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Quantum metrology exploits quantum mechanical effects to increase the precision of measurements of physical quantities. A wide variety of applications are currently being developed for scientific and technological purposes, however, most…
In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…
The histogram is an analysis tool in widespread use within many sciences, with high energy physics as a prime example. However, there exists an inherent bias in the choice of binning for the histogram, with different choices potentially…
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…
We propose a robust test for the equality of the covariance structures in two functional samples. The test statistic has a chi-square asymptotic distribution with a known number of degrees of freedom, which depends on the level of dimension…
We investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…
We define a Graphics Turing Test to measure graphics performance in a similar manner to the definition of the traditional Turing Test. To pass the test one needs to reach a computational scale, the Graphics Turing Scale, for which Computer…
Data similarity (or distance) computation is a fundamental research topic which underpins many high-level applications based on similarity measures in machine learning and data mining. However, in large-scale real-world scenarios, the exact…
We investigate the power of some common change-point tests as a function of the location of the change-point. The test statistics are maxima of weighted U-statistics, with the CUSUM test and the Wilcoxon change-point test as special…
Imagine that you could calculate of posttest probabilities, i.e. Bayes theorem with simple addition. This is possible if we stop thinking of probabilities as ranging from 0 to 1.0. There is a naturally occurring linear probability space…
The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…
Given the vast reservoirs of data stored worldwide, efficient mining of data from a large information store has emerged as a great challenge. Many databases like that of intrusion detection systems, web-click records, player statistics,…
This paper presents a derivation of the Two-Way Likelihood Ratio (G) Test and Comparison to the Two-Way Chi Squared Test
Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information.…
Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical…
Graph is a useful data structure to model various real life aspects like email communications, co-authorship among researchers, interactions among chemical compounds, and so on. Supporting such real life interactions produce a knowledge…
Applying the standard weighted mean formula, [sum_i {n_i sigma^{-2}_i}] / [sum_i {sigma^{-2}_i}], to determine the weighted mean of data, n_i, drawn from a Poisson distribution, will, on average, underestimate the true mean by ~1 for all…
The importance of exploring a potential integration among surveys has been acknowledged in order to enhance effectiveness and minimize expenses. In this work, we employ the alignment method to combine information from two different surveys…
Simulation and its variants (e.g., bisimulation and degree-preserving simulation) are useful in a wide spectrum of applications. However, all simulation variants are coarse "yes-or-no" indicators that simply confirm or refute whether one…
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…