The next All about that (Bayes) seminar will take place on Friday 24 Jan at SCAI, on the Jussieu campus, with the following talks. (Appearances to the contrary, I was not in the least involved in the program!)
13h30 – 14h30 Joshua Bon (OCEAN, Université Paris Dauphine) – Bayesian score calibration for approximate models
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often intractable and model simulation may be computationally burdensome. Fortunately, in many of these situations, it is possible to adopt a surrogate model or approximate likelihood function. It may be convenient to conduct Bayesian inference directly with the surrogate, but this can result in bias and poor uncertainty quantification. In this paper (https://arxiv.org/abs/2211.05357) we propose a new method for adjusting approximate posterior samples to reduce bias and produce more accurate uncertainty quantification. We do this by optimizing a transform of the approximate posterior that maximizes a scoring rule. Our approach requires only a (fixed) small number of complex model simulations and is numerically stable. We demonstrate beneficial corrections to several approximate posteriors using our method on several examples of increasing complexity.
14h30 – 15h30 Giacomo Zanella (Bocconi University) – Entropy contraction of the Gibbs sampler under log-concavity
In this talk I will present recent work (https://arxiv.org/abs/2410.00858) on the non-asymptotic analysis of the Gibbs sampler, a classical and popular MCMC algorithm for sampling. In particular, under the assumption that the probability measure π of interest is strongly log-concave, we show that the random scan Gibbs sampler contracts in relative entropy, and provide a sharp characterization of the associated contraction rate. The result implies that, under appropriate conditions, the number of full evaluations of π required for the Gibbs sampler to converge is independent of the dimension. If time permits, I will also discuss connections and applications of the above results to the problem of zero-order parallel sampling, as well as extensions to Hit-and-Run and Metropolis-within-Gibbs.
Based on joint work with Filippo Ascolani and Hugo Lavenant.
16h00 – 17h00 Paul Bastide (Université Paris Cité) – Goodness of Fit for Bayesian Generative Models with Applications in Population Genetics
In population genetics, inference about intractable likelihood models is common, and simulation methods, including Approximate Bayesian Computation (ABC) and Simulation-Based Inference (SBI), are essential. ABC/SBI methods work by simulating instrumental data sets of the models under study and comparing them with the observed data set y⁰. Advanced machine learning tools are used for tasks such as model selection and parameter inference. The present work focuses on model criticism. This type of analysis, called goodness of fit (GoF), is important for model validation. It can also be used for model pruning when the number of candidates to be considered is excessive, especially in the context where data simulation is expensive. We introduce two new GoF tests based on the local outlier factor (LOF), an indicator that was initially defined for outlier and novelty detection. We test whether y⁰ is distributed from the prior predictive distribution (pre-inference GoF) and whether there is a parameter value such that y⁰ is distributed from the likelihood with that value (post-inference GoF). We evaluate the performance of our two GoF tests on simulated datasets from three different model settings of varying complexity, and on a dataset of single nucleotide polymorphism (SNP) markers for the evaluation of complex evolutionary scenarios of modern human populations.
Joint work with Guillaume Le Mailloux, Jean-Michel Marin and Arnaud Estoup.
