On-line inference for multiple changepoint problems

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 69; no. 4; pp. 589 - 605
• Main Authors: Fearnhead, Paul, Liu, Zhen
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.09.2007; Blackwell Publishing Ltd; Blackwell Publishers; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Algorithms; Computational methods; Data models; Datasets; Direct simulation; Distribution theory; Exact sciences and technology; Filters; Filtration; General topics; Inference; Inference from stochastic processes; time series analysis; Isochores; Mathematics; Modeling; Monte Carlo simulation; Particle filtering; Particle mass; Probability and statistics; Probability theory and stochastic processes; Proposals; Quadratic programming; Regression analysis; Rejection control; Sciences and techniques of general use; Sequential Monte Carlo methods; Simulation; Statistical methods; Statistical models; Statistical variance; Statistics; Stochastic processes; Stratified sampling; Studies; Rejection control; Statistical distribution; Error estimation; Segmentation; Isochores; Prediction theory; Non parametric estimation; Stochastic method; Stochastic process; Stratified sampling; Direct simulation; Sequential method; Distribution function; Bootstrap; Jackknife method; Approximation theory; Sequential Monte Carlo methods; Sampling; Posterior distribution; Human; Monte Carlo method; Filtering; Statistical estimation; Joint distribution; Algorithm; Statistical method; Numerical analysis; Simulation; Particle filtering; Filtering theory; Resampling method
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2007.00601.x

We propose an on-line algorithm for exact filtering of multiple changepoint problems. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is quadratic in the number of observations. We further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations, at the expense of introducing small errors, and we propose two new, optimum resampling algorithms for this problem. One, a version of rejection control, allows the particle filter to choose the number of particles that are required at each time step automatically. The new resampling algorithms substantially outperform standard resampling algorithms on examples that we consider; and we demonstrate how the resulting particle filter is practicable for segmentation of human G+C content.