  Most of applied statistics involves regression analysis of data. This paper
presents a stand-alone and menu-driven software package, Bayesian Regression:
Nonparametric and Parametric Models. Currently, this package gives the user a
choice from 83 Bayesian models for data analysis. They include 47 Bayesian
nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture
models for density estimation; and 31 normal random effects models (HLMs),
including normal linear models. Each of the 78 regression models handles either
a continuous, binary, or ordinal dependent variable, and can handle multi-level
(grouped) data. All 83 Bayesian models can handle the analysis of weighted
observations (e.g., for meta-analysis), and the analysis of left-censored,
right-censored, and/or interval-censored data. Each BNP infinite-mixture model
has a mixture distribution assigned one of various BNP prior distributions,
including priors defined by either the Dirichlet process, Pitman-Yor process
(including the normalized stable process), beta (two-parameter) process,
normalized inverse-Gaussian process, geometric weights prior, dependent
Dirichlet process, or the dependent infinite-probits prior. The software user
can mouse-click to select a Bayesian model and perform data analysis via Markov
chain Monte Carlo (MCMC) sampling. After the sampling completes, the software
automatically opens text output that reports MCMC-based estimates of the
model's posterior distribution and model predictive fit to the data. Additional
text and/or graphical output can be generated by mouse-clicking other menu
options. This includes output of MCMC convergence analyses, and estimates of
the model's posterior predictive distribution, for selected functionals and
values of covariates. The software, constructed from MATLAB Compiler, is
illustrated through the BNP regression analysis of real data.
