GSoC 2017 Project: Hamiltonian Indirect Inference in Julia

This article details a Google Summer of Code 2017 project focused on implementing Indirect Inference within the Julia programming language. The primary objective was to address challenges in estimating models with intractable or computationally expensive likelihoods by utilizing Hamiltonian Monte Carlo for more efficient sampling. Under the mentorship of Tamás K. Papp, the author revised Bayesian estimation methods using Indirect Inference and developed the parametric Bayesian Indirect Likelihood for the Full Data (pdBIL) method. This approach substitutes intractable likelihoods with those from easier-to-handle auxiliary models. The writeup covers the theoretical framework, including the generation of data points and maximum likelihood estimation of auxiliary parameters. It also discusses practical implementation aspects, such as collaborating on the HamiltonianABC repository, handling type-stability issues, and applying the method to Stochastic Volatility models. The project highlights technical hurdles faced during development and outlines future work directions, serving as a comprehensive report on advancing statistical computation tools in Julia.