Related papers: Concatenation of Markov processes
This short note reviews the basic theory for quantifying both the asymptotic and preasymptotic convergence of Markov chain Monte Carlo estimators.
A method for tuning parameters in Monte Carlo generators is described and applied to a specific case. The method works in the following way: each observable is generated several times using different values of the parameters to be tuned.…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
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…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…
We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
The analytic properties of the Markov operator associated to a random walk are common tools in the study of the behaviour and some probabilistic features related to the walk. In this paper we consider a class of Markov operators which…
We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…
This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine…
Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a…
Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their infinitesimal…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
We prove what appears to be the first concentration of measure result for hidden Markov processes. Our bound is stated in terms of the contraction coefficients of the underlying Markov process, and strictly generalizes the Markov process…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
An introduction to the basics of Monte Carlo is given. The topics covered include, sample space, events, probabilities, random variables, mean, variance, covariance, characteristic function, chebyshev inequality, law of large numbers,…