Tree based credible set estimation

Estimating a joint Highest Posterior Density credible set for multivariate posterior density is challenging as dimension gets larger. Credible intervals univariate marginals are usually presented ease of computation and visualisation. There often two layers approximation, we may need to compute target which itself only an approximation the true density. We obtain sets estimation trees given by Li et al. (in: Lee, Sugiyama, Luxburg, Guyon, Garnett (eds) Advances in neural information processing systems, Curran Associates Inc, Red Hook, 2016) approximating truncated compact subset $$\mathbb {R}^d$$ this preferred copula construction. These approximate distribution from samples using piecewise constant function defined sequential binary splits. use consistent estimator measure symmetric difference between our estimate HPD samples. This quality can be computed without know set. show how true-posterior-coverage estimated doubly intractable cases where not available. illustrate methods with simulation studies find that competitive existing methods.