Likelihood-Free Schrödinger--Föllmer Sampling for Bayesian Inference with Fixed-Proposal Reuse
Abstract
We study Bayesian posterior sampling when the likelihood is an expectation that is costly to evaluate. We construct a likelihood-free Schrödinger--Föllmer sampler whose drift is written as a ratio of expectations over Gaussian variables and simulator outputs and is estimated directly from joint draws of the two. Importance sampling with a fixed proposal allows the simulator outputs to be generated once and reused across all time steps and trajectories. For the likelihood-free Schrödinger--Föllmer sampler, which draws new Monte Carlo samples at each step, we bound the terminal Wasserstein error under regularity and moment assumptions, separating time-discretization and integration errors. For the likelihood-free Schrödinger--Föllmer sampler with sample reuse, we prove that the output converges to the posterior in the Wasserstein distance, assuming only a finite posterior second moment. Numerical experiments illustrate the reduction in simulator calls and the benefits of randomized quasi-Monte Carlo for drift estimation.
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BibTeX
@misc{ren2026likelihoodfree,
title = {{Likelihood-Free Schrödinger--Föllmer Sampling for Bayesian Inference with Fixed-Proposal Reuse}},
author = {Xihan Ren and Zhijian He and Du Ouyang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01271},
eprint = {2611.01271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01271},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Likelihood-Free Schrödinger--Föllmer Sampling for Bayesian Inference with Fixed-Proposal Reuse
AU - Xihan Ren
AU - Zhijian He
AU - Du Ouyang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01271
UR - https://arxiv.org/abs/2611.01271
AB - We study Bayesian posterior sampling when the likelihood is an expectation that is costly to evaluate. We construct a likelihood-free Schrödinger--Föllmer sampler whose drift is written as a ratio of expectations over Gaussian variables and simulator outputs and is estimated directly from joint draws of the two. Importance sampling with a fixed proposal allows the simulator outputs to be generated once and reused across all time steps and trajectories. For the likelihood-free Schrödinger--Föllmer sampler, which draws new Monte Carlo samples at each step, we bound the terminal Wasserstein error under regularity and moment assumptions, separating time-discretization and integration errors. For the likelihood-free Schrödinger--Föllmer sampler with sample reuse, we prove that the output converges to the posterior in the Wasserstein distance, assuming only a finite posterior second moment. Numerical experiments illustrate the reduction in simulator calls and the benefits of randomized quasi-Monte Carlo for drift estimation.
ER -