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Full Description
This book presents a narrative account of Markov Chain Monte Carlo at a popular level. The author relies on history to provide a unifying narrative thread; on the centuries-old tension between "classical" and Bayesian approaches, as a plot theme that can highlight the importance of MCMC in changing the practice of statistics; and on applied examples and on metaphor in the hope of conveying the concepts without making technical demands of the reader.
Contents
An enduring controversy. The story of Bernoulli's Law of Averages. The story of Bayes's theorem. The triumphs of Laplace and Gauss. The triumphs of Fisher and Neyman. The provocations of Brinbaum, Savage, and de Finetti. The computational obstruction. A computational breakthrough. The bomb, the computer, and the origins of Monte Carlo methods. Metropolis and Hastings. The Gemans; Gelfand and Smith. The Gibbs sampler. Hierarchical models. Statistics: No definitive answers; only evolving questions. Subjective or objective? The role of priors. Equal ignorance and the paradox of flat priors. Jeffries and the attempt at "objective priors." Reanalysis and sensitivity analysis.
