Abstract. This paper deals with the ergodicity (convergence of the marginals) and the law of large numbers for adaptive MCMC algorithms built from transition kernels that are not necessarily geometrically ergodic. We develop a number of results that broaden significantly the class of adaptive MCMC algorithms for which rigorous analysis is now possible. As an example, we give a detailed analysis...

We present a new non-parametric deprojection algorithm DOPING (Deprojection of Observed Photometry using and INverse Gambit), that is designed to extract the three dimensional luminosity density distribution ρ, from the observed surface brightness profile of an astrophysical system such as a galaxy or a galaxy cluster, in a generalised geometry, while taking into account changes in the intrinsi...

The use of urban drainage models requires careful calibration, where model parameters are selected in order to minimize the difference between measured and simulated results. It has been recognized that often more than one set of calibration parameters can achieve similar model accuracy. A probability distribution of model parameters should therefore be constructed to examine the model’s sensit...

The basic idea of the proposed strategy is to use multiple chains sampled using the Metropolis Hasting algorithm (MH). The transition kernel we used for each chain is an isotropic Gaussian with small variance combined with a (randomly chosen) single parameter Gaussian proposal with same variance. The variance of the proposal kernel was determined based on early simulations in order to obtain an...

We estimate the mass of the central black hole in our Galaxy from stellar kinematical data published by Ghez et al. (1998) and Genzel et al. (2000). For this we develop a method, related to Merritt (1993), for non-parametrically reconstructing the mass profile and the stellar distribution function in the central region of the Galaxy from discrete kinematic data, including velocity errors. Model...

Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the values of its neighbors. We introduce the Metropolis weights, a simple choice for the averaging weight...

In this paper we develop tools for analyzing the rate at which a reversible Markov chain converges to stationarity. Our techniques are useful when the Markov chain can be decomposed into pieces which are themselves easier to analyze. The main theorems relate the spectral gap of the original Markov chains to the spectral gap of the pieces. In the first case the pieces are restrictions of the Mar...

W e resolve in the aff irmative a question of Boppana and B u i : whether simulated annealing can, w i th high probability and in polynomial t i m e , f ind the optimal bisection of a r a n d o m graph in Gnpr when p r = O(n*-’) f o r A 5 2 . ( T h e random graph model Gnpr specifies a “planted” bisection of density r , separating t w o n / 2 v e r t e x subsets of slightly higher density p . )...