Let 5 be a Boolean algebra; let Π be a set of relative (= conditional) probability functions on S, and IT a set of absolute ones; and let V be A Π A, with A here an arbitrary but fixed member of S. (i) A function P' in IT is then the V-restriction of a function P in Π (= P has P' as its K-restriction) if V(A) = P(,4, V) for each A in S; and (ii) the functions in Π relativize those in IT if each...

A utility function is an important tool for representing a DM’s preference. We adjoin utility functions to multi-objective optimization problems. In current studies, usually one utility function is used for each objective function. Situations may arise for a goal to have multiple utility functions. Here, we consider a constrained multi-objective problem with each objective having multiple utili...

A technique is presented for representing linear features as probability density functions in 2D or 3D affine space. Two chief advantages of this approach are (1) a unified representation and algebra for manipulating points, lines, and planes, and (2) seamless incorporation of uncertainty information. Applications to Euclidean and non-metric scene reconstruction are presented, with results on i...

We present an interpretation of Dempster-Shafer theory based on the probability of provability. We present two forms of revision (conditioning) that lead to the geometrical rule of conditioning and to Dempster rule of conditioning, respectively.

We give estimates of the distance between the densities of the laws of two functionals F and G on the Wiener space in terms of the Malliavin-Sobolev norm of F −G. We actually consider a more general framework which allows one to treat with similar (Malliavin type) methods functionals of a Poisson point measure (solutions of jump type stochastic equations). We use the above estimates in order to...

We present an algorithm for grouping families of probability density functions (pdfs). We exploit the fact that under the square-root re-parametrization, the space of pdfs forms a Riemannian manifold, namely the unit Hilbert sphere. An immediate consequence of this re-parametrization is that different families of pdfs form different submanifolds of the unit Hilbert sphere. Therefore, the proble...

Bhat et al. [1] developed an inductive compiler that computes density functions for probability spaces described by programs in a probabilistic functional language. In this work, we implement such a compiler for a modified version of this language within the theorem prover Isabelle and give a formal proof of its soundness w.r.t. the semantics of the source and target language. Together with Isa...

An exact expression is obtained for the probability density function (pdf) of any quantity measured in a general stationary process, in terms of conditional expectations of time derivatives of the signal. This expression indicates that the conditional expectations of both the time derivative squared and of the second time derivative influence the shape of the pdf, including its tails. A previou...

We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...