论文标题
贝叶斯cramér-rao绑定的物理风格的形式
Physics-inspired forms of the Bayesian Cramér-Rao bound
论文作者
论文摘要
使用差异几何形状，我得出了一种贝叶斯cramér-rao结合的形式，该形式在重新分析下保持不变。有了手头的不变配方，我发现吉尔·弗洛（Gill-Levit）界限中的最佳且自然不变。通过假设先前的概率密度是波函数的平方，我还以相对于波函数及其梯度为二次的功能方面表达了边界。在特殊情况下，在收紧之前找到不利的问题以进行最小值估计，等同于找到schrödinger方程的基态，而费舍尔的信息起着潜力的作用。为了说明该理论，讨论了两个量子估计问题，即，讨论了光学机械波形估计和细分不相互分的光学成像。
Using differential geometry, I derive a form of the Bayesian Cramér-Rao bound that remains invariant under reparametrization. With the invariant formulation at hand, I find the optimal and naturally invariant bound among the Gill-Levit family of bounds. By assuming that the prior probability density is the square of a wavefunction, I also express the bounds in terms of functionals that are quadratic with respect to the wavefunction and its gradient. The problem of finding an unfavorable prior to tighten the bound for minimax estimation is shown, in a special case, to be equivalent to finding the ground state of a Schrödinger equation, with the Fisher information playing the role of the potential. To illustrate the theory, two quantum estimation problems, namely, optomechanical waveform estimation and subdiffraction incoherent optical imaging, are discussed.
