## Statistics done wrong [book review]

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , , on March 16, 2015 by xi'an

no starch press (!) sent me the pdf version of this incoming book, Statistics done wrong, by Alex Reinhart, towards writing a book review for CHANCE, and I read it over two flights, one from Montpellier to Paris last week, and from Paris to B’ham this morning. The book is due to appear on March 16. It expands on a still existing website developed by Reinhart. (Discussed a year or so away on Andrew’s blog, most in comments, witness Andrew’s comment below.) Reinhart who is, incidentally or not, is a PhD candidate in statistics at Carnegie Mellon University. After apparently a rather consequent undergraduate foray into physics. Quite an unusual level of maturity and perspective for a PhD student..!

“It’s hard for me to evaluate because I am so close to the material. But on first glance it looks pretty reasonable to me.” A. Gelman

Overall, I found myself enjoying reading the book, even though I found the overall picture of the infinitely many mis-uses of statistics rather grim and a recipe for despairing of ever setting things straight..! Somehow, this is an anti-textbook, in that it warns about many ways of applying the right statistical technique in the wrong setting, without ever describing those statistical techniques. Actually without using a single maths equation. Which should be a reason good enough for me to let all hell break loose on that book! But, no, not really, I felt no compunction about agreeing with Reinhart’s warning and if you have reading Andrew’s blog for a while you should feel the same…

“Then again for a symptom like spontaneous human combustion you might get excited about any improvement.” A. Reinhart (p.13)

Maybe the limitation in the exercise is that statistics appears so much fraught with dangers of over-interpretation and false positive and that everyone (except physicists!) is bound to make such invalidated leaps in conclusion, willingly or not, that it sounds like the statistical side of Gödel’s impossibility theorem! Further, the book moves from recommendation at the individual level, i.e., on how one should conduct an experiment and separate data for hypothesis building from data for hypothesis testing, to a universal criticism of the poor standards of scientific publishing and the unavailability of most datasets and codes. Hence calling for universal reproducibility protocols that reminded of the directions explored in this recent book I reviewed on that topic. (The one the rogue bird did not like.) It may be missing on the bright side of things, for instance the wonderful possibility to use statistical models to produce simulated datasets that allow for an evaluation of the performances of a given procedure in the ideal setting. Which would have helped the increasingly depressed reader in finding ways of checking how wrongs things could get..! But also on the dark side, as it does not say much about the fact that a statistical model is most presumably wrong. (Maybe a physicist’s idiosyncrasy!) There is a chapter entitled Model Abuse, but all it does is criticise stepwise regression and somehow botches the description of Simpson’s paradox.

“You can likely get good advice in exchange for some chocolates or a beer or perhaps coauthorship on your next paper.” A. Reinhart (p.127)

The final pages are however quite redeeming in that they acknowledge that scientists from other fields cannot afford a solid enough training in statistics and hence should hire statisticians as consultants for the data collection, analysis and interpretation of their experiments. A most reasonable recommendation!

## Principles of scientific methods [not a book review]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , on November 11, 2014 by xi'an

Mark Chang, author of Paradoxes in Scientific Inference and vice-president of AMAG Pharmaceuticals, has written another book entitled Principles of Scientific Methods. As was clear from my CHANCE review of Paradoxes in Scientific Inference, I did not find much appeal in this earlier book, even after the author wrote a reply (first posted on this blog and later printed in CHANCE). Hence a rather strong reluctance [of mine] to engage into another highly critical review when I received this new opus by the same author. [And the brainwave cover just put me off even further, although I do not want to start a review by criticising the cover, it did not go that well with the previous attempts!]

After going through Principles of Scientific Methods, I became ever more bemused about the reason(s) for writing or publishing such a book, to the point I decided not to write a CHANCE review on it… (But, having spent some Métro rides on it, I still want to discuss why. Read at your own peril!)

## machine learning [book review, part 2]

Posted in Books, R, Statistics, University life with tags , , , , , , , on October 22, 2013 by xi'an

The chapter (Chap. 3) on Bayesian updating or learning (a most appropriate term) for discrete data is well-done in Machine Learning, a probabilistic perspective if a bit stretched (which is easy with 1000 pages left!). I like the remark (Section 3.5.3) about the log-sum-exp trick. While lengthy, the chapter (Chap. 4) on Gaussian models has the appeal of introducing LDA. The true chapter about Bayesian statistics (Chap. 5) only comes later, which seems a wee bit late to me, but it mentions the paper by Druilhet and Marin (2007) about the dependence of the MAP estimator on the dominating measure. The Bayesian chapter covers the Bayesian interpretation of false discovery rates, And decision-theory (shared with the following chapter on frequentist statistics). This later chapter also covers the pathologies of p-values. The chapter on regression has a paragraph on the g-prior and its extensions (p.238). There are chapters on DAGs, mixture models, EM (which mentions the early MCEM of Celeux and Diebolt!), factor and principal component analyses, Gaussian processes, CART models, HMMs and state-space models, MFRs, variational Bayes, belief and expectation propagations,  and more… Most of the methods are implemented within a MATLAB package called PMTK (probabilistic modelling toolkit) that I did not check (because it is MATLAB!).

