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The MCMC Procedure

The MCMC procedure is a flexible, general-purpose Markov chain Monte Carlo simulation procedure that is suitable for fitting a wide range of Bayesian models. To use the procedure, you specify a likelihood function for the data and a prior distribution for the parameters. If you are fitting hierarchical models, you can also specify hyperprior distributions or you can specify random effects and their prior distributions. PROC MCMC obtains samples from the corresponding posterior distributions, produces summary and diagnostic statistics, and saves the posterior samples in an output data set that can be used for further analysis. You can analyze data that have any likelihood, prior, or hyperprior with PROC MCMC, as long as these functions can be programmed by using the SAS DATA step functions. The parameters can enter the model in any linear or nonlinear functional form.

Sampling Algorithms

See the section "Sampling Methods" in the chapter "The MCMC Procedure" of the SAS/STAT^® User's Guide.

Priors

See the section "Standard Distributions" in the chapter "The MCMC Procedure" of the SAS/STAT^® User's Guide for the distributions that PROC MCMC recognizes. PROC MCMC also enables you to specify other distributions that are not included in the list of standard distributions, as explained in the section "Specifying a New Distribution".

Papers about PROC MCMC

• Bayesian Modeling Using the MCMC Procedure
• Fitting Your Favorite Mixed Models with PROC MCMC
• Getting Started with the MCMC Procedure
• Missing No More: Using the MCMC procedure to Model Missing Data
• The RANDOM Statement and More: Moving On with PROC MCMC

Videos

Getting Started with the MCMC Procedure By Fang Chen Air date: November 26, 2013

Fitting Bayesian Random-Effects Models Using PROC MCMC By Fang Chen Air date: December 12, 2011

Examples

• Simple Linear Regression
• The Behrens-Fisher Problem
• Random-Effects Model

• Example 77.1: Simulating Samples From a Known Density
• Example 77.2: Box-Cox Transformation
• Example 77.3: Logistic Regression Model with a Diffuse Prior
• Example 77.4: Logistic Regression Model with Jeffreys’ Prior
• Example 77.5: Poisson Regression
• Example 77.6: Nonlinear Poisson Regression Models
• Example 77.7: Logistic Regression Random-Effects Model
• Example 77.8: Nonlinear Poisson Regression Multilevel Random-Effects Model
• Example 77.9: Multivariate Normal Random-Effects Model
• Example 77.10: Missing at Random Analysis
• Example 77.11: Nonignorably Missing Data (MNAR) Analysis
• Example 77.12: Change Point Models
• Example 77.13: Exponential and Weibull Survival Analysis
• Example 77.14: Time Independent Cox Model
• Example 77.15: Time Dependent Cox Model
• Example 77.16: Piecewise Exponential Frailty Model
• Example 77.17: Normal Regression with Interval Censoring
• Example 77.18: Constrained Analysis
• Example 77.19: Implement a New Sampling Algorithm
• Example 77.20: Using a Transformation to Improve Mixing
• Example 77.21: Gelman-Rubin Diagnostics
• Example 77.22: One-Compartment Model with Pharmacokinetic Data

• Bayesian Zero-Inflated Poisson Regression
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• Bayesian Exponential Mixture Model
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• Bayesian Linear Regression with Standardized Covariates
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• Bayesian Hierarchical Poisson Regression Model for Overdispersed Count Data Using SAS/STAT 9.2
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• Bayesian Hierarchical Poisson Regression Model for Overdispersed Count Data Using SAS/STAT 9.3
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• Bayesian Binomial Model with Power Prior Using the MCMC Procedure
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• Bayesian Multivariate Prior for Multiple Linear Regression Using SAS/STAT 9.2
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• Bayesian Multivariate Prior for Multiple Linear Regression Using SAS/STAT 9.3
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• Bayesian Multinomial Model for Ordinal Data Using SAS/STAT 9.2
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• Bayesian Multinomial Model for Ordinal Data Using SAS/STAT 9.3
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• Bayesian Quantile Regression
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• Bayesian LASSO
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• Stochastic Search Variable Selection with PROC MCMC
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