Bernstein 多项式过程用于连续时间变化检测
Bernstein Polynomial Processes for Continuous Time Change Detection
AI总结：
针对连续时间变化检测缺乏方法的问题，提出基于 Bernstein 多项式过程的异质连续时间马尔可夫链模型，利用前向-后向算法高效推断变化点，并开发新损失函数及半参数均值函数以减少误检。
摘要：
由于非信息先验设定和高效后验推断在此背景下的挑战，连续时间变化检测缺乏方法论结果。迄今为止，大多数方法假设数据按均匀间隔的时间区间收集。这一假设在连续时间背景下会引入偏差，因为先验上，时间上紧密相邻的两个连续观测比时间上相距较远的两个连续观测更不可能发生变化。此背景下提出的模型需要 MCMC 采样，这并不理想。为解决这些问题，我们推导了异质连续时间马尔可夫链，该链以非信息方式对变化点转移概率进行建模。通过构造，该模型下的变化点可以使用前向-后向算法高效推断，且无需 MCMC 采样。随后，我们为连续时间背景开发了一种新颖的损失函数，推导了其贝叶斯估计量，并在合成数据上展示了其性能。然后，利用遥感观测的时间序列，在三个变化检测应用上进行了案例研究。为减少此背景下误检的变化，我们开发了一种半参数均值函数，该函数在趋势和季节成分之外捕捉由天气引起的年际变异性。
英文摘要：
There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are collected according to uniformly spaced time intervals. This assumption incurs bias in the continuous time setting where, a priori, two consecutive observations measured closely in time are less likely to change than two consecutive observations that are far apart in time. Models proposed in this setting have required MCMC sampling which is not ideal. To address these issues, we derive the heterogeneous continuous time Markov chain that models change point transition probabilities noninformatively. By construction, change points under this model can be inferred efficiently using the forward backward algorithm and do not require MCMC sampling. We then develop a novel loss function for the continuous time setting, derive its Bayes estimator, and demonstrate its performance on synthetic data. A case study using time series of remotely sensed observations is then carried out on three change detection applications. To reduce falsely detected changes in this setting, we develop a semiparametric mean function that captures interannual variability due to weather in addition to trend and seasonal components.
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