It is known that the robit regression model for binary data is a robust alternative to the more popular probit and logistic models. The robit model is obtained by replacing the normal distribution in the probit regression model with the Student’s t distribution. Unlike the probit and logistic models, the robit link has an extra degrees of freedom (df) parameter. It is shown that in practice it ...

In this paper we discuss auxiliary variable approaches to Bayesian binary and multinomial regression. These approaches are ideally suited to automated Markov chain Monte Carlo simulation. In the first part we describe a simple technique using joint updating that improves the performance of the conventional probit regression algorithm. In the second part we discuss auxiliary variable methods for...

Saddlepoint approximations of marginal densities and tail probabilities of general nonlinear statistics are derived. They are based on the expansion of the statistic up to the second order. Their accuracy is shown in a variety of examples, including logit and probit models and rank estimators for regression.

This article describes a method for efficient posterior simulation for Bayesian variable selection in probit regression models with many regressors but few observations. A proposal on model space is described which contains a tuneable parameter. An adaptive approach to choosing this tuning parameter is described which allows automatic, efficient computation in these models. The methods is appli...

We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation propagation algorithm respectively, are derived for hyperparameter learning and model selection. We compare t...