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

摘要

We consider the situation where a temporal process is composed of contiguoussegments with differing slopes and replicated noise-corrupted time seriesmeasurements are observed. The unknown mean of the data generating process ismodelled as a piecewise linear function of time with an unknown number ofchange-points. We develop a Bayesian approach to infer the joint posteriordistribution of the number and position of change-points as well as the unknownmean parameters. A-priori, the proposed model uses an overfitting number ofmean parameters but, conditionally on a set of change-points, only a subset ofthem influences the likelihood. An exponentially decreasing prior distributionon the number of change-points gives rise to a posterior distributionconcentrating on sparse representations of the underlying sequence. AMetropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed forapproximating the posterior distribution. Our method is benchmarked usingsimulated data and is applied to uncover differences in the dynamics of fungalgrowth from imaging time course data collected from different strains. Thesource code is available on CRAN.