Related papers: An improved implicit sampling for Bayesian inverse…

Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…

We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte…

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…

Bayesian inference often faces a trade-off between computational speed and sampling accuracy. We propose an adaptive workflow that integrates rapid amortized inference with gold-standard MCMC techniques to achieve a favorable combination of…

We introduce a deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling. As telescopes and simulations rapidly expand the volume and resolution of astrophysical data, fast simulation-based…

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…

We consider the Bayesian inverse homogenization problem of recovering the locally periodic two scale coefficient of a two scale elliptic equation, given limited noisy information on the solution. We consider both the uniform and the…

This paper proposes a novel approach to generate samples from target distributions that are difficult to sample from using Markov Chain Monte Carlo (MCMC) methods. Traditional MCMC algorithms often face slow convergence due to the…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

We investigate how ideas from covariance localization in numerical weather prediction can be used in Markov chain Monte Carlo (MCMC) sampling of high-dimensional posterior distributions arising in Bayesian inverse problems. To localize an…

Bayesian formulation of modern day signal processing problems has called for improved Markov chain Monte Carlo (MCMC) sampling algorithms for inference. The need for efficient sampling techniques has become indispensable for high…

The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities. Favorable scaling with dimension has led to wide adoption of HMC by the statistics community. Modern auto-differentiating software should allow more…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…

In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional…

This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

Standard Markov chain Monte Carlo methods struggle to explore distributions that are concentrated in the neighbourhood of low-dimensional structures. These pathologies naturally occur in a number of situations. For example, they are common…

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).…