ESTIMATION

• Thousands of built-in models, by combining
  • over 60 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, count, and survival outcomes
  • Univariate, multivariate, and multiple-equation models
  • Linear and nonlinear models
  • Continuous univariate, multivariate, and discrete priors
• bayes: prefix
  • Simply type bayes: in front of any of 58 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
• Multiple chains
• Use GUI to fit models
• Use command language to fit models
• Time-series operators

CLASSES OF MODELS

• Linear regression
• Nonlinear regression
• Multivariate regression
• Multivariate nonlinear regression
• Generalized linear models
• Generalized nonlinear models with canonical links
• Zero-inflated models
• Sample-selection model
• Survival models
• Panel-data models
• Multilevel models
• Autoregressive models
• Threshold autoregressive models
• Multivariate time-series models
• Multiple-equation models
• Lasso

LIKELIHOOD MODELS

• Normal
• Student’s t
• Lognormal
• Exponential
• Probit
• Logit/Logistic
• Binomial
• Ordered probit
• Ordered logistic
• Poisson
• Negative binomial
• Survival models
• Panel-data models
• Multilevel
  • Normal
  • Probit, logit/logistic, complementary log-log
  • Ordered probit and logit
  • Poisson and negative binomial
  • Generalized linear models
  • Survival
• Multivariate normal (MVN)
• Multivariate VAR
• Linear and nonlinear DSGE models
• User-defined

PRIOR DISTRIBUTIONS

• Normal
• Generalized (location-scale) t
• Lognormal
• Uniform
• Gamma
• Inverse gamma
• Exponential
• Laplace
• Cauchy
• Beta
• Chi-squared
• Pareto
• Multivariate normal
• Dirichlet
• Wishart
• Inverse Wishart
• Bernoulli
• Geometric
• Discrete
• Poisson
• User-defined density
• User-defined log density
• Specialized priors
  • MVN with exchangeable, independent, identity, and scaled covariances
  • Flat
  • Jeffreys
  • Multivariate Jeffreys
  • Zellner’s g

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

MARKOV CHAIN MONTE CARLO (MCMC) METHODS

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

SIMULATION

• Produce multiple chains
• Three MCMC methods
• Control burn-in iterations
• Control MCMC iterations
• Thinning
• Review model summary before simulation
• Save simulation results for future use

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
• May specify for some or all chains

POSTESTIMATION SELECTOR

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

TOOLS TO CHECK MCMC CONVERGENCE

• Diagnostic plots in compact form
• Trace plots
• Autocorrelation plots
• Histograms
• Density plots
• Cumulative sum plots
• Bivariate scatterplots
• Produce any of the above for parameters or functions of parameters
• Multiple separate graphs or multiple plots on one graph
• Pause between multiple graphs
• Customize the look of each graph
• Multiple chains
  • Use any of the above graphical tools
  • Gelman–Rubin convergence diagnostic

TOOLS TO CHECK MCMC EFFICIENCY

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

POSTERIOR SUMMARIES

• Means
• Medians
• Standard deviations
• Monte Carlo standard errors (MCSEs)
• Credible intervals (CrIs)
  • Equal-tailed
  • Highest posterior density (HPD)
• Compute any of the above for parameters or functions of parameters
• Summaries for log likelihood and log posterior
• Compute any of the above using multiple chains
• Summaries for simulated outcomes and their functions

MCSE ESTIMATION METHODS

• using effective sample size
• using batch means

HYPOTHESIS TESTING

• Interval-based by computing probability of an interval hypothesis
• Linear and nonlinear
• Single and joint
• Continuous parameters
• Discrete parameters
• Model-based by computing model posterior probabilities
• Perform tests for simulated outcomes and their functions

PREDICTIONS

• Generate predictions: simulate outcome values and their functions
• Save all or a subset of predictions in a separate dataset
• Save posterior summaries of predictions as variables in current dataset
• Save a subset of MCMC replicates as variables in current dataset
• Obtain graphical and posterior summaries, perform hypothesis tests, and more
• Use built-in tools to create functions of predictions or write your own Mata functions and Stata programs
• Generate replicated data for posterior predictive checks

MODEL COMPARISON

• Deviance information criterion (DIC)
• Bayes factors
• Model posterior probabilities
• Nested and nonnested models

MODEL GOODNESS OF FIT

• Posterior predictive p-values
• MCMC replicates
• Predictions

SPECIALIZED POSTESTIMATION

• Impulse–response functions (IRFs) after VAR and DSGE
  • Simple IRFs
  • Orthogonalized IRFs
  • Structural IRFs
  • Cumulative IRFs
• Postestimation after VAR
  • IRFs
  • Dynamic multipliers
  • Forecast-error variance decompositions (FEVD)
  • Static and dynamic forecasts
  • Stability analysis using eigenvalues

SAVE YOUR MCMC AND ESTIMATION RESULTS FOR FUTURE USE

FACTOR VARIABLES

• Automatically create indicators based on categorical variables
• Form interactions among discrete and continuous variables
• Include polynomial terms

• The basics
• Interactions
• More interaction