Minimax confidence intervals in geomagnetism
Minimax confidence intervals in geomagnetism
复制标题
地磁的极小极大置信区间
DOI：
10.1111/j.1365-246x.1992.tb00861.x
复制
发表时间：
1992
影响因子：
2.8
通讯作者：
P. Stark
中科院分区：
文献类型：
--
作者：
P. Stark
总结
Backus（1989）利用地球磁场的静止质量小于地球的质量，或者由产生主磁场的电流在地核释放的欧姆热小于表面热流的先验信息，计算磁场低阶高斯系数的置信区间长度。他的技术用于产生置信区间产生的区间比包含真实值的概率1 - α所需的时间更长。本文利用Donoho（1989）的理论，在热流约束下，求出了阶数为1 ≥ l ≥ 12的域的Gauss系数的最优短定长置信区间（minimax置信区间）长度的下界.最佳极小极大区间的界限比巴克斯区间短约40%：没有程序产生固定长度的置信区间，线性或非线性，可以给区间短于巴克斯的长度约60%在这个问题。虽然这两种方法都严格地考虑了核心场模型是无限维的这一事实，但这些技术在地磁问题中的应用涉及对数据误差的近似和反事实假设，因此这些结果可能是对高斯系数实际不确定性的极其乐观的估计。
SUMMARY
Backus (1989) uses the prior information that the rest mass of Earth's magnetic field is less than the mass of Earth, or that the Ohmic heat liberated in the core by the currents giving rise to the main magnetic field is less than the surface heat flow, to compute the lengths of confidence intervals for low-degree Gauss coefficients of the magnetic field. His technique for producing confidence intervals yields intervals that are longer than necessary to have probability 1 - α of containing the true values. The present paper uses theory of Donoho (1989) to find lower bounds on the lengths of optimally short fixed-length confidence intervals (minimax confidence intervals) for Gauss coefficients of the field of degree 1 ≥ l ≥ 12 using the heat flow constraint. The bounds on optimal minimax intervals are about 40 per cent shorter than Backus’ intervals: no procedure for producing fixed-length confidence intervals, linear or non-linear, can give intervals shorter than about 60 per cent the length of Backus’ in this problem. While both methods rigorously account for the fact that core field models are infinite-dimensional, the application of the techniques to the geomagnetic problem involves approximations and counterfactual assumptions about the data errors, and so these results are likely to be extremely optimistic estimates of the actual uncertainty in Gauss coefficients.