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Bayesian Data Analysis [BDA3]

Thu, 2014-03-27 19:14

Andrew Gelman and his coauthors, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Don Rubin, have now published the latest edition of their book Bayesian Data Analysis. David and Aki are newcomers to the authors’ list, with an extended section on non-linear and non-parametric models. I have been asked by Sam Behseta to write a review of this new edition for JASA (since Sam is now the JASA book review editor). After wondering about my ability to produce an objective review (on the one hand, this is The Competition  to Bayesian Essentials!, on the other hand Andrew is a good friend spending the year with me in Paris), I decided to jump for it and write a most subjective review, with the help of Clara Grazian who was Andrew’s teaching assistant this year in Paris and maybe some of my Master students who took Andrew’s course. The second edition was reviewed in the September 2004 issue of JASA and we now stand ten years later with an even more impressive textbook. Which truly what Bayesian data analysis should be.

This edition has five parts, Fundamentals of Bayesian Inference, Fundamentals of Bayesian Data Analysis, Advanced Computation, Regression Models, and Non-linear and Non-parametric Models, plus three appendices. For a total of xiv+662 pages. And a weight of 2.9 pounds (1395g on my kitchen scale!) that makes it hard to carry around in the metro…. I took it to Warwick (and then Nottingham and Oxford and back to Paris) instead.

We could avoid the mathematical effort of checking the integrability of the posterior density (…) The result would clearly show the posterior contour drifting off toward infinity.” (p.111)

While I cannot go into a detailed reading of those 662 pages (!), I want to highlight a few gems. (I already wrote a detailed and critical analysis of Chapter 6 on model checking in that post.) The very first chapter provides all the necessary items for understanding Bayesian Data Analysis without getting bogged in propaganda or pseudo-philosophy. Then the other chapters of the first part unroll in a smooth way, cruising on the B highway… With the unique feature of introducing weakly informative priors (Sections 2.9 and 5.7), like the half-Cauchy distribution on scale parameters. It may not be completely clear how weak a weakly informative prior, but this novel notion is worth including in a textbook. Maybe a mild reproach at this stage: Chapter 5 on hierarchical models is too verbose for my taste, as it essentially focus on the hierarchical linear model. Of course, this is an essential chapter as it links exchangeability, the “atom” of Bayesian reasoning used by de Finetti, with hierarchical models. Still. Another comment on that chapter: it broaches on the topic of improper posteriors by suggesting to run a Markov chain that can exhibit improperness by enjoying an improper behaviour. When it happens as in the quote above, fine!, but there is no guarantee this is always the case! For instance, improperness may be due to regions near zero rather than infinity. And a last barb: there is a dense table (Table 5.4, p.124) that seems to run contrariwise to Andrew’s avowed dislike of tables. I could also object at the idea of a “true prior distribution” (p.128), or comment on the trivia that hierarchical chapters seem to attract rats (as I also included a rat example in the hierarchical Bayes chapter of Bayesian Choice and so does the BUGS Book! Hence, a conclusion that Bayesian textbooks are better be avoided by muriphobiacs…)

“Bayes factors do not work well for models that are inherently continuous (…) Because we emphasize continuous families of models rather than discrete choices, Bayes factors are rarely relevant in our approach to Bayesian statistics.” (p.183 & p.193)

Part II is about “the creative choices that are required, first to set up a Bayesian model in a complex problem, then to perform the model checking and confidence building that is typically necessary to make posterior inferences scientifically defensible” (p.139). It is certainly one of the strengths of the book that it allows for a critical look at models and tools that are rarely discussed in more theoretical Bayesian books. As detailed in my  earlier post on Chapter 6, model checking is strongly advocated, via posterior predictive checks and… posterior predictive p-values, which are at best empirical indicators that something could be wrong, definitely not that everything’s allright! Chapter 7 is the model comparison equivalent of Chapter 6, starting with the predictive density (aka the evidence or the marginal likelihood), but completely bypassing the Bayes factor for information criteria like the Watanabe-Akaike or widely available information criterion (WAIC), and advocating cross-validation, which is empirically satisfying but formally hard to integrate within a full Bayesian perspective. Chapter 8 is about data collection, sample surveys, randomization and related topics, another entry that is missing from most Bayesian textbooks, maybe not that surprising given the research topics of some of the authors. And Chapter 9 is the symmetric in that it focus on the post-modelling step of decision making.

