Related papers: PGA Tour Scores as a Gaussian Random Variable
We present a new statistical test that examines the consistency of the tails of two empirical distributions at multiple thresholds. Such distributions are often encountered in counting experiments, in physics and elsewhere, where the…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major leagues to…
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…
The problem of eliminating the statistical fluctuations and extracting the event dynamics from event-by-event analysis is discussed. New moments $G_p$ (for continuous distribution), and $G_{q,p}$ (for anomalous distribution) are proposed,…
We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on $\mathbb{R}^d$ contained in compact domains. We also present two applications of this formula: (1) for fields whose…
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and…
We propose a novel ranking model that combines the Bradley-Terry-Luce probability model with a nonnegative matrix factorization framework to model and uncover the presence of latent variables that influence the performance of top tennis…
This paper extends an initial study [arXiv:0903.1762v1] where it was shown the tempo of the putting strokes of accomplished golfers can be explained by assuming these golfers drive their biomechanical system (i.e. golfer and putter)…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
A randomization test was developed to determine the statistical significance of QCD intermittency in single-event distributions. A total of 96 simulated intermittent distributions based on standard normal Gaussian distributions of size…
This paper presents a data-driven approach to model planar pushing interaction to predict both the most likely outcome of a push and its expected variability. The learned models rely on a variation of Gaussian processes with input-dependent…
Recording of events in National Hockey League rinks is done through the Real Time Scoring System. This system records events such as hits, shots, faceoffs, etc., as part of the play-by-play files that are made publicly available. Several…
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…
Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…
The golf swing is a complex movement requiring considerable full-body coordination to execute proficiently. As such, it is the subject of frequent scrutiny and extensive biomechanical analyses. In this paper, we introduce the notion of golf…
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…
Given a collection of historical sports rankings, can one tell which player is the greatest of all time (i.e., the GOAT)? In this work, we design a data-driven random walk on the symmetric group to obtain a stationary distribution over…
A new model, which uses the frequency of individuals' annual home run totals, is employed to predict future home run totals and records in Major League Baseball. Complete home run frequency data from 1903--2005 is analyzed, resulting in…
Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…