Related papers: Weak convergence of Metropolis algorithms for non-…
The exchange algorithm is one of the most popular extensions of the Metropolis--Hastings algorithm to sample from doubly-intractable distributions. However, the theoretical exploration of the exchange algorithm is very limited. For example,…
Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
Metropolis algorithms are classical tools for sampling from target distributions, with broad applications in statistics and scientific computing. Their convergence speed is governed by the spectral gap of the associated Markov operator.…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
In this study, we investigate the performance of the Metropolis-adjusted Langevin algorithm in a setting with constraints on the support of the target distribution. We provide a rigorous analysis of the resulting Markov chain, establishing…
The performance of Metropolis-Hastings algorithms is highly sensitive to the choice of step size, and miss-specification can lead to severe loss of efficiency. We study algorithms with randomized step sizes, considering both…
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown…
The purpose of this paper is to introduce a new Markov chain Monte Carlo method and exhibit its efficiency by simulation and high-dimensional asymptotic theory. Key fact is that our algorithm has a reversible proposal transition kernel,…
The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that…
This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…
It is well known in many settings that reversible Langevin diffusions in confining potentials converge to equilibrium exponentially fast. Adding irreversible perturbations to the drift of a Langevin diffusion that maintain the same…
We study asymptotic performance of distributed detection in large scale connected sensor networks. Contrasting to the canonical parallel network where a single node has access to local decisions from all other nodes, each node can only…
Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a…
There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…
The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm that incorporates the gradient of the logarithm of the target density in its proposal distribution. In an earlier joint work \citet{pill:stu:12}, the author had…
Adaptive importance sampling (AIS) methods are increasingly used for the approximation of distributions and related intractable integrals in the context of Bayesian inference. Population Monte Carlo (PMC) algorithms are a subclass of AIS…
We consider a multitask estimation problem where nodes in a network are divided into several connected clusters, with each cluster performing a least-mean-squares estimation of a different random parameter vector. Inspired by the…
Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…
The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for…