This paper presents exact solutions and convergent approximations for inferences in Bayesian networks associated with nitely generated convex sets of distributions. Robust Bayesian inference is the calculation of bounds on posterior values given perturbations in a probabilistic model. The paper presents exact inference algorithms and analyzes the circumstances where exact inference becomes intr...

Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based o...

Approach: We take a Bayesian approach to the inference problems (in particular, posterior estimation) that revolve around the bilinear model (1). In particular, we leverage the approximate message passing (AMP) framework of [2], [3] and extend it to the bilinear domain. Compared to Bayesian approaches that rely on Gibbs sampling methods or variational inference, the AMP framework allows us to f...

Fine airborne particulate matter (PM2.5) has adverse effects on human health. Assessing the long-term effects of PM2.5 exposure on human health and ecology is often limited by a lack of reliable PM2.5 measurements. In Taipei, PM2.5 levels were not systematically measured until August, 2005. Due to the popularity of geographic information systems (GIS), the landuse regression method has been wid...

The uncertainty in estimation of spatial animal density from line transect surveys depends on the degree of spatial clustering in the animal population. To quantify the clustering we model line transect data as independent thinnings of spatial shot-noise Cox processes. Likelihood-based inference is implemented using Markov chain Monte Carlo (MCMC) methods to obtain efficient estimates of spatia...

Modern cognitive experiments in functional Magnetic Resonance Imaging (fMRI) often aim at understanding the temporal dynamics of the brain response in regions activated by a given stimulus. The study of the variability of the hemodynamic response function (HRF) and its characteristics can provide some answers. In this context, we aim at improving the accuracy of the HRF estimation. To do so, we...

Modern geostatistical mapping methods are being applied to various types of data to produce more realistic and flexible characterizations of a natural random process. The Bayesian Maximum Entropy (BME) is a well-known geostatistical estimation method, especially for the use of soft knowledge as well as exact measurement data. Although development in geostatistical methods helps us to solve limi...

This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We demonstrate that an equivalent robustification may be made in Bayesian inference by substituting an appropriately scaled disparity for the log likelihood to whic...

Stochastic Bayesian detection has recently emerged as a competitive receiver design paradigm for wireless communications applications. It uses Monte Carlo simulations to perform Bayesian inference of a probabilistically modeled communication system so as to obtain the maximum a posterior (MAP) symbol detection and/or channel estimation results. The Monte Carlo concept is attractive in that it i...