Non-linear Regression Approaches in ABC
Michaël G. B. Blum · Nature Precedings · 2011
Abstract In this talk, we consider different methods of parameter inference for ABC. Derivations of the asymptotic bias and variance of the standard ABC estimators indicates that ABC may achieve poor performance when the dimension of the summary statistics is large. The linear adjustment introduced by Beaumont et al. (2002) is found to achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. To provide a more flexible adjustment method, we propose two innovations. The new method fits 1/a heteroscedatic rather than a homoscedastic regression model and consider 2/non linear instead of linear regression. The new algorithm is compared to the state-of-the-art approximate Bayesian methods and typically provides narrower credibility intervals.