Applications of dynamical inference to the analysis of noisy biological time series with hidden dynamical variables

We present a Bayesian framework for parameter inference in noisy, non-stationary, nonlinear, dynamical systems. The technique is implemented in two distinct ways: (i) Lightweight implementation: to be used for on-line analysis, allowing multiple parameter estimation, optimal compensation for dynamical noise, and reconstruction by integration of the hidden dynamical variables, but with some limitations on how the noise appears in the dynamics ; (ii) Full scale implementation: of the technique with extensive numerical simulations (MCMC), allowing for more sophisticated reconstruction of hidden dynamical trajectories and dealing better with sources of noise external to the dynamics (measurements noise).