Dresden 2014 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Statistical Physics far from Thermal Equilibrium - Part I

DY 3.3: Vortrag

Montag, 31. März 2014, 10:00–10:15, ZEU 160

Bayesian prior-predictive value for multi-modal distributions: thermodynamic integration, or fast-growth? — •Alberto Favaro, Elena Barykina, Daniel Nickelsen, and Andreas Engel — Institut für Physik, Carl-von-Ossietzky Universität, 26111 Oldenburg, Germany

In Bayesian inference, the prior-predictive value allows one to select the model, among different candidates, that fits the data best [Lartillot and Philippe, Syst. Biol. 55, 195-207 (2006)]. A common difficulty, when analysing data through Bayesian methods, is the evaluation of high-dimensional integrals. Techniques that originated in statistical physics, such as thermodynamic integration and fast-growth methods, can be used to mitigate this problem.

Naively, if the distribution of data is multi-modal, one expects that fast-growth algorithms, inspired by the Jarzynski equation, outperform thermodynamic integration. In fact, this last technique does not reliably sample all modes, as it often gets trapped around a maximum. The results of Ahlers and Engel for a bimodal Gaussian distribution appear to confirm this [Eur. Phys. J. B62, 357-364 (2008)]. Nevertheless, the estimate of the prior-predictive value, as obtained from a Jarzynski-like equation, is severely biased. By means of a careful error analysis, we determine the conditions under which a given method is to be preferred. Moreover, it is observed that fast-growth simulations are particularly efficient when computing averages with respect to the posterior distribution.