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DY: Fachverband Dynamik und Statistische Physik

DY 17: Modeling and Data Analysis

DY 17.4: Vortrag

Dienstag, 17. März 2015, 10:15–10:30, BH-N 333

A Bayesian method for the analysis of deterministic and stochastic time series — •Coryn Bailer-Jones — Max Planck Institute for Astronomy, Heidelberg, Germany

I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement uncertainties for arbitrary error models (not just Gaussian) on both the time and signal variables. Any model for the deterministic component of the variation of the signal with time is supported, as is any model of the stochastic component of the signal and time variables. The posterior probability distribution over model parameters is determined via Markov Chain Monte Carlo sampling. Models are then compared using the ``cross-validation likelihood'', a version of the Bayesian evidence which is less sensitive to the prior. I illustrate the method on astronomical time series data using both deterministic models and a purely stochastic model, the Ornstein-Uhlenbeck process. This latter process appears to be a good description of several astronomical phenomena, including the flux variability of objects as different as brown dwarfs and active galactic nuclei.