Title: Bayes calculations from quantile implied likelihood
Authors: George Karabatsos - University of Illinois-Chicago (United States) [presenting]
Fabrizio Leisen - University of Kent (United Kingdom)
Abstract: A Bayesian model can have a likelihood function that is analytically or computationally intractable, perhaps due to large data sample size or high parameter dimensionality. For such a model, a likelihood function is introduced which approximates the exact likelihood through its quantile function, and is defined by an asymptotic chi-square distribution based on confidence distribution theory. This Quantile Implied Likelihood (QIL) gives rise to an approximate posterior distribution, which can be estimated either by maximizing the penalized log-likelihood, or by any standard Monte Carlo algorithm. The QIL approach to Bayesian Computation is illustrated through the Bayesian analysis of simulated and real data sets having sample sizes that reach the millions, involving models for univariate or multivariate iid or non-iid data. They include the Student's t, g-and-h, and g-and-k distributions; the Bayesian logit regression model; Exponential random graph model, a doubly-intractable model for networks; the multivariate skew normal model for robust inference of large inverse-covariance matrices; the Wallenius distribution model for preference data; and a novel high-dimensional Bayesian nonparametric model for distributions under unknown stochastic precedence order-constraints.