Average

We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called "$p>n$" setup. When $\beta$ is sparse, or, more generally, when there is a sparse subset of covariates providing a close approximation to the unknown mean vector, we ask whether or not it is possible to accurately estimate $X\beta$ using a computationally tractable algorithm. We show that, in a surprisingly wide range of situations, the lasso happens to nearly select the best subset of variables. Quantitatively speaking, we prove that solving a simple quadratic program achieves a squared error within a logarithmic factor of the ideal mean squared error that one would achieve with an oracle supplying perfect information about which variables should and should not be included in the model. Interestingly, our results describe the average performance of the lasso; that is, the performance one can expect in an vast majority of cases where $X\beta$ is a sparse or nearly sparse superposition of variables, but not in all cases. Our results are nonasymptotic and widely applicable, since they simply require that pairs of predictor variables are not too collinear.

Summary.  The evaluation of results from mixtures of deoxyribonucleic acid (DNA) from two or more people in crime case investigations may be improved by taking not only the qualitative but also the quantitative part of the results into consideration. We present a statistical likelihood approach to assess the probability of observed peak heights and peak areas information for a pair of profiles matching the DNA mixture. Furthermore, we demonstrate how to incorporate this probability in the evaluation of the weight of the evidence by a likelihood ratio approach. Our model is based on a multivariate normal distribution of peak areas for assessing the weight of the evidence. On the basis of data from analyses of controlled experiments with mixed DNA samples, we exploited the linear relationship between peak heights and peak areas, and the linear relationships of the means and variances of the measurements. Furthermore, the contribution from one individual's allele to the mean area of this allele is assumed to be proportional to the average of peak height measurements of alleles, where the individual is the only contributor. For shared alleles in mixed DNA samples, it is possible to observe only the cumulative peak heights and areas. Complying with this latent structure, we used the EM algorithm to impute the missing variables on the basis of a compound symmetry model. The measurements were subject to intralocus and interlocus correlations not depending on the actual alleles of the DNA profiles. Owing to factorization of the likelihood, properties of the normal distribution and use of auxiliary variables, an ordinary implementation of the EM algorithm solved the missing data problem.

Euphotic zone depth (Zeu) products from ocean color measurements are now produced from MODIS ocean color measurements, one of which is based on inherent optical properties (IOP-approach) and the other is based on chlorophyll-a concentration (Chl-approach). For the first time, the quality of these satellite Zeu products is assessed with extensive field-measured Zeu (in the China Sea), where 78% of the measurements were made on the continental shelf (≤ 200 m). For the data with matching location and time window, we have found that the overall average difference (ε) between satellite and in situ Zeu is 21.8% (n = 218, Zeu ranges from 4 to 93 m) with a root mean square error in log scale (RMSE) of 0.118 by the IOP-approach, while it is 49.9% (RMSE = 0.205) by the Chl-approach. These results suggest that 1) MODIS Zeu products for waters in the China Sea are robust, even in shelf waters; and 2) Zeu produced with IOPs are more reliable than those produced with empirically derived Chl. Spatial and seasonal variations of Zeu in the China Sea are briefly described with Zeu products generated by the IOP-approach. These results will facilitate further research on carbon cycling and environmental changes on both local and global scales.

NOAA's Climate Prediction Center issues seasonal climate forecasts predicting total precipitation and average air temperature for three-month periods out to a year in advance. The utility of these seasonal forecasts for agricultural applications will depend on forecast characteristics, including dependability and effectiveness. Dependability is defined as the ability of the forecasts to correctly predict future climate probabilities. Effectiveness refers to the ability of the forecasts to provide information beyond that achieved by standard climatological considerations. Measures of dependability and effectiveness are developed for the NOAA probability of exceedance forecasts, and evaluated for the forecasts issued for 1997 through early 2005 for the contiguous U.S. Both measures require that forecasts satisfy a usefulness threshold of an 8% departure from climatological odds prior to inclusion in the evaluation. Results depend on forecast variable, direction of forecast (wetter...

The present study was conducted in Kohistan region, where mafic and ultramafic rocks (Kohistan island arc and Indus suture zone) and metasedimentary rocks (Indian plate) are exposed. Water samples were collected from the springs, streams and Indus river and analyzed for physical parameters, anions, cations and arsenic (As(3+), As(5+) and arsenic total). The water quality in Kohistan region was evaluated by comparing the physio-chemical parameters with permissible limits set by Pakistan environmental protection agency and world health organization. Most of the studied parameters were found within their respective permissible limits. However in some samples, the iron and arsenic concentrations exceeded their permissible limits. For health risk assessment of arsenic, the average daily dose, hazards quotient (HQ) and cancer risk were calculated by using statistical formulas. The values of HQ were found >1 in the samples collected from Jabba, Dubair, while HQ values were <1 in rest of the samples. This level of contamination should have low chronic risk and medium cancer risk when compared with US EPA guidelines. Furthermore, the inter-dependence of physio-chemical parameters and pollution load was also calculated by using multivariate statistical techniques like one-way ANOVA, correlation analysis, regression analysis, cluster analysis and principle component analysis.