Archive for the University life Category

the philosophical importance of Stein’s paradox

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , on November 30, 2015 by xi'an

I recently came across this paper written by three philosophers of Science, attempting to set the Stein paradox in a philosophical light. Given my past involvement, I was obviously interested about which new perspective could be proposed, close to sixty years after Stein (1956). Paper that we should actually celebrate next year! However, when reading the document, I did not find a significantly innovative approach to the phenomenon…

The paper does not start in the best possible light since it seems to justify the use of a sample mean through maximum likelihood estimation, which only is the case for a limited number of probability distributions (including the Normal distribution, which may be an implicit assumption). For instance, when the data is Student’s t, the MLE is not the sample mean, no matter how shocking that might sounds! (And while this is a minor issue, results about the Stein effect taking place in non-normal settings appear much earlier than 1998. And earlier than in my dissertation. See, e.g., Berger and Bock (1975). Or in Brandwein and Strawderman (1978).)

While the linear regression explanation for the Stein effect is already exposed in Steve Stigler’s Neyman Lecture, I still have difficulties with the argument in that for instance we do not know the value of the parameter, which makes the regression and the inverse regression of parameter means over Gaussian observations mere concepts and nothing practical. (Except for the interesting result that two observations make both regressions coincide.) And it does not seem at all intuitive (to me) that imposing a constraint should improve the efficiency of a maximisation program… Continue reading

superintelligence [book review]

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on November 28, 2015 by xi'an

“The first ultraintelligent machine is the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control.” I.J. Good

I saw the nice cover of Superintelligence: paths, dangers, strategies by Nick Bostrom [owling at me!] at the OUP booth at JSM this summer—nice owl cover that comes will a little philosophical fable at the beginning about sparrows—and, after reading an in-depth review [in English] by Olle Häggström, on Häggström hävdar, asked OUP for a review copy. Which they sent immediately. The reason why I got (so) interested in the book is that I am quite surprised at the level of alertness about the dangers of artificial intelligence (or computer intelligence) taking over. As reported in an earlier blog, and with no expertise whatsoever in the field, I was not and am not convinced that the uncontrolled and exponential rise of non-human or non-completely human intelligences is the number One entry in Doom Day scenarios. (As made clear by Radford Neal and Corey Yanovsky in their comments, I know nothing worth reporting about those issues, but remain presumably irrationally more concerned about climate change and/or a return to barbarity than by the incoming reign of the machines.) Thus, having no competence in the least in either intelligence (!), artificial or human, or in philosophy and ethics, the following comments on the book only reflect my neophyte’s reactions. Which means the following rant should be mostly ignored! Except maybe on a rainy day like today…

“The ideal is that of the perfect Bayesian agent, one that makes probabilistically optimal use of available information.  This idea is unattainable (…) Accordingly, one can view artificial intelligence as a quest to find shortcuts…” (p.9)

Overall, the book stands much more at a philosophical and exploratory level than at attempting any engineering or technical assessment. The graphs found within are sketches rather than outputs of carefully estimated physical processes. There is thus hardly any indication how those super AIs could be coded towards super abilities to produce paper clips (but why on Earth would we need paper clips in a world dominated by AIs?!) or to involve all resources from an entire galaxy to explore even farther. The author envisions (mostly catastrophic) scenarios that require some suspension of belief and after a while I decided to read the book mostly as a higher form of science fiction, from which a series of lower form science fiction books could easily be constructed! Some passages reminded me quite forcibly of Philip K. Dick, less of electric sheep &tc. than of Ubik, where a superpowerful AI(s) turn humans into jar brains satisfied (or ensnared) with simulated virtual realities. Much less of Asimov’s novels as robots are hardly mentioned. And the third laws of robotics dismissed as ridiculously too simplistic (and too human). Continue reading

The Richard Price Society

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , on November 26, 2015 by xi'an

As an item of news coming to me via ISBA News, I learned of the Richard Price Society and of its endeavour to lobby for the Welsh government to purchase Richard Price‘s birthplace as an historical landmark. As discussed in a previous post, Price contributed so much to Bayes’ paper that one may wonder who made the major contribution. While I am not very much inclined in turning old buildings into museums, feel free to contact the Richard Price Society to support this action! Or to sign the petition there. Which I cannot resist but  reproduce in Welsh:

Datblygwch Fferm Tynton yn Ganolfan Ymwelwyr a Gwybodaeth

​Rydym yn galw ar Lywodraeth Cymru i gydnabod cyfraniad pwysig Dr Richard Price nid yn unig i’r Oes Oleuedig yn y ddeunawfed ganrif, ond hefyd i’r broses o greu’r byd modern yr ydym yn byw ynddo heddiw, a datblygu ei fan geni a chartref ei blentyndod yn ganolfan wybodaeth i ymwelwyr lle gall pobl o bob cenedl ac oed ddarganfod sut mae ei gyfraniadau sylweddol i ddiwinyddiaeth, mathemateg ac athroniaeth wedi dylanwadu ar y byd modern.

