**A** book that I grabbed in Waterstones, Brussels, on a quick dash between two meetings. And which presumably attracted me because of the superficial [watery] similarity with the book series Rivers of London, which setting and style I like quite a lot. Or, one can always dream on, a light version of Jonathan Strange & Mr. Norrell… Rotherweird is the first book in a trilogy by Andrew Caldecott, taking place in a sort of time space hole in (very) rural England, the river Rother being a true river in South-East England, near Hastings, but this first book does not put me in a particularly eager mood to seek the next volumes, as I find the story, the plot, the characters, and the settings all quite disappointing. Maybe having a truly parallel universe does not help (although it worked pretty well with Jonathan Strange & Mr. Norrell!). Having a boarding school with weird teachers does not either, as they are never exhibited as particularly competent in their own field and as students are absolutely invisible in the novel, while supposed to be the brightest in the whole of England. (Which makes a comparison with Harry Potter megalogy pointless.) Having this town of Rotherweird stuck in a rather indefinite time (and banning any attempt at history) could have been a great start but characters are very shallow, despite some funny lines, and do not contribute to make the universe more conceivable, just the opposite. Without indulging in spoilers, the final resolution is very very unconvincing.

## Archive for book review

## rather dull, if rother weird… [book review]

Posted in Books, Kids, Travel with tags book review, Brussels, England, Harry Potter, Hastings, Jonathan Strange & Mr Norrell, Rivers of London, Ro, Rotherweird, Sussex, Waterstones on July 1, 2018 by xi'an## independent random sampling methods [book review]

Posted in Books, Statistics, University life with tags book review, inverse cdf, MCMC, Monte Carlo methods, Monte Carlo Statistical Methods, multiple try Metropolis, Non-Uniform Random Variate Generation, PRNG, random number generation, ratio of uniform algorithm, simulation, Springer-Verlag, Universidad Carlos III de Madrid, vertical density representation on May 16, 2018 by xi'an**L**ast week, I had the pleasant surprise to receive a copy of this book in the mail. Book that I was not aware had been written or published (meaning that I was not involved in its review!). The three authors, Luca Martino, David Luengo, and Joaquín Míguez, of Independent Random Sampling Methods are from Madrid universities and I have read (and posted on) several of their papers on (population) Monte Carlo simulation in the recent years. Including Luca’s survey of multiple try MCMC which was helpful in writing our WIREs own survey.

The book is a pedagogical coverage of most algorithms used to simulate independent samples from a given distribution, which of course recoups some of the techniques exposed with more details by [another] Luc, namely Luc Devroye’s Non-uniform random variate generation bible, often mentioned here (and studied in uttermost details by a dedicated reading group in Warwick). It includes a whole chapter on accept-reject methods, with in particular a section on Payne-Dagpunar’s band rejection I had not seen previously. And another entire chapter on ratio-of-uniforms techniques. On which the three authors had proposed generalisations [covered by the book], years before I attempted to go the same way, having completely forgotten reading their paper at the time… Or the much earlier 1991 paper by Jon Wakefield, Alan Gelfand and Adrian Smith!

The book also covers the “vertical density representation”, due to Troutt (1991), which consists in considering the distribution of the density p(.) of the random variable X as a random variable, p(X). I remember pondering about this alternative to the cdf transform and giving up on it as the outcome has a distribution depending on p, even when the density is monotonous. Even though I am not certain from reading the section that this is particularly appealing…

Given its title, the book contains very little about MCMC. Except for a last and final chapter that covers adaptive independent Metropolis-Hastings algorithms, in connection with some of the authors’ recent work. Like multiple try Metropolis. Relating to the (unidimensional) ARMS “ancestor” of adaptive MCMC methods. (As noted in a recent blog on Holden et al., 2009 , I have trouble understanding how recycling only rejected proposed values to build a better proposal distribution is enough to guarantee convergence of an adaptive algorithm, but the book does not delve much into this convergence.)

All in all and with the bias induced by me working in the very area, I find the book quite a nice entry on the topic, which can be used in a Monte Carlo course at both undergraduate and graduate levels if one want to avoid going into Markov chains. It is certainly less likely to scare students away than the comprehensive Non-uniform random variate generation and on the opposite may induce some of them to pursue a research career in this domain.

