Related papers: Analytic Approach to the Cloud-in-cloud Problem fo…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…
Multi-modal densities appear frequently in time series and practical applications. However, they cannot be represented by common state estimators, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which…
The mass function of galaxy clusters is a sensitive tracer of the gravitational evolution of the cosmic large-scale structure and serves as an important census of the fraction of matter bound in large structures. We obtain the mass function…
We calculate the maximum fraction of matter which is able to condense out of the expanding background universe, for any universe which will expand forever. We use a simple spherical model for the growth of density fluctuations in the…
We present initial results on the use of Mixture Models for density estimation in large astronomical databases. We provide herein both the theoretical and experimental background for using a mixture model of Gaussians based on the…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power-law form for power spectra of temporal fluctuations of all scales ranging…
Though very popular, it is well known that the EM for GMM algorithm suffers from non-Gaussian distribution shapes, outliers and high-dimensionality. In this paper, we design a new robust clustering algorithm that can efficiently deal with…
We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of non-Gaussianity which can be characterised by a set of numbers $S_p$ describing…
We propose to integrate the Vlasov-Poisson equations giving the evolution of a dynamical system in phase-space using a continuous set of local basis functions. In practice, the method decomposes the density in phase-space into small smooth…
Radio waves propagating from distant pulsars in the interstellar medium (ISM), are refracted by electron density inhomogeneities, so that the intensity of observed pulses fluctuates with time. The theory relating the observed pulse…
We consider whether the non-Gaussian scale-dependent halo bias can be used not only to constrain the local form of non-Gaussianity but also to distinguish among different shapes. In particular, we ask whether it can constrain the behavior…
A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as…
Based on the field theory of density fluctuation under Newtonian gravity, we obtain analytically the nonlinear equation of 3-pt correlation function $\zeta$ of galaxies in a homogeneous, isotropic, static universe. The density fluctuations…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
The nature of structure formation around the particle free streaming scale is still far from understood. Many attempts to simulate hot, warm, and cold dark matter cosmologies with a free streaming cutoff have been performed with…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…
We study the non-Gaussian dynamics of a quasiclassical electronic circuit inductively coupled to a mesoscopic conductor. Non-Gaussian noise accompanying the nonequilibrium transport through the conductor significantly modifies the…
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…
We present a particle filtering algorithm for stochastic models on infinite dimensional state space, making use of Girsanov perturbations to nudge the ensemble of particles into regions of higher likelihood. We argue that the optimal…