A Fast and Exact Simulation Algorithm for General Gaussian Markov Random Fields

This report has URL http://www.math.ntnu.no/preprint/statistics/1999/S8-1999.p

Printed in Great Britain Recursive computing and simulation-free inference

We illustrate how the recursive algorithm of Reeves & Pettitt (2004) for general factorizable models can be extended to allow exact sampling, maximization of distributions and computation of marginal distributions. All of the methods we describe apply to discrete-valued Markov random fields with nearest neighbour integrations defined on regular lattices; in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices. In this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as Markov chain Monte Carlo. In particular our work offers the basis for an automatic inference machine for such models

Modern Statistical Methods: A First Introduction

this paper we wish to give the more mathematically oriented reader a basic understanding of these new tools, and make him/her able to explore a part of the field him/her-self through the popular public domain software BUGS. We do not intend to give a complete review or exposition of all new developments nor to give all the standard references, but try to explain the main ideas and give some basic references to important WWW-pages and introductory books. We will focus on the following three aspects of modern computational statistics. GRAPHICAL MODELS are stochastic models that are defined via a graph or a network. In most cases, these models have a quite complicated global structure made up of simple local structures/buildingblocks. The graph for the model gives both an easy interpretation of the model, e.g. that smoking influences the risk for cancer, and provides a representation for the model well suited to be analyzed using Markov chain Monte Carlo methods. MARKOV CHAIN MONTE CARLO (MCMC) methods make use of the underlying graph structure to make computational efficient simulations from the stochastic model, in most cases conditioned on the observed data. We can then answer questions concerning properties of our model like parameter estimation, uncertainty bounds for the parameters, prediction for future observations and so on. The probability density for unknown parameters or predictions are often estimated using nonparametric methods, as the required densities seldom are known to be for example Gaussian or exponential. NONPARAMETRIC METHODS do not assume any parametric probability density functions or other functional relationship, but merely let the "data speak for them self". This is especially useful when the amount of data is large, a case that in our computeri..

Norges Teknisk-Naturvitenskapelige Universitet

This report has URL http://www.math.ntnu.no/preprint/statistics/1999/S5-1999.p

Parameter Estimation For A Deformable Template Model

This report has URL http://www.math.ntnu.no/preprint/statistics/1999/S5-1999.p

A Divide And Conquer Algorithm For Exact Simulation Of General Gaussian Markov Random Field

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Bayesian multiscale analysis for time series data

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