Probabilistic Model Fitting: Bayesian Parameter Estimation and Uncertainty Propagation

• Sanket Jantre (Brookhaven National Laboratory)

**Abstract**: In physical sciences, it is common to fit models to experimental data for the purposes of physical understanding (e.g., inferring unknown parameters) or prediction. Instead of seeking a single "best fit" model, probabilistic model fitting provides a probability distribution of possible fits, weighted by data-model agreement. In this talk, I will demonstrate an end-to-end probabilistic modeling workflow via a real-world application to Antarctic ice sheet disintegration and sea level rise using a massively parallel numerical model. We demonstrate two forms of uncertainty propagation from model input parameters to model output predictions of sea level rise: "prior" uncertainty via Monte Carlo sampling over an expert-specified distribution of model input parameters, and "posterior" uncertainty that further constrains the model parameters with observational data on model outputs. Posterior uncertainties are inferred via Bayesian parameter estimation (or calibration) of model input parameters. To further accelerate model fitting with computationally expensive simulations, our workflow incorporates statistical emulation of the computer model via Gaussian process regression, a statistical machine learning method trained to simulation data. We combine Gaussian process regression with principal component dimension reduction to emulate multivariate (time series) data. The statistical emulation is optional if the numerical simulation model is computationally inexpensive. The proposed probabilistic modeling workflow can be adopted for any scientific problem of interest which involves fitting numerical models to data. **Bio**: Sanket is the Amalie Emmy Noether Postdoctoral Fellow (2022-24) in the Applied Mathematics group at Brookhaven National Laboratory's Computational Science Initiative (CSI). He received his Ph.D. in Statistics from Michigan State University in 2022, M.S. in Economics, and B.Tech. in Computer Science and Engineering from the Indian Institute of Technology, Kanpur in 2017. Sanket is interested in the confluence of Bayesian Statistics and Machine Learning methods, focusing on Bayesian Deep Learning models.