# Introduction to Approximate Bayesian Computation

- Online Seminar of the NOMAD Laboratory
- Date: Jan 21, 2021
- Time: 14:15
- 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

*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.