相关论文: Measures of Variance on Windowed Gaussian Processe…
This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude…
Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including third and…
The solar brightness varies on timescales from minutes to decades. Determining the sources of such variations, often referred to as solar noise, is of importance for multiple reasons: a) it is the background that limits the detection of…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H>1/2 as a typical example. We establish infinite and finite past…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…
We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
Automatic classification methods applied to sky surveys have revolutionized the astronomical target selection process. Most surveys generate a vast amount of time series, or \quotes{lightcurves}, that represent the brightness variability of…
The use of statistical fluctuations as probes of the microscopic dynamics of hot and dense hadronic matter is reviewed. Critical fluctuations near the critical point of QCD matter are predicted to enhance fluctuations in pionic observables.…
A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are…
This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics during random time…
A very small dispersion in the speed of light may be observable in Fermi time- and energy-tagged data on variable sources, such as gamma-ray bursts (GRB) and active galactic nuclei (AGN). We describe a method to compute the size of this…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
Surveys with a narrow field-of-view can play an important role in probing cosmology, but inferences from these surveys suffer from large sample variance, arising from random fluctuations around the cosmic mean. The standard method for…
A variety of statistical methods for understanding variability in the time domain for low count rate X-ray and gamma-ray sources are explored. Variability can be detected using nonparametric (Anderson-Darling and overdispersion tests) and…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
We present a Monte Carlo analysis of the recently introduced variability indices $\tau$ (Tompkins 1999) and $I$ (Zhang et al. 2000 & Torres et al. 2001) for $\gamma$-ray sources. We explore different variability criteria and prove that…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…