alexa Exact Bayesian regression of piecewise constant functions
Biomedical Sciences

Biomedical Sciences

International Journal of Biomedical Data Mining

Author(s): Marcus Hutter

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We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary locations, and levels. The derivation works for any noise and segment level prior, e.g. Cauchy which can handle outliers. We derive simple but good estimates for the in-segment variance. We also propose a Bayesian regression curve as a better way of smoothing data without blurring boundaries. The Bayesian approach also allows straightforward determination of the evidence, break probabilities and error estimates, useful for model selection and significance and robustness studies. We discuss the performance on synthetic and real-world examples. Many possible extensions are discussed.

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This article was published in Bayesian Analysis and referenced in International Journal of Biomedical Data Mining

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