Testing conditional independence using maximal nonlinear conditional correlation

In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain desirable properties. When $Z$ is continuous, a test for testing the conditional independence of $X$ and $Y$ given $Z$ is constructed based on the estimator of a weighted average of the form $\sum_{k=1}^{n_Z}f_Z(z_k)\rho^2_1(X,Y|Z=z_k)$, where $f_Z$ is the probability density function of $Z$ and the $z_k$'s are some points in the range of $Z$. Under some conditions, it is shown that the test statistic is asymptotically normal under conditional independence, and the test is consistent.Comment: Published in at http://dx.doi.org/10.1214/09-AOS770 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effect of rootzone construction on soil physical properties and playing quality of golf greens under New Zealand conditions : a thesis presented in partial fulfilment of the requirements for the degree of Master of Applied Science in Plant Science at Massey University

A field experiment was designed to examine the effect of five different rootzone constructions (partially amended sand, silt soil, pure sand, fully amended sand and partially amended plus zeolite sand) and aeration methods (untreated control, HydroJect, Verti-drain and scarifying) on soil physical properties, root development and playing quality of golf greens. The five rootzone constructions were randomly arranged in three blocks. A split plot design was superimposed on the rootzone constructions using different aeration methods. Aeration treatments were carried out in the spring and autumn of 1998. Measurements of bulk density, total porosity, volumetric moisture content, air-filled porosity, infiltration rate, oxygen diffusion rate, saturated hydraulic conductivity, root mass, organic matter content, surface hardness and green speed were made to monitor differences between treatments. This study found there was no benefit of fully amended sand rootzone compared with partially amended sand rootzones (either plus or without zeolite). Although root development was greater in the pure sand rootzone, this occurred predominantly in the top 50 mm. Excessive accumulation near the surface of the profile can have detrimental impacts on turf growth. Rootzone construction had an important effect on surface hardness, i.e. pure sand rootzone produced the hardest surface, silt soil rootzone the softest and amended sand rootzones intermediate hardness. Rootzone construction had no effect on green speed in this study. Aeration treatment had no effect on any of the soil, plant or playing quality parameters measured in this study. This suggests either aeration treatments were very short lived or that long term effects of aeration treatments were not yet apparent

Convergence rates for posterior distributions and adaptive estimation

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000049

Physics Results From Alpha Magnetic Spectrometer 1998 Shuttle Flight

The Alpha Magnetic Spectrometer (AMS) is a particle detector designed to detect antimatter. During the 10-day test flight on the space shuttle in June 1998, AMS detected $10^8$ events. Upon analysis, no antimatter was found and the antimatter limit was reduced to $1.1\times10^{-6}$. The proton spectrum shows some differences with the cosmic ray flux used in atmospheric neutrino simulation. A large amount of protons, positrons, and electrons were found below the geomagnetic rigidity cutoff. The energy of these particles are as high as several GeV, one order of magnitude higher than any previously measured energy in radiation belts. These particles also exhibit many interesting features. This paper reviews the results in the four published papers of the AMS collaboration and provides explanation for some features of the albedo particles.Comment: 14 pages, 20 figures, The 7-th Taiwan Astrophysics Worksho