Wednesday, November 7, 3.15 pm, 2018

Conjugate Bayes for Probit Regression via Unified Skew-Normals
Daniele Durante, Department of Decision Sciences, Bocconi University, Italy
Abstract: Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, such methods are also fundamental building-blocks in more complex formulations, covering density regression, nonparametric classification, graphical models, and others. Within the Bayesian setting, inference typically proceeds by updating the Gaussian priors for the coefficients with the likelihood induced by probit or logit regressions for the binary responses. In this updating, the apparent absence of a tractable posterior has motivated a variety of computational methods, including Markov Chain Monte Carlo (MCMC) routines and algorithms which approximate the posterior. Despite being routinely implemented, current MCMC methodologies face mixing or time-efficiency issues in large p and small n studies, whereas approximate routines fail to capture the skewness typically observed in the posterior. In this seminar, I will show that the posterior distribution for the probit coefficients has indeed a unified skew-normal kernel, under Gaussian priors. This result allows fast and accurate Bayesian inference for a wide class of applications, especially in large p and small-to-moderate n studies where state-of-the-art computational methods face substantial issues. These notable advances are quantitatively outlined in a genetic study and are further generalized to improve classification via Bayesian Additive Regression Trees (BART).
Location: Ada Lovelace (Visionen)
Organizer: Hector Rodriguez-Deniz

Wednesday, December 5, 3.15 pm, 2018

Accelerating Sequential Monte Carlo and Markov chain Monte Carlo with (deterministic) approximations
Jouni Helske, Division of Media and Information Technology, Linköping University.
Abstract: Inference of Bayesian latent variable models can be grouped into deterministic and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases that are hard to quantify. The latter enjoy asymptotic consistency, but can suffer from high computational costs. In this talk I will show how these approaches can be combined in a way which provides more efficient sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) algorithms. Our proposed SMC strategy uses approximations for "twisted targets" with look-ahead property, allowing the use of less particles than "plain" SMC, while also being less sensitive to the processing order of the variables in probabilistic graphical model (PGM) context. The proposed MCMC approach first uses MCMC targeting an approximate marginal of the target distribution, while the subsequent weighting scheme (based on SMC or importance sampling (IS)) provides consistent weighted estimators. This IS-MCMC approach provides a natural alternative to delayed acceptance (DA) pseudomarginal/particle MCMC, and has many advantages over DA, including a straightforward parallelisation and additional flexibility in MCMC implementation.
Location: Ada Lovelace (Visionen)
Organizer: Mattias Villani