## practical Bayesian inference [book review]

Posted in Books, Kids, R, Statistics, University life with tags ABC model choice, Bayesian hypothesis testing, Bayesian inference, book review, Cambridge University Press, International Statistical Review, Monte Carlo Statistical Methods, practical Bayesian inference, R, textbook on April 26, 2018 by xi'an*[Disclaimer: I received this book of Coryn Bailer-Jones for a review in the International Statistical Review and intend to submit a revised version of this post as my review. As usual, book reviews on the ‘Og are reflecting my own definitely personal and highly subjective views on the topic!]*

**I**t is always a bit of a challenge to review introductory textbooks as, on the one hand, they are rarely written at the level and with the focus one would personally choose to write them. And, on the other hand, it is all too easy to find issues with the material presented and the way it is presented… So be warned and proceed cautiously! In the current case, Practical Bayesian Inference tries to embrace too much, methinks, by starting from basic probability notions (that should not be unknown to physical scientists, I believe, and which would avoid introducing a flat measure as a uniform distribution over the real line!, p.20). All the way to running MCMC for parameter estimation, to compare models by Bayesian evidence, and to cover non-parametric regression and bootstrap resampling. For instance, priors only make their apparition on page 71. With a puzzling choice of an improper prior (?) leading to an improper posterior (??), which is certainly not the smoothest entry on the topic. “*Improper posteriors are a bad thing*“, indeed! And using truncation to turn them into proper distributions is not a clear improvement as the truncation point will significantly impact the inference. Discussing about the choice of priors from the beginning has some appeal, but it may also create confusion in the novice reader (although one never knows!). Even asking about “*what is a good prior?*” (p.73) is not necessarily the best (and my recommended) approach to a proper understanding of the Bayesian paradigm. And arguing about the unicity of the prior (p.119) clashes with my own view of the prior being primarily a reference measure rather than an ideal summary of the available information. (The book argues at some point that there is no fixed model parameter, another and connected source of disagreement.) There is a section on assigning priors (p.113), but it only covers the case of a possibly biased coin without much realism. A feature common to many Bayesian textbooks though. To return to the issue of improper priors (and posteriors), the book includes several warnings about the danger of hitting an undefined posterior (still called a distribution), without providing real guidance on checking for its definition. (A tough question, to be sure.)

“One big drawback of the Metropolis algorithm is that it uses a fixed step size, the magnitude of which can hardly be determined in advance…”(p.165)

When introducing computational techniques, quadratic (or Laplace) approximation of the likelihood is mingled with kernel estimators, which does not seem appropriate. Proposing to check convergence and calibrate MCMC via ACF graphs is helpful in low dimensions, but not in larger dimensions. And while warning about the dangers of forgetting the Jacobians in the Metropolis-Hastings acceptance probability when using a transform like η=ln θ is well-taken, the loose handling of changes of variables may be more confusing than helpful (p.167). Discussing and providing *two* R codes for the (standard) Metropolis algorithm may prove too much. Or not. But using a four page R code for fitting a simple linear regression with a flat prior (pp.182-186) may definitely put the reader off! Even though I deem the example a proper experiment in setting a Metropolis algorithm and appreciate the detailed description around the R code itself. (I just take exception at the paragraph on running the code with two or even one observation, as the fact that “*the Bayesian solution always exists*” (p.188) [under a proper prior] is not necessarily convincing…)

“In the real world we cannot falsify a hypothesis or model any more than we “truthify” it (…) All we can do is ask which of the available models explains the data best.” (p.224)

In a similar format, the discussion on testing of hypotheses starts with a lengthy presentation of classical tests and p-values, the chapter ending up with a list of issues. Most of them reasonable in my own referential. I also concur with the conclusive remarks quoted above that what matters is a comparison of (all relatively false) models. What I less agree [as predictable from earlier posts and papers] with is the (standard) notion that comparing two models with a Bayes factor follows from the no information (in order to avoid the heavily loaded non-informative) prior weights of ½ and ½. Or similarly that the evidence is uniquely calibrated. Or, again, using a truncated improper prior under one of the assumptions (with the ghost of the Jeffreys-Lindley paradox lurking nearby…). While the Savage-Dickey approximation is mentioned, the first numerical resolution of the approximation to the Bayes factor is via simulations from the priors. Which may be very poor in the situation of vague and uninformative priors. And then the deadly harmonic mean makes an entry (p.242), along with nested sampling… There is also a list of issues about Bayesian model comparison, including (strong) dependence on the prior, dependence on irrelevant alternatives, lack of goodness of fit tests, computational costs, including calls to possibly intractable likelihood function, ABC being then mentioned as a solution (which it is not, mostly).

