A Bayesian Perspective on the Maximum Score Problem

TL;DR

This paper introduces a Bayesian inference framework for a binary choice model with median independence, leveraging Gaussian processes and Gibbs sampling for efficient computation, and showing equivalence to a heteroskedastic probit model.

Contribution

It develops a novel Bayesian approach for the maximum score problem using Gaussian processes, enabling flexible heteroskedastic modeling and efficient inference.

Findings

Bayesian framework matches maximum score model under median independence.

Gibbs sampling with Gaussian process priors is computationally efficient.

Model equivalence to heteroskedastic probit facilitates inference.

Abstract

This paper presents a Bayesian inference framework for a linear index threshold-crossing binary choice model that satisfies a median independence restriction. The key idea is that the model is observationally equivalent to a probit model with nonparametric heteroskedasticity. Consequently, Gibbs sampling techniques from Albert and Chib (1993) and Chib and Greenberg (2013) lead to a computationally attractive Bayesian inference procedure in which a Gaussian process forms a conditionally conjugate prior for the natural logarithm of the skedastic function.