(Second part of the review to appear on Monday, leaving readers the weekend to recover!)


Filed under: Books, Kids, R, Statistics, University life Tagged: Andrew Gelman, Bayesian data analysis, Bayesian model choice, Bayesian predictive, finite mixtures, graduate course, hierarchical Bayesian modelling, rats, STAN
Categories: Bayesian Bloggers

¼th i-like workshop in St. Anne’s College, Oxford

Wed, 2014-03-26 19:09

Due to my previous travelling to and from Nottingham for the seminar and back home early enough to avoid the dreary evening trains from Roissy airport (no luck there, even at 8pm, the RER train was not operating efficiently!, and no fast lane is planed prior to 2023…), I did not see many talks at the i-like workshop. About ¼th, roughly… I even missed the poster session (and the most attractive title of Lazy ABC by Dennis Prangle) thanks to another dreary train ride from Derby to Oxford.

As it happened I had already heard or read parts of the talks in the Friday morning session, but this made understanding them better. As in Banff, Paul Fearnhead‘s talk on reparameterisations for pMCMC on hidden Markov models opened a wide door to possible experiments on those algorithms. The examples in the talk were mostly of the parameter duplication type, somewhat creating unidentifiability to decrease correlation, but I also wondered at the possibility of introducing frequent replicas of the hidden chain in order to fight degeneracy. Then Sumeet Singh gave a talk on the convergence properties of noisy ABC for approximate MLE. Although I had read some of the papers behind the talk, it made me realise how keeping balls around each observation in the ABC acceptance step was not leading to extinction as the number of observations increased. (Summet also had a good line with his ABCDE algorithm, standing for ABC done exactly!) Anthony Lee covered his joint work with Krys Łatuszyński on the ergodicity conditions on the ABC-MCMC algorithm, the only positive case being the 1-hit algorithm as discussed in an earlier post. This result will hopefully get more publicity, as I frequently read that increasing the number of pseudo-samples has no clear impact on the ABC approximation. Krys Łatuszyński concluded the morning with an aggregate of the various results he and his co-authors had obtained on the fascinating Bernoulli factory. Including constructive derivations.

After a few discussions on and around research topics, it was too soon time to take advantage of the grand finale of a March shower to walk from St. Anne’s College to Oxford Station, in order to start the trip back home. I was lucky enough to find a seat and could start experimenting in R the new idea my trip to Nottingham had raised! While discussing a wee bit with my neighbour, a delightful old lady from the New Forest travelling to Coventry, recovering from a brain seizure, wondering about my LaTeX code syntax despite the tiny fonts, and who most suddenly popped a small screen from her bag to start playing Candy Crush!, apologizing all the same. The overall trip was just long enough for my R code to validate this idea of mine, making this week in England quite a profitable one!!! 


Filed under: pictures, Statistics, Travel, University life Tagged: ABC-MCMC, ABC-SMC, Bernouilli factory, Derby, HMM, i-like, Nottingham, pMCMC, St. Anne's College, University of Oxford, University of Warwick
Categories: Bayesian Bloggers

métro static

Wed, 2014-03-26 05:19

[heard in the métro this morning]

“…les équations à deux inconnues ça va encore, mais à trois inconnues, c’est trop dur!”

["...systems of equations with two unknowns are still ok, but with three variables it is too hard!"]


