Archive for discriminant analysis

Metropolis-Hastings via classification

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on February 23, 2021 by xi'an

Veronicka Rockova (from Chicago Booth) gave a talk on this theme at the Oxford Stats seminar this afternoon. Starting with a survey of ABC, synthetic likelihoods, and pseudo-marginals, to motivate her approach via GANs, learning an approximation of the likelihood from the GAN discriminator. Her explanation for the GAN type estimate was crystal clear and made me wonder at the connection with Geyer’s 1994 logistic estimator of the likelihood (a form of discriminator with a fixed generator). She also expressed the ABC approximation hence created as the actual posterior times an exponential tilt. Which she proved is of order 1/n. And that a random variant of the algorithm (where the shift is averaged) is unbiased. Most interestingly requiring no calibration and no tolerance. Except indirectly when building the discriminator. And no summary statistic. Noteworthy tension between correct shape and correct location.

ABC and discriminant analysis (and Molecular Ecology Ressources, ac’pted)

Posted in Statistics, University life with tags , , , on April 16, 2012 by xi'an

Our paper “Estimation of demo-genetic model probabilities with approximate Bayesian computation using linear discriminant analysis on summary statistics“, written with Arnaud Estoup, Eric Lombaert, Jean-Michel Marin, Thomas Guillemaud, Pierre Pudlo, et Jean-Marie Cornuet has now been accepted for publication in  Molecular Ecology Ressources. Great! This paper, written with members of our ANR (Agence Nationale de la Recherche) group in Montpelier (and to which I contributed a moderate amount), is considering the use of linear discriminant analysis for the selection of summary statistics. In this respect, it connects with the recent “Dimension reduction in ABC” posted on arXiv by Blum, Nunes, Prangle, and Sisson, I recently commented on the ‘Og.