# Gaussian likelihoods for ’intractable’ situations

Heikki Haario, Technische Universität Lappeenranta, Finland 2.28.0.108 (Campus Golm, building 28, room 0.108)10:00 - 11:00

Various modelling situations – including chaotic dynamics, stochastic differential equations, random patterns such as produced by the Turing reaction-diffusion systems, or the Cahn-Hilliard equation – share the analogy that a fixed model parameter corresponds to a family of solutions rather than a fixed deterministic one. This may be due to extreme sensitivity with respect to the initial values, randomized or unknown initial values, or the explicit stochasticity of the system. As a result, standard methods based on directly measuring the distance between model output and data are no more available. We discuss an approach that allows a unified construction of likelihoods for such ‘intractable’ situations. The starting point is the Donsker theorem stating that the cumulative distribution function of i.i.d scalar samples tends to a Gaussian distribution. But the approach can be extended also to weakly dependent, and vector-valued data. Several cases from the above list are presented as examples.

invited by Jana de Wiljes