Filed under: Kids, Travel Tagged: high school mathematics, métro, Paris
Categories: Bayesian Bloggers

Seminar in Nottingham

Tue, 2014-03-25 19:14

Last Thursday, I gave a seminar in Nottingham, the true birthplace of the Gibbs sampler!, and I had a quite enjoyable half-day of scientific discussions in the Department of Statistics, with a fine evening tasting a local ale in the oldest (?) inn in England (Ye Olde Trip to Jerusalem) and sampling Indian dishes at 4550 Miles [plus or minus epsilon, since the genuine distance is 4200 miles) from Dehli, plus a short morning run on the very green campus. In particular, I discussed with Theo Kypraios and Simon Preston parallel ABC and their recent paper in Statistics and Computing, their use of the splitting technique of Neiswanger et al. I discussed earlier but intended here towards a better ABC approximation since (a) each term in the product could correspond to a single observation and (b) hence no summary statistic was needed and a zero tolerance could be envisioned. The  paper discusses how to handle samples from terms in a product of densities, either by a Gaussian approximation or by a product of kernel estimates. And mentions connections with expectation propagation (EP), albeit not at the ABC level.

A minor idea that came to me during this discussion was to check whether or not a reparameterisation towards a uniform prior was a good idea: the plus of a uniform prior was that the power discussion was irrelevant, making both versions of the parallel MCMC algorithm coincide. The minus was not the computational issue since most priors are from standard families, with easily invertible cdfs, but rather why this was supposed to make a difference. When writing this on the train to Oxford, I started wondering as an ABC implementation is impervious to this reparameterisation. Indeed, simulate θ from π and pseudo-data given θ versus simulate μ from uniform and pseudo-data given T(μ) does not make a difference in the simulated pseudo-sample, hence in the distance selected θ’s, and still in one case the power does not matter while in the other case it does..!

Another discussion I had during my visit led me to conclude a bit hastily that a thesis topic I had suggested to a new PhD student a few months ago had already been considered locally and earlier, although it ended up as a different, more computational than conceptual, perspective (so not all was lost for my student!). In a wider discussion around lunch, we also had an interesting foray on possible alternatives to Bayes factors and their shortcomings, which was a nice preparation to my seminar on giving up posterior probabilities for posterior error estimates. And an opportunity to mention the arXival of a proper scoring rules paper by Phil Dawid, Monica Musio and Laura Ventura, related with the one I had blogged about after the Padova workshop. And then again about a connected paper with Steve Fienberg. This lunch discussion even included some (mild) debate about Murray Aitkin’s integrated likelihood.

As a completely irrelevant aside, this trip gave me the opportunity of a “pilgrimage” to Birmingham New Street train station, 38 years after “landing” for the first time in Britain! And to experience a fresco the multiple delays and apologies of East Midlands trains (“we’re sorry we had to wait for this oil train in York”, “we have lost more time since B’ham”, “running a 37 minutes delay now”, “we apologize for the delay, due to trespassing”, …), the only positive side being that delayed trains made delayed connections possible!


Filed under: Kids, pictures, Running, Statistics, Travel, University life Tagged: 4550 Miles from Dehli, English train, Gibbs sampler, Sherwood Forest, University of Nottingham, Ye Olde Trip to Jerusalem
Categories: Bayesian Bloggers

MCMC on zero measure sets

Sun, 2014-03-23 19:14

Simulating a bivariate normal under the constraint (or conditional to the fact) that x²-y²=1 (a non-linear zero measure curve in the 2-dimensional Euclidean space) is not that easy: if running a random walk along that curve (by running a random walk on y and deducing x as x²=y²+1 and accepting with a Metropolis-Hastings ratio based on the bivariate normal density), the outcome differs from the target predicted by a change of variable and the proper derivation of the conditional. The above graph resulting from the R code below illustrates the discrepancy!

targ=function(y){ exp(-y^2)/(1.52*sqrt(1+y^2))} T=10^5 Eps=3 ys=xs=rep(runif(1),T) xs[1]=sqrt(1+ys[1]^2) for (t in 2:T){ propy=runif(1,-Eps,Eps)+ys[t-1] propx=sqrt(1+propy^2) ace=(runif(1)<(dnorm(propy)*dnorm(propx))/ (dnorm(ys[t-1])*dnorm(xs[t-1]))) if (ace){ ys[t]=propy;xs[t]=propx }else{ ys[t]=ys[t-1];xs[t]=xs[t-1]}}

If instead we add the proper Jacobian as in

ace=(runif(1)<(dnorm(propy)*dnorm(propx)/propx)/ (dnorm(ys[t-1])*dnorm(xs[t-1])/xs[t-1]))

the fit is there. My open question is how to make this derivation generic, i.e. without requiring the (dreaded) computation of the (dreadful) Jacobian.


