Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood FunctionsSpringer Science & Business Media, 2012/12/06 - 208 ページ This book provides a unified introduction to a variety of computational algorithms for Bayesian and likelihood inference. In this third edition, I have attempted to expand the treatment of many of the techniques discussed. I have added some new examples, as well as included recent results. Exercises have been added at the end of each chapter. Prerequisites for this book include an understanding of mathematical statistics at the level of Bickel and Doksum (1977), some understanding of the Bayesian approach as in Box and Tiao (1973), some exposure to statistical models as found in McCullagh and NeIder (1989), and for Section 6. 6 some experience with condi tional inference at the level of Cox and Snell (1989). I have chosen not to present proofs of convergence or rates of convergence for the Metropolis algorithm or the Gibbs sampler since these may require substantial background in Markov chain theory that is beyond the scope of this book. However, references to these proofs are given. There has been an explosion of papers in the area of Markov chain Monte Carlo in the past ten years. I have attempted to identify key references-though due to the volatility of the field some work may have been missed. |
目次
1 | |
Nonnormal Approximations to Likelihoods and Posteriors | 40 |
The EM Algorithm | 65 |
The Data Augmentation Algorithm | 90 |
The Gibbs Sampler and | 137 |
Exercises | 188 |
203 | |
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American Statistical Association analysis approach assess convergence augmented data set augmented posterior B₁ Bayesian Biometrika calculate Carlin compute conditional distribution constant covariate curve data augmentation algorithm distribution with mean Draw EM algorithm equilibrium distribution estimate example flat prior Frequentist function Gelfand and Smith genetic linkage Gibbs sampler given grid histogram HPD region iid sample importance sampling imputation independent inference integration Journal latent data likelihood function linear model log p(0 loglikelihood M-step Markov chain maximizer maximum likelihood method Metropolis algorithm Monte Carlo Monte Carlo method multivariate Newton-Raphson noninformative prior normal approximation normal distribution Note observed data p(o² parameters plot PMDA points posterior density posterior distribution posterior mean present random variable Repeat Section simulated standard deviation standard error step sufficient statistics Tierney values variance variance-covariance matrix vector weights y₁ σ² дв