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Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…

Inference after model selection presents computational challenges when dealing with intractable conditional distributions. Markov chain Monte Carlo (MCMC) is a common method for sampling from these distributions, but its slow convergence…

We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant…

Bayesian variable selection requires sampling from a posterior distribution that combines discrete model indicators with continuously varying parameters, a challenge often addressed through reversible jump Markov chain Monte Carlo (RJMCMC).…

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…

In Bayesian inverse problems, one aims at characterizing the posterior distribution of a set of unknowns, given indirect measurements. For non-linear/non-Gaussian problems, analytic solutions are seldom available: Sequential Monte Carlo…

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the…

The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical…

We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…

Starting with a set of weighted items, we want to create a generic sample of a certain size that we can later use to estimate the total weight of arbitrary subsets. For this purpose, we propose priority sampling which tested on Internet…

The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…

In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…

Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…

We consider the problem of approximating the product of $n$ expectations with respect to a common probability distribution $\mu$. Such products routinely arise in statistics as values of the likelihood in latent variable models. Motivated…

This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses…

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…

Bayesian neural networks (BNNs) have received an increased interest in the last years. In BNNs, a complete posterior distribution of the unknown weight and bias parameters of the network is produced during the training stage. This…