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We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
Incorporating information about the target distribution in proposal mechanisms generally produces efficient Markov chain Monte Carlo algorithms (or at least, algorithms that are more efficient than uninformed counterparts). For instance, it…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in…
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…
Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target…
Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the target density with a local approximation based on a small number of carefully chosen density…
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…
This paper discusses the efficient Bayesian estimation of a multivariate factor stochastic volatility (Factor MSV) model with leverage. We propose a novel approach to construct the sampling schemes that converges to the posterior…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…
When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…
Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in generalized linear models; however, these algorithms are prohibitively slow in massive data…
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…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…