检测参数变化的贝叶斯Fisher信息与Shannon信息的关系
The Relation Between Bayesian Fisher Information and Shannon Information for Detecting a Change in a Parameter
摘要：
我们得到的性能估计的性能相关的检测任务的理想观察员之间的连接。具体来说，我们将展示如何香农信息的任务，检测参数的变化是相关的Fisher信息和贝叶斯Fisher信息。我们之前已经证明，这个香农信息通过积分变换与同一任务的最小错误概率相关。然后，我们通过Ziv-Zakai不等式从最小误差概率和包围均方误差开始，然后通过van Trees不等式从估计量的包围均方误差和贝叶斯Fisher信息开始，最后通过这里的工作从贝叶斯Fisher信息和检测任务的香农信息开始。
英文摘要：
We derive a connection between performance of estimators the performance of the ideal observer on related detection tasks. Specifically we show how Shannon Information for the task of detecting a change in a parameter is related to the Fisher Information and the Bayesian Fisher Information. We have previously shown that this Shannon Information is related via an integral transform to the Minimum Probability of Error on the same task. We then outline a circle of relations starting with this Minimum Probability of Error and Ensemble Mean Squared Error via the Ziv-Zakai inequality, then the Ensemble Mean Squared error for an estimator and the Bayesian Fisher Information via the van Trees Inequality, and finally the Bayesian Fisher Information and the Shannon Information for a detection task via the work here.
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