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
| PRIOR/HYPERPRIOR Statement |
- PRIOR parameter-list
distribution ;
- HYPERPRIOR parameter-list distribution ;
- HYPER parameter-list distribution ;
The PRIOR statement specifies the prior distribution of the model parameters. You must specify a single parameter or a list of parameters, a tilde 
, and then a distribution with its parameters. Multiple PRIOR statements are allowed for defining models with multiple independent prior components. The log of the prior is the sum of the log prior values from each of the PRIOR statements. See the section MODEL Statement for the names of the standard distributions and the section Standard Distributions for density specification.
The PRIOR statements are processed twice at every Markov chain simulation—that is, twice per pass through the data set. The statements are called at the first and the last observation of the data set. This is the same as how the BEGINNODATA and ENDNODATA statements are processed.
The HYPERPRIOR statement is internally treated the same as the PRIOR statement. It provides a notational convenience in case you want to fit a multilevel hierarchical model. It is used to specify the hyperprior distribution of the prior distribution parameters. The log of the hyperprior is the sum of the log hyperprior values from each of the HYPERPRIOR statements.
If you want to specify a multilevel hierarchical model, you can use either a PRIOR or a HYPERPRIOR statement as if it were a hyper-HYPERPRIOR statement. Your model can have as many hierarchical levels as desired.