Related papers: Comparison of continuity equation and Gaussian mix…
Galaxy evolution can be studied observationally by linking progenitor and descendant galaxies through an evolving cumulative number density selection. This procedure can reproduce the expected evolution of the median stellar mass from…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
Humans are exposed to complex mixtures of environmental pollutants rather than single chemicals, necessitating methods to quantify the health effects of such mixtures. Research on environmental mixtures provides insights into realistic…
Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…
We calculate the cosmological evolution of the 1-point probability distribution function (PDF), using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion of the PDF. Our method applies…
We investigate the cosmological evolution of interstellar dust with a semi-analytical galaxy formation model ($\nu^2$GC), focusing on the evolution of grain size distribution. The model predicts the statistical properties of dust mass and…
We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to…
Multivariate Gaussian distributions enjoy Gaussian conditional distributions that makes conditioning easy: conditioning boils down to implementing analytical formulae for conditional means and covariances. For more general distributions,…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
We investigate the evolution of the skewness of the distribution of density fluctuations in CDM models with both Gaussian and non--Gaussian initial fluctuations. We show that the method proposed by Coles \& Frenk (1991), which uses the…
Non-Gaussianity indicates complex dynamics related to extreme events or significant outliers. However, the correlation between non-Gaussianity and the dynamics of heterogeneous environments in anomalous diffusion remains uncertain. Inspired…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
Accurate modeling of contamination in subsurface flow and water aquifers is crucial for agriculture and environmental protection. Here, we demonstrate a parallel method to quantify the propagation of the uncertainty in the dispersal of…
In the present study we examine non-Gaussian spreading of solutes subject to advection, dispersion and kinetic sorption (adsorption/desorption). We start considering the behavior of a single particle and apply a random walk to describe…
We consider the behavior of the Gaussian concentration bound (GCB) under stochastic time evolution. More precisely, we consider a Markovian diffusion process on $\mathbb{R}^d$ and start the process from an initial distribution $\mu$ that…
Interstellar medium widely exists in the universe at multi-scales. In this study, we introduce the {\it Multi-scale Decomposition Reconstruction} method, an equation-based model designed to derive width maps of interstellar medium…
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate…