Speaker
Description
In the last couple of years, I have noticed an emerging theme in my work. Across multiple biological systems, colleagues and I have articulated models that involve particles that (1) emerge at random times from a fixed source-location distribution; (2) move throughout a local environment randomly (either diffusing, or switching between deterministic states); and (3) are removed from the system due to state-switching or escape from some predefined region.
We have been tentatively calling these systems “stochastic fountains” (in the classic Markov chain literature these are called “open systems”) and have been studying what these systems look like when you only have access to partial information. For example, what if you only have a snapshot of particles at one instant in time? Or, what happens if you can only observe particles at the moment they leave the domain? The associated inference problems arise naturally in mathematical biology applications, and I will give an overview of how they sit at an interesting intersection of stochastic processes, PDE-inverse theory, spatial point processes, and asymptotic statistics.
