Related papers: A Multi-Index Markov Chain Monte Carlo Method
In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…
Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty. The method…
We study Monte Carlo estimation of the expected value of sample information (EVSI) which measures the expected benefit of gaining additional information for decision making under uncertainty. EVSI is defined as a nested expectation in which…
Statistical inference in evolutionary models with site-dependence is a long-standing challenge in phylogenetics and computational biology. We consider the problem of approximating marginal sequence likelihoods under dependent-site models of…
The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and…
We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…
We introduce a new class of sequential Monte Carlo methods which reformulates the essence of the nested sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. Two new algorithms are proposed, nested sampling via…
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007)…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
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…
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…