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Description
This entry provides a software-free introduction to Bayesian analysis. See [BAYES] bayes for an
overview of the software for performing Bayesian analysis and for an overview example.

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.

Nonparametric series regression
Stata 16's new npregress series command fits nonparametric series regressions that approximate the mean of the dependent variable using polynomials, B-splines, or splines of the covariates. This means that you do not need to specify any predetermined functional form. You specify only which covariates you wish to include in your model. For instance, type
. npregress series wineoutput rainfall temperature i.irrigation
Instead of reporting coefficients, npregress series reports effects, meaning average marginal effects for continuous variables and contrasts for categorical variables. The results might be that the average marginal effect of rainfall is 1 and the contrast for irrigation is 2. This contrast can be interpreted as the average treatment effect of irrigation.
Being a nonparametric regression, the unknown mean is approximated by a series function of the covariates. And yet we can still obtain the inferences that we could from a parametric model. We use margins. We could type
. margins irrigation, at(temperature=(40(5)90))
and obtain a table of the expected effect of having irrigation at temperatures of 40, 50, ..., 90 degrees. And we could graph the result using marginsplot.
Even more, npregress series can fit partially parametric (semiparametric) models.

anyvalue(), anymatch(), and anycount() are for categorical or other variables taking integer
values. If we define a subset of values specified by an integer numlist (see [U] 11.1.8 numlist),
anyvalue() extracts the subset, leaving every other value missing; anymatch() defines an indicator
variable (1 if in subset, 0 otherwise); and anycount() counts occurrences of the subset across a set
of variables. Therefore, with one variable, anymatch(varname) and anycount(varname) are
equivalent.
With the auto dataset, we can generate a variable containing the high values of rep78 and a
variable indicating whether rep78 has a high value:
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