach to mixed models and models not generally studied by statisticianssuch as linear dynamic systems and changing parameter models ... and somethingpractical-clear graphs, eary-to-understand examples, end-of-chapter problems, numerousreferences, and a distribution appendix.Comprehensible, unique, and in-depth, Bayesian Analysis of Linear Models is the definitivemonograph for statisticians, econometricians, and engineers. In addition, this text isideal for students in graduate-level courses such as linear models, econometrics, andBayesian inference.

Download or read book Applied Bayesian Modeling and Causal Inference from Incomplete Data Perspectives written by Andrew Gelman and published by John Wiley & Sons. This book was released on 2004-09-03 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a collection of articles on statistical methods relating to missing data analysis, including multiple imputation, propensity scores, instrumental variables, and Bayesian inference. Covering new research topics and real-world examples which do not feature in many standard texts. The book is dedicated to Professor Don Rubin (Harvard). Don Rubin has made fundamental contributions to the study of missing data. Key features of the book include: Comprehensive coverage of an imporant area for both research and applications. Adopts a pragmatic approach to describing a wide range of intermediate and advanced statistical techniques. Covers key topics such as multiple imputation, propensity scores, instrumental variables and Bayesian inference. Includes a number of applications from the social and health sciences. Edited and authored by highly respected researchers in the area.

Download or read book Bayesian Analysis in Statistics and Econometrics written by Donald A. Berry and published by John Wiley & Sons. This book was released on 1996 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a definitive work that captures the current state of knowledge of Bayesian Analysis in Statistics and Econometrics and attempts to move it forward. It covers such topics as foundations, forecasting inferential matters, regression, computation and applications.

Download or read book Bayesian Nonparametric Methods for Causal Inference and Prediction written by Bret Michael Zeldow and published by . This book was released on 2017 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we present novel approaches to regression and causal inference using popular Bayesian nonparametric methods. Bayesian Additive Regression Trees (BART) is a Bayesian machine learning algorithm in which the conditional distribution is modeled as a sum of regression trees. We extend BART into a semiparametric generalized linear model framework so that a portion of the covariates are modeled nonparametrically using BART and a subset of the covariates have parametric form. This presents an attractive option for research in which only a few covariates are of scientific interest but there are other covariates must be controlled for. Under certain causal assumptions, this model can be used as a structural mean model. We demonstrate this method by examining the effect of initiating certain antiretroviral medications has on mortality among HIV/HCV coinfected subjects. In later chapters, we propose a joint model for a continuous longitudinal outcome and baseline covariates using penalized splines and an enriched Dirichlet process (EDP) prior. This joint model decomposes into local linear mixed models for the outcome given the covariates and marginals for the covariates. The EDP prior that is placed on the regression parameters and the parameters on the covariates induces clustering among subjects determined by similarity in their regression parameters and nested within those clusters, sub-clusters based on similarity in the covariate space. When there are a large number of covariates, we find improved prediction over the same model with Dirichlet process (DP) priors. Since the model clusters based on regression parameters, this model also serves as a functional clustering algorithm where one does not have to choose the number of clusters beforehand. We use the method to estimate incidence rates of diabetes when longitudinal laboratory values from electronic health records are used to augment diagnostic codes for outcome identification. We later extend this work by using our EDP model in a causal inference setting using the parametric g-formula. We demonstrate this using electronic health record data consisting of subjects initiating second generation antipsychotics.

Download or read book Bayesian Regression Tree Models for Causal Inference written by P. Richard Hahn and published by . This book was released on 2018 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a semi-parametric Bayesian regression model for estimating heterogeneous treatment effects from observational data. Standard nonlinear regression models, which may work quite well for prediction, can yield badly biased estimates of treatment effects when fit to data with strong confounding. Our Bayesian causal forests model avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. This new parametrization also allows treatment heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively “shrink to homogeneity”, in contrast to existing Bayesian non- and semi-parametric approaches.

