Stochastic Modeling and Inference with Multi-type Branching Processes

Start: 10/10/2016 - 4:15pm
End  : 10/10/2016 - 5:15pm

Applied Math Seminar

Jason Xu (UCLA)


Markov branching processes are a class of continuous-time Markov chains (CTMCs) with many applications such as modeling cellular differentiation, transposable element evolution, and infectious disease dynamics. Multi-type processes are necessary to model phenomena such as competition, predation, or infection, but often feature large or uncountable state spaces, rendering standard CTMC techniques impractical. We present new methodology that enables calculation of the likelihood in these settings using spectral techniques, enabling standard frequentist and Bayesian likelihood-based frameworks for inference. We examine the performance and limitations in several scientific examples, and explore compressed sensing techniques and moment-based estimators that scale to very large systems and datasets.

Emmy Noether Room Millikan 1021 Pomona College