Learning from data with ABC
10 Sep 2014. NUS statisticians extended the method of Approximate Bayesian Computation (ABC) to much higher dimensional problems than before.
It is common to have statistical models for random phenomena which are easily specified in terms of how those models might be simulated on a computer, without having an explicit formula for probabilities or likelihoods for possible observed data outcomes. In this situation there is a need for learning about unknown model process parameters using only simulations from the model. Approximate Bayesian Computation (ABC) is a class of methods which are useful. Traditional ABC approaches are applicable only when the set of unknowns is low-dimensional; recent research led by Prof David NOTT from Department of Statistics in NUS and their collaborators at University of New South Wales, Sydney, has extended the reach of ABC methods to problems where there may be hundreds of unknowns. This is done using an approximate approach that breaks a high-dimensional problem down into lower dimensional ones.
ABC methods find significant applications in ecology, population genetics, epidemiology, finance, cosmology and other fields.
The new approach attempts to give a careful treatment of the uncertainties in inferring each model parameter individually, and combines that information with a description of multivariate dependencies obtained using a regression based approach.
Image shows a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using MCMC for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. (Image credit: David NOTT)
Nott DJ, Fan Y, Marshall L, Sisson S. “Approximate Bayesian computation and Bayes linear analysis: Towards high-dimensional ABC.” Journal of Computational and Graphical Statistics. 23 (2014) 86.