Bayesian Methods
 Mon. 20.7.2015: 15.4517.15, building 20.14, room 103.2
 Wed. 22.7.2015: 11.3013.00, building 20.14, room 103.2
 Thu. 23.7.2015: 11.3013.00, building 20.14, room 103.2
 Fri. 24.7.2015: 11.3013.00, building 20.14, room 103.2
 Topics

 Introduction and Motivation
 An example: Linear Regression
 Finding posteriors
 Analytic
 Conjugate Priors
 MetropolisHastings
 Gibbs
 Checking convergence
 Analytic
 Applications:
 Robust regression
 Discrete Choice
 Instrumental Variables
 Errors in Variables
 Interval regression
 Hierarchical Models
 Nonparametric Methods?
 Identification
 Model Comparison
 Exercises
 Handout
 If you want to prepare for the lecture (or revise), you can have a look at the Handout
(this is a preliminary version only, please expect changes during the next few weeks).
 Exercises
 ... can also be found in the appendix of the handout.
 Literature:

 John K. Kruschke , Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan. Academic Press, 2nd Edition, 2014.
 Hoff, A First Course in Bayesian Statistical Methods. Springer, 2009.
 Christophe Andrieu, Nando de Freitas, Arnaud Doucet, Michael
I. Jordan. “An Introduction to MCMC for Machine Learning.” Machine Learning, 2003, 50(12), pp 543.
The paper can also be found on the homepage of the Arnaud Doucet.
 Software
 For our practical examples (during the entire course) we will use the software environment R. I think that it is helpful to coordinate on one environment and R has the advantage of being free and rather powerful.
For the Bayesian parts we will use JAGS. It helps if you have installed R and JAGS on your computer when we start the course.
 Documentation for R is
provided via the built in help system but also through the
R Homepage.
Useful are
 The R Guide, Jason Owen (Easy to read, explains R with the help of examples from basic statistics)
 Simple R, John Verzani (Explains R with the help of examples from basic statistics)
 Einführung in R, Günther Sawitzki (In German. Rather compact introduction.)
 Econometrics in R, Grant V. Farnsworth (The introduction to R is rather compact and pragmatic.)
 An Introduction to R, W. N. Venables und D. M. Smith (The focus is more on R as a programming language)
 The R language definition (Concentrates only on R as a programming language.)
 On the JAGS Homepage you go to the files pages, then to Manuals, to find the JAGS user manual.
 We will use the following packages:
runjags, coda, boot, Ecdat, boot, bootstrap, survival, lattice, latticeExtra, lme4, lmtest, quantreg, xtable, plyr, reshape2, sampleSelection
. If, e.g., the commandlibrary(Ecdat)
generates an error message (Error in library(Ecdat): There is no package called 'Ecdat'
), you have to install the package. Installing packages with Microsoft Windows:
 Start
Rgui.exe
and install packages from the menuPackages / Install Packages
).  Installing packages from advanced operating systems:
 From within R use the command
install.packages("Ecdat")
, e.g., to install the packageEcdat
 In the lecture we will use RStudio as a front end.
 Documentation for R is
provided via the built in help system but also through the
R Homepage.
Useful are