  This document is the Part IV of the book 'Stochastic Epidemic Models with
Inference' edited by Tom Britton and Etienne Pardoux. It is written by
Catherine Lar\'edo, with the contribution of Viet Chi Tran for the Chapter 4.
Epidemic data present challenging statistical problems, starting from the
recurrent issue of handling missing information. We review methods such as
MCMC, ABC or methods based on diffusion approximations. Plan of this document:
1) Observations and Asymptotic Frameworks; 2) Inference for Markov Chain
Epidemic Models; 3) Inference Based on the Diffusion Approximation of Epidemic
Models; 4) Inference for Continuous Time SIR models.
