Bayesian Optimal Experimental Design of Streaming Data Incorporating Machine Learning Generated Synthetic Data

This paper demonstrates two main innovations to aid in statistical inference using synthetic data in dynamic contexts. First, using a class of estimators which give valid statistical inference using synthetic and real data points, even when the operating characteristics of the synthetic data generation process are unknown, we illustrate how to incorporate our proposed estimators into dynamic linear models to analyze streaming data. Second, we combined our proposed estimators with Bayesian optimal experimental design to dynamically determine the optimal ratio of real and synthetic data to minimize model standard error.