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
| Assignments of Parameters |
In general, you cannot alter the values of any model parameters in PROC MCMC. For example, the following assignment statement produces an error:
parms alpha; alpha = 27;
This restriction prevents incorrect calculation of the posterior density—assignments of parameters in the program would override the parameter values generated by the procedure and lead to a constant value of the density function.
However, you can modify parameter values and assign initial values to parameters within the block defined by the BEGINCNST and ENDCNST statements. The following syntax is allowed:
parms alpha; begincnst; alpha = 27; endcnst;
The initial value of alpha is 
. Assignments within the BEGINCNST/ENDCNST block override initial values specified in the PARMS statement. For example, with the following statements, the Markov chain starts at alpha 
, not 
.
parms alpha 23; begincnst; alpha = 27; endcnst;
This feature enables you to systematically assign initial values. Suppose that z is an array parameter of the same length as the number of observations in the input data set. You want to start the Markov chain with each 
having a different value depending on the data set variable y. The following statements set 
for the first half of the observations and 
for the rest:
/* a rather artificial input data set. */
data inputdata;
do ind = 1 to 10;
y = rand('normal');
output;
end;
run;
proc mcmc data=inputdata;
array z[10];
begincnst;
if ind <= 5 then z[ind] = abs(y);
else z[ind] = 2.3;
endcnst;
parms z:;
prior z: ~ normal(0, sd=1);
model general(0);
run;
Elements of z are modified as PROC MCMC executes the programming statements between the BEGINCNST and ENDCNST statements. This feature could be useful when you use the GENERAL function and you find that the PARMS statements are too cumbersome for assigning starting values.