(Cancelled) Sung Woong Cho – Estimating the distribution of parameters in differential equations with repeated cross-sectional data

This presentation introduces an approach for estimating parameter distributions in dynamic systems modeled by differential equations. Traditional parameter estimation techniques often struggle with Repeated Cross-Sectional (RCS) data, characteristic of many real-world scenarios where continuous data collection is impractical or impossible. Previous approaches, like employing mean values or leveraging Gaussian Processes for time series generation, fail to capture system parameters’ true heterogeneity and distributions. We introduce a novel approach to infer accurate parameter distributions from RCS data. By constructing artificial trajectories from randomly selected observations at each time point and iteratively refining parameter estimates to minimize discrepancies between observed and modeled dynamics, our method enables the derivation of true parameter distributions even for RCS data. We demonstrate the efficacy of our method through its application to models including exponential growth, logistic population dynamics, and target cell-limited models with delayed virus production. Our findings offer a robust framework for understanding the full complexity of dynamic systems, paving the way for more precise and insightful analyses across various fields of study.