Bayesian Detection of Piecewise Linear Trends in Replicated Time-Series with Application to Growth Data Modelling

Papastamoulis Panagiotis (), Furukawa Takanori, Norman van Rhijn, Bromley Michael, Bignell Elaine and Rattray Magnus
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Papastamoulis Panagiotis: Department of Statistics, School of Information Sciences and Technology, Athens University of Economics and Business, Patision 76, 104 34Athens, Greece
Furukawa Takanori: Division of Infection, Immunity & Respiratory Medicine, Faculty of Biology, Medicine & Health, University of Manchester, Manchester, UK
Norman van Rhijn: Division of Infection, Immunity & Respiratory Medicine, Faculty of Biology, Medicine & Health, University of Manchester, Manchester, UK
Bromley Michael: Division of Infection, Immunity & Respiratory Medicine, Faculty of Biology, Medicine & Health, University of Manchester, Manchester, UK
Bignell Elaine: Division of Infection, Immunity & Respiratory Medicine, Faculty of Biology, Medicine & Health, University of Manchester, Manchester, UK
Rattray Magnus: Division of Informatics, Imaging and Data Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Michael Smith Building, Oxford Road, Manchester, M13 9PL, UK

The International Journal of Biostatistics, 2020, vol. 16, issue 1, 18

Abstract: We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. We develop a Bayesian approach to infer the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence. A Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed for approximating the posterior distribution. Our method is benchmarked using simulated data and is applied to uncover differences in the dynamics of fungal growth from imaging time course data collected from different strains. The source code is available on CRAN.

Keywords: Change-point detection; Fungal growth data; Markov chain Monte Carlo (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/ijb-2018-0052

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