A Hierarchical Spatio-Temporal Statistical Model Motivated by Glaciology

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Comment: Revision accepted for publication by the Journal of Agricultural, Biological, and Environmental Statistic

Penalising model component complexity:A principled, practical approach to constructing priors

In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations

A Hierarchical Spatiotemporal Statistical Model Motivated by Glaciology

This is a post-peer-review, pre-copyedit version of an article published in Journal of Agricultural, Biological and Environmental Statistics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s13253-019-00367-1In this paper, we extend and analyze a Bayesian hierarchical spatiotemporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Icelandic Centre for Research (152457).Peer reviewe

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

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..

Penalising model component complexity:A principled, practical approach to constructing priors

In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations