Related papers: Sampling through iterated approximation: Gradient-…

In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…

We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

In the quest for scalable Bayesian computational algorithms we need to exploit the full potential of existing methodologies. In this note we point out that message passing algorithms, which are very well developed for inference in graphical…

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…

Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted…

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

The likelihood-free sequential Approximate Bayesian Computation (ABC) algorithms, are increasingly popular inference tools for complex biological models. Such algorithms proceed by constructing a succession of probability distributions over…

We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

Credible microscopic traffic simulation requires car-following models that capture both the average response and the substantial variability observed across drivers and situations. However, most data-driven calibrations remain…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…

We propose an importance sampling (IS)-based transport map Hamiltonian Monte Carlo procedure for performing full Bayesian analysis in general nonlinear high-dimensional hierarchical models. Using IS techniques to construct a transport map,…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…