Bayesian detection of piecewise linear trends in replicated time-series with application to growth data modelling

TL;DR

This paper introduces a Bayesian method for detecting change-points in piecewise linear trends within replicated time-series data, effectively modeling growth dynamics and identifying structural changes.

Contribution

The authors develop a Bayesian framework with an MCMC sampler for joint inference of change-point number and locations, enhancing growth data analysis.

Findings

Method accurately detects change-points in simulated data

Effectively uncovers growth differences in fungal strains

Posterior concentrates on sparse change-point configurations

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.