2021/05/05 by Marco Tarsia, Tarsia, Marco, Antonietta Mira +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2105.01962
openalex publication_date 2021/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We research relations between optimal transport theory (OTT) and approximate\nBayesian computation (ABC) possibly connected to relevant metrics defined on\nprobability measures. Those of ABC are computational methods based on Bayesian\nstatistics and applicable to a given generative model to estimate its a\nposteriori distribution in case the likelihood function is intractable. The\nidea is therefore to simulate sets of synthetic data from the model with\nrespect to assigned parameters and, rather than comparing prospects of these\ndata with the corresponding observed values as typically ABC requires, to\nemploy just a distance between a chosen distribution associated to the\nsynthetic data and another of the observed values. Our focus lies in\ntheoretical and methodological aspects, although there would exist a remarkable\npart of algorithmic implementation, and more precisely issues regarding\nmathematical foundation and asymptotic properties are carefully analysed,\ninspired by an in-depth study of what is then our main bibliographic reference,\nthat is Bernton et al. (2019), carrying out what follows: a rigorous\nformulation of the set-up for the ABC rejection algorithm, also to regain a\ntransparent and general result of convergence as the ABC threshold goes to zero\nwhereas the number n of samples from the prior stays fixed; general technical\nproposals about distances leaning on OTT; weak assumptions which lead to lower\nbounds for small values of threshold and as n goes to infinity, ultimately\nshowing a reasonable possibility of lack of concentration which is contrary to\nwhat is proposed in Bernton et al. (2019) itself.\n