Numerical Computations of Separability Probabilities

Max-Min Posterior Pseudo-Probabilities Estimation of Posterior Class Probabilities to Maximize Class Separability

The estimation of the posterior class probabilities is desirable for optimal decision, decision confidence measure, and accurate performance evaluation of a classifier. In this paper, we address the problem of estimating posterior class probabilities by learning from samples for producing optimal classifiers. We introduce a posterior pseudo-probability function based on Bayes’ formula to transf...

Numerical computations of infinite products

The infinite product Q1 n1⁄40ð1 aqnÞ, plays a part in the theory of basic functions, similar to that of the Gamma function in the theoryof ordinaryhy pergeometric functions, so it is pertinent to enquire how such products can be evaluated numerically. In this paper we will discuss the numerical evaluation of the infinite products using the method of gridded data interpolation. 2004 Elsevier Inc...

Numerical computations concerning the GRH

Numerical Computations concerning the Erh

This paper describes a computation which established the ERH to height 10000 for all primitive Dirichlet ¿-series with conductor Q < 13 , and to height 2500 for all Q < 72, all composite Q < 112, and other moduli. The computations were based on Euler-Maclaurin summation. Care was taken to obtain mathematically rigorous results: the zeros were first located within 10~12 , then rigorously separat...

Numerical Computation of Multivariate Normal Probabilities

The numerical computation of a multivariate normal probability is often a diicult problem. This article describes a transformation that simpliies the problem and places it into a form that allows eecient calculation using standard numerical multiple integration algorithms. Test results are presented that compare implementations of two algorithms that use the transformation, with currently avail...