Archive for Monte Carlo Statistical Methods
mostly M[ar]C[h]
Posted in Books, Kids, Statistics, University life with tags diffusions, generative modelling, generative models, Monte Carlo methods, Monte Carlo Statistical Methods, mostly Monte Carlo seminar, normalizing flow, optimal transport, optimization, Paris, PariSanté campus, push-forward distribution, seminar, stochastic diffusions, The Prairie Chair on February 27, 2024 by xi'an
mostly MC[bruary]
Posted in Books, Kids, Statistics, University life with tags completion, contour algorithm, Gibbs sampling, insufficiency, IQR, mad, manifold, MCMC, median, Monte Carlo methods, Monte Carlo Statistical Methods, mostly Monte Carlo seminar, Paris, PariSanté campus, sample median, seminar, The Prairie Chair on February 18, 2024 by xi'an
histories of sign languages
Posted in Books, Statistics, University life with tags AAAS, American, Austrian, Bayesian computational methods, British, Chinese, computational phylogenetics, Czech, deaf people, Edinburgh, Estonian, French, German, Hong Kong, Italian, Japanese, language history, Latvian, Lithuanian, MCMC, Monte Carlo Statistical Methods, New Zealand, phylogenetic models, phylogenetic tree, Polish, Russian, Science, Scotland, sign language, Spanish, Taiwan, Ukrainian on February 8, 2024 by xi'an
Congrats to Grégoire Clarté (now in Edinburgh) and Robin Ryder who, along with coauthors from several instutions, published an article in Science this week about the philogenetic tree of (Asian and European) sign languages for the deaf people. Part of Grégoire’s thesis contained preliminary work on this problem.
Abstract
Sign languages are naturally occurring languages. As such, their emergence and spread reflect the histories of their communities. However, limitations in historical recordkeeping and linguistic documentation have hindered the diachronic analysis of sign languages. In this work, we used computational phylogenetic methods to study family structure among 19 sign languages from deaf communities worldwide. We used phonologically coded lexical data from contemporary languages to infer relatedness and suggest that these methods can help study regular form changes in sign languages. The inferred trees are consistent in key respects with known historical information but challenge certain assumed groupings and surpass analyses made available by traditional methods. Moreover, the phylogenetic inferences are not reducible to geographic distribution but do affirm the importance of geopolitical forces in the histories of human languages.
simulating signed mixtures
Posted in Books, pictures, R, Statistics, University life with tags accept-reject algorithm, arXiv, fundamental lemma of simulation, HAL, inverse cdf, mixtures of distributions, Monte Carlo Statistical Methods, pseudo-random generator, simulation on February 2, 2024 by xi'an
While simulating from a mixture of standard densities is relatively straightforward, when the component densities are easily simulated, to the point that many simulation methods exploit an intermediary mixture construction to speed up the production of pseudo-random samples from more challenging distributions (see Devroye, 1986), things get surprisingly more complicated when the mixture weights can take negative values. For instance, the naïve solution consisting in first simulating from the associated mixture of positive weight components and then using an accept-reject step may prove highly inefficient since the overall probability of acceptance
is the inverse of the sum of the positive weights and hence can be arbitrarily close to zero. The intuition for such inefficiency is that simulating from the positive weight components need not produce values within regions of high probability for the actual distribution
since its negative weight components may remove most of the mass under the positive weight components. In other words, the negative weight components do not have a natural latent variable interpretation and the resulting mixture can be anything, as the above graph testifies.
Julien Stoehr (Paris Dauphine) and I started investigating this interesting challenge when the Master students who had been exposed to said challenge could not dent it in any meaningful way. We have now arXived a specific algorithm that proves superior to the naïve accept-reject algorithm, but also to the numerical cdf inversion (which happens to be available in this setting). Compared with the naïve version, we construct an alternative accept-reject scheme based on pairing positive and negative components as well as possible, partitioning the real line, and finding tighter upper and lower bounds on positive and negative components, respectively, towards yielding a higher acceptance rate on average. Designing a random generator of signed mixtures with enough variability and representativity proved a challenge in itself!
mostly MC[nuary]
Posted in Books, Kids, Statistics, University life with tags Monte Carlo methods, Monte Carlo Statistical Methods, mostly Monte Carlo seminar, normalising flow, overdamped Langevin algorithm, Paris, PariSanté campus, quasi-Monte Carlo methods, seminar, The Prairie Chair on January 6, 2024 by xi'an
