Related papers: Bayesian Markov-Switching Vector Autoregressive Pr…

Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…

By mixing the target posterior distribution with a surrogate distribution, of which the normalizing constant is tractable, we propose a method for estimating the marginal likelihood using the Wang-Landau algorithm. We show that a faster…

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…

We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the…

Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…

We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…

A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…

We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…

We study a variance reduction strategy based on control variables for simulating the averaged macroscopic behavior of a stochastic slow-fast system. We assume that this averaged behavior can be written in terms of a few slow degrees of…

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…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

Recent variational Bayes methods for geospatial regression, proposed as an alternative to computationally expensive Markov chain Monte Carlo (MCMC) sampling, have leveraged Nearest Neighbor Gaussian processes (NNGP) to achieve scalability.…

Ensuring the safety of autonomous vehicles (AVs) requires both accurate estimation of their performance and efficient discovery of potential failure cases. This paper introduces Bayesian adaptive multifidelity sampling (BAMS), which…

Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers…

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…

Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…

Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of Layered Adaptive Importance Sampling…