Bayesian Core: A Practical Approach to Computational Bayesian Statistics
Springer Science & Business Media, May 26, 2007 - Mathematics - 258 pages
After that, it was down to attitude. —Ian Rankin, Black & Blue. — The purpose of this book is to provide a self-contained (we insist!) entry into practical and computational Bayesian statistics using generic examples from the most common models for a class duration of about seven blocks that roughly correspond to 13 to 15 weeks of teaching (with three hours of lectures per week), depending on the intended level and the prerequisites imposed on the students. (That estimate does not include practice—i. e. , programming labs—since those may have a variable duration, also depending on the s- dents’ involvement and their programming abilities. ) The emphasis on practice is a strong feature of this book in that its primary audience consists of gr- uate students who need to use (Bayesian) statistics as a tool to analyze their experiments and/or datasets. The book should also appeal to scientists in all ?elds, given the versatility of the Bayesian tools. It can also be used for a more classical statistics audience when aimed at teaching a quick entry to Bayesian statistics at the end of an undergraduate program for instance. (Obviously, it can supplement another textbook on data analysis at the graduate level.
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acceptance probability algorithm analysis approximation AR(p associated Bayes estimate Bayes factor capture capture–recapture Chapter choice complex roots components computation conditional distribution conjugate prior constraint convergence corresponding covariate defined denotes density dependence derived eurodip Exercise explanatory variables Figure flat prior full conditional distribution G-prior Gibbs sampler given hidden Markov model histogram hyperparameters importance sampling improper prior inference instance iterations joint distribution linear models MA(q marginal distribution Markov chain matrix MCMC MCMC algorithm Metropolis–Hastings algorithm mixture model mode Monte Carlo noninformative prior normal distribution normalizing constant observations obviously output parameters pixels posterior distribution posterior expectation posterior means posterior probability predictive distribution prior distribution prior information probit model random variables random walk regression representation reversible jump Robert and Casella Sampler Initialization Section sequence Show simulation state–space structure submodels Table target distribution variance vector