pseudo slice sampling

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

The workshop in Warwick last week made me aware of (yet) another arXiv posting I had missed: Pseudo-marginal slice sampling by Iain Murray and Matthew Graham. The idea is to mix the pseudo-marginal approach of Andrieu and Roberts (2009) with a noisy slice sampling scheme à la Neal (2003). The auxiliary random variable u used in the (pseudo-marginal) unbiased estimator of the target I(θ), Î(θ,u), and with distribution q(u) is merged with the random variable of interest so that the joint is


and a Metropolis-Hastings proposal on that target simulating from k(θ,θ’)q(u’) [meaning the auxiliary is simulated independently] recovers the pseudo-marginal Metropolis-Hastings ratio


(which is a nice alternative proof that the method works!). The novel idea in the paper is that the proposal on the auxiliary u can be of a different form, while remaining manageable. For instance, as a two-block Gibbs sampler. Or an elliptical slice sampler for the u component. The argument being that an independent update of u may lead the joint chain to get stuck. Among the illustrations in the paper, an Ising model (with no phase transition issue?) and a Gaussian process applied to the Pima Indian data set (despite a recent prohibition!). From the final discussion, I gather that the modification should be applicable to every (?) case when a pseudo-marginal approach is available, since the auxiliary distribution q(u) is treated as a black box. Quite an interesting read and proposal!

a programming bug with weird consequences

Posted in Kids, pictures, R, Statistics, University life with tags , , , , , , on November 25, 2015 by xi'an

One student of mine coded by mistake an independent Metropolis-Hastings algorithm with too small a variance in the proposal when compared with the target variance. Here is the R code of this implementation:

#target is N(0,1)
#proposal is N(0,.01)
for (t in 2:T){
  if (logu[t]>ratav){

It produces outputs of the following shape
smalvarwhich is quite amazing because of the small variance. The reason for the lengthy freezes of the chain is the occurrence with positive probability of realisations from the proposal with very small proposal density values, as they induce very small Metropolis-Hastings acceptance probabilities and are almost “impossible” to leave. This is due to the lack of control of the target, which is flat over the domain of the proposal for all practical purposes. Obviously, in such a setting, the outcome is unrelated with the N(0,1) target!

It is also unrelated with the normal proposal in that switching to a t distribution with 3 degrees of freedom produces a similar outcome:

It is only when using a Cauchy proposal that the pattern vanishes:

multiple importance sampling

Posted in Books, Statistics, University life with tags , , , , , , , , on November 20, 2015 by xi'an

“Within this unified context, it is possible to interpret that all the MIS algorithms draw samples from a equal-weighted mixture distribution obtained from the set of available proposal pdfs.”

In a very special (important?!) week for importance sampling!, Elvira et al. arXived a paper about generalized multiple importance sampling. The setting is the same as in earlier papers by Veach and Gibas (1995) or Owen and Zhou (2000) [and in our AMIS paper], namely a collection of importance functions and of simulations from those functions. However, there is no adaptivity for the construction of the importance functions and no Markov (MCMC) dependence on the generation of the simulations.

“One of the goals of this paper is to provide the practitioner with solid theoretical results about the superiority of some specific MIS schemes.”

One first part deals with the fact that a random point taken from the conjunction of those samples is distributed from the equiweighted mixture. Which was a fact I had much appreciated when reading Owen and Zhou (2000). From there, the authors discuss the various choices of importance weighting. Meaning the different degrees of Rao-Blackwellisation that can be applied to the sample. As we discovered in our population Monte Carlo research [which is well-referred within this paper], conditioning too much leads to useless adaptivity. Again a sort of epiphany for me, in that a whole family of importance functions could be used for the same target expectation and the very same simulated value: it all depends on the degree of conditioning employed for the construction of the importance function. To get around the annoying fact that self-normalised estimators are never unbiased, the authors borrow Liu’s (2000) notion of proper importance sampling estimators, where the ratio of the expectations is returning the right quantity. (Which amounts to recover the correct normalising constant(s), I believe.) They then introduce five (5!) different possible importance weights that all produce proper estimators. However, those weights correspond to different sampling schemes, so do not apply to the same sample. In other words, they are not recycling weights as in AMIS. And do not cover the adaptive cases where the weights and parameters of the different proposals change along iterations. Unsurprisingly, the smallest variance estimator is the one based on sampling without replacement and an importance weight made of the entire mixture. But this result does not apply for the self-normalised version, whose variance remains intractable.

I find this survey of existing and non-existing multiple importance methods quite relevant and a must-read for my students (and beyond!). My reservations (for reservations there must be!) are that the study stops short of pushing further the optimisation. Indeed, the available importance functions are not equivalent in terms of the target and hence weighting them equally is sub-efficient. The adaptive part of the paper broaches upon this issue but does not conclude.

OxWaSP seminar

Posted in Kids, Statistics, University life on November 19, 2015 by xi'an

Zeeman Building, University of WarwickThis Friday, I give a seminar talk on Rao-Blackwellisation for MCMC methods to the new students of the Oxford-Warwick Statistical Programme (OxWaSP). Here are my slides, working on three papers of mine on the topic, with George Casella  (1996), Randal Douc (2011), and Marco Banterle, Clara Grazian and Anthony Lee (2015).


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