Conjugate Sampling

The FMM procedure uses Bayesian analysis via a conjugate Gibbs sampler if the model belongs to a small class of mixture models for which a conjugate sampler is available. See the section Gibbs Sampler for a general discussion of Gibbs sampling. Table 37.8 summarizes the models for which conjugate and Metropolis-Hastings samplers are available.

Table 37.8 Availability of Conjugate and Metropolis Samplers in the FMM Procedure

Effects (exclusive

   

of intercept)

Distributions

Available Samplers

No

Normal or T

Conjugate or Metropolis-Hastings

Yes

Normal or T

Conjugate or Metropolis-Hastings

No

Binomial, binary, Poisson, exponential

Conjugate or Metropolis-Hastings

Yes

Binomial, binary, Poisson, exponential

Metropolis-Hastings only

The conjugate sampler enjoys greater efficiency than the Metropolis-Hastings sampler and has the advantage of sampling in terms of the natural parameters of the distribution.

You can always switch to the Metropolis-Hastings sampling algorithm in any model by adding the METROPOLIS option in the BAYES statement.