Archive for time series

ABC forecasts

Posted in Books, pictures, Statistics with tags , , , , , , , , on January 9, 2018 by xi'an

My friends and co-authors David Frazier, Gael Martin, Brendan McCabe, and Worapree Maneesoonthorn arXived a paper on ABC forecasting at the turn of the year. ABC prediction is a natural extension of ABC inference in that, provided the full conditional of a future observation given past data and parameters is available but the posterior is not, ABC simulations of the parameters induce an approximation of the predictive. The paper thus considers the impact of this extension on the precision of the predictions. And argues that it is possible that this approximation is preferable to running MCMC in some settings. A first interesting result is that using ABC and hence conditioning on an insufficient summary statistic has no asymptotic impact on the resulting prediction, provided Bayesian concentration of the corresponding posterior takes place as in our convergence paper under revision.

“…conditioning inference about θ on η(y) rather than y makes no difference to the probabilistic statements made about [future observations]”

The above result holds both in terms of convergence in total variation and for proper scoring rules. Even though there is always a loss in accuracy in using ABC. Now, one may think this is a direct consequence of our (and others) earlier convergence results, but numerical experiments on standard time series show the distinct feature that, while the [MCMC] posterior and ABC posterior distributions on the parameters clearly differ, the predictives are more or less identical! With a potential speed gain in using ABC, although comparing parallel ABC versus non-parallel MCMC is rather delicate. For instance, a preliminary parallel ABC could be run as a burnin’ step for parallel MCMC, since all chains would then be roughly in the stationary regime. Another interesting outcome of these experiments is a case when the summary statistics produces a non-consistent ABC posterior, but still leads to a very similar predictive, as shown on this graph.This unexpected accuracy in prediction may further be exploited in state space models, towards producing particle algorithms that are greatly accelerated. Of course, an easy objection to this acceleration is that the impact of the approximation is unknown and un-assessed. However, such an acceleration leaves room for multiple implementations, possibly with different sets of summaries, to check for consistency over replicates.

Bayesian Essentials with R [book review]

Posted in Books, R, Statistics, University life with tags , , , , , , , on July 28, 2016 by xi'an

[A review of Bayesian Essentials that appeared in Technometrics two weeks ago, with the first author being rechristened Jean-Michael!]

“Overall this book is a very helpful and useful introduction to Bayesian methods of data analysis. I found the use of R, the code in the book, and the companion R package, bayess, to be helpful to those who want to begin using  Bayesian methods in data analysis. One topic that I would like to see added is the use of Bayesian methods in change point problems, a topic that we found useful in a recent article and which could be added to the time series chapter. Overall this is a solid book and well worth considering by its intended audience.”
David E. BOOTH
Kent State University

Nonlinear Time Series just appeared

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , , , on February 26, 2014 by xi'an

My friends Randal Douc and Éric Moulines just published this new time series book with David Stoffer. (David also wrote Time Series Analysis and its Applications with Robert Shumway a year ago.) The books reflects well on the research of Randal and Éric over the past decade, namely convergence results on Markov chains for validating both inference in nonlinear time series and algorithms applied to those objects. The later includes MCMC, pMCMC, sequential Monte Carlo, particle filters, and the EM algorithm. While I am too close to the authors to write a balanced review for CHANCE (the book is under review by another researcher, before you ask!), I think this is an important book that reflects the state of the art in the rigorous study of those models. Obviously, the mathematical rigour advocated by the authors makes Nonlinear Time Series a rather advanced book (despite the authors’ reassuring statement that “nothing excessively deep is used”) more adequate for PhD students and researchers than starting graduates (and definitely not advised for self-study), but the availability of the R code (on the highly personal page of David Stoffer) comes to balance the mathematical bent of the book in the first and third parts. A great reference book!

