Off- and online detection of dynamical phases in time series

In this thesis we provide a consistent framework for the data analysis of time series exhibiting a complex dynamical behaviour. We show that, while Markov chains are a natural choice to model the change of dynamical phases, vector autoregressive (VAR) processes provide a convincing model for the flexibility within a dynamical phase. They arise naturally from the discretisation of stochastic differential equations, allow to include non-Markovian effects and can be used to unify several hidden Markov model (HMM) variants. A combination of a Markov model for the change of dynamical phases with VAR processes for the modelling of internal flexibility yields into a procedure which we name HMM-VAR. We demonstrate how to combine HMM-VAR with Perron cluster cluster analysis (PCCA) to analyse time series from complex systems. Furthermore, we develop an algorithm to detect dynamical changes in a time series on-line, i.e. reading the data sequently. Application of so-called objective Bayes techniques provide a change point detection procedure which is (i) sampling free, as all needed integrals can be solved analytically, (ii) applicable to high-dimensional time series and (iii) computationally cheap. It turns out, that the central object of our analysis is the so-called moment matrix, since it does not only allow a stable computation of the estimators for parameters of a VAR process, the compression of information contained in a time series and combination of information belonging to different time series by summing up their moment matrices, and therefore allowing efficient implementation of all algorithms presented here, but also a way to cluster obtained time series segments to the same dynamical phases without the computational effort of an HMM procedure. Finally, we demonstrate how to apply the change point detection algorithm within a rather complex computational setting to compute rate constants for a small biomolecular system with the help of distributed computing.

Author dc:creator

• Meerbach, Eike

• change point detection
• dynamical phases
• molecular dynamics
• pcca
• HMM-SDE
• HMM-VAR
• conformations
• peptides
• proteins
• hidden markov modell
• fractional bayes
• rate constants

Licence dc:rights.uri

• http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen

Language dc:language

eng

Identifier URI

http://dx.doi.org/10.17169/refubium-10799

OAI record oai:identifier

https://refubium.fu-berlin.de/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Arefubium.fu-berlin.de%3Afub188%2F6600