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中心极限定理型随机场的倾斜欧拉示性数密度及其“bubbles”数据应用AI 解读

Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level u chosen to control the tail probability or p-value of its maximum. This p-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statistic field above u, denoted $\mathbb{E}\varphi(A_{u})$. Under isotropy, one can use the expansion $\mathbb{E}\varphi(A_{u})=\sum_{k}\mathcal{V}_{k}\rho_{k}(u)$, where $\mathcal{V}_{k}$…

多元检验统计量随机场及其形状分析应用AI 解读

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the P-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main…

离散采样随机场的最大值及其在面部识别“气泡”技术中的应用AI 解读

A smooth Gaussian random field with zero mean and unit variance is sampled on a discrete lattice, and we are interested in the exceedance probability or P-value of the maximum in a finite region. If the random field is smooth relative to the mesh size, then the P-value can be well approximated by results for the continuously sampled smooth random field (Adler, 1981; Worsley, 1995a; Taylor & Adler, 2003; Adler & Taylor, 2007). If the random field is not smooth, so that…

利用超水平集的 Hadwiger 特征估计随机场峰值数：医学图像应用AI 解读

Certain three-dimensional images arising in medicine and astrophysics are modelled as a smooth random field, and experimenters are interested in the number of peaks or "hot-spots" present in such an image. This paper studies the Hadwiger characteristic of the excursion set of a random field. The excursion set is the set of points where the image exceeds a fixed threshold, and the Hadwiger characteristic, like the Euler characteristic, counts the number of connected…

多元正态均值变化的似然比检验AI 解读

A sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors, and we wish to test that the mean vectors have changed after an unknown point in the sequence. The likelihood ratio test is based on the maximum Hotelling T 2 for the sequences before and after the change point. The main result is a conservative approximation for its null distribution based on an improved Bonferroni inequality.…

指数族独立随机变量序列的变点检验与置信区域AI 解读

SUMMARY Maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables, with particular emphasis on the exponential distribution. The exact null and alternative distributions of the test statistics are found, and the power is compared with a test based on a linear trend statistic. Exact and approximate confidence regions for the change-point are based on the values accepted by a level x likelihood ratio test and a…

二项概率变化的似然比与累积和检验功效AI 解读

A simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio, cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables. It is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence, but that the likelihood ratio test is much more powerful near the ends. An example from epidemiology…

二项概率变化的似然比检验与累积和检验功效AI 解读

A simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio, cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables. It is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence, but that the likelihood ratio test is much more powerful near the ends. An example from epidemiology…

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正态总体位置突变的似然比检验AI 解读

An alternative to the hypothesis that the sequence X 1 ···, X n are independent and identically distributed normal random variables, with mean μ and variance σ2, is that the location parameter μ shifts at some unknown instant. The null distributions of likelihood ratio test statistics are given by Hawkins (1977) for the two cases of known and unknown σ2. Unfortunately, the null distribution for unknown σ2 obtained in that article is incorrect. In this article the correct…