Archive for Bayesian Essentials with R

mea culpa!

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , on October 9, 2017 by xi'an

An entry about our Bayesian Essentials book on X validated alerted me to a typo in the derivation of the Gaussian posterior..! When deriving the posterior (which was left as an exercise in the Bayesian Core), I just forgot the term expressing the divergence between the prior mean and the sample mean. Mea culpa!!!

relabelling in Bayesian mixtures by pivotal units

Posted in Statistics with tags , , , , on September 14, 2017 by xi'an

Yet another paper on relabelling for mixtures, when one would think everything and more has already be said and written on the topic… This one appeared in Statistics and Computing last August and I only became aware of it through ResearchGate which sent me an unsolicited email that this paper quoted one of my own papers. As well as Bayesian Essentials.

The current paper by Egidi, Pappadà, Pauli and Torelli starts from the remark that the similarity matrix of the probabilities for pairs of observations to be in the same component is invariant to label switching. A property we also used in our 2000 JASA paper. But here the authors assume it is possible to find pivots, that is, as many observations as there are components such that any pair of them is never in the same component with posterior probability one. These pivots are then used for the relabelling, as they define a preferential relabelling at each iteration. Now, this is not always possible since there are presumably iterations with empty components and there is rarely a zero probability that enough pairs never meet. The resolution of this quandary is then to remove the iterations for which this happens, a subsampling that changes the nature of the MCMC chain and may jeopardise its Markovian validation. The authors however suggest using alternative and computationally cheaper solutions to identify the pivots. (Which confuses me as to which solution they adopt.)

The next part of the paper compares this approach with seven other solutions found in the literature, from Matthew Stephens’ (2000) to our permutation reordering. Which does pretty well in terms of MSE in the simulation study (see the massive Table 3) while being much cheaper to implement than the proposed pivotal relabelling (Table 4). And which, contrary to the authors’ objection, does not require the precise computation of the MAP since, as indicated in our paper, the relative maximum based on the MCMC iterations can be used as a proxy. I am thus less than convinced at the improvement brought by this alternative…

a typo that went under the radar

Posted in Books, R, Statistics, University life with tags , , , , , , , on January 25, 2017 by xi'an

A chance occurrence on X validated: a question on an incomprehensible formula for Bayesian model choice: which, most unfortunately!, appeared in Bayesian Essentials with R! Eeech! It looks like one line in our LATEX file got erased and the likelihood part in the denominator altogether vanished. Apologies to all readers confused by this nonsensical formula!

tractable Bayesian variable selection: beyond normality

Posted in R, Statistics, University life with tags , , , , , , , on October 17, 2016 by xi'an

bird tracks in the first snow of Winter, Feb. 05, 2012 David Rossell and Francisco Rubio (both from Warwick) arXived a month ago a paper on non-normal variable selection. They use two-piece error models that preserve manageable inference and allow for simple computational algorithms, but also characterise the behaviour of the resulting variable selection process under model misspecification. Interestingly, they show that the existence of asymmetries or heavy tails leads to power losses when using the Normal model. The two-piece error distribution is made of two halves of location-scale transforms of the same reference density on the two sides of the common location parameter. In this paper, the density is either Gaussian or Laplace (i.e., exponential?). In both cases the (log-)likelihood has a nice compact expression (although it does not allow for a useful sufficient statistic). One is the L¹ version versus the other which is the L² version. Which is the main reason for using this formalism based on only two families of parametric distributions, I presume. (As mentioned in an earlier post, I do not consider those distributions as mixtures because the component of a given observation can always be identified. And because as shown in the current paper, maximum likelihood estimates can be easily derived.) The prior construction follows the non-local prior principles of Johnson and Rossell (2010, 2012) also discussed in earlier posts. The construction is very detailed and hence highlights how many calibration steps are needed in the process.

“Bayes factor rates are the same as when the correct model is assumed [but] model misspecification often causes a decrease in the power to detect truly active variables.”

