Sequential importance sampling for online Bayesian changepoint detection

Vladislav Vyshemirsky, Lida Mavrogonatou

Abstract:

Online detection of abrupt changes in the parameters of a generative model for a
time series is useful when modelling data in areas of application such as finance, robotics, and
biometrics. We present an algorithm based on Sequential Importance Sampling which allows
this problem to be solved in an online setting without relying on conjugate priors. Our results
are exact and unbiased as we avoid using posterior approximations, and only rely on Monte
Carlo integration when computing predictive probabilities. We apply the proposed algorithm to
three example data sets. In two of the examples we compare our results to previously published
analyses which used conjugate priors. In the third example we demonstrate an application where
conjugate priors are not available. Avoiding conjugate priors allows a wider range of models to
be considered with Bayesian changepoint detection, and additionally allows the use of arbitrary
informative priors to quantify the uncertainty more flexibly.