CMStatistics 2015: Start Registration
View Submission - CMStatistics
B1598
Topic: Contributions in statistical modeling and computation Title: Approximate Bayesian computation for model choice Authors:  Clara Grazian - Sapienza Universita di Roma (Italy) [presenting]
Abstract: Approximate Bayesian computation is a class of algorithms which is now an essential tool for handling complex models, for which the likelihood function is intractable. The idea is to compare the observed data set with a simulated data set by using a summary statistics bringing information on the parameter; unfortunately, in most real applications the summary statistics is unlikely to be sufficient. The ability of closely approximating the posterior distribution of the parameter of interest strongly depends on the choice of this statistics; some works which study how to choose the summary statistics already exist for inferential problems, nevertheless this aim is much more complicated to achieve in problems of model choice. It is now well known that there is a substantial discrepancy between the true Bayes factor and its ABC approximation, except for very few cases. We propose a way to compare observed and simulated data set inside an ABC algorithm based on the Bayes factor for a simpler version of the considered models and apply the methodology in the particular setting of quantiles distributions, a very flexible tool to model data far from normality (highly skewed or kurtotic), but which are difficult to manage without introducing ABC. The methodology only needs to be able to approximate the available models with simpler models; the distance between the models to compare and the models used as approximations gives a measure for the performance of the algorithm.