ABSTRACT
This chapter considers the question of whether it may be possible to conduct reliable approximate Bayesian computation (ABC) -based inference for high-dimensional models or when the number of summary statistics is large. It considers direct approximation of the posterior distribution p given the observed summary statistics sobs. The chapter shows an instructive toy example where marginal adjustment strategy fails to adequately estimate the posterior dependence structure. It discusses the Gaussian copula ABC approach, which extends the marginal adjustment to improve estimation of all pairwise dependences of the joint posterior, in combination with the marginal estimates, by use of a meta-Gaussian distribution. The high-dimensionality aspect of pilot analysis comes from the number of summary statistics, rather than the number of parameters. The chapter implements Gaussian copula ABC for two real data analyses: an analysis of multivariate currency exchange data, and simultaneous estimation of multiple quantile regressions.
