Related papers: Conditional Averages and Probability Density Funct…
Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…
The Delta-variance analysis is an efficient tool for measuring the structural scaling behaviour of interstellar turbulence in astronomical maps. In paper I we proposed essential improvements to the Delta-variance analysis. In this paper we…
In some applications it is necessary to estimate derivatives of probability densities defined on the positive semi-axis. The quality of nonparametric estimates of the probability densities and their derivatives are strongly influenced by…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
Using the random intensity of noise (RIN) approach to the one-dimensional Laval-Dubrulle-Nazarenko type model for the Lagrangian acceleration in developed turbulence [cond-mat/0305186, cond-mat/0305459] we study the probability density…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional…
In this paper, we introduce a new way to estimate the scaling parameter of a self-similar process by considering the maximum probability density function (pdf) of tis increments. We prove this for $H$-self-similar processes in general and…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
The spectral density for random matrix $\beta$ ensembles can be written in terms of the average of the absolute value of the characteristic polynomial raised to the power of $\beta$, which for even $\beta$ is a polynomial of degree…
The cascade rate of passive scalar and Bachelor's constant in scalar turbulence are calculated using the flux formula. This calculation is done to first order in perturbation series. Batchelor's constant in three dimension is found to be…
Probability density functions and conditional averages of velocity gradients derived from upper ocean observations are compared with results from forced simulations of the two-dimensional Navier-Stokes equations. Ocean data are derived from…
Experimental multi-scalar measurements in laboratory flames have provided important databases for the validation of turbulent combustion closure models. In this work, we present a framework for data-based closure in turbulent combustion and…
A common objective in the analysis of tabular data is estimating the conditional distribution (in contrast to only producing predictions) of a set of "outcome" variables given a set of "covariates", which is sometimes referred to as the…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Factor models are a parsimonious way to explain the dependence of variables using several latent variables. In Gaussian 1-factor and structural factor models (such as bi-factor, oblique factor) and their factor copula counterparts, factor…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…