Filed under: R, Statistics Tagged: conditional density, Hastings-Metropolis sampler, Jacobian, MCMC, measure theory, measure zero set, projected measure, random walk
Categories: Bayesian Bloggers

Bared Blade [book review]

Sat, 2014-03-22 19:14

As mentioned in my recent review of Broken Blade by Kelly McCullough, I had already ordered the sequel Bared Blade. And I read this second volume within a few days. Conditional on enjoying fantasy-world detective stories with supernatural beings popping in (or out) at the most convenient times, this volume is indeed very pleasant with a proper whodunnit, a fairly irrelevant McGuffin, a couple of dryads (that actually turn into…well, no spoiler!), several false trails, a radical variation on the “good cop-bad cop” duo, and the compulsory climactic reversal of fortune at the very end (not a spoiler since it is the same in every novel!). Once again, a very light read, to the point of being almost ethereal, with no pretence at depth or epics or myth, but rather funny and guaranteed 100% free of living-deads, which is a relief. I actually found this volume better than the first one, which is a rarity if you have had enough spare time to read thru my non-scientific book reviews, I am thus looking forward to the next break when I can skip through my next volume of Kelly McCullough, Crossed Blades. (And I hope I will not get more crossed with that one than I was bored with the current volume!)


Filed under: Books Tagged: barren blade, book reviews, broken blade, crossed blades, heroic fantasy, Kelly McCullough, magics
Categories: Bayesian Bloggers

to keep the werewolves at Bayes…

Sat, 2014-03-22 12:09


Filed under: Kids, pictures, University life Tagged: mug, puppies, werewolf
Categories: Bayesian Bloggers

Le Monde puzzle [#857]

Fri, 2014-03-21 19:14

A rather bland case of Le Monde mathematical puzzle :

Two positive integers x and y are turned into s=x+y and p=xy. If Sarah and Primrose are given S and P, respectively, how can the following dialogue happen?

  • I am sure you cannot find my number
  • Now you told me that, I can, it is 46.

and what are the values of x and y?

In the original version, it was unclear whether or not each person knew she had the sum or the product. Anyway, the first person in the dialogue has to be Sarah, since a product p equal to a prime integer would lead Primrose to figure out x=1 and hence s=p+1. (Conversely, having observed the sum s cannot lead to deduce x and y.) This means x+y-1 is not a prime integer. Now the deduction of Primrose that the sum is 46 implies p can be decomposed only once in a product such that x+y-1 is not a prime integer. If p=45, this is the case since 45=15×3 and 45=5×9 lead to 15+3-1=17 and 5+9-1=13, while 45=45×1 leads to 45+1-1=45.  Other solutions fail, as demonstrated by the R code:

> for (x in 1:23){ + fact=c(1,prime.factor(x*(46-x))) + u=0; + for (i in 1:(length(fact)-1)) + u=u+1-is.prim(prod(fact[1:i])+prod(fact[-(1:i)])-1) + if (u==1) print(x)} [1] 1

Busser and Cohen argue much more wisely in their solution that any non-prime product p other than 45 would lead to p+1 as an acceptable sum s, hence would prevent Primrose from guessing s.


