Regression adjustments for Approximate Bayesian computation (ABC): algorithms, theory and examples


Séminaire Probabilités & Statistique

7/06/2012 - 14:00 Michael BLUM (TIMC / BCM) Salle 1 - Tour IRMA

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. In a nutshell, ABC proceeds by comparing the observed summary statistics s to summary statistics simulated for different values of the parameter of interest. The posterior distribution is then approximated by the conditional distribution of the parameter given the observed summary statistics s. However the methods that use a simple rejection algorithm suffer from the curse of dimensionality when the number of summary statistics is increased. We will present two methods of regression adjustment that address the curse of dimensionality and we provide the asymptotic bias and variance of these different methods. In different examples borrowed from the population genetics and epidemiological literature, we show the potential of the methods with adjustment.