We consider here the case where our knowledge is partial and based on a betting density function which is n-dimensional Gaussian. The explicit formulation of the least committed basic belief density (bbd) of the multivariate Gaussian pdf is provided in the transferable belief model (TBM) framework. Beliefs are then assigned to hyperspheres and the bbd follows a χ2 distribution. Two applications...

The Eulerian mapping closure approach is developed for uncertainty propagation in computational uid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear ow. An analytical argument shows that uctuation of the concentration eld at one point in space is non-Gaussian and exhibits stretched exponential form. An Eu...

A number of printing errors have appeared in [1] some of which were typos in the original manuscript, and others were introduced during the typesetting. Certain equations appeared only in half, while others were repeated twice. The authors had not had a chance to correct the galley proofs due to their absence from their contact addresses, and unfortunately, these errors went unnoticed until rec...

We have suggested in a previous publication a method to estimate the Bit Error Rate (BER) of a digital communications system instead of using the famous Monte Carlo (MC) simulation. This method was based on the estimation of the probability density function (pdf) of soft observed samples. The kernel method was used for the pdf estimation. In this paper, we suggest to use a Gaussian Mixture (GM)...

The bit error rate (BER) of a code spread CDMA system, using low rate convolutional codes for spreading, is analyzed. The system is assumed to operate over a Rayleigh flat fading channel, and white Gaussian noise is added at the receiver front-end. Based on a Gaussian approximation, expressions for the pdf of the signal-to-noise ratios are derived for both upand downlink transmission. Computer ...

For a collection of distributions over a countable support set, the worst case universal compression formulation by Shtarkov attempts to assign a universal distribution over the support set. The formulation aims to ensure that the universal distribution does not underestimate the probability of any element in the support set relative to distributions in the collection. When the alphabet is unco...

The properties of the probability distribution function of the cosmological continuous density eld are studied. We present further developments and compare dynamically motivated methods to derive the PDF. One of them is based on the Zel'dovich approximation (ZA). We extend this method for arbitrary initial conditions, regardless of whether they are Gaussian or not. The other approach is based o...

Abstract: A Gaussian sum filter (GSF) is proposed in this paper on simultaneous localization and mapping (SLAM) for mobile robot navigation. In particular, the SLAM problem is tackled here for cases when only bearing measurements are available. Within the stochastic mapping framework using an extended Kalman filter (EKF), a Gaussian probability density function (pdf) is assumed to describe the ...

An algorithmic procedure is developed for the random expansion of a given training set to combat overfitting and improve the generalization ability of backpropagation trained multilayer perceptrons (MLPs). The training set is K-means clustered and locally most entropic colored Gaussian joint input-output probability density function (pdf) estimates are formed per cluster. The number of clusters...