Modeling and Estimation for Self-Exciting Spatio-Temporal Models of Terrorist Activity

Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal diffusion is placed, as a matter of convenience, in the process model allowing for straightforward estimation of the diffusion parameters through Bayesian techniques. However, this method of modeling does not allow for the existence of self-excitation, or a temporal data model dependency, that has been shown to exist in criminal and terrorism data. In this manuscript we will use existing theories on how violence spreads to create models that allow for both spatio-temporal diffusion in the process model as well as temporal diffusion, or self-excitation, in the data model. We will further demonstrate how Laplace approximations similar to their use in Integrated Nested Laplace Approximation can be used to quickly and accurately conduct inference of self-exciting spatio-temporal models allowing practitioners a new way of fitting and comparing multiple process models. We will illustrate this approach by fitting a self-exciting spatio-temporal model to terrorism data in Iraq and demonstrate how choice of process model leads to differing conclusions on the existence of self-excitation in the data and differing conclusions on how violence is spreading spatio-temporally

An Extended Laplace Approximation Method for Bayesian Inference of Self-Exciting Spatial-Temporal Models of Count Data

Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as temporal self-excitation. For large spatial or temporal regions, however, the model leads to an intractable likelihood. An increasingly common method for dealing with large spatio-temporal models is by using Laplace approximations (LA). This method is convenient as it can easily be applied and is quickly implemented. However, as we will demonstrate in this manuscript, when applied to self-exciting Poisson spatial-temporal models, Laplace Approximations result in a significant bias in estimating some parameters. Due to this bias, we propose using up to sixth-order corrections to the LA for fitting these models. We will demonstrate how to do this in a Bayesian setting for Self-Exciting Spatio-Temporal models. We will further show there is a limited parameter space where the extended LA method still has bias. In these uncommon instances we will demonstrate how a more computationally intensive fully Bayesian approach using the Stan software program is possible in those rare instances. The performance of the extended LA method is illustrated with both simulation and real-world data

Review of A Primer of Ecological Statistics

Ecological statistics usually refers to the distinctive statistical methods used for ecological questions and data. Little of that information will be found in this book. Instead, Gotelli and Ellison have written a wonderful overview of statistics for ecologists. This volume contains all the material one would expect in an introductory statistical methods book, and is illustrated using ecological data: random variables and probability, descriptive statistics, comparison of means, regression, analysis of variance (ANOVA), and contingency tables

Review of Biomeasurement

In spite of the title, this is really a textbook for a one‐semester, introductory statistics course for biologists. It covers the standard material: descriptive statistics, concepts of sampling, inference and testing, one‐ and two‐sample Chi‐square tests, one‐, two‐, and k‐sample tests of location, regression, and correlation. Both parametric methods (e.g., one‐way ANOVA) and nonparametric methods (e.g., the Kruskal‐Wallis test) are presented. The style is very conversational and nonmathematical. Methods are illustrated using biological examples. Instructions are given for both hand calculation and the SPSS package. Each chapter includes self‐help questions, with answers at the back of the volume, but there are no homework problems. Assignments from the author’s course at Anglia Ruskin University and other supporting material are included on a companion website, although some of the material is password protected and available only to instructors who adopt the book for their course

FIVE THINGS I WISH MY MOTHER HAD TOLD ME, ABOUT STATISTICS THAT IS

I present five short stories, each describing something I wish I had known and appreciated earlier in my statistical life. The five are Simpson\u27s paradox is everywhere, numerical optimization algorithms can be deceived, you can\u27t always trust the Satterthwaite approximation, BLUP\u27s are wonderful things, and It\u27s good to know Reverend Bayes

Pooling of Variances: The Skeleton in the Mixed Model Closet?

I explore three related issues concerning pooling of error variances: when is it appropriate (or not) to pool, how best to evaluate equality of variances, and whether there is a cost to never pooling. I focus on pooling decisions in a combined analysis of a multi-site experiment. A-priori, sites should have different error variances. My primary question is whether an analysis that ignores unequal variances is wrong. I find that ignoring heteroscedasticity between sites maintains, or provides slightly conservative, tests of average treatment effects and treatment-by-site interactions. Models with site-specific variances do provide more powerful tests when variances are different. Never pooling, i.e., using site-specific variances when variances are equal, also reduces power. In contrast to the relatively benign effects of pooling across sites, incorrectly pooling across treatments is much more serious. AIC-based evaluations of variances are very sensitive to non-normality, with a strong tendency to indicate unequal variances when that is incorrect and the data are non-normal. While Levene’s test is somewhat liberal when errors are skewed or heavy-tailed, it is much more robust than AIC. I conclude that ignoring site-specific error variances is not wrong, but modeling that heterogeneity will increase power. If there is any possibility that errors are non-normal, I suggest that variance models be evaluated using Levene’s test instead of AIC

Review of A Primer of Ecological Statistics. Second Edition

The second edition of this ecological statistics textbook adds two chapters on distinctive statistical methods used for ecological questions. One new chapter covers estimating species richness and other diversity metrics; this chapter focuses on rarefaction curves, although there is a short discussion of Chao’s estimators of assemblage richness. The second new chapter focuses on occupancy modeling with short discussions of mark-recapture models for closed and open populations. Combined with the chapter on ordination that was in the first edition, this volume now provides an introduction to the major areas of ecological statistics