## look, look, confidence! [book review]

Posted in Books, Statistics, University life with tags ABC, amazon associates, Bayesian foundations, BibTeX, book review, confidence distribution, confidence intervals, epistemic probability, fiducial distribution, frequentist coverage, Neyman-Scott problem, Nobel Prize, Norway, prior free posterior, Quenouille, survey, whales on April 23, 2018 by xi'an**A**s it happens, I recently bought [with Amazon Associate earnings] a (used) copy of Confidence, Likelihood, Probability (Statistical Inference with Confidence Distributions), by Tore Schweder and Nils Hjort, to try to understand this confusing notion of confidence distributions. (And hence did not get the book from CUP or anyone else towards purposely writing a review. Or a ½-review like the one below.)

“Fisher squared the circle and obtained a posterior without a prior.” (p.419)

Now that I have gone through a few chapters, I am no less confused about the point of this notion. Which seems to rely on the availability of confidence intervals. Exact or asymptotic ones. The authors plainly recognise (p.61) that a confidence distribution is neither a posterior distribution nor a fiducial distribution, hence cutting off any possible Bayesian usage of the approach. Which seems right in that there is no coherence behind the construct, meaning for instance there is no joint distribution corresponding to the resulting marginals. Or even a specific dominating measure in the parameter space. (Always go looking for the dominating measure!) As usual with frequentist procedures, there is always a feeling of arbitrariness in the resolution, as for instance in the Neyman-Scott problem (p.112) where the profile likelihood and the deviance do not work, but considering directly the distribution of the (inconsistent) MLE of the variance “saves the day”, which sounds a bit like starting from the solution. Another statistical freak, the Fieller-Creasy problem (p.116) remains a freak in this context as it does not seem to allow for a confidence distribution. I also notice an ambivalence in the discourse of the authors of this book, namely that while they claim confidence distributions are both outside a probabilisation of the parameter and inside, “producing distributions for parameters of interest given the data (…) with fewer philosophical and interpretational obstacles” (p.428).

“Bias is particularly difficult to discuss for Bayesian methods, and seems not to be a worry for most Bayesian statisticians.” (p.10)

The discussions as to whether or not confidence distributions form a synthesis of Bayesianism and frequentism always fall short from being convincing, the choice of (or the dependence on) a prior distribution appearing to the authors as a failure of the former approach. Or unnecessarily complicated when there are nuisance parameters. Apparently missing on the (high) degree of subjectivity involved in creating the confidence procedures. Chapter 1 contains a section on “Why not go Bayesian?” that starts from Chris Sims‘ Nobel Lecture on the appeal of Bayesian methods and goes [softly] rampaging through each item. One point (3) is recurrent in many criticisms of B and I always wonder whether or not it is tongue-in-cheek-y… Namely the fact that parameters of a model are rarely if ever stochastic. This is a misrepresentation of the use of prior and posterior distributions [which are in fact] as summaries of information cum uncertainty. About a true fixed parameter. Refusing as does the book to endow posteriors with an epistemic meaning (except for “Bayesian of the Lindley breed” (p.419) is thus most curious. (The debate is repeating in the final(e) chapter as “why the world need not be Bayesian after all”.)

