Abbey C K, Clarkson E, Barrett H H, Müller S P, Rybicki F J
Department of Radiology, University of Arizona, Tucson, USA.
Med Image Anal. 1998 Dec;2(4):395-403. doi: 10.1016/s1361-8415(98)80019-4.
The performance of maximum-likelihood (ML) and maximum a posteriori (MAP) estimates in non-linear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive a point approximation to density values of the conditional distribution of such estimates. In an example problem, this approximate distribution captures the essential features of the distribution of ML estimates in the presence of Gaussian-distributed noise.
在低数据信噪比的非线性问题中，最大似然（ML）估计和最大后验（MAP）估计的性能并不能通过克拉美 - 罗（Cramér-Rao）方差下界或其他方差下界得到很好的预测。为了更好地表征在这些条件下ML估计和MAP估计的分布，我们推导了此类估计的条件分布密度值的点近似。在一个示例问题中，这种近似分布捕捉了存在高斯分布噪声时ML估计分布的基本特征。
