Related papers: Intrinsic effective sample size for manifold-value…
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…
Approximate Bayesian computation has emerged as a standard computational tool when dealing with the increasingly common scenario of completely intractable likelihood functions in Bayesian inference. We show that many common Markov chain…
We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
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…
We consider Bayesian analysis on high-dimensional spheres with angular central Gaussian priors. These priors model antipodally symmetric directional data, are easily defined in Hilbert spaces and occur, for instance, in Bayesian binary…
We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…
Markov chain Monte Carlo (MCMC) methods provide powerful framework for sampling unknown probability measures across a wide range of scientific applications. In some settings, the target distribution is supported on a lower-dimensional…
Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities?…
Markov chain Monte Carlo (MCMC) samplers are numerical methods for drawing samples from a given target probability distribution. We discuss one particular MCMC sampler, the MALA-within-Gibbs sampler, from the theoretical and practical…
Markov chain Monte Carlo methods have become popular in statistics as versatile techniques to sample from complicated probability distributions. In this work, we propose a method to parameterize and train transition kernels of Markov chains…
In this paper, we provide bounds on the asymptotic variance for a class of sequential Monte Carlo (SMC) samplers designed for approximating multimodal distributions. Such methods combine standard SMC methods and Markov chain Monte Carlo…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
We introduce inherent measures for effective quality control of brain segmentation based on a Bayesian fully convolutional neural network, using model uncertainty. Monte Carlo samples from the posterior distribution are efficiently…
We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our new sampler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of…
Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC)…