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

We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…

Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…

In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…

Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. Two critical…

This lecture note provides a self-contained introduction to Bayesian inference and Markov Chain Monte Carlo (MCMC) methods for parameter estimation in epidemic models. Using the classical Susceptible-Infectious-Recovered (SIR) compartmental…

The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework.…

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…

A new methodology is presented for the construction of control variates to reduce the variance of additive functionals of Markov Chain Monte Carlo (MCMC) samplers. Our control variates are definedthrough the minimization of the asymptotic…

In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A…

Two popular classes of methods for approximate inference are Markov chain Monte Carlo (MCMC) and variational inference. MCMC tends to be accurate if run for a long enough time, while variational inference tends to give better approximations…

The term ``sequential Monte Carlo methods'' or, equivalently, ``particle filters,'' refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (\pi_t). We…

Effective sample size is a standard summary of Markov chain Monte Carlo output, but it is usually attached to scalar or Euclidean summaries chosen by the analyst. For manifold-valued samples this choice is not canonical: coordinate-wise…

We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…

We study frequentist confidence intervals based on graphical profile likelihoods (Wilks' theorem, likelihood integration), and the Feldman-Cousins (FC) prescription, a generalisation of the Neyman belt construction, in a setting with…

We apply a Bayesian data analysis scheme known as the Markov Chain Monte Carlo (MCMC) to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical…

Battery impedance spectroscopy models are given by fractional order (FO) differential equations. In the discrete-time domain, they give rise to state-space models where the latent process is not Markovian. Parameter estimation for these…

We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics.…