Applied Bayesian Statistics

With R and OpenBUGS Examples

Author: Mary Kathryn Cowles

Publisher: Springer Science & Business Media

ISBN: 1461456967

Category: Mathematics

Page: 232

View: 3604

This book is based on over a dozen years teaching a Bayesian Statistics course. The material presented here has been used by students of different levels and disciplines, including advanced undergraduates studying Mathematics and Statistics and students in graduate programs in Statistics, Biostatistics, Engineering, Economics, Marketing, Pharmacy, and Psychology. The goal of the book is to impart the basics of designing and carrying out Bayesian analyses, and interpreting and communicating the results. In addition, readers will learn to use the predominant software for Bayesian model-fitting, R and OpenBUGS. The practical approach this book takes will help students of all levels to build understanding of the concepts and procedures required to answer real questions by performing Bayesian analysis of real data. Topics covered include comparing and contrasting Bayesian and classical methods, specifying hierarchical models, and assessing Markov chain Monte Carlo output. Kate Cowles taught Suzuki piano for many years before going to graduate school in Biostatistics. Her research areas are Bayesian and computational statistics, with application to environmental science. She is on the faculty of Statistics at The University of Iowa.
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Introduction to Applied Bayesian Statistics and Estimation for Social Scientists

Author: Scott M. Lynch

Publisher: Springer Science & Business Media

ISBN: 0387712658

Category: Social Science

Page: 359

View: 2797

This book outlines Bayesian statistical analysis in great detail, from the development of a model through the process of making statistical inference. The key feature of this book is that it covers models that are most commonly used in social science research - including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models - and it thoroughly develops each real-data example in painstaking detail.
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Applied Bayesian Statistical Studies in Biology and Medicine

Author: M. di Bacco,G. d'Amore,F. Scalfari

Publisher: Springer Science & Business Media

ISBN: 146130217X

Category: Medical

Page: 258

View: 1157

This volume presents the results of biological and medical research with the statistical methods used to obtain them. Nowadays the fields of biology and experimental medicine rely on techniques for processing of experimental data and for the evaluation of hypotheses. It is increasingly necessary to stimulate awareness of the importance of statistical techniques (and of the possible traps that they can hide) by using real data in concrete situations drawn from research activity.
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Applied Bayesian Modelling

Author: Peter Congdon

Publisher: Wiley

ISBN: 9780471486954

Category: Mathematics

Page: 478

View: 2219

The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author’s best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS – a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example – explaining fully the choice of model for each particular problem. The book · Provides a broad and comprehensive account of applied Bayesian modelling. · Describes a variety of model assessment methods and the flexibility of Bayesian prior specifications. · Covers many application areas, including panel data models, structural equation and other multivariate structure models, spatial analysis, survival analysis and epidemiology. · Provides detailed worked examples in WINBUGS to illustrate the practical application of the techniques described. All WINBUGS programs are available from an ftp site. The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.
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The Oxford Handbook of Applied Bayesian Analysis

Author: Anthony O' Hagan,Mike West

Publisher: OUP Oxford

ISBN: 0191613894

Category: Mathematics

Page: 924

View: 1510

Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
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Applied Bayesian Hierarchical Methods

Author: Peter D. Congdon

Publisher: CRC Press

ISBN: 9781584887218

Category: Mathematics

Page: 604

View: 3842

The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables and in methods where parameters can be treated as random collections. Emphasizing computational issues, the book provides examples of the following application settings: meta-analysis, data structured in space or time, multilevel and longitudinal data, multivariate data, nonlinear regression, and survival time data. For the worked examples, the text mainly employs the WinBUGS package, allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. It also incorporates BayesX code, which is particularly useful in nonlinear regression. To demonstrate MCMC sampling from first principles, the author includes worked examples using the R package. Through illustrative data analysis and attention to statistical computing, this book focuses on the practical implementation of Bayesian hierarchical methods. It also discusses several issues that arise when applying Bayesian techniques in hierarchical and random effects models.
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Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives

Author: Donald B. Rubin,Andrew Gelman,Xiao-Li Meng

Publisher: John Wiley & Sons

ISBN: 9780470090435

Category: Mathematics

Page: 407

View: 4750

This book brings together a collection of articles onstatistical methods relating to missing data analysis, includingmultiple imputation, propensity scores, instrumental variables, andBayesian inference. Covering new research topicsand real-world examples which do not feature in manystandard texts. The book is dedicated to Professor Don Rubin(Harvard). Don Rubin has made fundamental contributions tothe study of missing data. Key features of the book include: Comprehensive coverage of an imporant area for both researchand applications. Adopts a pragmatic approach to describing a wide range ofintermediate and advanced statistical techniques. Covers key topics such as multiple imputation, propensityscores, instrumental variables and Bayesian inference. Includes a number of applications from the social and healthsciences. Edited and authored by highly respected researchers in thearea.
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Introduction to Bayesian Statistics

