postdoctoral research positions at PariSanté

Thanks to the 2023-2029 ERC Synergy grant OCEAN (On intelligenCE And Networks: Synergistic research in Bayesian Statistics, Microeconomics and Computer Sciences), I am seeking one or two postdoctoral researchers with an interest in Bayesian federated learning, distributed MCMC, approximate Bayesian inference and computing, and data privacy.

The project is based at Université Paris Dauphine, on the new PariSanté Campus.  The postdocs will join the OCEAN teams of researchers directed by Éric Moulines and myself (Christian P Robert) to work on the above themes with multiple possibilities of focus from statistical theory, to Bayesian methodology, to decision theory, to algorithms, to medical applications. Collaborations with the OCEAN teams of researchers directed by Michael Jordan (Berkeley) and Gareth Roberts (Warwick) will further be encouraged and related travel will be supported.

Qualifications

The candidates should hold a doctorate in applied maths, statistics or machine learning, with demonstrated skills in Bayesian analysis, game theory, Monte Carlo methodology or numerical probability, an excellent record of publications in these domains, and an interest in working as part of an interdisciplinary international team. Scientific maturity and research autonomy are a must for applying. There is no deadline for the positions, which will be filled when a suitable candidate is selected.

Funding

Besides a 2 year postdoctoral contract at Université Paris Dauphine (with possible extension for another year), at a salary of 31K€ per year, the project will fund travel to OCEAN partners’ institutions (University of Warwick or University of Berkeley) and participation to yearly summer schools and conferences. Standard French university benefits are attached to the position and no teaching duty is involved, as per ERC rules.

The starting date of the postdoctoral positions is negotiable depending on the applicants’ availability.

Application Procedure

• To apply, please send the following entries in one pdf file to Christian Robert (bayesianstatistics@gmail.com).
• a letter of application,
• a CV,

Letters of recommendation are to be sent directly by their author.

Estimating means of bounded random variables by betting

Ian Waudby-Smith and Aaditya Ramdas are presenting next month a Read Paper to the Royal Statistical Society in London on constructing a conservative confidence interval on the mean of a bounded random variable. Here is an extended abstract from within the paper:

For each m ∈ [0, 1], we set up a “fair” multi-round game of statistician
against nature whose payoff rules are such that if the true mean happened
to equal m, then the statistician can neither gain nor lose wealth in
expectation (their wealth in the m-th game is a nonnegative martingale),
but if the mean is not m, then it is possible to bet smartly and make
money. Each round involves the statistician making a bet on the next
observation, nature revealing the observation and giving the appropriate
(positive or negative) payoff to the statistician. The statistician then plays
all these games (one for each m) in parallel, starting each with one unit of
wealth, and possibly using a different, adaptive, betting strategy in each.
The 1 − α confidence set at time t consists of all m 2 [0, 1] such that the
statistician’s money in the corresponding game has not crossed 1/α. The
true mean μ will be in this set with high probability.

I read the paper on the flight back from Venice and was impressed by its universality, especially for a non-asymptotic method, while finding the expository style somewhat unusual for Series B, with notions late into being defined if at all defined. As an aside, I also enjoyed the historical connection to Jean Ville‘s 1939 PhD thesis (examined by Borel, Fréchet—his advisor—and Garnier) on a critical examination of [von Mises’] Kollektive. (The story by Glenn Shafer of Ville’s life till the war is remarkable, with the de Beauvoir-Sartre couple making a surprising and rather unglorious appearance!). Himself inspired by a meeting with Wald while in Berlin. The paper remains quite allusive about Ville‘s contribution, though, while arguing about its advance respective to Ville’s work… The confidence intervals (and sequences) depend on a supermartingale construction of the form

which allows for a universal coverage guarantee of the derived intervals (and can optimised in λ). As I am getting confused by that point about the overall purpose of the analysis, besides providing an efficient confidence construction, and am lacking in background about martingales, betting, and sequential testing, I will not contribute to the discussion. Especially since ChatGPT cannot help me much, with its main “criticisms” (which I managed to receive while in Italy, despite the Italian Government banning the chabot!)

