Related papers: Testing Universality in Critical Exponents: the Ca…
Testing whether the observed data conforms to a purported model (probability distribution) is a basic and fundamental statistical task, and one that is by now well understood. However, the standard formulation, identity testing, fails to…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution…
Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws…
In order to reach the supply/demand balance, electricity providers need to predict the demand and production of electricity at different time scales. This implies the need of modeling weather variables such as temperature, wind speed, solar…
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…
Nowadays there is an increasing interest of physicists in finding regularities related to social phenomena. This interest is clearly motivated by applications that a statistical mechanical description of the human behavior may have in our…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are…
Turbulence is a complex spatial and temporal structure created by the strong non-linear dynamics of fluid flows at high Reynolds numbers. Despite being an ubiquitous phenomenon that has been studied for centuries, a full understanding of…
It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…
The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity…
Rainfall from ice-free cumulus clouds requires collisions of large numbers of microscopic droplets to create every raindrop. The onset of rain showers can be surprisingly rapid, much faster than the mean time required for a single…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially…
Climate models robustly imply that some significant change in precipitation patterns will occur. Models consistently project that the intensity of individual precipitation events increases by approximately 6-7%/K, following the increase in…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
Two-sample testing is a fundamental problem in statistics, and many famous two-sample tests are designed to be fully non-parametric. These existing methods perform well with location and scale shifts but are less robust when faced with more…