Download or read book Bayesian Inference in Statistical Analysis written by George E. P. Box and published by Addison Wesley Longman. This book was released on 1973 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nature of Bayesian inference; Standard normal theory inference problems; Bayesian assessment of assumptions; Bayesian assessment of assumptions; Random effect models; Analysis of cross classification designs; Inference about means with information from more than one source: one-way classification and block designs; Some aspects of multivariate analysis; Estimation of common regression coefficients; Transformation of data.

Download or read book The Bayesian Paradigm of Robustness Indices of Causal Inferences written by Tenglong Li and published by . This book was released on 2018 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Data Analysis Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Download or read book Regression and Other Stories written by Andrew Gelman and published by Cambridge University Press. This book was released on 2020-07-23 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical approach to using regression and computation to solve real-world problems of estimation, prediction, and causal inference.

Download or read book Targeted Learning written by Mark J. van der Laan and published by Springer Science & Business Media. This book was released on 2011-06-17 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistics profession is at a unique point in history. The need for valid statistical tools is greater than ever; data sets are massive, often measuring hundreds of thousands of measurements for a single subject. The field is ready to move towards clear objective benchmarks under which tools can be evaluated. Targeted learning allows (1) the full generalization and utilization of cross-validation as an estimator selection tool so that the subjective choices made by humans are now made by the machine, and (2) targeting the fitting of the probability distribution of the data toward the target parameter representing the scientific question of interest. This book is aimed at both statisticians and applied researchers interested in causal inference and general effect estimation for observational and experimental data. Part I is an accessible introduction to super learning and the targeted maximum likelihood estimator, including related concepts necessary to understand and apply these methods. Parts II-IX handle complex data structures and topics applied researchers will immediately recognize from their own research, including time-to-event outcomes, direct and indirect effects, positivity violations, case-control studies, censored data, longitudinal data, and genomic studies.

Download or read book Doing Bayesian Data Analysis written by John Kruschke and published by Academic Press. This book was released on 2010-11-25 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and BUGS software Comprehensive coverage of all scenarios addressed by non-bayesian textbooks- t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis). Coverage of experiment planning R and BUGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment

Download or read book Bayesian Nonparametrics written by Nils Lid Hjort and published by Cambridge University Press. This book was released on 2010-04-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.

Download or read book Bayesian Nonparametrics written by J.K. Ghosh and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.

Download or read book Data Analysis written by Devinderjit Sivia and published by OUP Oxford. This book was released on 2006-06-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the strengths of this book is the author's ability to motivate the use of Bayesian methods through simple yet effective examples. - Katie St. Clair MAA Reviews.

Download or read book Pattern Recognition and Machine Learning written by Christopher M. Bishop and published by Springer. This book was released on 2016-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.

Download or read book Reliability and Risk written by Nozer D. Singpurwalla and published by John Wiley & Sons. This book was released on 2006-08-14 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: We all like to know how reliable and how risky certain situations are, and our increasing reliance on technology has led to the need for more precise assessments than ever before. Such precision has resulted in efforts both to sharpen the notions of risk and reliability, and to quantify them. Quantification is required for normative decision-making, especially decisions pertaining to our safety and wellbeing. Increasingly in recent years Bayesian methods have become key to such quantifications. Reliability and Risk provides a comprehensive overview of the mathematical and statistical aspects of risk and reliability analysis, from a Bayesian perspective. This book sets out to change the way in which we think about reliability and survival analysis by casting them in the broader context of decision-making. This is achieved by: Providing a broad coverage of the diverse aspects of reliability, including: multivariate failure models, dynamic reliability, event history analysis, non-parametric Bayes, competing risks, co-operative and competing systems, and signature analysis. Covering the essentials of Bayesian statistics and exchangeability, enabling readers who are unfamiliar with Bayesian inference to benefit from the book. Introducing the notion of “composite reliability”, or the collective reliability of a population of items. Discussing the relationship between notions of reliability and survival analysis and econometrics and financial risk. Reliability and Risk can most profitably be used by practitioners and research workers in reliability and survivability as a source of information, reference, and open problems. It can also form the basis of a graduate level course in reliability and risk analysis for students in statistics, biostatistics, engineering (industrial, nuclear, systems), operations research, and other mathematically oriented scientists, wherein the instructor could supplement the material with examples and problems.