Related papers: sgmcmc: An R Package for Stochastic Gradient Marko…

In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…

Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the…

Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo…

Sequential Monte Carlo (SMC) is a class of algorithms that approximate high-dimensional expectations of a Markov chain. SMC algorithms typically include a resampling step. There are many possible ways to resample, but the relative…

In this work we define a unified mathematical framework to deepen our understanding of the role of stochastic gradient (SG) noise on the behavior of Markov chain Monte Carlo sampling (SGMCMC) algorithms. Our formulation unlocks the design…

We present JaxSGMC, an application-agnostic library for stochastic gradient Markov chain Monte Carlo (SG-MCMC) in JAX. SG-MCMC schemes are uncertainty quantification (UQ) methods that scale to large datasets and high-dimensional models,…

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…

In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior…

In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…

Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…

Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…

This work discusses the implementation of Markov Chain Monte Carlo (MCMC) sampling from an arbitrary Gaussian mixture model (GMM) within SRAM. We show a novel architecture of SRAM by embedding it with random number generators (RNGs),…

We propose locally stable sparse hard-disk packings, as introduced by B\"or\"oczky, as a model for the analysis and benchmarking of Markov-chain Monte Carlo (MCMC) algorithms. We first generate such packings in a square box with periodic…

The R package sns implements Stochastic Newton Sampler (SNS), a Metropolis-Hastings Monte Carlo Markov Chain algorithm where the proposal density function is a multivariate Gaussian based on a local, second-order Taylor series expansion of…

Sequential Monte Carlo (SMC) methods, also known as particle filters, constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those…