Saddlepoint Monte Carlo and its application to vote transfers
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.
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