We provide estimates for the xed point ratios in the permutation representations of a nite classical group over a eld of order q on k-subspaces of its natural n-dimensional module. For suuciently large n each element must either have a negligible ratio or act linearly with a large eigenspace. We obtain an asymptotic estimate in the latter case, which in most cases is q ?dk where d is the codime...

The main result of this paper is the derivation of the probability density function of the cross ratio k a b c d c a d b d a c b when the numbers a, b, c and d are independent stochastic variables with identical rectangular distribution. The probability density function of the cross ratio is needed to study the effectiveness of invariant based recognition systems. A short background into invari...

In this paper we discuss abundance ratios and their relation to stellar nucleosynthesis and other parameters of chemical evolution models, reviewing and clarifying the correct use of the observed abundance ratios in several astrophysical contests. In particular, we start from the well known fact that abundance ratios depend on stellar yields, initial mass function and stellar lifetimes and we s...

Likelihood ratios are extensively used to evaluate the performances of diagnostic tests and to update prior odds of disease to posttest odds. Since few tests are truly 100% accurate, including many used as “gold standards,” it is important to be able to estimate likelihood ratios in cases where no such standard is available. In this paper, methods to calculate point and interval estimates for l...

We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. This approach offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the nonnegativity of our integrands, and the correlations that exist b...