Filed under: Books, Kids, R Tagged: is.prim, Le Monde, mathematical puzzle, number theory, prime factor decomposition, prime.factor, R, schoolmath
Categories: Bayesian Bloggers

Pre-processing for approximate Bayesian computation in image analysis

Thu, 2014-03-20 19:14

With Matt Moores and Kerrie Mengersen, from QUT, we wrote this short paper just in time for the MCMSki IV Special Issue of Statistics & Computing. And arXived it, as well. The global idea is to cut down on the cost of running an ABC experiment by removing the simulation of a humongous state-space vector, as in Potts and hidden Potts model, and replacing it by an approximate simulation of the 1-d sufficient (summary) statistics. In that case, we used a division of the 1-d parameter interval to simulate the distribution of the sufficient statistic for each of those parameter values and to compute the expectation and variance of the sufficient statistic. Then the conditional distribution of the sufficient statistic is approximated by a Gaussian with these two parameters. And those Gaussian approximations substitute for the true distributions within an ABC-SMC algorithm à la Del Moral, Doucet and Jasra (2012).

Across 20 125 × 125 pixels simulated images, Matt’s algorithm took an average of 21 minutes per image for between 39 and 70 SMC iterations, while resorting to pseudo-data and deriving the genuine sufficient statistic took an average of 46.5 hours for 44 to 85 SMC iterations. On a realistic Landsat image, with a total of 978,380 pixels, the precomputation of the mapping function took 50 minutes, while the total CPU time on 16 parallel threads was 10 hours 38 minutes. By comparison, it took 97 hours for 10,000 MCMC iterations on this image, with a poor effective sample size of 390 values. Regular SMC-ABC algorithms cannot handle this scale: It takes 89 hours to perform a single SMC iteration! (Note that path sampling also operates in this framework, thanks to the same precomputation: in that case it took 2.5 hours for 10⁵ iterations, with an effective sample size of 10⁴…)

Since my student’s paper on Seaman et al (2012) got promptly rejected by TAS for quoting too extensively from my post, we decided to include me as an extra author and submitted the paper to this special issue as well.


Filed under: R, Statistics, University life Tagged: ABC, Chamonix, image processing, MCMC, MCMSki IV, Monte Carlo Statistical Methods, path sampling, Potts model, QUT, simulation, SMC-ABC, Statistics and Computing, sufficient statistics, summary statistics
Categories: Bayesian Bloggers

fine-sliced Poisson [a.k.a. sashimi]

Wed, 2014-03-19 19:14

As my student Kévin Guimard had not mailed me his own Poisson slice sampler of a Poisson distribution, I could not tell why the code was not working! My earlier post prompted him to do so and a somewhat optimised version is given below:

nsim = 10^4 lambda = 6 max.factorial = function(x,u){ k = x parf=1 while (parf*u<1){ k = k + 1 parf = parf * k } k = k - (parf*u>1) return (k) } x = rep(floor(lambda), nsim) for (t in 2:nsim){ v1 = ceiling((log(runif(1))/log(lambda))+x[t-1]) ranj=max(0,v1):max.factorial(x[t-1],runif(1)) x[t]=sample(ranj,size=1) } barplot(as.vector(rbind( table(x)/length(x),dpois(min(x):max(x), lambda))),col=c("sienna","gold"))

As you can easily check by running the code, it does not work. My student actually majored my MCMC class and he spent quite a while pondering why the code was not working. I did ponder as well for a part of a morning in Warwick, removing causes for exponential or factorial overflows (hence the shape of the code), but not eliciting the issue… (This now sounds like lethal fugu sashimi! ) Before reading any further, can you spot the problem?!

The corrected R code is as follows:

x = rep(lambda, nsim) for (t in 2:nsim){ v1=ceiling((log(runif(1))/log(lambda))+x[t-1]) ranj=max(0,v1):max.factorial(x[t-1],runif(1)) if (length(ranj)>1){ x[t] = sample(ranj, size = 1) }else{ x[t]=ranj} }

The culprit is thus the R function sample which simply does not understand Dirac masses and the basics of probability! When running

> sample(150:150,1) [1] 23

you can clearly see where the problem stands…! Well-documented issue with sample that already caused me woes… Another interesting thing about this slice sampler is that it is awfully slow in exploring the tails. And to converge to the centre from the tails. This is not very pronounced in the above graph with a mean of 6. Moving to 50 makes it more apparent:

This is due to the poor mixing of the chain, as shown by the raw sequence below, which strives to achieve a single cycle out of 10⁵ iterations! In any case, thanks to Kévin for an interesting morning!