Author: William M. Bolstad,James M. Curran

Publisher: John Wiley & Sons

ISBN: 1118593227

Category: Mathematics

Page: 624

View: 6457

"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.
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Applied Bayesian and Classical Inference

The Case of The Federalist Papers

Author: F. Mosteller,D. L. Wallace

Publisher: Springer Science & Business Media

ISBN: 1461252563

Category: Mathematics

Page: 303

View: 3336

The new version has two additions. First, at the suggestion of Stephen Stigler I we have replaced the Table of Contents by what he calls an Analytic Table of Contents. Following the title of each section or subsection is a description of the content of the section. This material helps the reader in several ways, for example: by giving a synopsis of the book, by explaining where the various data tables are and what they deal with, by telling what theory is described where. We did several distinct full studies for the Federalist papers as well as many minor side studies. Some or all may offer information both to the applied and the theoretical reader. We therefore try to give in this Contents more than the few cryptic words in a section heading to ~peed readers in finding what they want. Seconq, we have prepared an extra chapter dealing with authorship work published from. about 1969 to 1983. Although a chapter cannot compre hensively Gover a field where many books now appear, it can mention most ofthe book-length works and the main thread of authorship' studies published in English. We founq biblical authorship studies so extensive and com plicated that we thought it worthwhile to indicate some papers that would bring out the controversies that are taking place. We hope we have given the flavor of developments over the 15 years mentioned. We have also corrected a few typographical errors.
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Statistical Rethinking

A Bayesian Course with Examples in R and Stan

Author: Richard McElreath

Publisher: CRC Press

ISBN: 1315362619

Category: Mathematics

Page: 487

View: 8287

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.
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Bayesian Data Analysis, Third Edition

Author: Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin

Publisher: CRC Press

ISBN: 1439840954

Category: Mathematics

Page: 675

View: 9836

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.
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Elements of Bayesian Statistics

Author: Florens

Publisher: CRC Press

ISBN: 9780824781231

Category: Mathematics

Page: 544

View: 7465

The ingratiating title notwithstanding, this is in no standard sense a text but a monograph, based largely upon the authors' research over a period of years, and intended to be read by sophisticated students of theoretical statistics. No exercises attach to the nine chapters, nor are they interrup
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Bayesian Statistics and Marketing

Author: Peter E. Rossi,Greg M. Allenby,Rob McCulloch

Publisher: John Wiley & Sons

ISBN: 0470863684

Category: Mathematics

Page: 368

View: 9667

The past decade has seen a dramatic increase in the use of Bayesian methods in marketing due, in part, to computational and modelling breakthroughs, making its implementation ideal for many marketing problems. Bayesian analyses can now be conducted over a wide range of marketing problems, from new product introduction to pricing, and with a wide variety of different data sources. Bayesian Statistics and Marketing describes the basic advantages of the Bayesian approach, detailing the nature of the computational revolution. Examples contained include household and consumer panel data on product purchases and survey data, demand models based on micro-economic theory and random effect models used to pool data among respondents. The book also discusses the theory and practical use of MCMC methods. Written by the leading experts in the field, this unique book: Presents a unified treatment of Bayesian methods in marketing, with common notation and algorithms for estimating the models. Provides a self-contained introduction to Bayesian methods. Includes case studies drawn from the authors’ recent research to illustrate how Bayesian methods can be extended to apply to many important marketing problems. Is accompanied by an R package, bayesm, which implements all of the models and methods in the book and includes many datasets. In addition the book’s website hosts datasets and R code for the case studies. Bayesian Statistics and Marketing provides a platform for researchers in marketing to analyse their data with state-of-the-art methods and develop new models of consumer behaviour. It provides a unified reference for cutting-edge marketing researchers, as well as an invaluable guide to this growing area for both graduate students and professors, alike.
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Introduction to Hierarchical Bayesian Modeling for Ecological Data

Author: Eric Parent,Etienne Rivot

Publisher: CRC Press

ISBN: 1584889195

Category: Mathematics

Page: 427

View: 5529

Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts and techniques of the Bayesian paradigm from a practical point of view using real case studies. They emphasize how hierarchical Bayesian modeling supports multidimensional models involving complex interactions between parameters and latent variables. Data sets, exercises, and R and WinBUGS codes are available on the authors’ website. This book shows how Bayesian statistical modeling provides an intuitive way to organize data, test ideas, investigate competing hypotheses, and assess degrees of confidence of predictions. It also illustrates how conditional reasoning can dismantle a complex reality into more understandable pieces. As conditional reasoning is intimately linked with Bayesian thinking, considering hierarchical models within the Bayesian setting offers a unified and coherent framework for modeling, estimation, and prediction.
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Applied Bayesian Forecasting and Time Series Analysis

