2.1 The Main Theorem We first start with the simplest case where A and B are both subsets of the real line R. Let x ∈ A. The number pA(x) means that, in the infinitesimal interval [x, x+ δx), there exists pA(x)δx amount of “probability mass.” Here, δx is a “differential quantity” such that (δx) = 0. Assume that f is continuous and infinitely differentiable. The function f sends the interval [x,...

We report experimental results on the acceleration component probability distribution function at R λ = 690 to probabilities of less than 10 −7. This is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55. We compare our probability distribution to those predicted by several mode...

C. Pereira and J. Stern have recently introduced a measure of evidence of a precise hypothesis consisting of the posterior probability of the set of points having smaller density than the supremum over the hypothesis. The related procedure is seen to be a Bayes test for specific loss functions. The nature of such loss functions and their relation to stylised inference problems are investigated....

This paper presents conditions under which a person’s beliefs about the occurrence of uncertain events are quantified by a capacity measure, i.e., a nonadditive probability. Additivity of probability is violated in a large number of applications where probabilities are vague or ambiguous due to lack of information. The key feature of the theory presented in this paper is a separation of the der...

we propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on lp-losses for such estimators. we suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quad...