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Exact and efficient Bayesian inference for multiple changepoint problems

机译：针对多个变更点问题的精确而有效的贝叶斯推断

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摘要

We demonstrate how to perform direct simulation from the posterior distribution of a class of multiple change-point models where the number of changepoints is unknown. The class of models assumes independence between the posterior distribution of the parameters associated with segments of data between successive changepoints. This approach is based on the use of recursions, and is related to work on product partition models. The computational complexity of the approach is quadratic in the number of observations, but an approximate version, which introduces negligible error, and whose computational cost is roughly linear in the number of observations, is also possible. Our approach can be useful, for example within an MCMC algorithm, even when the independence assumptions do not hold. We demonstrate our approach on coal-mining disaster data and on well-log data. Our method can cope with a range of models, and exact simulation from the posterior distribution is possible in a matter of minutes.
机译：我们演示了如何从一类多个变更点模型的后验分布执行直接仿真，其中变更点的数量未知。该类模型假定与连续变化点之间的数据段相关联的参数的后验分布之间的独立性。此方法基于递归的使用，并且与产品分区模型上的工作有关。该方法的计算复杂度在观察次数上为二次方，但是也可以采用引入误差可忽略的近似版本，并且其计算成本在观察次数上大致呈线性。即使在独立性假设不成立的情况下，例如在MCMC算法中，我们的方法也可能有用。我们展示了有关煤矿灾害数据和测井数据的方法。我们的方法可以处理各种模型，并且可以在几分钟内从后验分布进行精确的仿真。

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