Related papers: Federated Bayesian Computation via Piecewise Deter…

Differential privacy formalises privacy-preserving mechanisms that provide access to a database. We pose the question of whether Bayesian inference itself can be used directly to provide private access to data, with no modification. The…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Employing Bayesian inference to calibrate constitutive model parameters has grown substantially in recent years. Among the available techniques, Markov Chain Monte Carlo (MCMC) sampling remains one of the most widely used approaches for…

Differential Privacy (DP) is a probabilistic framework that protects privacy while preserving data utility. To protect the privacy of the individuals in the dataset, DP requires adding a precise amount of noise to a statistic of interest;…

In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…

For engineering applications of artificial intelligence, Bayesian learning holds significant advantages over standard frequentist learning, including the capacity to quantify uncertainty. Langevin Monte Carlo (LMC) is an efficient…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…

Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…

Since the mid-2000s, there has been a resurrection of interest in modern modifications of fiducial inference. To date, the main computational tool to extract a generalized fiducial distribution is Markov chain Monte Carlo (MCMC). We propose…

We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by Davis (1984), are a very general class of Markov processes and are…

Performing model selection for coupled hidden Markov models (CHMMs) is highly challenging, owing to the large dimension of the hidden state process. Whilst in principle the hidden state process can be marginalized out via forward filtering,…

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…

Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…

This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…

Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…