We consider Stochastic Hybrid Systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an approach based on a set of Volterra equations to compute any statistical moment of the state of the SHS. Moreover, we provide a method to compute the Lyapunov exponents of a given degree, i.e., the exponential rat...

We develop a complete convergence theory for the Maximum Entropy method based on moment matching for a sequence of approximate statistical moments estimated by the Multilevel Monte Carlo method. Under appropriate regularity assumptions on the target probability density function, the proposed method is superior to the Maximum Entropy method with moments estimated by the Monte Carlo method. New t...

This paper provides a concise de nition for ignorable dropout. This is done primarily from a frequentist perspective. The de nition of ignorable dropout depends on both the population of inference and the type of statistical methodology used for inference. Di erent types of dropouts are described and compared to those found in the literature. Ignorability conditions are then given for the follo...

The simplest system in Levermore’s moment hierarchy involving moments higher than second order is the five–moment closure. It is obtained by taking velocity moments of the one–dimensional Boltzmann equation under the assumption that the velocity distribution is a maximum–entropy function. The moment vectors for which a maximum–entropy function exist consequently make up the domain of definition...

We study statistical properties of the random variables Xσ(π), the number of occurrences of the pattern σ in the permutation π. We present two contrasting approaches to this problem: traditional probability theory and the “less traditional” computational approach. Through the perspective of the first one, we prove that for any pair of patterns σ and τ , the random variables Xσ and Xτ are jointl...

Face recognition using different imaging modalities, particularly infrared imaging sensors, has become an area of growing interest. The use of thermal IR images can improve the performance of face recognition in uncontrolled illumination conditions. In this paper, we present a new technique for face recognition based on statistical calculations of thermal images. We propose the use of moments i...

This paper presents a new, univariate dimension-reduction method for calculating statistical moments of response of mechanical systems subject to uncertainties in loads, material properties, and geometry. The method involves an additive decomposition of a multi-dimensional response function into multiple one-dimensional functions, an approximation of response moments by moments of single random...

The Rayleigh-Taylor instability of an interface separating uids of distinct density is driven by an acceleration across the interface. Low order statistical moments of uctuating uid quantities characterize the hydrodynamics of the mixing zone. A new model is proposed for the momentum coupling between the two phases. This model is validated against computational data for compressible ows, includ...