“To obtain frequentist unbiasedness, the Bayesian will have to choose her prior with unbiasedness in mind. Is she then a Bayesian?” (p.430)

A general puzzling feature of the book is that notions are not always immediately defined, but rather discussed and illustrated first. As for instance for the central notion of fiducial probability (Section 1.7, then Chapter 6), maybe because Fisher himself did not have a general principle to advance. The construction of a confidence distribution most often keeps a measure of mystery (and arbitrariness), outside the rather stylised setting of exponential families and sufficient (conditionally so) statistics. (Incidentally, our 2012 ABC survey is [kindly] quoted in relation with approximate sufficiency (p.180), while it does not sound particularly related to this part of the book. Now, is there an ABC version of confidence distributions? Or an ABC derivation?) This is not to imply that the book is uninteresting!, as I found reading it quite entertaining, with many humorous and tongue-in-cheek remarks, like “From Fraser (1961a) and until Fraser (2011), and hopefully even further” (p.92), and great datasets. (Including one entitled *Pornoscope*, which is about *drosophilia* mating.) And also datasets with lesser greatness, like the 3000 mink whales that were killed for Example 8.5, where the authors if not the whales “are saved by a large and informative dataset”… (Whaling is a recurrent [national?] theme throughout the book, along with sport statistics usually involving Norway!)

Miscellanea: The interest of the authors in the topic is credited to bowhead whales, more precisely to Adrian Raftery’s geometric merging (or melding) of two priors and to the resulting Borel paradox (xiii). Proposal that I remember Adrian presenting in Luminy, presumably in 1994. Or maybe in Aussois the year after. The book also repeats Don Fraser’s notion that the likelihood is a sufficient statistic, a point that still bothers me. (On the side, I realised while reading Confidence, &tc., that ABC cannot comply with the likelihood principle.) To end up on a French nitpicking note (!), Quenouille is typ(o)ed Quenoille in the main text, the references and the index. (Blame the .bib file!)

## fiducial simulation

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags book review, conditional density, English train, fiducial statistics, Jeffreys prior, Monte Carlo Statistical Methods, Oxford, pseudo-random generator, simulation, Student's t distribution, sufficient statistics, University of Warwick on April 19, 2018 by xi'an**W**hile reading Confidence, Likelihood, Probability), by Tore Schweder and Nils Hjort, in the train from Oxford to Warwick, I came upon this unexpected property shown by Lindqvist and Taraldsen (Biometrika, 2005) that to simulate a sample **y** conditional on the realisation of a sufficient statistic, T(**y**)=t⁰, it is sufficient (!!!) to simulate the components of **y** as y=G(u,θ), with u a random variable with fixed distribution, e.g., a U(0,1), and to solve in θ the fixed point equation T(**y**)=t⁰. Assuming there exists a single solution. Brilliant (like an aurora borealis)! To borrow a simple example from the authors, take an exponential sample to be simulated given the sum statistics. As it is well-known, the conditional distribution is then a (rescaled) Beta and the proposed algorithm ends up being a standard Beta generator. For the method to work in general, T(**y**) must factorise through a function of the u’s, a so-called pivotal condition which brings us back to my post title. If this condition does not hold, the authors once again brilliantly introduce a pseudo-prior distribution on the parameter θ to make it independent from the u’s conditional on T(**y**)=t⁰. And discuss the choice of the Jeffreys prior as optimal in this setting even when this prior is improper. While the setting is necessarily one of exponential families and of sufficient conditioning statistics, I find it amazing that this property is not more well-known [at least by me!]. And wonder if there is an equivalent outside exponential families, for instance for simulating a ** t** sample conditional on the average of this sample.

## A Closed and Common Orbit

Posted in Statistics with tags A Closed and Common Orbit, A Long Way to a Small Angry Planet, AI, Arthur C. Clarke, Becky Chambers, book review, Hugo Awards, science fiction on February 27, 2018 by xi'an**T**his book by Becky Chambers comes as a sequel of sorts to her first [science-fiction] book, A Long Way to a Small Angry Planet. Book that I liked a lot for its construction of relationships between the highly different team members of a spaceship. In this new book, the author pursues a similar elaboration of unlikely friendships between human and alien species, and AIs. If the first book felt homey, this one is even more so, with essentially two principal characters followed alternatively throughout the book, until the stories predictably cross. It is fairly well-written, with again a beautiful cover, but I cannot say it is as magisterial as the first book. The book-long considerations on the nature of AI and of cloned humans are certainly interesting and deep enough, but the story tension ebbs at time, especially for the story in the past since we know from the beginning that the main character will reappear in the current time. Not reaching the superlatives of a Hugo or Clarke Award in my opinion (albeit nominated for these prizes). Still a most enjoyable read!