Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029, USA.
J Acoust Soc Am. 2012 Feb;131(2):1087-101. doi: 10.1121/1.3672709.
A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations.
从最大熵原理推导出了一个适用于估计从声学测量推断出的海洋海底参数值的统计特性的条件概率分布。误差函数的期望值的指定约束了熵泛函的最大化。这个约束确定了所得概率分布的误差函数的敏感因子 (β)，这是一种规范形式，为参数值的不确定性提供了保守估计。从条件分布中，可以通过对其他参数进行积分来确定各个参数的边缘分布。该方法是替代在没有中间确定似然函数然后应用贝叶斯规则的情况下获得后验概率分布的一种方法。在本文中，指定约束的期望值是从从少量数据样本中获得的模型解的误差函数的值确定的。该方法应用于新泽西大陆架上的海洋声学测量。对于不同的地球声学模型表示，检查了海底表面声速比和拖曳源的声源级的概率分布的边缘分布。
