Bayesian Analysis

Exact Bayesian regression of piecewise constant functions

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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Bayesian Anal. Volume 2, Number 4 (2007), 635-664.

First available in Project Euclid: 22 June 2012

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Bayesian regression exact polynomial algorithm non-parametric inference piecewise constant function dynamic programming change point problem


Hutter, Marcus. Exact Bayesian regression of piecewise constant functions. Bayesian Anal. 2 (2007), no. 4, 635--664. doi:10.1214/07-BA225.

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