Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers
This book describes the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students. It is unusual in presenting Bayesian statistics with a practical flavor and an emphasis on mainstream statistics, showing how to infer scientific, medical, and social conclusions from numerical data. The authors draw on many years of experience with practical and research programs and describe many statistical methods, not readily available elsewhere. A first chapter on Fisherian methods, together with a strong overall emphasis on likelihood, makes the text suitable for mainstream statistics courses whose instructors wish to follow mixed or comparative philosophies. The other chapters contain important sections relating to many areas of statistics such as the linear model, categorical data analysis, time series and forecasting, mixture models, survival analysis, Bayesian smoothing, and non-linear random effects models. The text includes a large number of practical examples, worked examples, and exercises. It will be essential reading for all statisticians, statistics students, and related interdisciplinary researchers.
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analysis applied assume Bayes estimate beta chi-squared distribution choices computed confidence interval Consider covariance matrix criterion curve degrees of freedom denotes depend described distributed with mean distribution of 9 equal equation exact posterior example expected utility hypothesis exponential family Figure finite frequency properties Gamma given independent inferences Laplacian approximation likelihood approximation likelihood function likelihood of 9 likelihood principle linear logistic loss function lurking variable marginal posterior density maximized maximum likelihood estimate mean and variance mean squared error mean vector Model Answer multivariate normal distribution nonlinear Note observations Poisson possess posterior distribution posterior expectation posterior mean posterior mode posterior probability prior density prior distribution prior information prior probability probability distribution procedure profile likelihood random sample regression respect sampling model satisfies Section SELF-STUDY EXERCISES Show shrinkage estimators simulations specified squared error loss statistic Table theorem unknown parameters utility function zero