Concept# Sufficient statistic

Summary

In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter". In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than the statistic, as to which of those probability distributions is the sampling distribution.
A related concept is that of linear sufficiency, which is weaker than sufficiency but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic.
The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in descriptive sta

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Henning Paul-Julius Stahlberg, Jasenko Zivanov

Urease converts urea into ammonia and carbon dioxide and makes urea available as a nitrogen source for all forms of life except animals. In human bacterial pathogens, ureases also aid in the invasion of acidic environments such as the stomach by raising the surrounding pH. Here, we report the structure of urease from the pathogen Yersinia enterocolitica at 2 Å resolution from cryo-electron microscopy. Y. enterocolitica urease is a dodecameric assembly of a trimer of three protein chains, ureA, ureB and ureC. The high data quality enables detailed visualization of the urease bimetal active site and of the impact of radiation damage. The obtained structure is of sufficient quality to support drug development efforts.

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Switzerland has about 6,000 shooting ranges, of which 2,000 are still in use. These activities generate a significant lead pollution. FOEN estimated 200 tons of lead is fired each year. This Master Project has been realized with the consultancy office CSD Ingénieurs Conseils SA in Lausanne. The project is divided into three parts related to investigations and remediation of shooting ranges. Eleven shooting ranges of the army and two communal shooting ranges have formed the field study of this project. On these sites, 20 samples were taken for laboratory analysis. Nearly 350 field tests with a portable X-ray fluorescence (XRF) were also performed. The first part of the study focused on sample preparation methods. Based on several assumptions, they often give conflicting results. It has been shown that not taking into account the size fraction between 1 cm and 2 mm leads to underestimating the lead concentration by 10% on average. Taking into account the bullets, and how, is even more important. The original content of lead in standard military bullets is 74% of the weight. A common use is to assume this content for the bullets found in soils samples. The lead content measured in bullets is from 64% for those in good shape to 17% for fragments. Lead seems to spread more easily than the steel jacket of the bullets. These results are of major importance for the calculation of the lead content of samples. A strong correlation between lead and bullet amount in soils has not been found. The condition of the bullets seemed to be a significant factor, but the representativeness of the samples was not sufficient due too few mass samples. Taking into account these results, a preparation method was proposed. The second part of the study concern leachate analysis. In particular, OSites leachate and OTD1 (acid) leachate was studied. These leachates are used respectively for polluted sites risk assessment and for choosing treatment solution of excavated materials. Correlations were looked for, between concentrations in leachate and soils parameters. CEC, clay content, organic carbon content and aquous pH has been used as soils parameters. Leachate OTD1 (neutral) has been preferred to leachate Osites for economic reasons, these two tests provide similar results for lead. Good correlations were obtained with non-linear models taking into account all the soils parameters. Models based only on the lead content and aqueous pH (better correlation) give interesting results, but have greater error. The third part focused on the study of geostatistics shooting ranges with fixed targets. Variogram were made from field measurements. A metric sampling grid metric was used. The variogram showed a remedy made from a range of 3 meters. Although the site shows a clear anisotropy, an isotropic spherical variogram with nugget effect has been adjusted. The data were insufficient to fit an anisotropic model. Calculations showed that the kriging interpolation provides better results than those obtained with conventional interpolation. The study also showed that the uncertainty of the kriging interpolation decreases when the mesh sampling is lower. An optimum between accuracy and number of tests could not be found, because the variogram used has too much variability. The results are very promising and will continue to be worked out in order to produce the means of zoning and estimate for the remediation of shooting range.

2009Abstract—Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. A necessary condition for the validity of this approach is the existence and uniqueness of a solution to a fixed point equation. However, it was also recently pointed out that this condition is not sufficient; in contrast, a necessary and sufficient condition is a global stability property of the associated ordinary differential equation. Such a property was established only for a specific case, namely for a homogeneous system (all nodes have the same parameters) and when the number of backoff stages is either 1 or infinite and with other restrictive conditions. In this paper, we give a simple condition that establishes the validity of the decoupling assumption for the homogeneous case. We also discuss the heterogeneous and the differentiated service cases and show that the uniqueness condition is not sufficient; we exhibit one case where the fixed point equation has a unique solution but the decoupling assumption is not valid.

2010