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• W893480 abstract "Bayesian methods have become increasingly popular in modern statistical analysis and are being applied to a broad spectrum of scientific fields and research areas. This paper introduces the new MCMC procedure in SAS/STAT 9.2, which is designed for general-purpose Bayesian computations. The MCMC procedure enables you to carry out analysis on a wide range of complex Bayesian statistical models. The procedure uses the Markov chain Monte Carlo (MCMC) algorithm to draw samples from an arbitrary posterior distribution, which is defined by the prior distributions for the parameters and the likelihood function for the data that you specify. This paper describes how to use the MCMC procedure for estimation, inference, and prediction. The MCMC procedure is based on Markov chain Monte Carlo methods; it performs posterior sampling and statistical inference for Bayesian parametric models. The procedure fits single-level or multilevel models. These models can take various forms, from linear to nonlinear models, by using standard or nonstandard distributions. To use the procedure, you declare parameters in the model and specify prior distributions of the parameters and a conditional distribution for the response variable given the parameters. The MCMC procedure enables you to fit models by using either a keyword for a standard form (normal, binomial, gamma) or SAS programming statements to specify a general distribution. The MCMC procedure uses a random walk Metropolis algorithm to simulate samples from the model you specify. You can also choose an optimization technique (such as the quasi-Newton algorithm) to estimate the posterior mode and approximate the covariance matrix around the mode. The procedure computes a number of posterior estimates, and it also outputs the posterior samples to a data set for further analysis. Successful Bayesian inference that uses this sampling-based approach depends on the convergence of the Markov chain. The MCMC procedure provides a number of convergence diagnostics so you can assess the convergence of the chains. This paper first provides a brief overview of some relevant concepts in Bayesian methods and sampling-based infer- ence, and then explains the mechanisms that drive the MCMC procedure. A number of examples, ordered from simple to more complex, demonstrate how to use the procedure. The examples show a single-parameter binomial model, inference on functions of parameters, power priors, nonstandard distributions, sensitivity analysis, a random-effects model, and meta-analysis. In addition to the models that are demonstrated in this paper, you can use PROC MCMC to fit zero-inflated Poisson regression, survival analysis, ordinal multinomial models, time series, missing data analysis, and so on. Detailed examples and discussions can be found in the PROC MCMC documentation in the SAS/STAT User's Guide and on SAS web site (see the section CONTACT INFORMATION on page 22 for more details)." @default.
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• W893480 date "2009-01-01" @default.
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• W893480 title "Bayesian Modeling Using the MCMC Procedure" @default.
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