When there are too many models to compare at once, the authors propose a random walk on the finite set of models (which does not require advanced measure-theoretic tools like reversible jump MCMC). One interesting aspect is that moving away from the normal to another member of this small family is driven by the density of the data under the marginal densities, which means moving only to interesting alternatives. But also sticking to the normal only for adequate datasets. In a sense this is not extremely surprising given that the marginal likelihoods (model-wise) are available. It is also interesting that on real datasets, one of the four models is heavily favoured against the others, be it Normal (6.3) or Laplace (6.4). And that the four model framework returns almost identical values when compared with a single (most likely) model. Although not immensely surprising when acknowledging that the frequency of the most likely model is 0.998 and 0.998, respectively.

“Our framework represents a middle-ground to add flexibility in a parsimonious manner that remains analytically and computationally tractable, facilitating applications where either p is large or n is too moderate to fit more flexible models accurately.”

Overall, I find the experiment quite conclusive and do not object [much] to this choice of parametric family in that it is always more general and generic than the sempiternal Gaussian model. That we picked in our Bayesian Essentials, following tradition. In a sense, it would be natural to pick the most general possible parametric family that allows for fast computations, if this notion does make any sense…

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

Statistical rethinking [book review]

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , on April 6, 2016 by xi'an

Statistical Rethinking: A Bayesian Course with Examples in R and Stan is a new book by Richard McElreath that CRC Press sent me for review in CHANCE. While the book was already discussed on Andrew’s blog three months ago, and [rightly so!] enthusiastically recommended by Rasmus Bååth on Amazon, here are the reasons why I am quite impressed by Statistical Rethinking!

“Make no mistake: you will wreck Prague eventually.” (p.10)

While the book has a lot in common with Bayesian Data Analysis, from being in the same CRC series to adopting a pragmatic and weakly informative approach to Bayesian analysis, to supporting the use of STAN, it also nicely develops its own ecosystem and idiosyncrasies, with a noticeable Jaynesian bent. To start with, I like the highly personal style with clear attempts to make the concepts memorable for students by resorting to external concepts. The best example is the call to the myth of the golem in the first chapter, which McElreath uses as an warning for the use of statistical models (which almost are anagrams to golems!). Golems and models [and robots, another concept invented in Prague!] are man-made devices that strive to accomplish the goal set to them without heeding the consequences of their actions. This first chapter of Statistical Rethinking is setting the ground for the rest of the book and gets quite philosophical (albeit in a readable way!) as a result. In particular, there is a most coherent call against hypothesis testing, which by itself justifies the title of the book. Continue reading

Introduction to Monte Carlo methods with R and Bayesian Essentials with R

Posted in Books, R, Statistics, University life with tags , , , , , , on June 26, 2015 by xi'an

sales1Here are the  download figures for my e-book with George as sent to me last week by my publisher Springer-Verlag.  With an interesting surge in the past year. Maybe simply due to new selling strategies of the published rather to a wider interest in the book. (My royalties have certainly not increased!) Anyway thanks to all readers. As an aside for wordpress wannabe bloggers, I realised it is now almost impossible to write tables with WordPress, another illustration of the move towards small-device-supported blogs. Along with a new annoying “simpler” (or more accurately dumber) interface and a default font far too small for my eyesight. So I advise alternatives to wordpress that are more sympathetic to maths contents (e.g., using MathJax) and comfortable editing.

salesBessAnd the same for the e-book with Jean-Michel, which only appeared in late 2013. And contains more chapters than Introduction to Monte Carlo methods with R. Incidentally, a reader recently pointed out to me the availability of a pirated version of The Bayesian Choice on a Saudi (religious) university website. And of a pirated version of Introducing Monte Carlo with R on a Saõ Paulo (Brazil) university website. This may be alas inevitable, given the diffusion by publishers of e-chapters that can be copied with no limitations…