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 Nonparametrics for Causal Inference and Missing Data written by Michael Joseph Daniels and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Nonparametrics for Causal Inference and Missing Data provides an overview of flexible Bayesian nonparametric (BNP) methods for modeling joint or conditional distributions and functional relationships, and their interplay with causal inference and missing data. This book emphasizes the importance of making untestable assumptions to identify estimands of interest, such as missing at random assumption for missing data and unconfoundedness for causal inference in observational studies. Unlike parametric methods, the BNP approach can account for possible violations of assumptions and minimize concerns about model misspecification. The overall strategy is to first specify BNP models for observed data and then to specify additional uncheckable assumptions to identify estimands of interest. The book is divided into three parts. Part I develops the key concepts in causal inference and missing data and reviews relevant concepts in Bayesian inference. Part II introduces the fundamental BNP tools required to address causal inference and missing data problems. Part III shows how the BNP approach can be applied in a variety of case studies. The datasets in the case studies come from electronic health records data, survey data, cohort studies, and randomized clinical trials. Features Thorough discussion of both BNP and its interplay with causal inference and missing data How to use BNP and g-computation for causal inference and non-ignorable missingness How to derive and calibrate sensitivity parameters to assess sensitivity to deviations from uncheckable causal and/or missingness assumptions Detailed case studies illustrating the application of BNP methods to causal inference and missing data R code and/or packages to implement BNP in causal inference and missing data problems The book is primarily aimed at researchers and graduate students from statistics and biostatistics. It will also serve as a useful practical reference for mathematically sophisticated epidemiologists and medical researchers.
Download or read book Bayesian Nonparametric Methods for Missing Data and Causal Inference written by Michael Joseph Daniels and published by Chapman & Hall/CRC. This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Bayesian nonparametric (BNP) methods can be used to flexibly model joint or conditional distributions, as well as functional relationships. These methods, along with causal and/or missingness assumptions, can be used with the g-formula to infer causal effects"--
Download or read book Nonparametric Bayesian Inference in Biostatistics written by Riten Mitra and published by Springer. This book was released on 2015-07-25 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: As chapters in this book demonstrate, BNP has important uses in clinical sciences and inference for issues like unknown partitions in genomics. Nonparametric Bayesian approaches (BNP) play an ever expanding role in biostatistical inference from use in proteomics to clinical trials. Many research problems involve an abundance of data and require flexible and complex probability models beyond the traditional parametric approaches. As this book's expert contributors show, BNP approaches can be the answer. Survival Analysis, in particular survival regression, has traditionally used BNP, but BNP's potential is now very broad. This applies to important tasks like arrangement of patients into clinically meaningful subpopulations and segmenting the genome into functionally distinct regions. This book is designed to both review and introduce application areas for BNP. While existing books provide theoretical foundations, this book connects theory to practice through engaging examples and research questions. Chapters cover: clinical trials, spatial inference, proteomics, genomics, clustering, survival analysis and ROC curve.
Download or read book Bayesian Nonparametric Data Analysis written by Peter Müller and published by Springer. This book was released on 2015-06-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.
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 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 Nonparametric Prediction and Statistical Inference written by Bruce M. Hill and published by . This book was released on 1989 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of Bayesian nonparametric prediction and statistical inference is formulated and discussed. A solution is proposed based upon A sub n and H sub n as in Hill (1968). The meaning of parameters in the subjective Bayesian theory of Bruno de Finetti is discussed in connection both with A sub n and with conventional parametric models. It is argued that the usual sharp distinction between prediction and parametric inference is largely illusory. The finite version of de Finetti's theorem is emphasized for the practice of statistics, with the infinite case used only to obtain approximations and insight. (kr).
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 Methods for Nonlinear Classification and Regression written by David G. T. Denison and published by John Wiley & Sons. This book was released on 2002-05-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bei der Regressionsanalyse von Datenmaterial erhält man leider selten lineare oder andere einfache Zusammenhänge (parametrische Modelle). Dieses Buch hilft Ihnen, auch komplexere, nichtparametrische Modelle zu verstehen und zu beherrschen. Stärken und Schwächen jedes einzelnen Modells werden durch die Anwendung auf Standarddatensätze demonstriert. Verbreitete nichtparametrische Modelle werden mit Hilfe von Bayes-Verfahren in einen kohärenten wahrscheinlichkeitstheoretischen Zusammenhang gebracht.
