The MCMC Procedure
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Overview
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Getting Started
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Syntax
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Details
How PROC MCMC Works Blocking of Parameters Sampling Methods Tuning the Proposal Distribution Conjugate Sampling Initial Values of the Markov Chains Assignments of Parameters Standard Distributions Usage of Multivariate Distributions Specifying a New Distribution Using Density Functions in the Programming Statements Truncation and Censoring Some Useful SAS Functions Matrix Functions in PROC MCMC Create Design Matrix Modeling Joint Likelihood Regenerating Diagnostics Plots Caterpillar Plot Posterior Predictive Distribution Handling of Missing Data Floating Point Errors and Overflows Handling Error Messages Computational Resources Displayed Output ODS Table Names ODS Graphics
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Examples
Simulating Samples From a Known Density Box-Cox Transformation Logistic Regression Model with a Diffuse Prior Logistic Regression Model with Jeffreys’ Prior Poisson Regression Nonlinear Poisson Regression Models Logistic Regression Random-Effects Model Nonlinear Poisson Regression Random-Effects Model Multivariate Normal Random-Effects Model Change Point Models Exponential and Weibull Survival Analysis Time Independent Cox Model Time Dependent Cox Model Piecewise Exponential Frailty Model Normal Regression with Interval Censoring Constrained Analysis Implement a New Sampling Algorithm Using a Transformation to Improve Mixing Gelman-Rubin Diagnostics
- References
Getting Started: MCMC Procedure
There are three examples in this "Getting Started" section: a simple linear regression, the Behrens-Fisher estimation problem, and a random-effects model. The regression model is chosen for its simplicity; the Behrens-Fisher problem illustrates some advantages of the Bayesian approach; and the random-effects model is one of the most prevalently used models.
Keep in mind that PARMS statements declare the parameters in the model, PRIOR statements declare the prior distributions, and MODEL statements declare the likelihood for the data. In most cases, you do not need to supply initial values. The procedure advises you if it is unable to generate starting values for the Markov chain.