Optimal properties of some Bayesian inferences

Relative surprise regions are shown to minimize, among Bayesian credible regions, the prior probability of covering a false value from the prior. Such regions are also shown to be unbiased in the sense that the prior probability of covering a false value is bounded above by the prior probability of covering the true value. Relative surprise regions are shown to maximize both the Bayes factor in favor of the region containing the true value and the relative belief ratio, among all credible regions with the same posterior content. Relative surprise regions emerge naturally when we consider equivalence classes of credible regions generated via reparameterizations.Comment: Published in at http://dx.doi.org/10.1214/07-EJS126 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Az\'ema-Yor processes, their optimal properties and the Bachelier-drawdown equation

We study the class of Az\'ema-Yor processes defined from a general semimartingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. Solutions of the latter have the drawdown property: they always stay above a given function of their past maximum. We then show that any process which satisfies the drawdown property is in fact an Az\'ema-Yor process. The proofs exploit group structure of the set of Az\'ema-Yor processes, indexed by functions, which we introduce. We investigate in detail Az\'ema-Yor martingales defined from a nonnegative local martingale converging to zero at infinity. We establish relations between average value at risk, drawdown function, Hardy-Littlewood transform and its inverse. In particular, we construct Az\'ema-Yor martingales with a given terminal law and this allows us to rediscover the Az\'ema-Yor solution to the Skorokhod embedding problem. Finally, we characterize Az\'ema-Yor martingales showing they are optimal relative to the concave ordering of terminal variables among martingales whose maximum dominates stochastically a given benchmark.Comment: Published in at http://dx.doi.org/10.1214/10-AOP614 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal embeddings of ultradistributions into differential algebras

We construct embeddings of spaces of non-quasianalytic ultradistributions into differential algebras enjoying optimal properties in view of a Schwartz type impossibility result, also shown in this article. We develop microlocal analysis in these algebras consistent with the microlocal analysis in the corresponding spaces of ultradistributions

Optimal Properties of Experimental Designs

Abstract Not Provided

Multidimensional Binning Techniques for a Two Parameter Trilinear Gauge Coupling Estimation at LEP II

This paper describes two generalization schemes of the Optimal Variables technique in estimating simultaneously two Trilinear Gauge Couplings. The first is an iterative procedure to perform a 2-dimensional fit using the linear terms of the expansion of the probability density function with respect to the corresponding couplings, whilst the second is a clustering method of probability distribution representation in five dimensions. The pair production of W's at 183 GeV center of mass energy, where one W decays leptonically and the other hadronically, was used to demonstrate the optimal properties of the proposed estimation techniques.Comment: (25 pages, 11 figures

A First Mass Production of Gas Electron Multipliers

We report on the manufacture of a first batch of approximately 2,000 Gas Electron Multipliers (GEMs) using 3M's fully automated roll to roll flexible circuit production line. This process allows low-cost, reproducible fabrication of a high volume of GEMs of dimensions up to 30$\times$30 cm$^{2}$. First tests indicate that the resulting GEMs have optimal properties as radiation detectors. Production techniques and preliminary measurements of GEM performance are described. This now demonstrated industrial capability should help further establish the prominence of micropattern gas detectors in accelerator based and non-accelerator particle physics, imaging and photodetection.Comment: 11 pages, 10 figures, to be submitted to Nucl. Instr. Meth.