Archive for Springer-Verlag

Monte Carlo Markov chains

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , on May 12, 2020 by xi'an

Darren Wraith pointed out this (currently free access) Springer book by Massimiliano Bonamente [whose family name means good spirit in Italian] to me for its use of the unusual Monte Carlo Markov chain rendering of MCMC.  (Google Trend seems to restrict its use to California!) This is a graduate text for physicists, but one could nonetheless expect more rigour in the processing of the topics. Particularly of the Bayesian topics. Here is a pot-pourri of memorable quotes:

“Two major avenues are available for the assignment of probabilities. One is based on the repetition of the experiments a large number of times under the same conditions, and goes under the name of the frequentist or classical method. The other is based on a more theoretical knowledge of the experiment, but without the experimental requirement, and is referred to as the Bayesian approach.”

“The Bayesian probability is assigned based on a quantitative understanding of the nature of the experiment, and in accord with the Kolmogorov axioms. It is sometimes referred to as empirical probability, in recognition of the fact that sometimes the probability of an event is assigned based upon a practical knowledge of the experiment, although without the classical requirement of repeating the experiment for a large number of times. This method is named after the Rev. Thomas Bayes, who pioneered the development of the theory of probability.”

“The likelihood P(B/A) represents the probability of making the measurement B given that the model A is a correct description of the experiment.”

“…a uniform distribution is normally the logical assumption in the absence of other information.”

“The Gaussian distribution can be considered as a special case of the binomial, when the number of tries is sufficiently large.”

“This clearly does not mean that the Poisson distribution has no variance—in that case, it would not be a random variable!”

“The method of moments therefore returns unbiased estimates for the mean and variance of every distribution in the case of a large number of measurements.”

“The great advantage of the Gibbs sampler is the fact that the acceptance is 100 %, since there is no rejection of candidates for the Markov chain, unlike the case of the Metropolis–Hastings algorithm.”

Let me then point out (or just whine about!) the book using “statistical independence” for plain independence, the use of / rather than Jeffreys’ | for conditioning (and sometimes forgetting \ in some LaTeX formulas), the confusion between events and random variables, esp. when computing the posterior distribution, between models and parameter values, the reliance on discrete probability for continuous settings, as in the Markov chain chapter, confusing density and probability, using Mendel’s pea data without mentioning the unlikely fit to the expected values (or, as put more subtly by Fisher (1936), “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel’s expectations”), presenting Fisher’s and Anderson’s Iris data [a motive for rejection when George was JASA editor!] as a “a new classic experiment”, mentioning Pearson but not Lee for the data in the 1903 Biometrika paper “On the laws of inheritance in man” (and woman!), and not accounting for the discrete nature of this data in the linear regression chapter, the three page derivation of the Gaussian distribution from a Taylor expansion of the Binomial pmf obtained by differentiating in the integer argument, spending endless pages on deriving standard properties of classical distributions, this appalling mess of adding over the conditioning atoms with no normalisation in a Poisson experiment

P(X=4|\mu=0,1,2) = \sum_{\mu=0}^2 \frac{\mu^4}{4!}\exp\{-\mu\},

botching the proof of the CLT, which is treated before the Law of Large Numbers, restricting maximum likelihood estimation to the Gaussian and Poisson cases and muddling its meaning by discussing unbiasedness, confusing a drifted Poisson random variable with a drift on its parameter, as well as using the pmf of the Poisson to define an area under the curve (Fig. 5.2), sweeping the improperty of a constant prior under the carpet, defining a null hypothesis as a range of values for a summary statistic, no mention of Bayesian perspectives in the hypothesis testing, model comparison, and regression chapters, having one-dimensional case chapters followed by two-dimensional case chapters, reducing model comparison to the use of the Kolmogorov-Smirnov test, processing bootstrap and jackknife in the Monte Carlo chapter without a mention of importance sampling, stating recurrence results without assuming irreducibility, motivating MCMC by the intractability of the evidence, resorting to the term link to designate the current value of a Markov chain, incorporating the need for a prior distribution in a terrible description of the Metropolis-Hastings algorithm, including a discrete proof for its stationarity, spending many pages on early 1990’s MCMC convergence tests rather than discussing the adaptive scaling of proposal distributions, the inclusion of numerical tables [in a 2017 book] and turning Bayes (1763) into Bayes and Price (1763), or Student (1908) into Gosset (1908).

[Usual disclaimer about potential self-plagiarism: this post or an edited version of it could possibly appear later in my Books Review section in CHANCE. Unlikely, though!]

free Springer textbooks [incl. Bayesian essentials]

Posted in Statistics with tags , , , , , , , , , on May 4, 2020 by xi'an

EntropyMCMC [R package]

Posted in Statistics with tags , , , , , , , , , , , , on March 26, 2019 by xi'an

My colleague from the Université d’Orléans, Didier Chauveau, has just published on CRAN a new R package called EntropyMCMC, which contains convergence assessment tools for MCMC algorithms, based on non-parametric estimates of the Kullback-Leibler divergence between current distribution and target. (A while ago, quite a while ago!, we actually collaborated with a few others on the Springer-Verlag Lecture Note #135 Discretization and MCMC convergence assessments.) This follows from a series of papers by Didier Chauveau and Pierre Vandekerkhove that started with a nearest neighbour entropy estimate. The evaluation of this entropy is based on N iid (parallel) chains, which involves a parallel implementation. While the missing normalising constant is overwhelmingly unknown, the authors this is not a major issue “since we are mostly interested in the stabilization” of the entropy distance. Or in the comparison of two MCMC algorithms. [Disclaimer: I have not experimented with the package so far, hence cannot vouch for its performances over large dimensions or problematic targets, but would as usual welcome comments and feedback on readers’ experiences.]

independent random sampling methods [book review]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , on May 16, 2018 by xi'an

Last 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.

Springer no more!

Posted in Books, Kids, Statistics, University life with tags , , , , , on April 4, 2018 by xi'an

Just learned that, starting from tomorrow night, I will not have access to any of the Springer journals, as the negotiations between the consortium of French universities, research institutes, higher educations schools, and museums, failed. The commercial published refusing to stem the ever increasing fees, while happily taking in the fast increasing open access fees it pressures from authors, a unique example of triple taxation (researchers’ salaries, open access duties, and enormous non-negotiable subscription rates for the whole package of journals)… Following their German counterparts. Well, this is an opportunity for the boards of all these journals to withdraw and create the phantom version of their formal journal, evaluating and reviewing papers already available on arXiv! And I should definitely get my acts together, rise from my winter-is-coming lethargy, and launch PCI Comput Stat now!!!