This paper examines two approaches to estimating implied risk-neutral probability density functions from the prices of European-style options. It sets up a monte carlo test to evaluate alternative techniques’ ability to recover simulated distributions based on Heston’s (1993) stochastic volatility model. The paper tests both for the accuracy and stability of the estimated summary statistics fro...

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 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...

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...

Many regression schemes deliver a point estimate only, but often it is useful or even essential to quantify the uncertainty inherent in a prediction. If a conditional density estimate is available, then prediction intervals can be derived from it. In this paper we compare three techniques for computing conditional density estimates using a class probability estimator, where this estimator is ap...

In ‘inverse problems’ data from indirect measurements are used to estimate unknown parameters of physical systems. Uncertain data, (possibly vague) prior information on model parameters, and a physical theory relating the model parameters to the observations are the fundamental elements of any inverse problem. Using concepts from probability theory, a consistent formulation of inverse problems ...