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Paper No. 11-19

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CFH Nam, JAD Aston and AM Johansen

Date: 31 May 2011

Abstract: Quantifying the uncertainty in the location and nature of change points in time series is important in a variety of applications. Many existing methods for estimation of the number and location of change points fail to capture fully or explicitly the uncertainty regarding these estimates, whilst others require explicit simulation of large vectors of dependent latent variables.This paper proposes methodology for approximating the full posterior distribution of various change point characteristics in the presence of parameter uncertainty. The methodology combines recent work on evaluation of exact change point distributions conditional on model parameters via Finite Markov Chain Imbedding in a Hidden Markov Model setting, and accounting for parameter uncertainty and estimation via Bayesian modelling and Sequential Monte Carlo. The combination of the two leads to a exible and computationally efficient procedure, which does not require estimates of the underlying state sequence. We illustrate that good estimation of posterior distributions regarding change point characteristics is provided for simulated and functional magnetic resonance imaging data. We use the methodology to show that the modelling of relevant physical properties of the scanner can inuence detection of change points and their uncertainty.

Keywords: Change Points; Finite Markov Chain Imbedding; Functional Magnetic Resonance Imaging; Hidden Markov Models; Sequential Monte Carlo; Segmentation.