Comments on "Particle Markov chain Monte Carlo" by C. Andrieu, A. Doucet, and R. Hollenstein

This is the compilation of our comments submitted to the Journal of the Royal Statistical Society, Series B, to be published within the discussion of the Read Paper of Andrieu, Doucet and Hollenstein.Comment: 7 pages, 4 figure

Non-stationary Gaussian models with physical barriers

The classical tools in spatial statistics are stationary models, like the Matern field. However, in some applications there are boundaries, holes, or physical barriers in the study area, e.g. a coastline, and stationary models will inappropriately smooth over these features, requiring the use of a non-stationary model. We propose a new model, the Barrier model, which is different from the established methods as it is not based on the shortest distance around the physical barrier, nor on boundary conditions. The Barrier model is based on viewing the Matern correlation, not as a correlation function on the shortest distance between two points, but as a collection of paths through a Simultaneous Autoregressive (SAR) model. We then manipulate these local dependencies to cut off paths that are crossing the physical barriers. To make the new SAR well behaved, we formulate it as a stochastic partial differential equation (SPDE) that can be discretised to represent the Gaussian field, with a sparse precision matrix that is automatically positive definite. The main advantage with the Barrier model is that the computational cost is the same as for the stationary model. The model is easy to use, and can deal with both sparse data and very complex barriers, as shown in an application in the Finnish Archipelago Sea. Additionally, the Barrier model is better at reconstructing the modified Horseshoe test function than the standard models used in R-INLA. (C) 2019 Elsevier B.V. All rights reserved.Peer reviewe

...you might like to give a talk about how priors are useful for modelling spatial data but we certainly would not hold you to that

Non UBCUnreviewedAuthor affiliation: King Abdullah University of Science and TechnologyFacult

Gaussian Markov random fields: theory and applications

Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important

Exact Simulation Using Markov Chains

This reports gives a review of the new exact simulation algorithms using Markov chains. The first part covers the discrete case. We consider two different algorithms, Propp and Wilsons "coupling from the past" (CFTP) technique and Fills rejection sampler. The algorithms are tested on the Ising model, with and without an external field. The second part covers continuous state spaces

Loss Functions for Bayesian Image Analysis

This paper discusses the role of loss functions in Bayesian image classification, object recognition and identification, and reviews the use of a particular loss function which produces visually attractive estimates. 1 INTRODUCTION Bayesian image analysis often involves calculating point estimates of some appropriate quantity, for example the grey level at each pixel (in image reconstruction), the label type of each pixel (in image classification), or the number of objects together with their contours and types (in object recognition and identification). Within a decision theoretic framework, the approach to finding an estimator is first to select an appropriate loss function L(x; z), which gives the loss when the true value is x but we estimate it by z. The optimal Bayes estimator (OBE) x is then computed by minimising the posterior expectation of this loss (the Bayes risk), x = arg min z EL(x; z): (1) Commonly used L(x; z) are LMAP = 1 [x6=z] , LMPM = P i 1 [x i 6=z i ] ..