Bayesian Regression of Piecewise Constant Functions

Details Bayesian Regression of Piecewise Constant Functions Bayesian Regression of Piecewise Constant Functions

2006-06-13

arxiv.org/abs/math/0606315v1

Mathematics

Statistics Theory

27 pages, 18 figures, 1 table, 3 algorithms

Scientific paper

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It 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 will be discussed.

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