TY - BOOK

T1 - Inference from Stochastic Processes with Application to Birdsongs and Biomedicine

AU - Grosse Ruse, Mareile

PY - 2017

Y1 - 2017

N2 - 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. Thestochastic processes are bird songs and we approach inference from their time-frequency domainrepresentation. We suggest an algorithm for the automated structural analysis of bird songs, whichis particularly suitable for noisy recordings and complex song structures. The novel way of assessingsimilarity between syllables is based on a particular feature representation, which is derived fromthe syllables’ Ambiguity spectra. The other two articles, which present research carried out at theUniversity of Copenhagen, base inference on time-domain representations of stochastic processes.Focus lies on deterministic and stochastic differential equations models with random effects andapplications to biomedical data. In Paper II we employ a delay differential equations model withrandom effects to gain hitherto unknown insights on the initial distribution and metabolism ofselenomethionine in the human body. Paper III considers inference for multivariate stochasticdifferential mixed effects models and has a stronger theoretical spirit. By allowing the inclusionof subject-specific covariate information in the drift, we leave the setting of identically distributedprocesses. 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 fromepileptic patients.

AB - 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. Thestochastic processes are bird songs and we approach inference from their time-frequency domainrepresentation. We suggest an algorithm for the automated structural analysis of bird songs, whichis particularly suitable for noisy recordings and complex song structures. The novel way of assessingsimilarity between syllables is based on a particular feature representation, which is derived fromthe syllables’ Ambiguity spectra. The other two articles, which present research carried out at theUniversity of Copenhagen, base inference on time-domain representations of stochastic processes.Focus lies on deterministic and stochastic differential equations models with random effects andapplications to biomedical data. In Paper II we employ a delay differential equations model withrandom effects to gain hitherto unknown insights on the initial distribution and metabolism ofselenomethionine in the human body. Paper III considers inference for multivariate stochasticdifferential mixed effects models and has a stronger theoretical spirit. By allowing the inclusionof subject-specific covariate information in the drift, we leave the setting of identically distributedprocesses. 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 fromepileptic patients.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122482380505763

M3 - Ph.D. thesis

BT - Inference from Stochastic Processes with Application to Birdsongs and Biomedicine

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -