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Multi-messenger astronomy is becoming the key to understanding the Universe from a comprehensive perspective. In most cases, the data and the technology are already in place, therefore it is important to provide an easily-accessible package…
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
The problem of detecting changes in the statistical properties of a stochastic system and time series arises in various branches of science and engineering. It has a wide spectrum of important applications ranging from machine monitoring to…
Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are…
This paper summarizes a presentation for a panel discussion on "The Future of Astrostatistics" held at the Statistical Challenges in Modern Astronomy V conference at Pennsylvania State University in June 2011. I argue that the emerging…
We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of…
In recent years, there has been a proliferation of wide-field sky surveys to search for a variety of transient objects. Using relatively short focal lengths, the optics of these systems produce undersampled stellar images often marred by a…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
In this paper, we propose a class of monitoring statistics for a mean shift in a sequence of high-dimensional observations. Inspired by the recent U-statistic based retrospective tests developed by Wang et al.(2019) and Zhang et al.(2020),…
The definition of anomaly detection is the identification of an unexpected event. Real-time detection of extreme events such as wildfires, cyclones, or floods using satellite data has become crucial for disaster management. Although several…
A direct sampling method (DSM) is designed herein for a real-time detection of small anomalies from scattering parameters measured by a small number of dipole antennas. Applicability of the DSM is theoretically demonstrated by proving that…
To address the problem that traditional network traffic anomaly detection algorithms do not suffi-ciently mine potential features in long time domain, an anomaly detection method based on mul-ti-scale residual features of network traffic is…
Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral…
Anomaly and similarity detection in multidimensional series have a long history and have found practical usage in many different fields such as medicine, networks, and finance. Anomaly detection is of great appeal for many different…
Ultra Fast Astronomy is a new frontier becoming enabled by improved detector technology allowing discovery of optical transients on millisecond to nanosecond time scales. These may reveal counterparts of energetic processes such as fast…
Anomaly detection is a longstanding and active research area that has many applications in domains such as finance, security, and manufacturing. However, the efficiency and performance of anomaly detection algorithms are challenged by the…
Dynamic networks, also called network streams, are an important data representation that applies to many real-world domains. Many sets of network data such as e-mail networks, social networks, or internet traffic networks are best…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a…