Approximate maximum likelihood estimation using data-cloning ABC

Abstract

A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC sampler with so-called "data cloning" for maximum likelihood estimation. Accuracy of ABC methods relies on the use of a small threshold value for comparing simulations from the model and observed data. The proposed methodology shows how to use large threshold values, while the number of data-clones is increased to ease convergence towards an approximate maximum likelihood estimate. We show how to exploit the methodology to reduce the number of iterations of a standard ABC-MCMC algorithm and therefore reduce the computational effort, while obtaining reasonable point estimates. Simulation studies show the good performance of our approach on models with intractable likelihoods such as g-and-k distributions, stochastic differential equations and state-space models.

25 pages. Minor revision. It includes a parametric bootstrap for the exact MLE for the first example; includes mean bias and RMSE calculations for the third example. Forthcoming in Computational Statistics and Data Analysis

References in corpus (2)

• MCMC using Hamiltonian dynamics
• Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Cited by in corpus (4)

• Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
• Kernel Recursive ABC: Point Estimation with Intractable Likelihood
• Sequentially guided MCMC proposals for synthetic likelihoods and correlated synthetic likelihoods
• Likelihood-free stochastic approximation EM for inference in complex models