🤖 AI Summary
This work proposes a simulation-based Bayesian inference framework to address the challenges posed by intractable or computationally prohibitive likelihood functions. By learning efficient summary statistics to construct an empirical likelihood and incorporating the Cressie–Read divergence criterion under moment constraints, the method transforms simulated data to enable conditioning on observed data. The approach achieves both statistical efficiency and valid conditional inference, naturally accommodating weakly dependent data and distributed computing environments. The resulting unified framework is readily extensible to complex simulator-based models and large-scale data settings, facilitating accurate and computationally efficient Bayesian inference even when the likelihood is unavailable.
📝 Abstract
This paper, which is Part 1 of a two-part paper series, considers a simulation-based inference with learned summary statistics, in which such a learned summary statistic serves as an empirical-likelihood with ameliorative effects in the Bayesian setting, when the exact likelihood function associated with the observation data and the simulation model is difficult to obtain in a closed form or computationally intractable. In particular, a transformation technique which leverages the Cressie-Read discrepancy criterion under moment restrictions is used for summarizing the learned statistics between the observation data and the simulation outputs, while preserving the statistical power of the inference. Here, such a transformation of data-to-learned summary statistics also allows the simulation outputs to be conditioned on the observation data, so that the inference task can be performed over certain sample sets of the observation data that are considered as an empirical relevance or believed to be particular importance. Moreover, the simulation-based inference framework discussed in this paper can be extended further, and thus handling weakly dependent observation data. Finally, we remark that such an inference framework is suitable for implementation in distributed computing, i.e., computational tasks involving both the data-to-learned summary statistics and the Bayesian inferencing problem can be posed as a unified distributed inference problem that will exploit distributed optimization and MCMC algorithms for supporting large datasets associated with complex simulation models.