The analysis of ordinal time-series data via a transition (Markov) model

2011 ◽  
Vol 38 (9) ◽  
pp. 1883-1897 ◽  
Author(s):  
Kathryn Bartimote-Aufflick ◽  
Peter C. Thomson
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Time Series Data ◽  
Series Data ◽  
Ordinal Time Series

scholarly journals An Approximate Markov Model for the Wright–Fisher Diffusion and Its Application to Time Series Data

Genetics ◽  
2016 ◽  
Vol 203 (2) ◽  
pp. 831-846 ◽  
Author(s):  
Anna Ferrer-Admetlla ◽  
Christoph Leuenberger ◽  
Jeffrey D. Jensen ◽  
Daniel Wegmann
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Time Series Data ◽  
Series Data

scholarly journals Modelling the Dynamics of Biological Systems with the Geometric Hidden Markov Model

2017 ◽  
Author(s):  
Borislav Vangelov ◽  
Mauricio Barahona
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Time Series Data ◽  
Hidden Markov ◽  
Stem Cell Differentiation ◽  
Coarse Grained ◽  
Genetic Circuit ◽  
Series Data ◽  
Biological Processes

ABSTRACTMany biological processes can be described geometrically in a simple way: stem cell differentiation can be represented as a branching tree and cell division can be depicted as a cycle. In this paper we introduce the geometric hidden Markov model (GHMM), a dynamical model whose goal is to capture the low-dimensional characteristics of biological processes from multivariate time series data. The framework integrates a graph-theoretical algorithm for dimensionality reduction with a latent variable model for sequential data. We analyzed time series data generated by an in silico model of a biomolecular circuit, the represillator. The trained model has a simple structure: the latent Markov chain corresponds to a two-dimensional lattice. We show that the short-term and long-term predictions of the GHMM reflect the oscillatory behaviour of the genetic circuit. Analysis of the inferred model with a community detection methods leads to a coarse-grained representation of the process.

scholarly journals Symbol Encoding Method of Time Series Data and Markov Model

1991 ◽  
Vol 3 (2) ◽  
pp. 124-127
Author(s):  
Takafumi Katayama ◽  
◽  
Eiji Suzuki ◽  
Masao Saito ◽  
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Linear Prediction ◽  
Time Series Data ◽  
Series Data ◽  
Likelihood Ratios ◽  
Model Parameter ◽  
Alphabetic Character ◽  
Log Likelihood ◽  
Encoding Method

A symbol encoding method is proposed for the purpose of data classification. The parameters of a sample are obtained by linear prediction analysis. Log likelihood ratios are computed between the parameters of a sample and several templates. A sample is classified to the template distance, and then the parameters of the template is modified. A symbol (e.g. an alphabetic character) is assigned to each template. The whole time series data are encoded into the stream of symbols. A Markov model which produced the same symbol series is constructed. A model parameter is represented as a structure of the time series data.

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