Introduction to Bayesian Statistics

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesia

Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesia

Engaging and accessible, this book teaches readers how to use inferential statistical thinking to check their assumptions, assess evidence about their beliefs, and avoid overinterpreting results that

Engaging and accessible, this book teaches readers how to use inferential statistical thinking to check their assumptions, assess evidence about their beliefs, and avoid overinterpreting results that

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 importan

This book provides an introduction to elementary probability and to Bayesian mathematical statistics using de Finetti's subjectivistic approach. One of the features of this approach is that it does no

This textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It defines the likelihood function, prior distributions and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics and other applied fields. New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit, item response, factor analysis, ARCH-GARCH and stochastic volatility models. The new ed

This textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It defines the likelihood function, prior distributions and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics and other applied fields. New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit, item response, factor analysis, ARCH-GARCH and stochastic volatility models. The new ed

Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, b

This book presents Bayes' theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a s

A 2008 introduction to econometrics using the Bayesian approach to statistics at the graduate or advanced undergraduate level. In contrast to the frequentist approach to statistics, the Bayesian appro

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 mo

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

The two parts of this book treat probability and statistics as mathematical disciplines and with the same degree of rigour as is adopted for other branches of applied mathematics at the level of a British honours degree. They contain the minimum information about these subjects that any honours graduate in mathematics ought to know. They are written primarily for general mathematicians, rather than for statistical specialists or for natural scientists who need to use statistics in their work. No previous knowledge of probability or statistics is assumed, though familiarity with calculus and linear algebra is required. The first volume takes the theory of probability sufficiently far to be able to discuss the simpler random processes, for example, queueing theory and random walks. The second volume deals with statistics, the theory of making valid inferences from experimental data, and includes an account of the methods of least squares and maximum likelihood; it uses the results of the

The two parts of this book treat probability and statistics as mathematical disciplines and with the same degree of rigour as is adopted for other branches of applied mathematics at the level of a British honours degree. They contain the minimum information about these subjects that any honours graduate in mathematics ought to know. They are written primarily for general mathematicians, rather than for statistical specialists or for natural scientists who need to use statistics in their work. No previous knowledge of probability or statistics is assumed, though familiarity with calculus and linear algebra is required. The first volume takes the theory of probability sufficiently far to be able to discuss the simpler random processes, for example, queueing theory and random walks. The second volume deals with statistics, the theory of making valid inferences from experimental data, and includes an account of the methods of least squares and maximum likelihood; it uses the results of the

This book presents the theory and practice of non-parametric statistics, with an emphasis on motivating principals. The course is a combination of traditional rank based methods and more computational

Fun guide to learning Bayesian statistics and probability through unusual and illustrative examples.Many professionals use statistics and probabilities in their everyday work but struggle to make much

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving you a way to check your answers.