## January 31, 2019

### Books to Read While the Algae Grow in Your Fur, January 2019

Attention conservation notice: I have no taste. I also have no qualifications to discuss the history of millenarianism, or really even statistical graphics.

Bärbel Finkenstädt, Leonhard Held and Valerie Isham (eds.), Statistical Methods for Spatio-Temporal Systems
This is an edited volume arising from a conference, with all the virtues and vices that implies. (Several chapters have references to the papers which first published the work expounded in other chapters.) I will, accordingly, review the chapters in order.
Chapter 1: "Spatio-Temporal Point Processes: Methods and Applications" (Diggle). Mostly a precis of case studies from Diggle's (deservedly standard) books on the subject, which I will get around to finishing one of these years.
Chapter 2: "Spatio-Temporal Modelling --- with a View to Biological Growth" (Vedel Jensen, Jónsdóttir, Schmiegel, and Barndorff-Nielsen). This chapter divides into two parts. One is about "ambit stochastics". In a random field $Z(s,t)$, the "ambit" of the space-time point-instant $(s,t)$ is the set of point-instants $(q,u)$, $u < t$, where $Z(q,u)$ is (causally) relevant to $Z(r,t)$. (This is what, in my own work, I've called the "past cone" of $(s,t)$.) Having a regular geometry for the ambit imposes some tractable restrictions on random fields, which are explored here for models of growth-without-decay. The second part of this chapter will only make sense to hardened habituees of Levy processes, and perhaps not even to all of them.
Chapter 3: "Using Transforms to Analyze Space-Time Processes" (Fuentes, Guttorp, and Sampson): A very nice survey of Fourier transform, wavelet transform, and PCA approaches to decomposing spatio-temporal data. There's a good account of some tests for non-stationarity, based on the idea that (essentially) we should get the nearly same transforms for different parts of the data if things really are stationary. (I should think carefully about the assumptions and the implied asymptotic regime here, since the argument makes sense, but it also makes sense that sufficiently slow mean-reversion is indistinguishable from non-stationarity.)
Chapter 4: "Geostatistical Space-Time Models, Stationarity, Seperability, and Full Symmetry" (Gneiting, Genton, and Guttorp): "Geostatistics" here refers to "kriging", or using linear prediction on correlated data. As every schoolchild knows, this boils down to finding the covariance function, $\mathrm{Cov}[Z(s_1, t_1), Z(s_2, t_2)]$. This chapter considers three kinds of symmetry restrictions on the covariance functions: "separability", where $\mathrm{Cov}[Z(s_1, t_1), Z(s_2, t_2)] = C_S(s_1, s_2) C_T(t_1, t_2)$; the weaker notion of "full symmetry", where $\mathrm{Cov}[Z(s_1, t_1), Z(s_2, t_2)] =$\mathrm{Cov}[Z(s_1, t_2), Z(s_2, t_1)]$; and "stationarity", where$\mathrm{Cov}[Z(s_1, t_1), Z(s_2, t_2)] = $\mathrm{Cov}[Z(s_1+q, t_1+h), Z(s_2+q, t_2+h)]$. As the authors explain, while separable covariance functions are often used because of their mathematical tractability, they look really weird; "full symmetry" can do a lot of the same work, at less cost in implausibility.
Chapter 5: "Space-Time Modelling of Rainfall for Continuous Simulations" (Chandler, Isham, Belline, Yang and Northrop): A detailed exposition of two models for rainfall, at different spatio-temporal scales, and how they are both motivated by and connected to data. I appreciate their frankness about things that didn't work, and the difficulties of connecting the different models.
Chapter 6, "A Primer on Space-Time Modeling from a Bayesian Perspective" (Higdon): Here "space-time modeling" means "Gaussian Markov random fields". Does what it says on the label.
All the chapters combine theory with examples --- chapter 2 is perhaps the most mathematically sophisticated one, and also the one where the examples do the least work. The most useful, from my point of view, were Chapters 3 and 4, but that's because I was teaching a class where I did a lot of kriging ad PCA, and (with some regret) no point processes. If you have a professional interest in spatio-temporal statistics, and a fair degree of prior acquaintance, I can recommend this as a useful collection of examples, case studies, and expositions of some detailed topics.
Errata, of a sort: There are supposed to be color plates between pages 142 and 143. Unfortunately, in my copy these are printed in grey, not in color.
Disclaimer: The publisher sent me a copy of this book, but that was part of my fee for reviewing a (different) book proposal for them.
Kieran Healy, Data Visualization: A Practical Introduction
Anyone who has looked at my professional writings will have noticed that my data visualizations are neither fancy nor even attractive, and they never go beyond basic R graphics. This is because I have never learned any other system for statistical visualization. And I've not done that because I'm lazy, and have little visual sense anyway. This book is the best guide I've seen to (1) learning the widely-used, and generally handsome, ggplot library in R, (2) learning the "grammar of graphics" principles on which it is based, and (3) learning the underlying psychological principles which make some graphics better or worse visualizations than others. (This is not to be confused with learning the maxims or even the tacit taste of a particular designer, even one of genius.) The writing is great, the examples are interesting, well-chosen and complete, and the presumptions about how much R, or statistics, you know coming in are minimal. I wish something like this had existed long ago, and I'm tempted, after reading it, to totally re-do the figures in my book. (Aside to my editor: I am not going to totally re-do the figures in my book.) I strongly recommend it, and will be urging it on my graduate students for the foreseeable future.
ObLinkage: The book is online, pretty much.
ObDisclaimer: Kieran and I have been saying good things about each other's blogs since the High Bronze Age of the Internet. But I paid good cash money for my copy, and have no stake in the success of this book.
Anna Lee Huber, Mortal Arts
More historical-mystery mind candy, this time flavored by the (dismal) history of early 19th century psychiatry. (Huber is pretty good, though not perfect, at avoiding anachronistic language, so nobody says "psychiatry" in the novel.) --- Further in the series.
Norman Cohn, The Pursuit of the Millennium: Revolutionary Millenarians and Mystical Anarchists of the Middle Ages
I vividly remember finding a used copy of this in the UW-Madison student bookstore when I began graduate school, in the fall of 1993, and having my mind blown by reading it that fall*. Coming back to it now, I find it still fascinating and convincing, and does an excellent job of tracing millenarian movements among the poor in Latinate Europe from the fall of Rome through the Reformation. (There are a few bits where he gets a bit psychoanalytic, but the first edition was published in 1957.) If I no longer find it mind-blowing, that's in large part because reading it sparked an enduring interest in millenarianism, and so I've long since absorbed what then (you should forgive the expression) came as a revelation.
The most controversial part of the book, I think, is the conclusion, where Cohn makes it very clear that he thinks there is a great deal of similarity, if not actual continuity, between his "revolutionary millenarians and mystical anarchists" and 20th century political extremism, both of the Fascist and the Communist variety. He hesitates --- wisely, I think --- over whether this is just a similarity, or there is an actual thread of historical continuity; but I think his case for the similarity is sound.
*: I was supposed to be having my mind blown by Sakurai. In retrospect, this incident sums up both why I was not a very good graduate student, and why I will never be a great scientist.

Posted at January 31, 2019 23:59 | permanent link