However, there are also some potential limitations and challenges to this approach. One limitation is that the accuracy of the method is dependent on the quality of the prior distribution used to set the odds. If the prior distribution is poorly chosen, the resulting estimates may be inaccurate. Additionally, the method may not work well for more complex or high-dimensional problems, where there may not be a clear and intuitive way to set up the betting framework.

and

Another potential consequence is that the use of a betting framework could raise ethical concerns. For example, if the bets are placed on sensitive or controversial topics, such as medical research or political outcomes, there may be concerns about the potential for manipulation or bias in the betting markets. Additionally, the use of betting as a method for scientific or policy decision-making may raise questions about the appropriate role of gambling in these contexts.

being totally off the radar… (No prior involved, no real-life consequence for betting, no gambling.)

bean bag win

A quick riddle from The Riddler, where a multiple step game sees a probability of a 3 point increase of .4 and a probability of a 1 point increase of .3 with a first strategy (A), versus a probability of a 3 point increase of .4 and a probability of a 1 point increase of .3 with a second strategy (B), and a sure miss third strategy (C). The goal is to optimise the probability of hitting exactly 3 points after 4 steps.

The optimal strategy is to follow A while the score is zero, C when the score is 3, and B otherwise. The corresponding winning probability is 0.8548, as checked by the following code

win=function(n=1,s=0){
  if(n==4)return((s==3)+.4*(!s)+.8*(s==2))
  else{return(max(c(
    .4*win(n+1,s+3)+.3*win(n+1,s+1)+.3*win(n+1,s),
    .1*win(n+1,s+3)+.8*win(n+1,s+1)+.1*win(n+1,s),
    win(n+1,s))))}}

asymmetric information

The Riddler of 16 October had the following puzzle:

Take a real number θ uniformly distributed over (0,100). Among three players, the winner is whoever guessed the closest price without going over θ. In the event all guesses exceeded θ, the contestant with the lowest (and therefore closest) guess is declared the winner. The second player knows the first player’s guess and the third player knows both other guesses. What is the optimal guess for the first player, assuming all players maximise their probability of winning?

Looking at the optimal solution z for the third player leads to six possible choices, depending on the connection between the other guesses, x and y. Which translates in the R code

topz=function(x,y){
  if((2*y>=x)&(y>=1-x))  z=y-.001
  if(max(4*y,1+y)<=2*x)  z=y+.001
  if((2*x<=1+y)&(x<=1-y))z=x+.001
  z}
  
third=function(x,y) ifelse(y<x,topz(x,y),topz(y,x))

For there, the optimal choice y for the second player follows and happens on a boundary of one of the six regions, which itself returns that the optimal choice for the first player is x=2/3, leading to equal chances of winning (although there is some uncertainty on the boundaries). It is thus feasible to beat the asymmetric information. The picture above was my attempt at representing the probabilities of gain for all three players, some of the six regions being clearly visible, with first axis being x and second being y [and z is one of x⁻,x⁺,y⁻,y⁺]. The R code is too pedestrian to be reproduced!

the biggest bluff [not a book review]

It came as a surprise to me that the book reviewed in the book review section of Nature of 25 June was a personal account of a professional poker player, The Biggest Bluff by Maria Konnikova.  (Surprise enough to write a blog entry!) As I see very little scientific impetus in studying the psychology of poker players and the associated decision making. Obviously, this is not a book review, but a review of the book review. (Although the NYT published a rather extensive extract of the book, from which I cannot detect anything deep from a game-theory viewpoint. Apart from the maybe-not-so-deep message that psychology matters a lot in poker…) Which does not bring much incentive for those uninterested (or worse) in money games like poker. Even when “a heap of Bayesian model-building [is] thrown in”, as the review mixes randomness and luck, while seeing the book as teaching the reader “how to play the game of life”, a type of self-improvement vending line one hardly expects to read in a scientific journal. (But again I have never understood the point in playing poker…)