论文标题
整合多通态和计算分类测量的方法
Methods to integrate multinormals and compute classification measures
论文作者
论文摘要
在不确定性下对决策进行建模时，单变量和多元正常概率分布将被广泛使用。计算此类模型的性能需要在特定域上集成这些分布，这些域可能会在模型之间差异很大。除某些特殊情况外，这些积分没有一般分析表达式，标准数值方法或软件。 Here we present mathematical results and open-source software that provide (i) the probability in any domain of a normal in any dimensions with any parameters, (ii) the probability density, cumulative distribution, and inverse cumulative distribution of any function of a normal vector, (iii) the classification errors among any number of normal distributions, the Bayes-optimal discriminability index and relation to the operating characteristic, (iv) ways to scale the对此类问题的两个分布的可区分性，（v）维度减小和可视化，以及（vi）测试如何可靠地在给定数据上使用这些方法。我们通过视觉研究应用来证明这些工具，该应用程序在自然场景中检测遮挡物体并检测伪装。
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases, there exist no general analytical expressions, standard numerical methods or software for these integrals. Here we present mathematical results and open-source software that provide (i) the probability in any domain of a normal in any dimensions with any parameters, (ii) the probability density, cumulative distribution, and inverse cumulative distribution of any function of a normal vector, (iii) the classification errors among any number of normal distributions, the Bayes-optimal discriminability index and relation to the operating characteristic, (iv) ways to scale the discriminability of two distributions, (v) dimension reduction and visualizations for such problems, and (vi) tests for how reliably these methods may be used on given data. We demonstrate these tools with vision research applications of detecting occluding objects in natural scenes, and detecting camouflage.
