Math Biology Seminar: Amit Apte

The problems of estimation of state of a high dimensional chaotic system such as the atmosphere or estimation of parameters of models of highly nonlinear real life phenomena involving multiple parameters can both be considered in the Bayesian framework as problems of the study of the posterior distributions of the state or the parameters, conditioned on the observed data. The former is commonly known as data assimilation in the earth sciences. This talk will focus on discussing the connection between the properties of this posterior distribution and the characteristics of the dynamics of the system, in particular the unstable subspace (in the context of data assimilation [1,2]) and the bifurcations of the system as well as the characteristics of the data sets (in the context of parameter estimation [3]). Ref: [1] doi:10.1137/15M1025839, [2] doi:10.1137/16M1068712, [3] arXiv:1705.03868