Mechanistic and Data-Adaptive Bayesian Methods for Scientific Inference

• Main Author: Hansen, Derek
• Other Authors: Regier, Jeffrey, Avestruz, Camille, Chen, Yang, Ionides, Edward
• Format: Thesis
• Language: English
• Published: 2023
• Subjects: Bayesian methods; Scientific machine learning; Controlled feature selection; Deep generative models; Variational inference; Statistics and Numeric Data; Science; Southern Ocean
• Online Access: https://hdl.handle.net/2027.42/176420; https://doi.org/10.7302/7269

To draw rigorous conclusions from scientific data, Bayesian statistics requires computationally efficient methods for posterior inference as well as models that are both flexible and interpretable. This dissertation investigates the use of Bayesian methods in cases with both mechanistic and data-adaptive models. Mechanistic models are based on an interpretable understanding of the underlying process that generated the data, whereas data-adaptive models can adapt to unknown structure in the data but are often black-boxes that lack interpretability. In the first half of this dissertation, we develop two methods for efficient and scalable Bayesian inference for well-understood mechanistic models. In the second chapter, we present a mechanistic state-space model of Argo float trajectories called ArgoSSM. ArgoSSM utilizes a physical model of floats' movement and incorporates daily ice-cover images and potential vorticity information to infer the missing locations of Argo floats while under ice in the Southern ocean. Inference is achieved by developing an efficient proposal distribution within sequential Monte Carlo (SMC). In the third chapter, we present the Bayesian Light Source Separator (BLISS), a new probabilistic method for detecting, deblending, and cataloging stars and galaxies. BLISS utilizes a mechanistic model for the placement of stars and galaxies and a deep generative model of galaxy shapes. By training neural networks via Forward Amortized Variational Inference (FAVI) for posterior inference, BLISS can perform fully Bayesian inference on megapixel images in seconds and produce highly accurate catalogs. The latter two chapters of this dissertation describe methods that provide interpretable results while maintaining the flexibility of black-box data-adaptive models. In the fourth chapter, we propose the ProbConserv framework for incorporating physical constraints into a black-box probabilistic model. ProbConserv integrates the integral form of a conservation law into a Bayesian update, with a detailed ...