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The MCMC Procedure
Overview
PROC MCMC Compared with Other SAS Procedures
Getting Started
Simple Linear Regression
The Behrens-Fisher Problem
Random-Effects Model
Syntax
PROC MCMC Statement
ARRAY Statement
BEGINCNST/ENDCNST Statement
BEGINNODATA/ENDNODATA Statements
BY Statement
MODEL Statement
PARMS Statement
PREDDIST Statement
PRIOR/HYPERPRIOR Statement
Programming Statements
RANDOM Statement
UDS Statement
Details
How PROC MCMC Works
Blocking of Parameters
Sampling Methods
Tuning the Proposal Distribution
Direct Sampling
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
Autocall Macros for Postprocessing
Gamma and Inverse-Gamma Distributions
Posterior Predictive Distribution
Handling of Missing Data
Functions of Random-Effects Parameters
Floating Point Errors and Overflows
Handling Error Messages
Computational Resources
Displayed Output
ODS Table Names
ODS Graphics
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 Multilevel Random-Effects Model
Multivariate Normal Random-Effects Model
Missing at Random Analysis
Nonignorably Missing Data (MNAR) Analysis
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
Examples: MCMC Procedure
Subsections:
61.1 Simulating Samples From a Known Density
61.2 Box-Cox Transformation
61.3 Logistic Regression Model with a Diffuse Prior
61.4 Logistic Regression Model with Jeffreys’ Prior
61.5 Poisson Regression
61.6 Nonlinear Poisson Regression Models
61.7 Logistic Regression Random-Effects Model
61.8 Nonlinear Poisson Regression Multilevel Random-Effects Model
61.9 Multivariate Normal Random-Effects Model
61.10 Missing at Random Analysis
61.11 Nonignorably Missing Data (MNAR) Analysis
61.12 Change Point Models
61.13 Exponential and Weibull Survival Analysis
61.14 Time Independent Cox Model
61.15 Time Dependent Cox Model
61.16 Piecewise Exponential Frailty Model
61.17 Normal Regression with Interval Censoring
61.18 Constrained Analysis
61.19 Implement a New Sampling Algorithm
61.20 Using a Transformation to Improve Mixing
61.21 Gelman-Rubin Diagnostics
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