Erik Vanem: Bayesian hierarchical space-time models with application to significant wave height

Abstract

1 Forristall Ocean Engineering, Inc., 101 Chestnut St., Camden, ME 04843, USA rithms for estimating the necessary integrals has been crucial in these applications. The core of this book is the development of a space-time model for significant wave heights. The data come from a wave hindcast for the area of the North Atlantic between Iceland and theUnitedKingdom. Spatial dependence of the data is modeled using a Markov random field. The time evolution is modeled as a Markov chain. Because the main motivation of the study is to determine long-term trends in the data, linear and quadratic terms are explicitly included in the temporal model. Most of the priors are specified as simple Gaussian distributions. The integrals necessary for theBayesian update are calculated using Markov Chain Monte Carlo techniques. These techniques are explained in a detailedAppendix.Other Appendices describe extreme value modeling, Markov random fields, and sampling from a multi-normal distribution. These Appendices are the most useful part of the book. But it would have been helpful to novices tomore fully describe the path from the probability integrals to Bayesian simulations. The book beginswith a literature reviewof 215 references. The review is broad but not deep. Most of the references are described in a sentence or two, and the connections between references are not clear. For example, forecasts of significant wave height are mixed up with statistics of individual waves in a section on short-term models. Many variations of the model were run. As is generally true, changing the prior distributions had very little effect on the results. The basic model sums the time-independent, space-time, seasonal, and secular time components. Taking a log transform of the data leads to a multiplicative model. The author was unable to find a convincing argument to prefer one model over the others. But almost all of the models show an increasing trend of significant wave height over the 42years of hindcast data. The modeled increase in monthly maximum wave heights is about 70cm. The author is reluc-