Related papers: The zero degree of freedom non-central chi squared…
Weather forecasts are typically given in the form of forecast ensembles obtained from multiple runs of numerical weather prediction models with varying initial conditions and physics parameterizations. Such ensemble predictions tend to be…
Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…
Many experiments utilize the precession of trapped particles in magnetic fields to perform high precision measurements. It had been presumed that after free precession, initially polarized particles will form a Gaussian phase distribution…
The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally obtain the {\em nonsymmetric indefinite system} [Chen et al., IMA J. Numer. Anal., (2021)]. In this case, the discrete maximum…
Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (XC) free energy functional accurate over a wide range of state conditions.…
Exact expressions are given for the distribution function of the ratio of a weighted sum of independent chi-squared variables to a single chi-square variable, scaled appropriately. This distribution is the generalization of the classical F…
Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…
This paper focuses on inhomogeneous quadratic tests, which involve the sum of a dependent non-central chi-square with a Gaussian random variable. Unfortunately, no closed-form expression is available for the statistical distribution of the…
A massive dataset often consists of a growing number of (potentially) heterogeneous sub-populations. This paper is concerned about testing various forms of heterogeneity arising from massive data. In a general nonparametric framework, a set…
We derive a fully analytical, one-line closed-form expression for the cumulative distribution function (CDF) of the product of two correlated zero-mean normal random variables, avoiding any series representation. This result complements the…
We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded…
The analysis of seasonal or annual block maxima is of interest in fields such as hydrology, climatology or meteorology. In connection with the celebrated method of block maxima, we study several tests that can be used to assess whether the…
The phase transition of the three--dimensional random field Ising model with a discrete ($\pm h$) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific…
The phase transition of the three--dimensional random field Ising model with a discrete ($\pm h$) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific…
There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the…
Non-Gaussian distributions are commonly observed in collisionless space plasmas. Generating samples from non-Gaussian distributions is critical for the initialization of particle-in-cell simulations that investigate their driven and…
In this paper non-asymptotic exact exponential estimates are derived for the tail of maximum distribution of random field in the terms of majoring measures or, equally, generic chaining.
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…