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Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
The likelihood ratio test (LRT) and the related $F$ test, do not (even asymptotically) adhere to their nominal $\chi^2$ and $F$ distributions in many statistical tests common in astrophysics, thereby casting many marginal line or source…
The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing…
There are many research works and methods about change point detection in the literature. However, there are only a few that provide inference for such change points after being estimated. This work mainly focuses on a statistical analysis…
A fundamental functional in nonparametric statistics is the Mann-Whitney functional ${\theta} = P (X < Y )$ , which constitutes the basis for the most popular nonparametric procedures. The functional ${\theta}$ measures a location or…
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…
It is shown that the conventional approach to microcosm investigations uses an incorrect supposition (incorrect space-time model) whose incorrectness is compensated by means of additional hypotheses, known as quantum mechanics principles.…
Various Bell inequalities are trivial algebraic properties satisfied by each line of particular data spreadsheets.It is surprising that their violation in some experiments, allows to speculate about the existence of nonlocal influences in…
This article provides a thorough meta-analysis of the anomaly detection problem. To accomplish this we first identify approaches to benchmarking anomaly detection algorithms across the literature and produce a large corpus of anomaly…
The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the…
The problem of compressive detection of random subspace signals is studied. We consider signals modeled as $\mathbf{s} = \mathbf{H} \mathbf{x}$ where $\mathbf{H}$ is an $N \times K$ matrix with $K \le N$ and $\mathbf{x} \sim…
The False Discovery Rate (FDR) method has recently been described by Miller et al (2001), along with several examples of astrophysical applications. FDR is a new statistical procedure due to Benjamini and Hochberg (1995) for controlling the…
We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…
These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…
The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…
In this paper, we introduce two robust, nonparametric methods for multiple change-point detection in the variability of a multivariate sequence of observations. We demonstrate that changes in ranks generated from data depth functions can be…
A topological multiple testing scheme is presented for detecting peaks in images under stationary ergodic Gaussian noise, where tests are performed at local maxima of the smoothed observed signals. The procedure generalizes the…
As image tampering becomes ever more sophisticated and commonplace, the need for image forensics algorithms that can accurately and quickly detect forgeries grows. In this paper, we revisit the ideas of image querying and retrieval to…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…