There are two (late!) chapters dedicated to simulation methods, Monte Carlo Inference (Chap. 23) and MCMC Inference (Chap.24). (I am somehow unhappy with the label Inference in those titles as those are simulation methods.) They cover the basics and more, including particle filters to some extent (but missing some of the most recent stuff, like Del Moral, Doucet & Jasra, 2006, or Andrieu, Doucet & Hollenstein, 2010). (When introducing the Metropolis-Hastings algorithm, the author states the condition that the union of the supports of the proposal should include the support of the target but this is a rather formal condition as the Markov chain may still fail to be irreducible in that case.) My overall feeling is that too much is introduced in too little space, potentially confusing the student. See, e.g., the half-page Section 24.3.7 (p.855) on reversible jump MCMC. Or the other half-page on Hamiltonian MCMC (p.868). An interesting entry is the study of the performances of the original Gibbs sampler of Geman & Geman (1984), which started the field (to some extent). It states that, unless the hyperparameters are extremely well-calibrated, the Gibbs sampler suggested therein fails to produce a useful segmentation algorithm! The section on convergence diagnoses is rather limited and referring to rather oldish methods, rather than suggesting a multiple-chain empirical exploratory approach. Similarly, there is only one page (p.872) of introduction to marginal likelihood approximation techniques, half of which is wasted on the harmonic mean “worst Monte Carlo method ever”. And the other half is spent on criticising Besag‘s candidate method exploited by Chib (1995).

Now, a wee bit more into detailed nitpicking (if only to feed the ‘Og!): first, the mathematical rigour is not always “au rendez-vous” and the handling of Dirac masses and conditionals and big-Oh (Exercise 3.20)( is too hand-waving for my taste (see p.39 for an example). I also dislike the notion of the multinoulli distribution (p.35), first because it is a poor pun on Bernoulli‘s name, second because sufficiency makes this distribution somewhat irrelevant when compared with the multinomial distribution. Although the book rather fairly covers the dangers and shortcomings of MAP estimators in Section 5.2.1.3 (p.150), this remains the default solution. Monte Carlo is not “a city in Europe known for its plush gambling casinos” but the district of Monaco where the casino stands. And it writes Monte-Carlo in the original. The approximation of π by Monte Carlo is the one I used in my Aussie public lecture, but it would have been nice to know the number of iterations (p.54). The book unnecessarily and most vaguely refers to Taleb about the black swan paradox (p.77). The first introduction of Bayesian tests is to use the HPD  interval and check whether the null value is inside, with a prosecutor’s fallacy in conclusion (p.137). BIC then AIC are introduced (p.162) and the reader remains uncertain about which one to use. If any. Not! The fact that the MLE and the posterior mean differ (p.165) is not a sign of informativeness in the prior. The processing of the label switching problem for mixtures (p.841) is confusing in that the inference problem (invariance by permutation that prohibits using posterior means) is compounded by the simulation problem (failing to observe this behaviour in simulations). The Rao-Blackwellisation Theorem (p.841) does not apply to other cases than two-stage Gibbs sampling, but this is not clear from the text. The adaptive MCMC amcmc package of Jeff Rosenthal is not mentioned (because it is in R?). The proof of detailed balance (p.854-855) should take a line. Having so many references (35 pages) is both a bonus and a nuisance in a textbook, where students dislike the repeated occurrence of “see (so-&-so….”. I also dislike references being given with a parenthesis at all time, as in “See (Doucet et al. 2001) for details”.  And, definitely the least important remark!, the quotes at the beginning are not particularly novel or relevant: the book could do without them. (Same thing for the “no free lunch theorem” which is not particularly helpful as presented…)

In conclusion, Machine Learning, a probabilistic perspective offers a fairly wide, unifying, and comprehensive perspective on the field of statistics, aka machine learning, that can certainly be used as the textbook in a Master program where this is the only course of statistics, aka machine learning. (Having not read other machine learning books thoroughly, I cannot judge how innovative it is. The beginning is trying to build the intuition of what the book is about before introducing the models. Just not my way of proceeding but mostly a matter of taste and maybe of audience…) The computational aspects are not treated in enough depth for my taste and my courses, but there are excellent books on those aspects. The Bayesian thread sometimes run a wee bit thin, but remains a thread nonetheless throughout the book. Thus, a nice textbook for the appropriate course and a reference for many.

