This is an entry for The Encyclopedia of Statistics in Behavioral Science, to be published by Wiley in 2005. In regression analysis there are n observations yi on a dependent variable(also known as outcome or criterion) that are related to n corresponding observations xi on p independent variables (also known as inputs or predictors). Fitting regression models of some form or another is by far ...

These lectures give a detailed introduction to constructing and analyzing string vacua suitable for phenomenological model building, with particular emphasis on F-theory flux vacua. Topics include (1) general challenges and overview of some proposed scenarios, (2) an extensive introduction to F-theory and its relation to M-theory and perturbative IIB string theory, (3) F-theory flux vacua and m...

In this paper we extend Chandrasekhar and von Neumann’s analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function W (F, dF/dt) giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt. We calculate the first m...

A general solution of the functional equation J f{x+y)dfii(y) = f(x) where / is a nonnegative function and ?i is a o--finite positive Borel measure on [0, oo ) is shown to be f(x) = p(x) exp (xa?) where p is a periodic function with every yep, the support of ft as a period. The solution is applied in characterizing Pareto, exponential and geometric distributions by properties of integrated lack...

We develop numerical methods for computing statistics of stochastic processes on surfaces general shape with drift-diffusion dynamics dXt=a(Xt)dt+b(Xt)dWt. formulate descriptions Brownian motion and surfaces. consider the form u(x)=Ex[∫0τg(Xt)dt]+Ex[f(Xτ)] a domain Ω exit stopping time τ=inft⁡{t>0|Xt∉Ω}, where f,g are smooth functions. For these statistics, we high-order Generalized Moving Leas...

A framework fo r statistical modeling of the wideband characterABSTRACT ist ics o f the frequency-selective fad ing mul t ipa th indoor radio channel fo r geolocation applications is presented. Mul t ipath characteristics o f the channel are divided into three classes according t o availability and the strength of the direct line of sight (DLOS) path w i th respect t o the other paths. Statisti...

In this paper we extend Chandrasekhar and von Neumann’s analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function W (F, dF/dt) giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt. We calculate the first m...

A Martin, D Nolan, S Gaudieri, C Almeida, F Carvalho, C Witt, D Sayer , R Nolan , S Herrmann, F Christiansen and S Mallal Centre for Clinical Immunology and Biomedical Statistics, Murdoch University and Royal Perth Hospital, Perth, Western Australia; Department of Pathology, University of Western Australia; and Department of Clinical Immunology and Biochemical Genetics, Royal Perth Hospital, We...

Comparison Theorems for Small Deviations of Random Series F. Gao, J. Hannig and F. Torcaso Department of Mathematics, University of Idaho Moscow, ID 83844-1103, USA [email protected] Department of Statistics, Colorado State University Ft. Collins, CO 80523-1877, USA [email protected] Department of Mathematical Sciences, Johns Hopkins University Baltimore, MD 21218-2682, USA torcaso@mts...

The package Hierfstat for the statistical software R (R Development Core Team [2003]) allows to estimate hierarchical F-statistics from a hierarchy with any numbers of levels. In addition, it allows testing the statistical significance of population differentiation for these different levels, using a generalized likelihood-ratio test. The package Hierfstat is available from http://www.unil.ch/p...