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UP: Fachverband Umweltphysik

UP 10: Data Analysis and Stochastic Modeling; jointly with Fachverband Dynamik und Statistische Physik (DY)

UP 10.1: Vortrag

Donnerstag, 17. März 2011, 17:00–17:15, ZEU 255

Changepoint detection in stochastic diffusion processes — •Andreas Ruttor¹, Florian Stimberg¹, Guido Sanguinetti², and Manfred Opper¹ — ¹Technische Universität Berlin — ²University of Edinburgh, UK

While diffusion processes are often suitable for modelling the dynamics of a system driven by both deterministic and stochastic forces, their parameters may change suddenly at certain time points. Detecting such changepoints is possible by extending the model with a latent Markovian jump process. Each state of this unobserved process corresponds to one set of parameters for the diffusion process. Here the prior probabilities of jumps denote the expected frequency of changepoints. We derive partial differential equations describing the time evolution of the posterior probability distribution over system states, which can be used for exact inference in low-dimensional systems. We also present a Markov-Chain Monte Carlo algorithm suitable for larger models. In both cases only observations of the diffusion process at discrete points in time are used to estimate the position of the changepoints as well as the parameters of the model. Our results on both simulated and real data show that the approach is very successful in capturing latent dynamics and is suitable for a number of real data modelling tasks.