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How can I run multiple Markov chains in parallel?

The nchains() option produces multiple chains with the bayes: prefix and the bayesmh command. The chains are simulated sequentially. But you may want to simulate the chains simultaneously to save time. You can do this by using the unofficial bayesparallel: prefix.

You can install bayesparallel: by typing

. net install bayesparallel, from("http://www.stata.com/users/nbalov")

After installation, type

. help bayesparallel

Below, we demonstrate a quick example of how to use this command. Let's fit a simple Bayesian linear regression of mpg on weight using our auto dataset.

First, we will simulate multiple chains sequentially using the standard syntax. To demonstrate, we will generate only two chains:

. webuse auto
(1978 automobile data)

. bayes, nchains(2) rseed(16): regress mpg weight

Chain 1
  Burn-in ...
  Simulation ...
  
Chain 2
  Burn-in ...
  Simulation ...

Model summary


Likelihood: 
  mpg ~ regress(xb_mpg,{sigma2})

Priors: 
  {mpg:weight _cons} ~ normal(0,10000)                                     (1)
            {sigma2} ~ igamma(.01,.01)

(1) Parameters are elements of the linear form xb_mpg.

Bayesian linear regression                    Number of chains    =          2
Random-walk Metropolis–Hastings sampling      Per MCMC chain:
                                                  Iterations      =     12,500
                                                  Burn-in         =      2,500
                                                  Sample size     =     10,000
                                              Number of obs       =         74
                                              Avg acceptance rate =      .3448
                                              Avg efficiency: min =      .1256
                                                              avg =      .1469
                                                              max =      .1864
Avg log marginal-likelihood = -218.62073      Max Gelman–Rubin Rc =      1.003


             
 
                                                Equal-tailed    
             
 
      Mean   Std. dev.     MCSE     Median  [95% cred. interval]

mpg          
 
                                                                
      weight 
 
 -.0060058   .0005249    .00001  -.0060001  -.0070166  -.0049596
       _cons 
 
  39.43578   1.637784   .032675   39.42489   36.08263   42.60404

      sigma2 
 
  12.16568   2.067553   .033858   11.94594   8.770868   16.81322


Note: Default priors are used for model parameters.
Note: Default initial values are used for multiple chains.

We now use bayesparallel: to simulate these same chains simultaneously:

. bayesparallel, nproc(2): bayes, nchains(2) rseed(16): regress mpg weight 

Simulating multiple chains ...

Done.

We simply prefixed our initial bayes: specification with the bayesparallel: prefix, also providing the number of processors to use simultaneously in the nproc() option.

We can now use any of the Bayesian features that are available after bayes, nchains():. The bayesparallel prefix does not produce any output, but we can display the results by typing

. bayes

Model summary

Likelihood: 
  mpg ~ regress(xb_mpg,{sigma2})

Priors: 
  {mpg:weight _cons} ~ normal(0,10000)                                     (1)
            {sigma2} ~ igamma(.01,.01)

(1) Parameters are elements of the linear form xb_mpg.

Bayesian linear regression                    Number of chains    =          2
Random-walk Metropolis-Hastings sampling      Per MCMC chain:
                                                  Iterations      =     12,250
                                                  Burn-in         =      2,500
                                                  Sample size     =     10,000
                                              Number of obs       =         74
                                              Avg acceptance rate =      .3448
                                              Avg efficiency: min =      .1256
                                                              avg =      .1469
                                                              max =      .1864
Avg log marginal-likelihood = -218.62073      Max Gelman-Rubin Rc =      1.003



             
 
                                                Equal-tailed    
             
 
      Mean   Std. dev.     MCSE     Median  [95% cred. interval]

mpg          
 
                                                                
      weight 
 
 -.0060058   .0005249    .00001  -.0060001  -.0070166  -.0049596
       _cons 
 
  39.43578   1.637784   .032675   39.42489   36.08263   42.60404

      sigma2 
 
  12.16568   2.067553   .033858   11.94594   8.770868   16.81322


Note: Default priors are used for model parameters.

We obtain the same parameter estimates but faster.

We can now use any standard Bayesian postestimation command, just as we do after the bayes prefix (or bayesmh). For instance, we can use bayesgraph diagnostics to check MCMC convergence visually:

. bayesgraph diagnostics {mpg:weight}

Or we can use bayestest interval to perform interval hypothesis testing:

. bayestest interval {mpg:weight}, lower(-.005)

Interval tests     Number of chains =         2
                   MCMC sample size =    20,000

       prob1 : {mpg:weight} > -.005



             
 
      Mean    Std. dev.      MCSE

       prob1 
 
      .028     0.16510   .0028899

We used bayes, nchains(): in our demonstration, but you can just as easily use bayesmh, nchains() with the bayesparallel prefix.

See Bayesian analysis and, in particular, Multiple chains and Convergence diagnostics using multiple chains in [BAYES] bayesmh. Read more about Bayesian analysis in the Stata Bayesian Analysis Reference Manual.