Related papers: On the Poisson equation for Metropolis-Hastings ch…
We consider the random walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. In the limit $n\to\infty$, it is well known (see [Ann.…
We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
This article presents a complete second order theory for a large class of geometric functionals on homogeneous Poisson input. In particular, the results don't require the existence of a radius of stabilisation. Hence they can be applied to…
Given F:[a,b]^k\to [a,b] and a nonconstant X_0 with P(X_0\in [a,b])=1, define the hierarchical sequence of random variables {X_n}_{n\ge 0} by X_{n+1}=F(X_{n,1},...,X_{n,k}), where X_{n,i} are i.i.d. as X_n. Such sequences arise from…
In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One of the main results of this paper is as follows: Let $a\in…
The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete…
Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that…
The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…
The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…
An approximate analytical solution to the fluctuation potential problem in the modified Poisson-Boltzmann theory of electrolyte solutions in the restricted primitive model is presented. The solution is valid for all inter-ionic distances,…
In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and…
Consider a Markov chain $\{X_n\}_{n\ge 0}$ with an ergodic probability measure $\pi$. Let $\Psi$ a function on the state space of the chain, with $\alpha$-tails with respect to $\pi$, $\alpha\in (0,2)$. We find sufficient conditions on the…
This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force. When the magnetic field is large, the so-called drift-fluid approximation is obtained. In this…
In a recent paper `The equi-energy sampler with applications statistical inference and statistical mechanics' [Ann. Stat. 34 (2006) 1581--1619], Kou, Zhou & Wong have presented a new stochastic simulation method called the equi-energy (EE)…
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure…
We present a technique for approximating generic normalization constants subject to constraints. The method is then applied to derive the exact asymptotics for the conditional normalization constant of constrained exponential random graphs.
We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…