Abstract: I’ll discuss some work in progress on Bayesian parameter estimation for chaotic nonlinear dynamical systems with noisy observations. This is a tricky problem, largely because trajectories in chaotic systems have the well-known property that small perturbations in initial conditions lead to large trajectory deviations in finite time. As a consequence, a naively constructed Bayesian posterior density over parameter space based on trajectory data has an unusable, essentially cryptographic structure — parameter values adjoining the true parameters are assigned negligible probability. I’ll describe an alternate approach, adapted to Bayesianism from the SINDY dynamical-law inference method, in which the analysis is cleverly conducted in ODE law space rather than in trajectory space. This approach mostly works, although some frustration results from the determined efforts of chaos to defy cleverness by creeping back in over a subtle side-channel. I’ll try to provide some suitable rant, since Jeff seems to expect this of me for some reason.
LANS Informal Seminar