Related papers: A numerically stable algorithm for integrating Bay…
Bayesian inference involves two main computational challenges. First, in estimating the parameters of some model for the data, the posterior distribution may well be highly multi-modal: a regime in which the convergence to stationarity of…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…
The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…
Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an…
In this work, we propose a two-stage algorithm based on Bayesian modeling and computation aiming at quantifying analyte concentrations or quantities in complex mixtures with Raman spectroscopy. A hierarchical Bayesian model is built for…
Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
In large-scale genomic applications vast numbers of molecular features are scanned in order to find a small number of candidates which are linked to a particular disease or phenotype. This is a variable selection problem in the "large p,…
Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to…
Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has…
Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in…
In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…
Weinberg (2012) described a constructive algorithm for computing the marginal likelihood, Z, from a Markov chain simulation of the posterior distribution. Its key point is: the choice of an integration subdomain that eliminates subvolumes…
This paper presents a new Markov chain Monte Carlo method to sample from the posterior distribution of conjugate mixture models. This algorithm relies on a flexible split-merge procedure built using the particle Gibbs sampler. Contrary to…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The…