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State Space Modeling of Event Count Time Series

This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated exten...

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Detalles Bibliográficos
Autores principales: Moontaha, Sidratul, Arnrich, Bert, Galka, Andreas
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10606130/
https://www.ncbi.nlm.nih.gov/pubmed/37895494
http://dx.doi.org/10.3390/e25101372
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author Moontaha, Sidratul
Arnrich, Bert
Galka, Andreas
author_facet Moontaha, Sidratul
Arnrich, Bert
Galka, Andreas
author_sort Moontaha, Sidratul
collection PubMed
description This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated extended Kalman filter is employed. Positive definiteness of covariance matrices is preserved by a square-root filtering approach, based on singular value decomposition. Non-negativity of the count data is ensured, either by an exponential observation function, or by a newly introduced “affinely distorted hyperbolic” observation function. The resulting algorithm is applied to time series of the daily number of seizures of drug-resistant epilepsy patients. This number may depend on dosages of simultaneously administered anti-epileptic drugs, their superposition effects, delay effects, and unknown factors, making the objective analysis of seizure counts time series arduous. For the purpose of validation, a simulation study is performed. The results of the time series analysis by state space modeling, using the dosages of the anti-epileptic drugs as external control inputs, provide a decision on the effect of the drugs in a particular patient, with respect to reducing or increasing the number of seizures.
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spelling pubmed-106061302023-10-28 State Space Modeling of Event Count Time Series Moontaha, Sidratul Arnrich, Bert Galka, Andreas Entropy (Basel) Article This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated extended Kalman filter is employed. Positive definiteness of covariance matrices is preserved by a square-root filtering approach, based on singular value decomposition. Non-negativity of the count data is ensured, either by an exponential observation function, or by a newly introduced “affinely distorted hyperbolic” observation function. The resulting algorithm is applied to time series of the daily number of seizures of drug-resistant epilepsy patients. This number may depend on dosages of simultaneously administered anti-epileptic drugs, their superposition effects, delay effects, and unknown factors, making the objective analysis of seizure counts time series arduous. For the purpose of validation, a simulation study is performed. The results of the time series analysis by state space modeling, using the dosages of the anti-epileptic drugs as external control inputs, provide a decision on the effect of the drugs in a particular patient, with respect to reducing or increasing the number of seizures. MDPI 2023-09-23 /pmc/articles/PMC10606130/ /pubmed/37895494 http://dx.doi.org/10.3390/e25101372 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Moontaha, Sidratul
Arnrich, Bert
Galka, Andreas
State Space Modeling of Event Count Time Series
title State Space Modeling of Event Count Time Series
title_full State Space Modeling of Event Count Time Series
title_fullStr State Space Modeling of Event Count Time Series
title_full_unstemmed State Space Modeling of Event Count Time Series
title_short State Space Modeling of Event Count Time Series
title_sort state space modeling of event count time series
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10606130/
https://www.ncbi.nlm.nih.gov/pubmed/37895494
http://dx.doi.org/10.3390/e25101372
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