A common class of shielding problems involves the calculation of biological dose rates from large distributed sources at localised positions. A typical example is that of calculating the dose at points around a transport cask. Sophisticated variance reduction methods must be used in Monte Carlo calculations to sample from the important parts of the source and to propagate particles towards the ...

In this paper we propose a methodology for minimizing the variance of a cube (mosaicked) representation of a scene imaged by a pan-tilt camera. The minimization is based on the estimation of the vignetting image distortion, using the pan and tilt degrees of freedom instead of color calibrating patterns. Experiments with real images show that variance minimization is effective for improving even...

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of populations tends to infinity. We consider several cases of various orders of the sample sizes and show that the maximum likelihood estimator of the variance may or m...

We introduce a new version of Stein’s method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance has to be bounded has an explicit formula that makes it possible to carry out the program more easily. As an applicatio...

This chapter addresses models that incorporate more than one kind of variability, variously called mixed, multilevel, multistratum, or hierarchical models. It starts by considering data with (1) changing amounts of variability or (2) correlation among data points. These kinds of data can be modeled adequately with the tools introduced in previous chapters. The last part of the chapter considers...

The general form for the probability density and for the transition probability of a nonequilibrium system is given. Maximization of the latter gives a generalized fluctuation-dissipation theorem by providing a molecular basis for Langevin's friction force that avoids continuum hydrodynamics. The result shows that the friction coefficient must be proportional to the variance of the stochastic e...

We consider a mean-variance hedging (MVH) problem for an arbitrage-free large financial market, i.e. a financial market with countably many risky assets modelled by a sequence of continuous semimartingales. By using the stochastic integration theory for a sequence of semimartingales developed in De Donno and Pratelli (2003), we extend the results about change of numéraire and MVH of Gourieroux,...

We have established a compact and transportable I2-stabilized Nd:YAG laser for international comparisons of laser frequency. The root Allan variance of the portable laser has reached 3 9 10 14 when the integration time is longer than 200 s. The results of an international comparison between the National Research Laboratory of Metrology (NRLM), Tsukuba, Japan and the JILA (formerly the Joint Ins...

We present results for the strangeness contribution to the nucleon, 〈N|s̄s|N〉 and to the spin of the nucleon, ∆s. By combining several variance reduction techniques for all-to-all propagators we are able to obtain gains in terms of computer time of factors of 25–30 for the disconnected loop that is needed within the calculation of ∆s, relative to the standard approach of just employing time part...