953 research outputs found
Bayesian Model Search for Nonstationary Periodic Time Series
We propose a novel Bayesian methodology for analyzing nonstationary time
series that exhibit oscillatory behaviour. We approximate the time series using
a piecewise oscillatory model with unknown periodicities, where our goal is to
estimate the change-points while simultaneously identifying the potentially
changing periodicities in the data. Our proposed methodology is based on a
trans-dimensional Markov chain Monte Carlo (MCMC) algorithm that simultaneously
updates the change-points and the periodicities relevant to any segment between
them. We show that the proposed methodology successfully identifies time
changing oscillatory behaviour in two applications which are relevant to
e-Health and sleep research, namely the occurrence of ultradian oscillations in
human skin temperature during the time of night rest, and the detection of
instances of sleep apnea in plethysmographic respiratory traces.Comment: Received 23 Oct 2018, Accepted 12 May 201
Stochastic reaction networks with input processes: Analysis and applications to reporter gene systems
Stochastic reaction network models are widely utilized in biology and
chemistry to describe the probabilistic dynamics of biochemical systems in
general, and gene interaction networks in particular. Most often, statistical
analysis and inference of these systems is addressed by parametric approaches,
where the laws governing exogenous input processes, if present, are themselves
fixed in advance. Motivated by reporter gene systems, widely utilized in
biology to monitor gene activation at the individual cell level, we address the
analysis of reaction networks with state-affine reaction rates and arbitrary
input processes. We derive a generalization of the so-called moment equations
where the dynamics of the network statistics are expressed as a function of the
input process statistics. In stationary conditions, we provide a spectral
analysis of the system and elaborate on connections with linear filtering. We
then apply the theoretical results to develop a method for the reconstruction
of input process statistics, namely the gene activation autocovariance
function, from reporter gene population snapshot data, and demonstrate its
performance on a simulated case study
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