Michael Betancourt, PhD
Postdoctoral Research Associate
Department of Statistics
University of Warwick

Research Interests

Fueled by advances in measurement technologies and computation, the questions at the heart of the physical sciences have surpassed the antiquated statistical methods in which young scientists are traiend today. Only the comprehensive perspective of Bayesian inference admits the full utilization of experimental results, pushing scientfic inquiry to its limits. My research is focused on developing robust and transparent Bayesian modeling techniques and the tools needed to fit those models.

Bayesian Modeling Techniques

Ultimately Bayesian models encode all information about an analyses, including every assumption made by the user. In order to make this process more transparent and reproducible, I am working on techniques that facilitate the identification and contextual understanding of these assumptions, as well as their criticism and eventual validation. This includes, for example, the development of readily interpretable prior distributions, implementing compenents such as ordinary differential equations needed to build complex generative models, and establishing robust visual and numerical model validation procedures.

Implementing Bayesian Inference

One of the most welcoming features of Bayesian inference is that implementing, or "fitting", a model reduces to computing expectations with respect to the posterior distribution. Although conceptually straightforward, inference can be hampered by the computational cost of these expectations without powerful new tools. Markov Chain Monte Carlo has a long history of success in estimating expectations for Bayesian applications, but early implementations are often impractical given the immense scope of modern analyses. By appealing to techniques from differential geometry, however, Hamiltonian Monte Carlo dramatically improves on these early methods, and has quickly proven one of the most computationally efficient methods in modern Bayesian inference. Much of my work focuses on understanding the theoretical foundations of Hamiltonian Monte Carlo, in particular identifying the properties that manifest in high practical performance and robust estimation. These insights help users apply Hamiltonian Monte Carlo to the most demanding problems in applied statistics today, especially when combined with the development of state of the art computational tools such as automatic differentiation.
"Because no matter where you go, there you are."