Filed under: Books, Kids, pictures, R, Running, Statistics, University life Tagged: convergence assessment, ENSAE, Gibbs sampling, Monte Carlo Statistical Methods, Poisson distribution, R, sample, sampling from an atomic population, slice sampling, slow convergence
Categories: Bayesian Bloggers

The 8th Rimini Bayesian Econometrics Workshop

Wed, 2014-03-19 12:56

Just reporting the announcement for the 8th Rimini Bayesian Econometrics Workshop, June 9-10, 2014, in the very pleasant beach resort of Rimini, workshop that I attended a few years ago:

This Workshop is organized by the Rimini Centre for Economic Analysis (RCEA) and will be run within the  RIMINI CONFERENCE in ECONOMICS and FINANCE RCEF-2014 

Call for papers:  Authors should submit an extended abstract of up to 500 words by Monday 31st of March 2014. Please include with the submission JEL classification codes for the paper, keywords as well as JEL classification codes of the author(s) specialization field(s). Complete papers may be submitted but the extended abstract is required. In case of more than one author, please note the corresponding author. Proposals for sessions, consisting of three papers, are particularly welcome. If you are interested in submitting a session please send the session topic, paper titles and names of authors and arrange for the abstracts to be sent to the addresses provided below.


Filed under: Running, Statistics, Travel, University life Tagged: Bayesian econometrics, Italy, Rimini
Categories: Bayesian Bloggers

Annual Review of Statistics and its Application, vol. 1

Tue, 2014-03-18 19:14

Got this book in my mailbox the other day. It is somewhat a unique object in that it is a high quality book with solid bindings, glossy paper, colours on every page and a nice layout… And even my name (as well as all other authors’) on the cover!

I am somewhat surprised there are still books “like that” (private joke for Sempé‘s aficionadi) as I wonder at which niche “they” are aiming at. What is basically unclear to me is the nature and business model of the “non-profit” Annual Reviews. Presumably selling the entire collection of Annual Reviews for $9312 helps in making the scheme “non-profitable”, at $339 for this single volume. If just a few libraries buy them. Especially when authors get no perks other than a single copy of the book. (To be completely fair, the book is available on-line for free for the first year.) So, in retrospect, (a) I should have been more careful in checking the fundamentals of this publication, as I foolishly assumed when contacted that it was a new journal (!), and (b) I should also have taken better advantage of the editing and printing facilities, using margins for highlights and comments, adding markers on important bibliographical references, and including vignettes as those Sam Behesta suggested for my CHANCE book reviews… (It did not come at the best of times, but still I should have tried harder.)


Filed under: Books, Statistics
Categories: Bayesian Bloggers

sliced Poisson

Mon, 2014-03-17 19:14

One of my students complained that his slice sampler of a Poisson distribution was not working when following the instructions in Monte Carlo Statistical Methods (Exercise 8.5). This puzzled me during my early morning run and I checked on my way back, even before attacking the fresh baguette I had brought from the bakery… The following R code is the check. And it does work! As the comparison above shows…

slice=function(el,u){ #generate uniform over finite integer set mode=floor(lambda) sli=mode   x=mode+1   while (dpois(x,el)>u){       sli=c(sli,x);x=x+1}   x=mode-1   while (dpois(x,el)>u){    sli=c(sli,x);x=x-1}   return(sample(sli,1))} #example T=10^4 lambda=2.414 x=rep(floor(lambda),T) for (t in 2:T) x[t]=slice(lambda,runif(1)*dpois(x[t-1],lambda)) barplot(as.vector(rbind( table(x)/length(x),dpois(0:max(x), lambda))),col=c("sienna","gold"))
Filed under: Books, Kids, pictures, R, Running, Statistics, University life Tagged: ENSAE, Monte Carlo Statistical Methods, Poisson distribution, R, slice sampling
Categories: Bayesian Bloggers

misty dawn [#3]

