TY - JOUR
T1 - Bayesian Detection of Piecewise Linear Trends in Replicated Time-Series with Application to Growth Data Modelling
AU - Papastamoulis, Panagiotis
AU - Furukawa, Takanori
AU - Van Rhijn, Norman
AU - Bromley, Michael
AU - Bignell, Elaine
AU - Rattray, Magnus
N1 - Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85082779529&partnerID=8YFLogxK
U2 - 10.1515/ijb-2018-0052
DO - 10.1515/ijb-2018-0052
M3 - Article
C2 - 31343979
AN - SCOPUS:85082779529
SN - 1557-4679
VL - 16
JO - International Journal of Biostatistics
JF - International Journal of Biostatistics
IS - 1
M1 - 20180052
ER -