PROC MCMC how to specify a spike and slab prior

[blund]

I would like to specify a "spike and slab" prior in PROC MCMC. Let beta be the parameter. I need beta ~ (1 - p)*D + p*Normal(0,var) where D is a point mass at zero and p is a beta(a,b) ... or perhaps more simply, p = 0.5

[sbxkoenk · Accepted solution]

Hello,

You cannot specify a spike and slab prior in PROC MCMC!

• There are some standard “Univariate Distributions” that PROC MCMC recognizes in the PRIOR statement.
• There are some standard “Multivariate Distributions” that PROC MCMC recognizes in the PRIOR statement. The exception is the multinomial distribution (only supported in MODEL statement).
• To specify an arbitrary distribution (any distribution), you can use the DGENERAL and GENERAL functions.
  • The DGENERAL function is for discrete distributions.
  • The GENERAL function is for continuous distributions.
• You can work with truncated distributions and censoring data.
• You can work with a mixture distribution (like a mixture of a Poisson distribution and a distribution that is constant at zero).

The spike and slab prior (S&S prior) is actually a mixture of the dgeneral() and the general() prior and PROC MCMC wouldn’t know how to handle that. In PROC MCMC it (the parameter) needs to be either discrete or continuous.

BR, Koen

[blund]

Thanks for the answer!

I think SAS should consider adding functionality to PROC MCMC to include spike and slab priors.

[sbxkoenk]

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@blund wrote:

I think SAS should consider adding functionality to PROC MCMC to include spike and slab priors.

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Koen