A multifidelity approximate Bayesian computation with pre-filtering

TL;DR

This work tackles the computational burden of likelihood-free ABC when simulators are expensive by integrating multifidelity modeling with a pre-filtering strategy. The authors introduce MAPS, a pre-filtering hierarchical importance sampling method, and prove posterior concentration under mild assumptions, quantifying how the false-filtering rate $a_L$ bounds estimation error. They further develop an adaptive MF-ABC-SMC algorithm that dynamically selects filtering thresholds to reduce HF simulations while preserving accuracy, and they provide practical model-suitability checks for LF models. Numerical experiments on toy, Ornstein–Uhlenbeck, and Kuramoto problems show substantial reductions in HF evaluations (around 34–44%) with competitive or improved posterior accuracy, highlighting MAPS as a scalable approach for expensive simulators. An R package MAPS accompanies the method to facilitate adoption in real applications.

Abstract

Approximate Bayesian Computation (ABC) methods often require extensive simulations, resulting in high computational costs. This paper focuses on multifidelity simulation models and proposes a pre-filtering hierarchical importance sampling algorithm. Under mild assumptions, we theoretically prove that the proposed algorithm satisfies posterior concentration properties, characterize the error upper bound and the relationship between algorithmic efficiency and pre-filtering criteria. Additionally, we provide a practical strategy to assess the suitability of multifidelity models for the proposed method. Finally, we develop a multifidelity ABC sequential Monte Carlo with adaptive pre-filtering strategy. Numerical experiments are used to demonstrate the effectiveness of the proposed approach. We develop an R package that is available at https://github.com/caofff/MAPS

Figures (11)

• Figure 1: An overview of the MAPS algorithm (Steps 6-10 of Algorithm \ref{['alg:MAPS-filter']}). Given a set of weighted particles ${\boldsymbol{\theta}}_t^{1:N}$, the MAPS algorithm performs the following steps to approximate ${\boldsymbol{\theta}}_{t+1}^{1:N}$: (1) decreasing the auxiliary threshold to filter out low-activity particles; (2) adaptive resampling based on effective sample size; (3) multi-fidelity MCMC moves with LF pre-filtering and HF refinement; (4) final threshold reduction.
• Figure 2: (a) Variation of HF and LF simulation data as a function of the parameter $\theta$. Solid lines denote mean values; shaded areas represent 95% confidence intervals. Gray dashed lines mark observed values $y_{\text{obs}}=0$, $0.5$, and $1$. (b) Likelihood functions for both fidelity models at $y_{\text{obs}}=0.5$.
• Figure 3: Comparison of posterior density estimates over iterations for ABC-ASMC and MAPS methods, as well as the true posterior density, when $y_{obs} = 0.5$.
• Figure 4: Comparison of results from 50 repetitions of ABC-ASMC and MAPS methods with $y_{\mathrm{obs}} = 0.5$. (a) effective sample size, (b) KL divergence, (c) posterior mean and total number of HF simulations, (d) the threshold evolution and (e) the number of HF simulations as a function of iterations.
• Figure 5: HF and LF simulation data generated using parameters $\mu = 2$, $\sigma = 0.5$, $\gamma = 1$, and $\mu_{\mathrm{offset}} = 3$.

Theorems & Definitions (3)

• Proposition 1
• Theorem 1
• Proposition 2