This paper announces support in the form of the Spearman rank correlation test for the hypothesis: stock variance is a stable commodity, but the covariance of stocks varies randomly. Among the consequences of this hypothesis are: 1. Arbitrage equations involving covariances do not constrain the marketplace. 2. Variance is a stable commodity whose price is set by the arbitrage opportunities it p...

In this paper, low-complexity distributed fusion filtering algorithm for mixed continuous-discrete multisensory dynamic systems is proposed. To implement the algorithm a new recursive equations for local cross-covariances are derived. To achieve an effective fusion filtering the covariance intersection (CI) algorithm is used. The CI algorithm is useful due to its low-computational complexity fo...

This paper derives a fundamental result for processing two correlated random vectors with unknown cross–correlation, where constraints on the maximum absolute correlation coefficient are given. A tight upper bound for the joint covariance matrix is derived on the basis of the individual covariances and the correlation constraint. For symmetric constraints, the bounding covariance matrix natural...

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density – the Fourier transform of a kernel – with a Gaussian mixture. The propos...

A statistical method is reported to determine the pairs of fragment ions in a mass spectrum that are most susceptible to control by adaptive optimization of the laser pulse shapes in the strong-field regime. The proposed method is based on covariance analysis of the mass spectral fragmentation patterns generated by a set of randomly shaped pulses. The pairs of fragment ions that have higher neg...

This paper deals with the fusion of random variables when cross covariances are unknown. This is a vital problem in nearly every real world application since cross covariances are often impossible to obtain but also cannot be ignored. We provide a rigorous derivation of the fusion equations which are also known as covariance intersection. This approach allows us to derive an iterative scheme fo...

Nei and Gojobori (1986) developed a simple method to estimate the numbers of synonymous (ds) and nonsynonymous (dN) substitutions per site. In the present paper, we have developed a method for computing variances and covariances of ds's and dN's and of the proportions of synonymous (ps) and nonsynonymous (pN) differences. We also have developed a method for computing the variances of mean dS, d...

Models based on stationary covariance functions, such as the Matérn family, are commonly used in spatial statistics. For large grid resolutions, the computational effort can be substantial, as well as the memory requirements. A solution to this problem is to approximate the stationary covariances with aMarkov random field model on the grid. This report contains the theoretical basis for one suc...

By using a model of gene conversion for treating concerted evolution of multigene families, a theory for calculating the variances and covariances of identity coefficients has been developed. Six coefficients on triple identity and 15 coefficients on quadruple identity are needed. The variances and covariances are obtained from the quadruple identity coefficients and divided into within-populat...

We study the trajectories of a single colloidal particle as it hops between two energy wells which are sculpted using optical traps. Whereas the dynamical behaviors of such systems are often treated by master-equation methods that focus on particles as actors, we analyze them instead using a trajectory-based variational method called maximum caliber (MaxCal). We show that the MaxCal strategy ac...