Description

In a Bayesian analysis one fixes a prior on the unknown parameter, observes the data, and obtains the posterior distribution of the parameter given the data. For a number of problems the posterior cannot be obtained in closed form and one uses instead the Markov chain simulation method, which in effect produces a sequence of random variables distributed approximately from the posterior distribution. These random variables can be used to estimate the posterior or features of it like the posterior expectation and variance. Unfortunately, the Markov chain simulation method requires non-negligible computer time and this precludes consideration of a large number of priors and an interactive analysis. We present a computing environment within which one can interactively change the prior and immediately see the corresponding changes in the posterior. The environment is based on the object-oriented programming language LISP-STAT and an importance sampling procedure which enables one to use the output of one or a small number of Markov chains to obtain estimates of the posterior for a large class of priors. The environment is developed for the particular case of Bayesian Poisson regression but the programs have been deliberately structured in such a way that the environment can be easily modified to handle a wide range of Bayesian problems requiring use of Markov chain simulation.

Authors

Hani Doss, Ohio State University, and B. Narasimhan, Penn State Erie, The Behrend College.

How to get the programs

A preliminary (and still incomplete) document containing the latest version is available as a hyperps file at http://euler.bd.psu.edu/~naras/bpois.ps.

If you want a quick glimpse of what the software does, see this snapshot. Note: Your browser could take some time to display the pictures which are at the normal size.

If you have the new xlispstat distribution installed, version 3.39 or later, you can get the full software and technical report from here.

If you have the old version of xlispstat, then please click here. If you want only the technical report, click here.

In case of trouble, you can contact B. Narasimhan at naras@euler.bd.psu.edu.