Some R scripts for Bayesian inference

by Luca La Rocca
This is a collection of R scripts for Bayesian inference,
first coded on the occasion of ABS07: Summer School on Bayesian Methods and Econometrics.

These scripts come under the terms of GNU General Public License;
packages coda and LearnBayes are needed to run them.

The following models have been considered:

• normal linear regression (script)


• binary probit regression (script1, script2)
  reviewed on the occasion of ABS09: Summer School on Bayesian Methodology for Clustering, Classification and Categorical Data Analysis


• linear regression with independent Student errors (script)


• binary regression with Student link function (script)


• multiple change point model for binary time series (script, data, dataplot)


• beta-binomial model for overdispersed counts (script)
  reviewed on the occasion of ABS09: Summer School on Bayesian Methodology for Clustering, Classification and Categorical Data Analysis

The last script was coded on the occasion of my seminars on Bayesian Computation
supplementing the mini-course on Bayesian Statistics given by Guido Consonni at the
Laboratoire de Mathématiques Appliquées de l'Université de Pau et des Pays de l'Adour
during the months of October and November 2007; it only needs package LearnBayes.

Notice that the data analysed by means of the multiple change point model are simulated
as in Chib (1998) but they are not the same data analysed by Chib (1998).

The following references are relevant:

• Albert (2007). Bayesian Computation with R. Springer.
• Albert & Chib (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669-679.
• Chib (1995). Marginal likelihood from the Gibbs output. Journal of the American Statistical Association, 90, 1313-1321.
• Chib & Greenberg (1995). Understanding the Metropolis-Hastings algorithm. American Statistician, 49, 327-335.
• Chib (1998). Estimation and comparison of multiple change-point models. Journal of Econometrics, 86, 221-241.