Bayesian MCMC Probit

To access the report only, please click here

To access the repository, please click here

Implementation & theory of a Metropolis Hastings and a Gibbs Algorithm to estimate the parameters of a Probit linear model on simulated and real data.

Abstract

Markov Chain Monte Carlo sampling methods are efficient procedures to generate distributions sequentially. Our work proposes two ways to estimate the parameters of a Generalized Linear Model of a binary target variable linked with a probit function to the covariates. The former is a Metropolis Hastings with a Random Walk proposal algorithm. The latter method is inspired from Albert and Chib (1983), using an instrumental variable Gibbs algorithm framework. Once full conditional closed forms of the parameter are retrievable, we can sample from them. The procedure is carried out in blocks, to increase efficiency. After a theoretical introduction to the techniques, we explicitly derive characterizing features of both and provide a code to present results. Given that the distribution needs additionally to come with ergodic properties, we construct a collection of diagnostic checks to ensure this through plots. A randomly generated dataset and a real dataset are used to graphically derive stable parameters’ specifications. The two methods are then compared in terms of performance and appearance of the resulting chains.

Authors

• Chiavarino Federico
• Giancola Simone
• Liscai Dario
• Marchetti Simone