We consider the optimal scaling problem for proposal distributions in Hastings-Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that...

Classifiers based on Bayesian networks are usually learned with a fixed structure or a small subset of possible structures. In the presence of unlabeled data this strategy can be detrimental to classification performance, when the assumed classifier structure is incorrect. In this paper we present a classification driven learning method for Bayesian network classifiers that is based on Metropol...

This paper addresses pixel-level segmentation of a human body from a single image. The problem is formulated as a multi-region segmentation where the human body is constrained to be a collection of geometrically linked regions and the background is split into a small number of distinct zones. We solve this problem in a Bayesian framework for jointly estimating articulated body pose and the pixe...

This paper is concerned with the online public engagement ‘Leitbild Metropolis Hamburg – Growing City’ which has been conducted in the context of the EU project DEMOS (Delphi Mediation Online System). The result of DEMOS is an innovative Internet platform facilitating democratic discussions and participative public opinion formation. The test of the DEMOS approach and the software system during...

This paper examines the constraints to physical planning in Kano Metropolis. Kano been one of the most populous cities in Nigeria, is undergoing tremendous urban expansion particularly at the edge of the city. This expansion could be attributed to not only population growth but also redistribution of activities within the metropolitan area. Rapid population growth has increased the tendency of ...

In this article we examine two relatively new MCMC methods which allow for Bayesian inference in diffusion models. First, the Monte Carlo within Metropolis (MCWM) algorithm (O’Neil, Balding, Becker, Serola and Mollison, 2000) uses an importance sampling approximation for the likelihood and yields a limiting stationary distribution that can be made arbitrarily “close” to the posterior distributi...

In this paper we shall consider optimal scaling problems for highdimensional Metropolis–Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropolis algorithm, which tunes the overall algorithm acceptance rate to be 0.234, holds for the so-called Metropolis-within-Gibbs algorithm as well. Further...

This article contains an overview of the literature concerning the computational complexity of Metropolis-Hastings based MCMC methods for sampling probability measures on Rd , when the dimension d is large. The material is structured in three parts addressing, in turn, the following questions: (i) what are sensible assumptions to make on the family of probability measures indexed by d ?; (ii) w...

We present advances in Bayesian modeling and computation for CART (classification and regression tree) models. The modeling innovations include a formal prior distributional structure for tree generation – the pinball prior – that allows for the combination of an explicit specification of a distribution for both the tree size and the tree shape. The core computational innovations involve a nove...

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, decisions and predictions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data. Specifically, we consider learning of probabilistic nonlinear state space models. There is no closedform solution available for this problem, implying that we...