Mon, 2014-03-17 12:12
Categories: Bayesian Bloggers

Approximate Bayesian model choice

Sun, 2014-03-16 19:14

The above is the running head of the arXived paper with full title “Implications of  uniformly distributed, empirically informed priors for phylogeographical model selection: A reply to Hickerson et al.” by Oaks, Linkem and Sukuraman. That I (again) read in the plane to Montréal (third one in this series!, and last because I also watched the Japanese psycho-thriller Midsummer’s Equation featuring a physicist turned detective in one of many TV episodes. I just found some common features with The Devotion of Suspect X, only to discover now that the book has been turned into another episode in the series.)

“Here we demonstrate that the approach of Hickerson et al. (2014) is dangerous in the sense that the empirically-derived priors often exclude from consideration the true values of the models’ parameters. On a more fundamental level, we question the value of adopting an empirical Bayesian stance for this model-choice problem, because it can mislead model posterior probabilities, which are inherently measures of belief in the models after prior knowledge is updated by the data.”

This paper actually is a reply to Hickerson et al. (2014, Evolution), which is itself a reply to an earlier paper by Oaks et al. (2013, Evolution). [Warning: I did not check those earlier references!] The authors object to the use of “narrow, empirically informed uniform priors” for the reason reproduced in the above quote. In connection with the msBayes of Huang et al. (2011, BMC Bioinformatics). The discussion is less about ABC used for model choice and posterior probabilities of models and more about the impact of vague priors, Oaks et al. (2013) arguing that this leads to a bias towards models with less parameters, a “statistical issue” in their words, while Hickerson et al. (2014) think this is due to msBayes way of selecting models and their parameters at random.

“…it is difficult to choose a uniformly distributed prior on divergence times that is broad enough to confidently contain the true values of parameters while being narrow enough to avoid spurious support of models with less parameter space.”

So quite an interesting debate that takes us in fine far away from the usual worries about ABC model choice! We are more at the level empirical versus natural Bayes, seen in the literature of the 80′s. (The meaning of empirical Bayes is not that clear in the early pages as the authors seem to involve any method using the data “twice”.) I actually do not remember reading papers about the formal properties of model choice done through classical empirical Bayes techniques. Except the special case of Aitkin’s (1991,2009) integrated likelihood. Which is essentially the analysis performed on the coin toy example (p.7)

“…models with more divergence parameters will be forced to integrate over much greater parameter space, all with equal prior density, and much of it with low likelihood.”

The above argument is an interesting rephrasing of Lindley’s paradox, which I cannot dispute, but of course it does not solve the fundamental issue of how to choose the prior away from vague uniform priors… I also like the quote “the estimated posterior probability of a model is a single value (rather than a distribution) lacking a measure of posterior uncertainty” as this is an issue on which we are currently working. I fully agree with the statement and we think an alternative assessment to posterior probabilities could be more appropriate for model selection in ABC settings (paper soon to come, hopefully!).


Filed under: Books, R, Statistics, Travel, University life Tagged: ABC, ABC model selection, 真夏方程式, Detective Galileo, empirical Bayes methods, integrated likelihood, Jeffreys-Lindley paradox, model posterior probabilities, Montréal, vague priors
Categories: Bayesian Bloggers

ISBA 2016 in Banff???

Sat, 2014-03-15 19:14

Scott Schmidler, Steve Scott and myself just submitted a proposal for holding the next World ISBA Conference in 2016 in Banff, Canada! After enjoying the superb environment of the Advanced in Scalable Bayesian computation workshop last week, we thought it would be worth a try as a potential location for the next meeting, esp. when considering the superlative infrastructure of the Banff Centre (meaning we really do not have to be local to be local organisers!), the very reasonable rates for renting the site and securing two hundred rooms, the potential for a special collaboration with BIRS, the scarcity of alternative proposals (as far as I can fathom) and the ultimate mountain environment… I remember fondly the IMS annual meeting of 2002 there,  with a great special lecture by Hans Künsch and, exceptionally, an RSS Read Paper by Steve Brooks, Paulo Guidici and Gareth Roberts.  (Not mentioning en exhilarating solo scramble up Mount Temple and another one with Arnaud Guillin up the chimneys of Mount Edith!)  Since the deadline was this Saturday, March 15, we should hear pretty soon if we are successful in this bid. (Good luck to our Scottish friends from Edinburgh for their bid for holding ISBA 2018! Moving from the feet of Mount Rundle [above] to the feet of Arthur’s Seat would make for a great transition.)