## Carnon [and Core, end]

Posted in Books, Kids, pictures, R, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , on June 16, 2012 by xi'an

Yet another full day working on Bayesian Core with Jean-Michel in Carnon… This morning, I ran along the canal for about an hour and at last saw some pink flamingos close enough to take pictures (if only to convince my daughter that there were flamingos in the area!). Then I worked full-time on the spatial statistics chapter, using a small dataset on sedges that we found in Gaetan and Guyon’s Spatial Statistics and Modelling. I am almost done tonight, with both path sampling and ABC R codes documented and working for this dataset. But I’d like to re-run both codes for longer to achieve smoother outcomes.

## yet more questions about Monte Carlo Statistical Methods

Posted in Books, Statistics, University life with tags , , , , , , , , , , on December 8, 2011 by xi'an

As a coincidence, here is the third email I this week about typos in Monte Carlo Statistical Method, from Peng Yu this time. (Which suits me well in terms of posts as  I am currently travelling to Provo, Utah!)

I’m reading the section on importance sampling. But there are a few cases in your book MCSM2 that are not clear to me.

On page 96: “Theorem 3.12 suggests looking for distributions g for which |h|f/g is almost constant with finite variance.”

What is the precise meaning of “almost constant”? If |h|f/g is almost constant, how come its variance is not finite?

“Almost constant” is not a well-defined property, I am afraid. By this sentence on page 96 we meant using densities g that made |h|f/g as little varying as possible while being manageable. Hence the insistence on the finite variance. Of course, the closer |h|f/g is to a constant function the more likely the variance is to be finite.

“It is important to note that although the finite variance constraint is not necessary for the convergence of (3.8) and of (3.11), importance sampling performs quite poorly when (3.12) ….”

It is not obvious to me why when (3.12) importance sampling performs poorly. I might have overlooked some very simple facts. Would you please remind me why it is the case? From the previous discussion in the same section, it seems that h(x) is missing in (3.12). I think that (3.12) should be (please compare with the first equation in section 3.3.2)

$\int h^2(x) f^2(x) / g(x) \text{d}x = + \infty$

The preference for a finite variance of f/g and against (3.12) is that we would like the importance function g to work well for most integrable functions h. Hence a requirement that the importance weight f/g itself behaves well. It guarantees some robustness across the h‘s and also avoids checking for the finite variance (as in your displayed equation) for all functions h that are square-integrable against g, by virtue of the Cauchy-Schwarz inequality.

## Time series

Posted in Books, R, Statistics with tags , , , , , , on March 29, 2011 by xi'an

(This post got published on The Statistics Forum yesterday.)

The short book review section of the International Statistical Review sent me Raquel Prado’s and Mike West’s book, Time Series (Modeling, Computation, and Inference) to review. The current post is not about this specific book, but rather on why I am unsatisfied with the textbooks in this area (and correlatively why I am always reluctant to teach a graduate course on the topic). Again, I stress that the following is not specifically about the book by Raquel Prado and Mike West!

With the noticeable exception of Brockwell and Davis’ Time Series: Theory and Methods, most time-series books seem to suffer (in my opinion) from the same difficulty, which sums up as being unable to provide the reader with a coherent and logical description of/introduction to the field. (This echoes a complaint made by Håvard Rue a few weeks ago in Zurich.) Instead, time-series books appear to haphazardly pile up notions and techniques, theory and methods, without paying much attention to the coherency of the presentation. That’s how I was introduced to the field (even though it was by a fantastic teacher!) and the feeling has not left me since then. It may be due to the fact that the field stemmed partly from signal processing in engineering and partly from econometrics, but such presentations never achieve a Unitarian front on how to handle time-series. In particular, the opposition between the time domain and the frequency domain always escapes me. This is presumably due to my inability to see the relevance of the spectral approach, as harmonic regression simply appears (to me) as a special type of non-linear regression with sinusoidal regressors and with a well-defined likelihood that does not require Fourier frequencies nor periodogram (nor either spectral density estimation). Even within the time domain, I find the handling of stationarity  by time-series book to be mostly cavalier. Why stationarity is important is never addressed, which leads to the reader being left with the hard choice between imposing stationarity and not imposing stationarity. (My original feeling was to let the issue being decided by the data, but this is not possible!) Similarly, causality is often invoked as a reason to set constraints on MA coefficients, even though this resorts to a non-mathematical justification, namely preventing dependence on the future. I thus wonder if being an Unitarian (i.e. following a single logical process for analysing time-series data) is at all possible in the time-series world! E.g., in Bayesian Core, we processed AR, MA, ARMA models in a single perspective, conditioning on the initial values of the series and imposing all the usual constraints on the roots of the lag polynomials but this choice was far from perfectly justified…