A transport approach to sequential simulation-based inference

TL;DR

This paper introduces a transport-based method for efficient sequential Bayesian inference that constructs explicit surrogate models for likelihoods using structured transport maps, suitable for complex noise models and black-box forward models.

Contribution

It proposes a novel transport approach for sequential inference that leverages structured maps to create explicit likelihood surrogates, enabling gradient-based posterior analysis in complex scenarios.

Findings

Effective in complex noise models including nuisance parameters

Provides explicit surrogate models for likelihood functions

Applicable to black-box forward models

Abstract

We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters. The strategy is based on the extraction of conditional distribution from the joint distribution of parameters and data, via the estimation of structured (e.g., block triangular) transport maps. This gives explicit surrogate models for the likelihood functions and their gradients. This allow gradient-based characterizations of posterior density via transport maps in a model-free, online phase. This framework is well suited for parameter estimation in case of complex noise models including nuisance parameters and when the forward model is only known as a black box. The numerical application of this method is performed in the context of characterization of ice thickness with conductivity measurements.