Exact Bayesian Regression of Piecewise Constant Functions
Exact Bayesian Regression of Piecewise Constant Functions
复制标题
DOI：
10.1214/07-ba225
复制
发表时间：
2007-01-01
影响因子：
4.4
通讯作者：
Hutter, Marcus
中科院分区：
文献类型：
--
作者：
Hutter, Marcus
我们针对未知段数、边界位置和级别的分段常数函数推导了精确且有效的贝叶斯回归算法。该推导适用于任何噪声和先验段级别，例如柯西可以处理异常值。我们对段内方差进行了简单但良好的估计。我们还提出了贝叶斯回归曲线作为平滑数据而不模糊边界的更好方法。贝叶斯方法还可以直接确定证据、破坏概率和误差估计，这对于模型选择以及显着性和鲁棒性研究非常有用。我们讨论合成示例和现实示例的性能。讨论了许多可能的扩展。
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.