Statistics for spatio-temporal data [book review]

Posted in Books, Statistics, University life with tags , , , , , , on October 14, 2013 by xi'an

Here is the new reference book about spatial and spatio-temporal statistical modelling!  Noel Cressie wrote the earlier classic Statistics for Spatial Data in 1993 and he has now co-authored with Christopher Wikle (a plenary speaker at ISBA 2014 in Cancún) the new bible on the topic. And with a very nice cover of a Guatemaltec lienzo about the Spanish conquest. (Disclaimer: as I am a good friend of Noel, do not expect this review to remain unbiased!)

“…we state the obvious, that political boundaries cannot hold back a one-meter rise in sea level; our environment is ultimately a global resource and its stewardship is an international responsibility.” (p.11)

The book is a sum (in the French/Latin meaning of somme/summa when applied to books—I am not sure this explanation makes any sense!) and, as its predecessor, it covers an enormous range of topics and methods. So do not expect a textbook coverage of most notions and prepare to read further articles referenced in the text. One of the many differences with the earlier book is that MCMC appears from the start as a stepping stone that is necessary to handle

“…there are model-selection criteria that could be invoked (e.g., AIC, BIC, DIC, etc.), which concentrate on the twin pillars of predictability and parsimony. But they do not address the third pillar, namely scientific interpretability (i.e., knowledge).” (p.33)

The first chapter of the book is actually a preface motivating the topics covered by the book, which may be confusing on a first read, esp. for a graduate student, as there is no math formula and no model introduced at this stage. Anyway, this is not really a book made for a linear read. It is quite  witty (with too many quotes to report here!) and often funny (I learned for instance that Einstein’s quote “Everything should be made as simple as possible, but not simpler” was a paraphrase of an earlier lecture, invented by the Reader’s Digest!).

“Thus, we believe that it is not helpful to try to classify probability distributions that determine the statistical models, as subjective or objective. Better questions to ask are about the sensitivity of inferences to model choices and whether such choices make sense scientifically.” (p.32)

The overall tone of the book is mostly Bayesian, in a non-conflictual conditional probability way, insisting on hierarchical (Bayesian) model building. Incidentally, it uses the same bracket notation for generic distributions (densities) as in Gelfand and Smith (JASA, 1990), i.e. [X|Y] and [X|Z,y][Z|y,θ], notation that did not get much of a fan club. (I actually do not know where it stemmed from.) The second chapter contains an illustration of the search for the USS Scorpion using a Bayesian model (including priors built from experts’ opinions), example which is also covered [without the maths!] in Sharon McGrayne’s Theory that would not die.

The book is too rich and my time is too tight (!) to cover each chapter in details.  (For instance, I am not so happy with the temporal chapter in that it moves away from the Bayesian perspective without much of a justification.) Suffice to say then that it appears like an updated and improved version of its predecessor, with 45 pages of references, some of them quite recent. If I was to teach from this book at a Master level, it would take the whole academic year and then some, assuming enough mathematical culture from the student audience.

As an addendum, I noticed several negative reviews on amazon due to the poor quality of the printing, but the copy I received from John Wiley was quite fine, with the many colour graphs well-rendered. Maybe an earlier printing or a different printing agreement?

non-stationary AR(10)

Posted in Books, R, Statistics, University life with tags , , , , , on January 19, 2012 by xi'an

In the revision of Bayesian Core on which Jean-Michel Marin and I worked together most of last week, having missed our CIRM break last summer (!), we have now included an illustration of what happens to an AR(p) time series when the customary stationarity+causality condition on the roots of the associated polynomial is not satisfied.  More specifically, we generated several time-series with the same underlying white noise and random coefficients that have a fair chance of providing non-stationary series and then plotted the 260 next steps of the series by the R code

p=10
T=260
dat=seri=rnorm(T) #white noise

par(mfrow=c(2,2),mar=c(2,2,1,1))
for (i in 1:4){
  coef=runif(p,min=-.5,max=.5)
  for (t in ((p+1):T))
    seri[t]=sum(coef*seri[(t-p):(t-1)])+dat[t]
  plot(seri,ty="l",lwd=2,ylab="")
  }

leading to outputs like the following one