We review work on how to perform exact online inference for a class of multiple changepoint models. These models have a conditional independence structure, and require you to be able to integrate out (either analytically or numerically) the parameters associated within each segment. The computational cost per observation increases linearly with the number of observations. This algorithm is closely related to a particle filter algorithm, and we describe how efficient resampling algorithms can be used to produce an accurate particle filter for this class of models.
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