09: Bayesian Likelihood-free Inference with High-dimensional Data

Music City Center 

With the growing availability of high-dimensional data, variable selection has become an inevitable step in regression analysis. Traditional Bayesian inference, however, depends on correctly specifying the likelihood, which is often impractical. The loss-likelihood bootstrap (LLB) has recently gained attention as a tool for likelihood-free Bayesian inference. In this paper, we aim to overcome the limited applicability of LLB for high-dimensional regression problems. To this end, we develop a likelihood-free Markov Chain Monte Carlo Model Composition (MC3) method. Traditional MC3 requires marginal likelihoods, which are not available in our likelihood-free setting. To address this, we propose a novel technique that utilizes the Laplace approximation to estimate marginal likelihood ratios without requiring explicit likelihood evaluations. This advancement allows for efficient and accurate model comparisons within the likelihood-free context. Our proposed method is applicable to various high-dimensional regression methods including machine learning techniques. The performance of the proposed method is examined via simulation studies and real data analysis.

Bayesian variable selection

High-dimensional regression

Likelihood-free Bayesian inference

Loss-likelihood bootstrap (LLB) 

Section on Bayesian Statistical Science