Inverse Gaussian Process regression for likelihood-free inference

2021/02/21 by Hongqiao Wang, Ziqiao Ao, Wang, Hongqiao +5
Computer Science · Engineering · #Computation (stat.CO) #Control Systems and Identification #FOS: Computer and information sciences #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2102.10583

openalex publication_date 2021/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian Process regression (IGPR), i.e., one from the output of a simulation model to the input of it. Within the method, we provide an adaptive algorithm with a tempering procedure to construct the approximations of the marginal posterior distributions. With examples we demonstrate that IGPR has a competitive performance compared to some commonly used algorithms, especially in terms of statistical stability and computational efficiency, while the price to pay is that it can only compute a weighted Gaussian approximation of the marginal posteriors.

Citations

• Statistical inference for noisy nonlinear ecological dynamic systems
• Variational Bayesian Monte Carlo
• Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows
• Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation
• Variational Inference: A Review for Statisticians

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