Author: Andy Pole,Mike West,Jeff Harrison

Publisher: CRC Press

ISBN: 9780412044014

Category: Mathematics

Page: 480

View: 4075

Practical in its approach, Applied Bayesian Forecasting and Time Series Analysis provides the theories, methods, and tools necessary for forecasting and the analysis of time series. The authors unify the concepts, model forms, and modeling requirements within the framework of the dynamic linear mode (DLM). They include a complete theoretical development of the DLM and illustrate each step with analysis of time series data. Using real data sets the authors: Explore diverse aspects of time series, including how to identify, structure, explain observed behavior, model structures and behaviors, and interpret analyses to make informed forecasts Illustrate concepts such as component decomposition, fundamental model forms including trends and cycles, and practical modeling requirements for routine change and unusual events Conduct all analyses in the BATS computer programs, furnishing online that program and the more than 50 data sets used in the text The result is a clear presentation of the Bayesian paradigm: quantified subjective judgements derived from selected models applied to time series observations. Accessible to undergraduates, this unique volume also offers complete guidelines valuable to researchers, practitioners, and advanced students in statistics, operations research, and engineering.
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Applied Statistical Inference

Likelihood and Bayes

Author: Leonhard Held,Daniel Sabanés Bové

Publisher: Springer Science & Business Media

ISBN: 3642378870

Category: Mathematics

Page: 376

View: 1797

This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective. A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.
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Bayesian Core: A Practical Approach to Computational Bayesian Statistics

Author: Jean-Michel Marin,Christian Robert

Publisher: Springer Science & Business Media

ISBN: 0387389830

Category: Mathematics

Page: 258

View: 9266

This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book.
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Bayesian Statistical Modelling

Author: Peter Congdon

Publisher: John Wiley & Sons

ISBN: 0470035935

Category: Mathematics

Page: 596

View: 5415

Bayesian methods combine the evidence from the data at hand with previous quantitative knowledge to analyse practical problems in a wide range of areas. The calculations were previously complex, but it is now possible to routinely apply Bayesian methods due to advances in computing technology and the use of new sampling methods for estimating parameters. Such developments together with the availability of freeware such as WINBUGS and R have facilitated a rapid growth in the use of Bayesian methods, allowing their application in many scientific disciplines, including applied statistics, public health research, medical science, the social sciences and economics. Following the success of the first edition, this reworked and updated book provides an accessible approach to Bayesian computing and analysis, with an emphasis on the principles of prior selection, identification and the interpretation of real data sets. The second edition: Provides an integrated presentation of theory, examples, applications and computer algorithms. Discusses the role of Markov Chain Monte Carlo methods in computing and estimation. Includes a wide range of interdisciplinary applications, and a large selection of worked examples from the health and social sciences. Features a comprehensive range of methodologies and modelling techniques, and examines model fitting in practice using Bayesian principles. Provides exercises designed to help reinforce the reader’s knowledge and a supplementary website containing data sets and relevant programs. Bayesian Statistical Modelling is ideal for researchers in applied statistics, medical science, public health and the social sciences, who will benefit greatly from the examples and applications featured. The book will also appeal to graduate students of applied statistics, data analysis and Bayesian methods, and will provide a great source of reference for both researchers and students. Praise for the First Edition: “It is a remarkable achievement to have carried out such a range of analysis on such a range of data sets. I found this book comprehensive and stimulating, and was thoroughly impressed with both the depth and the range of the discussions it contains.” – ISI - Short Book Reviews “This is an excellent introductory book on Bayesian modelling techniques and data analysis” – Biometrics “The book fills an important niche in the statistical literature and should be a very valuable resource for students and professionals who are utilizing Bayesian methods.” – Journal of Mathematical Psychology
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Statistical Inference

An Integrated Bayesian/Likelihood Approach

Author: Murray Aitkin

Publisher: CRC Press

ISBN: 1420093444

Category: Mathematics

Page: 254

View: 9698

Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct Bayesian counterparts of frequentist t-tests and other standard statistical methods for hypothesis testing. After an overview of the competing theories of statistical inference, the book introduces the Bayes/likelihood approach used throughout. It presents Bayesian versions of one- and two-sample t-tests, along with the corresponding normal variance tests. The author then thoroughly discusses the use of the multinomial model and noninformative Dirichlet priors in "model-free" or nonparametric Bayesian survey analysis, before covering normal regression and analysis of variance. In the chapter on binomial and multinomial data, he gives alternatives, based on Bayesian analyses, to current frequentist nonparametric methods. The text concludes with new goodness-of-fit methods for assessing parametric models and a discussion of two-level variance component models and finite mixtures. Emphasizing the principles of Bayesian inference and Bayesian model comparison, this book develops a unique methodology for solving challenging inference problems. It also includes a concise review of the various approaches to inference.
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Mathematical Theory of Bayesian Statistics

Author: Sumio Watanabe

Publisher: CRC Press

ISBN: 148223808X

Category: Mathematics

Page: 320

View: 1836

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.
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