PhD Defense Mareile Grosse Ruse

Title:

Inference From stochastic processes with application to birdsongs and biomedicine

Abstract: 

This thesis contains three contributions on inference from stochastic processes.

The first article, which originates from research conducted at Lund University, has a signal processing spirit. The stochastic processes are bird songs and we approach inference from their time-frequency domain representation. We suggest an algorithm for the automated structural analysis of bird songs, which is particularly suitable for noisy recordings and complex song structures. The novel way of assessing similarity between syllables is based on a particular feature representation, which is derived from the syllables’ Ambiguity spectra.

The other two articles, which present research carried out at the University of Copenhagen, base inference on time-domain representations of stochastic processes. Focus lies on deterministic and stochastic differential equations models with random effects and applications to biomedical data.

In Paper II we employ a delay differential equations model with random effects to gain hitherto unknown insights on the initial distribution and metabolism of selenomethionine in the human body.

Paper III considers inference for multivariate stochastic differential mixed effects models and has a stronger theoretical spirit. By allowing the inclusion of subject-specific covariate information in the drift, we leave the setting of identically distributed processes. We derive the Maximum-Likelihood estimator from the continuous-time likelihood, prove its consistency and asymptotic normality, and study the bias arising from time-discretization. The method is applied to the statistical analysis of a data set containing EEG recordings from epileptic patients.

Supervisor: Prof. Susanne Ditlevsen, Math, University of Copenhagen
Co-Supervisor: Adeline Samson, l’Université Grenoble Alpes, France and
Maria Sandsten, Lund University

Assessment committee:
Prof. Helle Sørensen (Chairman), MATH, University of Copenhagen
Chargée de Recherches. Sophie Donnet, Unité MIA-Paris, AgroParisTech
Senior Researcher Dan Stowell, University of London