相关论文: Non-asymptotic confidence intervals for MCMC in pr…

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…

We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…

Testing between hypotheses, when independent sampling is possible, is a well developed subject. In this paper, we propose hypothesis tests that are applicable when the samples are obtained using Markov chain Monte Carlo. These tests are…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC…

I show how any reversible Markov chain on a finite state space that is irreducible, and hence suitable for estimating expectations with respect to its invariant distribution, can be used to construct a non-reversible Markov chain on a…

We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…

For a reversible and ergodic Markov chain $\{X_n,n\geq0\}$ with invariant distribution $\pi$, we show that a valid confidence interval for $\pi(h)$ can be constructed whenever the asymptotic variance $\sigma^2_P(h)$ is finite and positive.…

Markov chain Monte Carlo (MCMC) provides asymptotically consistent estimates of intractable posterior expectations as the number of iterations tends to infinity. However, in large data applications, MCMC can be computationally expensive per…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

Markov chain Monte Calro methods (MCMC) are commonly used in Bayesian statistics. In the last twenty years, many results have been established for the calculation of the exact convergence rate of MCMC methods. We introduce another rate of…

Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the…

Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…

The spectral gap $\gamma$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to…

We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain…

Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…