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
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.