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Sequential change-point detection plays a critical role in numerous real-world applications, where timely identification of distributional shifts can greatly mitigate adverse outcomes. Classical methods commonly rely on parametric density…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
We present a careful frequentist analysis of one- and two-point statistics of the hot and cold spots in the cosmic microwave background (CMB) data obtained by the Wilkinson Microwave Anisotropy Probe (WMAP). Our main result is the detection…
This Point spread function (PSF) plays a crucial role in many computational imaging applications, such as shape from focus/defocus, depth estimation, and fluorescence microscopy. However, the mathematical model of the defocus process is…
The level-set method is a prominent approach to modelling the evolution of a fire over time based on a characterised rate of spread. It however does not provide a direct means for assimilating new data and quantifying uncertainty. Fire…
The effects of anisoplanatism on the adaptive optics point spread function are investigated. A model is derived that combines observations of the guide star with an analytic formulation of anisoplanatism to generate predictions for the…
The goal of the change-point detection is to discover changes of time series distribution. One of the state of the art approaches of the change-point detection are based on direct density ratio estimation. In this work we show how existing…
We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares estimator and obtain component-wise and…
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…
Astrometric precision and knowledge of the point spread function are key ingredients for a wide range of astrophysical studies including time-delay cosmography in which strongly lensed quasar systems are used to determine the Hubble…
The estimation of regression parameters in one dimensional broken stick models is a research area of statistics with an extensive literature. We are interested in extending such models by aiming to recover two or more intersecting…
The point spread function reflects the state of an optical telescope and it is important for data post-processing methods design. For wide field small aperture telescopes, the point spread function is hard to model, because it is affected…
The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…
We examined the anisotropic point spread function (PSF) of Suprime-Cam data utilizing dense star field data. We decomposed the PSF ellipticities into three components, the optical aberration, atmospheric turbulence, and chip-misalignment in…
A two-dimensional model of wildfire spread and merger is presented. Three features affect the fire propagation: (i) a constant basic rate of spread term accounting for radiative and convective heat transfer, (ii) the unidirectional,…
Change-point analysis has been successfully applied to the detect changes in multivariate data streams over time. In many applications, when data are observed over a graph/network, change does not occur simultaneously but instead spread…
We propose Adaptive Diffusion Denoised Smoothing, a method for certifying the predictions of a vision model against adversarial examples, while adapting to the input. Our key insight is to reinterpret a guided denoising diffusion model as a…
Due to recent climate changes, we have seen more frequent and severe wildfires in the United States. Predicting wildfires is critical for natural disaster prevention and mitigation. Advances in technologies in data processing and…
Change point estimation in its offline version is traditionally performed by optimizing over the data set of interest, by considering each data point as the true location parameter and computing a data fit criterion. Subsequently, the data…
Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries).…