The problem of determining surface shape from shading is formulated in terms of Bayesian estimation. The goal is to select an estimate of surface shape that best fits some criterion on the posterior probability of the surface conditional on the image data. This conditional probability is a function of the imaging function and the prior probability of the surface. A gradient descent technique is...

暴雨强度公式在水文、气象、工程设计等各领域都是非常关注的问题,而常用降雨概率分布函数的适用性欠缺,理论分布函数一直处于争鸣之中。从逐时降雨概率密度函数的适用性分析入手,有利于发现普适且恰当的理论密度函数。本文从我国暴雨洪涝灾害易发区中沿30°N选取4个经纬度长方形区域(雅安附近、鄂西南、江汉平原南部、杭州湾西),并在其南、北各选一对比分区(海南岛、郑州),对6个分区内降雨资料直接采用全样本,统计逐时降雨的三类概率密度经验函数,对照这些函数的特性,从理论上分析了众多分布函数的适用性,筛选适用函数并进行拟合试验,优选出理论密度函数。研究结果表明:三参广义伽玛函数拟合误差最小,而两参广义正态函数更恰当、被首推为理论密度函数;拟合参数寻优时的目标函数综合了乘性与加性误差模型,能使拟合曲线兼顾头尾;本研究有别于极值降雨概率分布中仅采用极少部分样本的方法,采用降雨概率密度方法替代传统的年极值法,...

Allowing for misspecification in the linear conditional quantile function, this paper provides a new interpretation and the semiparametric efficiency bound for the quantile regression parameter β(τ) in Koenker and Bassett (1978). The first result on interpretation shows that under a mean-squared loss function, the probability limit of the Koenker–Bassett estimator minimizes a weighted distribut...

We describe a new approach for modeling the distribution of high-dimensional vectors of discrete variables. This model is inspired by the restricted Boltzmann machine (RBM), which has been shown to be a powerful model of such distributions. However, an RBM typically does not provide a tractable distribution estimator, since evaluating the probability it assigns to some given observation require...

Let (X,Y ) be a bivariate random vector. The estimation of a probability of the form P (Y ≤ y | X > t) is challenging when t is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector (X,Y ), suitably normalized, given that X is large. There already exists a wide literature on bivariate models for which this limiting distribu...

A unified treatment is presented here of compounding with the bivariate Poisson distribution. Exploiting the exponential nature of its probability generating function, it is shown that the pgf of the compound distribution is the moment generating function of the compounding random variable. This relationship leads to rather interesting general results. Particularly, the development of the condi...