Filed under: Mountains, pictures, Statistics, Travel, University life Tagged: Alberta, Arthur's Seat, Banff, Banff Centre, Canada, Canadian Rockies, Edinburgh, ISBA, ISBA 2016, ISBA 2018, Mount Rundle, Mount Temple, Scotland
Categories: Bayesian Bloggers

Clockers [book review]

Fri, 2014-03-14 19:14

Throughout my recent trip to Canada, I read bits and pieces of Clockers by Richard Price and I finished reading it last Sunday. It is an impressive piece of literature and I am surprised I was not aware of its existence until amazon.com suggested it to me (as I was checking for recent books by another Richard, Richard Morgan!). Guessing from the summary it could be of interest and from comments it was sort of a classic, I ordered it more or less on a whim (given a comfortable balance on my amazon.com account, thanks to ‘Og’s readers!) It took me a few pages to realise the plot was deeply set in the 1990′s, not only because this was the high of the crack epidemics, but also since the characters (drug dealers and policemen) therein are all using beepers, instead of cellphones, and street phone booths).

“It’s like a math problem. Juan got whacked at point X, he drove away losing blood at the rate of a pint every ninety seconds. He was driving forty-five miles an hour and he bought the farm two miles inside the tunnel (…) So for ten points, [who] in what New Jersey town did Juan?” Clockers (p.272)

The plot of Clockers is vaguely a detective story as an aging and depressed homicide officer, Rosso, hunts the murderer of a drug dealer, being convinced from the start that the self-declared murderer Victor did not do it. In parallel, and somewhat more closely, the book follows the miserable plight and thoughts and desires of Victor’s brother, Strike, who is head of a local crack dealing network, under the domination of the charismatic and berserk Rodney Little… But the resolution of the crime matters very little, much less than the exposure of the deadly economics of the drug traffic in inner cities (years before Freakonomics!), of the constant fight of single mothers to bring food and structure to their dysfunctional families, to the widespread recourse to moonlighting, and above all to the almost physical impossibility to escape one’s environment (even for smart and decent kids like Victor and, paradoxically enough, the drug-dealing Strike) by lack of prospect and exposure to anything or anywhere else, as well as social pressure, early pregnancies and gang-related micro-partitioning of cities.

When I mentioned Clockers to Andrew, he told me that he also liked it very much but that the characters were not quite “real”. I somewhat agree in that, while the economics, the sociology and the practice of drug-dealing sound very accurately reproduced (for all I know!), the characters are more caricaturesque or picturesque than natural. The stomach disease of Strike sounds too much like an allegory of both his schizophrenic split between running the drug trade and looking for a definitive quit, while the sacrifice of his brother makes little sense, except as a form either of suicide or of escape from an environment he can no longer stand. What is most surprising is that Richard Price (just like Michael Crichton) is  a practised screenwriter (who collaborated to Spike Lee’s 1995 Clockers). So he knows how to run an efficient story with convincing characters and plot(s). Hence my little theory of a picaresque novel… (Here is Jim Shepard’s enthusiastic review of Clockers. With the definitely accurate title of “Sympathy for the dealer”.)


Filed under: Books, Travel Tagged: Amazon, Clockers, crack epidemics, drug dealers, Freakonomics, Jim Shepard, New Jersey, Richard Price, Spike Lee, The New York Times
Categories: Bayesian Bloggers

misty dawn

Fri, 2014-03-14 05:56
Categories: Bayesian Bloggers