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STATA BAYESIAN ANALYSIS REFERENCE MANUAL
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Bayesian analysis is a statistical analysis that answers research questions about unknown parameters of statistical models by using probability statements. Bayesian analysis rests on the assumption that all model parameters are random quantities and thus can incorporate prior knowledge.
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STATA BAYESIAN ANALYSIS
REFERENCE MANUAL
RELEASE 14
®
A Stata Press Publication
StataCorp LLC
College Station, Texas

®
Copyright
c
1985–2015 StataCorp LLC
All rights reserved
Version 14
Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845
Typeset in T
E
X
ISBN-10: 1-59718-149-8
ISBN-13: 978-1-59718-149-5
This manual is protected by copyright. All rights are reserved. No part of this manual may be reproduced, stored
in a retrieval system, or transcribed, in any form or by any means—electronic, mechanical, photocopy, recording, or
otherwise—without the prior written permission of StataCorp LLC unless permitted subject to the terms and conditions
of a license granted to you by StataCorp LLC to use the software and documentation. No license, express or implied,
by estoppel or otherwise, to any intellectual property rights is granted by this document.
StataCorp provides this manual “as is” without warranty of any kind, either expressed or implied, including, but
not limited to, the implied warranties of merchantability and fitness for a particular purpose. StataCorp may make
improvements and/or changes in the product(s) and the program(s) described in this manual at any time and without
notice.
The software described in this manual is furnished under a license agreement or nondisclosure agreement. The software
may be copied only in accordance with the terms of the agreement. It is against the law to copy the software onto
DVD, CD, disk, diskette, tape, or any other medium for any purpose other than backup or archival purposes.
The automobile dataset appearing on the accompanying media is Copyright
c
1979 by Consumers Union of U.S.,
Inc., Yonkers, NY 10703-1057 and is reproduced by permission from CONSUMER REPORTS, April 1979.
Stata, , Stata Press, Mata, , and NetCourse are registered trademarks of StataCorp LLC.
Stata and Stata Press are registered trademarks with the World Intellectual Property Organization of the United Nations.
NetCourseNow is a trademark of StataCorp LLC.
Other brand and product names are registered trademarks or trademarks of their respective companies.
For copyright information about the software, type help copyright within Stata.
The suggested citation for this software is
StataCorp. 2015. Stata: Release 14. Statistical Software. College Station, TX: StataCorp LLC.

Contents
intro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction to Bayesian analysis 1
bayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction to commands for Bayesian analysis 24
bayesmh . . . . . . . . . . . . . . . . . . . . . Bayesian regression using Metropolis–Hastings algorithm 40
bayesmh evaluators . . . . . . . . . . . . . . . . . . . . . . . . . . . . User-defined evaluators with bayesmh 169
bayesmh postestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . Postestimation tools for bayesmh 190
bayesgraph . . . . . . . . . . . . . . . . . . . . . . . . . Graphical summaries and convergence diagnostics 194
bayesstats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bayesian statistics after bayesmh 213
bayesstats ess . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective sample sizes and related statistics 214
bayesstats ic . . . . . . . . . . . . . . . . . . . . . . . . . . Bayesian information criteria and Bayes factors 220
bayesstats summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bayesian summary statistics 229
bayestest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bayesian hypothesis testing 240
bayestest interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interval hypothesis testing 241
bayestest model . . . . . . . . . . . . . . . . . . Hypothesis testing using model posterior probabilities 252
set clevel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Set default credible level 264
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Subject and author index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
i


Cross-referencing the documentation
When reading this manual, you will find references to other Stata manuals. For example,
[U] 26 Overview of Stata estimation commands
[R] regress
[D] reshape
The first example is a reference to chapter 26, Overview of Stata estimation commands, in the User’s
Guide; the second is a reference to the regress entry in the Base Reference Manual; and the third
is a reference to the reshape entry in the Data Management Reference Manual.
All the manuals in the Stata Documentation have a shorthand notation:
[GSM] Getting Started with Stata for Mac
[GSU] Getting Started with Stata for Unix
[GSW] Getting Started with Stata for Windows
[U] Stata User’s Guide
[R] Stata Base Reference Manual
[BAYES] Stata Bayesian Analysis Reference Manual
[D] Stata Data Management Reference Manual
[FN] Stata Functions Reference Manual
[G] Stata Graphics Reference Manual
[IRT] Stata Item Response Theory Reference Manual
[XT] Stata Longitudinal-Data/Panel-Data Reference Manual
[ME] Stata Multilevel Mixed-Effects Reference Manual
[MI] Stata Multiple-Imputation Reference Manual
[MV] Stata Multivariate Statistics Reference Manual
[PSS] Stata Power and Sample-Size Reference Manual
[P] Stata Programming Reference Manual
[SEM] Stata Structural Equation Modeling Reference Manual
[SVY] Stata Survey Data Reference Manual
[ST] Stata Survival Analysis Reference Manual
[TS] Stata Time-Series Reference Manual
[TE] Stata Treatment-Effects Reference Manual:
Potential Outcomes/Counterfactual Outcomes
[I ] Stata Glossary and Index
[M] Mata Reference Manual
iii
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