Download or read book Bayesian Nonparametrics via Neural Networks written by Herbert K. H. Lee and published by SIAM. This book was released on 2004-01-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Nonparametrics via Neural Networks is the first book to focus on neural networks in the context of nonparametric regression and classification, working within the Bayesian paradigm. Its goal is to demystify neural networks, putting them firmly in a statistical context rather than treating them as a black box. This approach is in contrast to existing books, which tend to treat neural networks as a machine learning algorithm instead of a statistical model. Once this underlying statistical model is recognized, other standard statistical techniques can be applied to improve the model. The Bayesian approach allows better accounting for uncertainty. This book covers uncertainty in model choice and methods to deal with this issue, exploring a number of ideas from statistics and machine learning. A detailed discussion on the choice of prior and new noninformative priors is included, along with a substantial literature review. Written for statisticians using statistical terminology, Bayesian Nonparametrics via Neural Networks will lead statisticians to an increased understanding of the neural network model and its applicability to real-world problems.
Download or read book Bayesian Nonparametric Methods for Non exchangeable Data written by Nicholas J. Foti and published by . This book was released on 2013 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian nonparametric methods have become increasingly popular in machine learning for their ability to allow the data to determine model complexity. In particular, Bayesian nonparametric versions of common latent variable models can learn as effective dimension of the latent space. Examples include mixture models, latent feature models and topic models, where the number of components, features, or topics need not be specified a priori. A drawback of many of these models is that they assume the observations are exchangeable, that is, any dependencies between observations are ignored. This thesis contributes general methods to incorporate covariates into Bayesian nonparametric models and inference algorithms to learn with these models. First, we will present a flexible class of dependent Bayesian nonparametric priors to induce covariate-dependence into a variety of latent variable models used in machine learning. The proposed framework has nice analytic properites and admits a simple inference algorithm. We show how the framework can be used to construct a covariate-dependent latent feature model and a time-varying topic model. Second, we describe the first general purpose inference algorithm for a large family of dependent mixture models. Using the idea of slice-sampling, the algorithm is truncation-free and fast, showing that inference can de done efficiently despite the added complexity that covariate-dependence entails. Last, we construct a Bayesian nonparametric framework to couple multiple latent variable models and apply the framework to learning from multiple views of data.
Download or read book Fundamentals of Nonparametric Bayesian Inference written by Subhashis Ghosal and published by Cambridge University Press. This book was released on 2017-06-26 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.
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 Bayesian Nonparametrics written by J.K. Ghosh and published by Springer Science & Business Media. This book was released on 2003-04-08 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 Fundamentals of Nonparametric Bayesian Inference written by Subhashis Ghosal and published by . This book was released on 2017 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.
Download or read book Bayesian Nonparametric Probabilistic Methods in Machine Learning written by Justin C. Sahs and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many aspects of modern science, business and engineering have become data-centric, relying on tools from Artificial Intelligence and Machine Learning. Practitioners and researchers in these fields need tools that can incorporate observed data into rich models of uncertainty to make discoveries and predictions. One area of study that provides such models is the field of Bayesian Nonparametrics. This dissertation is focused on furthering the development of this field. After reviewing the relevant background and surveying the field, we consider two areas of structured data: - We first consider relational data that takes the form of a 2-dimensional array--such as social network data. We introduce a novel nonparametric model that takes advantage of a representation theorem about arrays whose column and row order is unimportant. We then develop an inference algorithm for this model and evaluate it experimentally. - Second, we consider the classification of streaming data whose distribution evolves over time. We introduce a novel nonparametric model that finds and exploits a dynamic hierarchical structure underlying the data. We present an algorithm for inference in this model and show experimental results. We then extend our streaming model to handle the emergence of novel and recurrent classes, and evaluate the extended model experimentally.
