B0341
Title: Posterior inference in the sequential probit model with applications to medical data
Authors: Daniele Durante - Bocconi University (Italy)
Augusto Fasano - Universita` Cattolica del Sacro Cuore and Collegio Carlo Alberto (Italy) [presenting]
Abstract: The sequential probit regression model represents a natural extension of the widely-used probit model to deal with ordinal categorical data that may appear in many medical applications, as, for instance, in the case of the severity of an injury or the days spent in hospital. In its Bayesian formulation, the apparent absence of a tractable class of conjugate priors motivated the development of effective Markov chain Monte Carlo methods to perform posterior inference. However, such solutions still face severe computational bottlenecks, especially in large p settings. Leveraging on results for the probit model, it is shown that the class of unified skew-normal (SUN) distributions is conjugate to the sequential probit model likelihood, improving over available methods both in terms of closed-form results for key functionals of interest and via the development of novel computational methods via i.i.d. sampling. Moreover, accurate partially-factorized variational Bayes and expectation propagation procedures are developed, leading to computational gains when the sample size increases. The improvements of such methods are shown in a medical application.
