Related papers: Uniform ergodicity of the Particle Gibbs sampler

This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-reversible trans-dimensional Markov chains, under mild conditions,…

The emergence of big data has led to a growing interest in so-called convergence complexity analysis, which is the study of how the convergence rate of a Monte Carlo Markov chain (for an intractable Bayesian posterior distribution) scales…

We introduce a Markov Chain Monte Carlo (MCMC) algorithm to generate samples from probability distributions supported on a $d$-dimensional lattice $\Lambda = \mathbf{B}\mathbb{Z}^d$, where $\mathbf{B}$ is a full-rank matrix. Specifically,…

We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of probability spaces. It also gives an isomorphism between…

We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax…

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…

We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…

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…

In this paper, we give quantitative bounds on the $f$-total variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a sub-geometric rate. These…

We study the convergence rate to stationarity for a class of exchangeable partition-valued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain are determined by products of i.i.d. stochastic…

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

We consider Markov processes that alternate continuous motions and jumps in a general locally compact polish space. Starting from a mechanistic construction, a first contribution of this article is to provide conditions on the dynamics so…

We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…

We establish verifiable general sufficient conditions for exponential or subexponential ergodicity of Markov processes that may lack the strong Feller property. We apply the obtained results to show exponential ergodicity of a variety of…

The logistic linear mixed model (LLMM) is one of the most widely used statistical models. Generally, Markov chain Monte Carlo algorithms are used to explore the posterior densities associated with the Bayesian LLMMs. Polson, Scott and…

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…

We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…

The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of…

We consider a particle system with uniform coupling between a macroscopic component and individual particles. The constraint for each particle is of full rank, which implies that each movement of the macroscopic component leads to a…

We propose a unified mixture sampler (UMS) that provides a universal estimation framework for nonlinear state-space models with "exp-exp" likelihood kernels. Unlike existing methods that require deriving new mixture approximations for each…