Introduction to Approximate Bayesian Computation

Online Seminar of the NOMAD Laboratory
Date: Jan 21, 2021
Time: 02:15 PM (Local Time Germany)
Speaker: Prof. Antonietta Mira
Director of the Data Science Lab, Università della Svizzera italiana, and University of Insubria
Location: Join the webinar: https://us02web.zoom.us/j/87487369698?pwd=TnNaQmhoOUFxMXY5QUU0R1I0Z2xCdz09
Room: Webinar ID: 874 8736 9698 I Password: NOMAD
Host: NOMAD Laboratory

The goal of statistical inference is to draw conclusions about properties of a population given a finite observed sample. This typically proceeds by first specifying a parametric statistical model (that identifies a likelihood function) for the data generating process which is indexed by parameters that need to be calibrated (estimated). There is always a trade-off between model simplicity / inferencial effort / prediction power.

When we want to work with a realistic model, the likelihood function may not be analytically available, for example because it involves complex integrals besides the ones needed to compute normalizing constants. Still we can retain the ability to simulate pseudo samples from the model once a set or parameter values has been specified. These simulator-based models are very natural in several contexts such as Astrophysics, Neuroscience, Econometrics, Epidemiology, Ecology, Genetics and so on.

When a simulator-based model is available we can rely on Approximate Bayesian Computation (ABC) to calibrate it. Indeed, ABC is a class of algorithms which has been developed to perform statistical inference (from point estimation all the way to hypothesis testing, model selection and prediction) in the absence of a likelihood function but in a setting where there exists a data generating mechanism able to return pseudo-samples.

In this talk I will introduce the basic idea behind ABC and explain some of the algorithms useful for statistical inference. I will conclude with an example related to epidemiological models for Covid-19 data.