Perfect Sampling for the Wavelet Reconstruction of Signals

The coupling from the past (CFTP) procedure described in [1] is a protocol for nite state Markov chain Monte Carlo (MCMC) methods whereby the algorithm itself determines the necessary run-time to stationarity. In this paper we demonstrate how this protocol can be applied to the problem of signal reconstruction using Bayesian wavelet analysis where the observations are distorted by Gaussian white noise of unknown variance. MCMC simulation is used to account for model uncertainty by approximating integrals (or summations) on the model space that are either too complex or too computationally demanding to perform analytically. We extend the CFTP protocol of [1] by making use of the central limit theorem to show how the algorithm can determine for itself the approximation error induced by MCMC. In this way we can assess the number of MCMC samples needed to approximate the integral to within a user specied tolerance level. Hence the method automatically ensures convergence and the minimum ..

Bayesian Partitioning for Estimating Disease Risk

This paper presents a Bayesian nonparametric approach for the analysis of spatial count data. It extends the Bayesian partition methodology of Holmes, Denison and Mallick (1999) to handle data which involves counts. A demonstration involving incidence rates of leukemia in New York state is used to highlight the methodology. The model allows us to make probability statements on the incidence rates around point sources without making any parametric assumptions about the nature of the influence between the sources and the surrounding location. Keywords: Bayesian computation; Leukemia incidence data; Markov chain Monte Carlo (MCMC); Point source; Spatial count data; Voronoi tessellation. 1 Introduction The analysis of spatial data is of great importance to researches in many fields, with the greatest interest shown by environmental engineers (e.g. studying the extent of pollution from a source) and medical statisticians (e.g. estimating spatially-varying disease incidence). A good review..

Classification Trees

The generalized linear model framework is often used in classification problems and the importance and effect of the predictor variables on the response is generally judged by examination of the relevant regression coefficients. This chapter describes classification trees which can also be used for performing classification but lead to more appealing `rule-based' models which are simple to interpret. We utilise Markov chain Monte Carlo methods to formulate a Bayesian `search' strategy to find good tree models which, in general, outperform the usual tree search methods. 1 Introduction This chapter deals with the general classification problem. We wish to find a model, using a training set of data, which we can use to predict the (categorical) response of future observations given just their covariates. Using classical generalized linear model (GLM) theory for categorical data (Chapter 5, McCullagh and Nelder, 1989) is restrictive and the resulting model can be difficult to interpret. D..

Semiparametric generalized linear models: Bayesian approaches

Generalized linear models are one of the most widely used tools of the data analyst. However, the model assumes that the structure of the regression relationship between the response and the covariates is linear on a known transformed scale. We focus here on different methods to perform the same type of analyses. These involve using nonparametric models to determine the relationship between the response and covariates after the usual transformation has been carried out. We demonstrate how such a semiparametric model performs for binary regression. 1 Introduction Regression techniques are among some of the most widely used methods in applied statistics. Given a response variable Y , and a set of covariates X = (X 1 ; X 2 ; \Delta \Delta \Delta ; X p ), one is often interested in estimating an assumed functional relationship between Y and X, and in predicting further responses for new values of the covariates. One way of modelling such a relationship is to present the expected value of..

Efficient sampling schemes for Bayesian MARS models with many predictors

10.1007/s11222-005-6201-xStatistics and Computing15293-10