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Bayesian analysis

Fit Bayesian models using one of the Markov chain Monte Carlo (MCMC) methods.You can choose from a variety of supported models or even program your own. Extensive graphical tools are available to check convergence visually. Compute posterior mean estimates and credible intervals for model parameters and functions of model parameters. You can perform both interval and model-based hypothesis testing. Compare models using Bayes factors. And much more.

Learn about Bayesian analysis.

Also see an Overview example.

Estimation Updated

  • Thousands of built-in models, by combining
    • over 50 likelihood models, including univariate and multivariate normal, logit, probit, ordered logit, ordered probit, Poisson ...
    • Many prior distributions, including normal, lognormal, multivariate normal, gamma, beta, Wishart ...
    • Continuous, binary, ordinal, and count outcomes
    • Univariate, multivariate, and multiple-equation models
    • Linear and nonlinear models
    • Continuous univariate, multivariate, and discrete priors
  • bayes: prefix New
    • Simply type bayes: in front of any of 45 estimation commands to fit Bayesian regression models
    • Change any of the default priors
    • Change any of the simulation or sampling settings
    • Time-series operators
    • Control Panel lets you specify and fit models from an easy-to-use interface
  • Use GUI to fit models
  • Use command language to fit models

Classes of models Updated

Likelihood models Updated

Prior distributions

Markov chain Monte Carlo (MCMC) methods

  • Adaptive Metropolis-Hastings (MH)
  • Hybrid MH (adaptive MH with Gibbs updates)
  • Full Gibbs sampling for some models

Adaptive MH sampling

  • Blocking of parameters
  • Adaptation within each block
  • Diminishing adaptation
  • Random-effects parameters
  • Control scale and covariance of the proposal distribution
  • Control adaptation
    • Length of adaptation
    • Maximum and minimum numbers of adaptive iterations
    • Acceptance rate
    • Adaptation rate
    • Target acceptance rate
    • Acceptance rate tolerance


Starting values

  • Automatic
  • May specify for some or all parameters

Add your own models

  • Write your own programs to calculate likelihood function and choose built-in priors
  • Write your own programs to calculate posterior density directly
  • Use built-in adaptive MH sampling to simulate marginal posterior

Postestimation Selector

  • View and run all postestimation features for your command
  • Automatically updated as estimation commands are run

Graphical tools to check MCMC convergence

Tools to check MCMC efficiency

  • Effective sample sizes
  • Autocorrelation times
  • Efficiencies
  • Compute any of above for parameters or functions of parameters

Posterior summaries

MCSE estimation methods

  • using effective sample size
  • using batch means

Hypothesis testing

Model comparison

Save your MCMC and estimation results for future use

Factor variables Updated

  • Automatically create indicators based on categorical variables
  • Form interactions among discrete and continuous variables
  • Include polynomial terms
Watch Introduction to Factor Variables in Stata tutorials

Additional resources

See New in Stata 15 for more about what was added in Stata 15.





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