Our former Dauphine Master student Théo Voldoire (now PhD-ing at Harvard), along with Nicolas Chopin, Guillaume Rateau, and Robin Ryder (now at Imperial), arXived a month ago a paper with title Saddlepoint Monte Carlo and its Application to Exact Ecological Inference, essentially the outcome of his Master thesis last summer. Nicolas came to present the paper at our Mostly MC seminar. The motivating example is about vote transfers (to surviving candidates for a second round, as in the French presidential and deputorial elections) based on results from polling stations across rounds, which equates filling a contingency table with known margins, exploiting multiple tools like characteristic functions, inverse Fourier transform, its Monte Carlo version, pseudo-marginal MCMC, tilting, exponential families, quasi Monte Carlo! Which also reminded me of the time Reuven Rubinstein was occasionally visiting Paris, defending the cross entropy approach. Among multiple questions raised by this original approach to an “old” problem, one may think of the model misspecification issue that political analysts would not fail to raise, namely that the transfer estimates are based on multinomial models, that all models are wrong, &tc. We discussed briefly about this during the seminar, the suggestion being a predictive check by cross validation. The talk also brought to mind highly probable applications to privacy, and possibly to capture recapture.
Archive for saddlepoint
Saddlepoint Monte Carlo and its application to vote transfers
Posted in Books, Statistics, University life with tags characteristic function, cross-entropy method, ecological models, exponential families, exponential tilting, French elections, French politics, marginalisation, presidential elections, pseudo-marginal MCMC, quasi-Monte Carlo, Reuven Rubinstein, saddlepoint on January 3, 2024 by xi'ananother easy Riddler
Posted in Books, Kids, R with tags optimisation, R, riddle, saddlepoint, The Riddler on January 31, 2020 by xi'an
A quick riddle from the Riddler
In a two-person game, Abigail and Zian both choose between a and z. Abigail win one point with probability .9 if they choose (a,a) and with probability 1 if they choose (a,z), and two points with probability .4 if they choose (z,z) and with probability .6 if they choose (z,a). Find the optimal probabilities δ and ς of choosing a for both Abigail and Zian when δ is known to Zian.
Since the average gain for Abigail is δ(1-.1ς)+2(1-δ)(.4+.2ς) the riddle sums up as solving the minmax problem
the solution in ς is either 0 or 1 depending on δ being smaller or larger than 12/22, which leads to this value as the expected gain. The saddlepoint is hardly visible in the above image. While ς is either 0 or 1 in the optimal setting, a constant choice of 1 or 0 would modify the optimal for δ except that Abigail must declare her value of δ!
