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含干扰参数的多尺度扫描AI 解读

Abstract We develop a multiscale scanning method to find anomalies in a d-dimensional random field in the presence of nuisance parameters. This covers the common situation that either the baseline-level or additional parameters such as the variance are unknown and have to be estimated from the data. We argue that state of the art approaches to determine asymptotically correct critical values for multiscale scanning statistics will in general fail when such parameters are…

何谓分辨率：超分辨显微成像的统计极小极大检验视角AI 解读

As a general rule of thumb the resolution of a light microscope (i.e., the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)—the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well-known Abbe and Rayleigh criteria, dating back to the end of the 19th century. However, during the last…

指数族中的多维多尺度扫描：极限理论与统计结论AI 解读

We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_{i}\}_{i\in \{1,\ldots,n\}^{d}}$, each distributed according to a one-dimensional natural exponential family $\mathcal{F}=\{F_{\theta }\}_{\theta \in \Theta }$. Given some baseline parameter $\theta _{0}\in \Theta $, the field is scanned using local likelihood ratio tests to detect from a (large) given system of regions $\mathcal{R}$ those regions $R\subset \{1,\ldots,n\}^{d}$…

逆问题中的多尺度扫描AI 解读

In this paper, we propose a multiscale scanning method to determine active components of a quantity $f$ w.r.t. a dictionary $\mathcal{U}$ from observations $Y$ in an inverse regression model $Y=Tf+\xi$ with linear operator $T$ and general random error $\xi$. To this end, we provide uniform confidence statements for the coefficients $\langle\varphi,f\rangle$, $\varphi\in\mathcal{U}$, under the assumption that $(T^{*})^{-1}(\mathcal{U})$ is of wavelet-type. Based on this, we…