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Stata 16 New in Bayesian analysis—Multiple chains, predictions, and more
Multiple chains.
Bayesian inference based on an MCMC (Markov chain Monte Carlo) sample is valid only if the Markov chain has converged. One way we can evaluate this convergence is to simulate and compare multiple chains.
The new nchains() option can be used with both the bayes: prefix and the bayesmh command. For instance, you type
. bayes, nchains(4): regress y x1 x2
and four chains will be produced. The chains will be combined to produce a more accurate final result. Before interpreting the result, however, you can compare the chains graphically to evaluate convergence. You can also evaluate convergence using the Gelman–Rubin convergence diagnostic that is now reported by bayes: regress and other Bayesian estimation commands when multiple chains are simulated. When you are concerned about noncovergence, you can investigate further using the bayesstats grubin command to obtain individual Gelman–Rubin diagnostics for each parameter in your model.
Bayesian predictions.
Bayesian predictions are simulated values from the posterior predictive distribution. These predictions are useful for checking model fit and for predicting out-of-sample observations. After you fit a model with bayesmh, you can use bayespredict to compute these simulated values or functions of them and save those in a new Stata dataset. For instance, you can type
. bayespredict (ymin:@min({_ysim})) (ymax:@max({_ysim})), saving(yminmax)
to compute minimums and maximums of the simulated values. You can then use other postestimation commands such as bayesgraph to obtain summaries of the predictions.
The dataset created by bayespredict may include thousands of simulated values for each observation in your dataset. Sometimes, you do not need all of these individual values. To instead obtain posterior summaries such as posterior means or medians, you can use bayespredict, pmean or bayespredict, pmedian. Alternatively, you may be interested in a random sample of the simulated values. You can use, for instance, bayesreps, nreps(100) to obtain 100 replicates.
Finally, you may want to evaluate model goodness of fit using posterior predictive p-values, also known as PPPs or as Bayesian predictive p-values. PPPs measure agreement between observed and replicated data and can be computed using the new bayesstats ppvalues command. For instance, using our earlier example
. bayesstats ppvalues {ymin} {ymax} using yminmax

Stata 16 has a new suite of commands for performing meta-analysis. This suite lets you explore and combine the results from different studies. For instance, if you have collected results from 20 studies about the effect of a particular drug on blood pressure, you can summarize these studies and estimate the overall effect using meta-analysis.
The new meta suite is broad, but what sets it apart is its simplicity.
You can type, for instance,
. meta set effectsize stderr
to declare precomputed effect sizes or use meta esize to compute effects from summary data. With this, you can perform random-effects, fixed-effects, or common-effect meta-analysis.
To estimate an overall effect size and its confidence interval, obtain heterogeneity statistics, and more, you simply type
. meta summarize
And visualizing the results is as easy as typing
. meta forestplot
But the meta suite provides much more.
Meta-regression and subgroup analysis allow you to evaluate the heterogeneity of studies. These are available via meta regress and meta forestplot, subgroup() or meta summarize, subgroup().
You can investigate potential publication bias. Check visually for funnel-plot asymmetry using meta funnelplot; formally test for funnel-plot asymmetry using meta bias; and assess publication bias using the trim-and-fill method with meta trimfill.
You can even perform cumulative meta-analysis with meta summarize, cumulative().
All the meta-analysis features are documented in the new Meta-analysis Reference Manual.

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