Proc MCMC cannot generate stable results

[Beki]

Hello there,

I've tried a simple regression on both SAS and Winbugs, but SAS generated different estimates everytime I hit "run" even though I didn't change any values (just press "run" again and again), while Winbugs gave me quite stable results.

Here is my SAS code, would someone tell me anything I missed in the program? Or SAS MCMC itself is not functioning well?

Thank you.

===============================

Data Base;

Input ID $ Y X_mu X_sigma;

Datalines;

A 15 4 1.1

B 8 1.2 0.8

C 12 2.8 1

;

run;

Proc MCMC Data=base nmc=10000 Autocorlag=10000 thin=1 nbi=10000 monitor = (intercept beta X);

Parms intercept beta X;

       Model Y ~ normal(Intercept + beta * X , sd=1);

                Prior Intercept ~ normal(0, sd=100);

                Prior beta ~ normal(0, sd=100);

                Prior X ~ lognormal(X_mu, sd= X_sigma);

Run;

===================================

For running five times, SAS generated estimates of beta as -1.3, 7.8, -2.3, 0.4, 2.3 (and kept changing...), 

and Winbugs generated a stable range 0.70, 0.75, 0.70, 0.70, 0.70.

[Rick_SAS]

If you want the same results, use the SEED= option in the PROC MCMC statement:

    proc MCMC Data=base SEED=12345 ...;

This sets the random number seed. By default, SEED=0, and PROC MCMC gets a random number seed from the time of day.

[Beki]

Thank you, @Rick_SAS. The Seed option did work, and the results are the same now.

But I checked the posterior values for each iteration, found that the values were barely moved no matter the seed was set or not (the first 20 values are as belows.) I need to increase the thinning rate, say 10, or the nmc to 200,000 to maker sure the results are right, but then it takes a lot of running time. Is this normal for SAS?

Thanks.

Iteration	intercept	beta	x	Log Prior Density	Log-Likelihood	Log Posterior
1	9.6	0.1	23.7	-14.3	-15.8	-30.2
2	9.5	0.1	23.7	-14.3	-15.4	-29.8
3	9.4	0.1	23.5	-14.4	-15.4	-29.8
4	9.4	0.1	23.5	-14.4	-15.4	-29.8
5	9.4	0.1	23.5	-14.4	-15.4	-29.8
6	9.1	0.1	23.9	-14.3	-15.9	-30.2
7	9.2	0.1	23.8	-14.3	-15.8	-30.1
8	9.2	0.1	23.8	-14.3	-15.8	-30.1
9	9.5	0.1	25.2	-14.3	-15.8	-30.1
10	9.5	0.1	26.0	-14.3	-15.1	-29.4
11	9.1	0.1	27.0	-14.3	-15.2	-29.5
12	9.0	0.1	27.4	-14.3	-15.2	-29.5
13	9.0	0.1	27.4	-14.3	-15.2	-29.5
14	9.0	0.1	27.4	-14.3	-15.2	-29.5
15	9.0	0.1	27.4	-14.3	-15.2	-29.5
16	9.0	0.1	27.4	-14.3	-15.2	-29.5
17	9.0	0.1	27.4	-14.3	-15.2	-29.5
18	9.0	0.1	27.4	-14.3	-15.2	-29.5
19	8.9	0.1	25.5	-14.3	-15.7	-30.0
20	8.9	0.1	25.5	-14.3	-15.7	-30.0

[lvm]

You are not getting any mixing at all in the chain. Your profile plots must look very strange. It is probably related to the fact that you do not have a free residual variance parameter. You are fixing the standard deviation (variance) at a constant in the model. This usually is a parameter with a prior.

I don't know why you are treating X as a parameter rather than as a fixed predictor variable. I assume you have a good reason (perhaps, as a measurement-error model).

[lvm]

The problem is your treatment of X as a parameter. I tried this with some data, and MCMC cannot mix. If you just had a model with X_mu as the predictor variable, it runs fine. Of course, you may have a reason to treat the predictor as a variable, although I am not aware of a reason for doing so.

[Beki]

Thank you, @lvm. This helps a lot.

yeah, I was guessing the "X" was the reason. When I set X constant, everything looks fine. But since X is an estimation instead of an observation in my work, I need to assign a distribution for X. I may need to figure out a way to solve this problem.