The Energy Response of Calorimeters

2018 ◽  
Author(s):  
Richard Wigmans
Keyword(s):  
Sampling Frequency ◽  
Integration Time ◽  
Signal Integration ◽  
Energy Response ◽  
Absorption Process ◽  
Active Materials ◽  
Unit Energy ◽  
Sampling Fraction ◽  
Signal Integration Time ◽  
Calorimeter Response

This chapter deals with the signals produced by particles that are being absorbed in a calorimeter. The calorimeter response is defined as the average signal produced per unit energy deposited in this absorption process, for example in terms of picoCoulombs per GeV. Defined in this way, a linear calorimeter has a constant response. Typically, the response of the calorimeter depends on the type of particle absorbed in it. Also, most calorimeters are non-linear for hadronic shower detection. This is the essence of the so-called non-compensation problem, which has in practice major consequences for the performance of calorimeters. The origins of this problem, and its possible solutions are described. The roles of the sampling fraction, the sampling frequency, the signal integration time and the choice of the absorber and active materials are examined in detail. Important parameters, such as the e/mip and e/h values, are defined and methods to determine their value are described.

Excavation Sample Size: A Cautionary Tale

1993 ◽  
Vol 58 (3) ◽  
pp. 523-529 ◽  
Author(s):  
Dennis H. O'Neil
Keyword(s):  
Cultural Resource Management ◽  
Small Sample ◽  
Sampling Strategies ◽  
Cautionary Tale ◽  
Complete Understanding ◽  
Cultural Resource ◽  
Sampling Fraction ◽  
Small Sample Sizes ◽  
A Site ◽  
Management Work

Frequently, only five percent or less of a midden site is excavated for environmental-analysis purposes before it is turned over to the bulldozers for destruction. Such exceptionally small sample sizes have become accepted in cultural-resource-management work as adequate for gaining a good understanding of the chronology and cultural activities at a site. This assumption was tested by the author with a 63 percent excavation sampling fraction from a southern California midden. The data indicate that a far-from-complete understanding of a site may result from small sampling fractions and that more carefully designed sampling strategies and statistical manipulation of the data may not overcome this problem.

Equal probability sampling

2019 ◽  
pp. 23-47
Author(s):  
David G. Hankin ◽  
Michael S. Mohr ◽  
Ken B. Newman
Keyword(s):  
Sample Size ◽  
Relative Efficiency ◽  
Finite Population ◽  
Simple Random Sampling ◽  
Sampling Distribution ◽  
Equal Probability ◽  
Sampling Variance ◽  
Selection Methods ◽  
Target Variable ◽  
Sampling Fraction

This chapter presents a formal quantitative treatment of material covered conceptually in Chapter 2, all with respect to equal probability with replacement (SWR) and without replacement selection simple random sampling, (SRS) of samples of size n from a finite population of size N. Small sample space examples are used to illustrate unbiasedness of mean-per-unit estimators of the mean, total and proportion of the target variable, y, for SWR and SRS. Explicit formulas for sampling variance indicate how estimator uncertainty depends on finite population variance, sample size and sampling fraction. Measures of the relative performance of alternative sampling strategies (relative precision, relative efficiency, net relative efficiency) are introduced and applied to mean-per-unit estimators used for the SWR and SRS selection methods. Normality of the sampling distribution of the SRS mean-per-unit estimator depends on sample size but also on the shape of the distribution of the target variable, y, values over the finite population units. Normality of the sampling distribution is required to justify construction of valid 95% confidence intervals that may be constructed around sample estimates based on unbiased estimates of sampling variance. Methods to calculate sample size to achieve accuracy objectives are presented. Additional topics include Bernoulli sampling (a without replacement selection scheme for which sample size is a random variable), the Rao–Blackwell theorem (which allows improvement of estimators that are based on selection methods which may result in repeated selection of the same units), oversampling and nonresponse.

Estimating Diversification Rates on Incompletely Sampled Phylogenies: Theoretical Concerns and Practical Solutions

2019 ◽  
Vol 69 (3) ◽  
pp. 602-611 ◽  
Author(s):  
Jonathan Chang ◽  
Daniel L Rabosky ◽  
Michael E Alfaro
Keyword(s):  
Statistical Power ◽  
Likelihood Function ◽  
Point Of View ◽  
Death Process ◽  
Rate Variation ◽  
Sampled Data ◽  
Diversification Rates ◽  
Sampling Fraction ◽  
Incomplete Sampling ◽  
Birth Death

Abstract Molecular phylogenies are a key source of information about the tempo and mode of species diversification. However, most empirical phylogenies do not contain representatives of all species, such that diversification rates are typically estimated from incompletely sampled data. Most researchers recognize that incomplete sampling can lead to biased rate estimates, but the statistical properties of methods for accommodating incomplete sampling remain poorly known. In this point of view, we demonstrate theoretical concerns with the widespread use of analytical sampling corrections for sparsely sampled phylogenies of higher taxonomic groups. In particular, corrections based on “sampling fractions” can lead to low statistical power to infer rate variation when it is present, depending on the likelihood function used for inference. In the extreme, the sampling fraction correction can lead to spurious patterns of diversification that are driven solely by unbalanced sampling across the tree in concert with low overall power to infer shifts. Stochastic polytomy resolution provides an alternative to sampling fraction approaches that avoids some of these biases. We show that stochastic polytomy resolvers can greatly improve the power of common analyses to estimate shifts in diversification rates. We introduce a new stochastic polytomy resolution method (Taxonomic Addition for Complete Trees [TACT]) that uses birth–death-sampling estimators across an ultrametric phylogeny to estimate branching times for unsampled taxa, with taxonomic information to compatibly place new taxa onto a backbone phylogeny. We close with practical recommendations for diversification inference under several common scenarios of incomplete sampling. [Birth–death process; diversification; incomplete sampling; phylogenetic uncertainty; rate heterogeneity; rate shifts; stochastic polytomy resolution.]

I. The Theoretical Framework

1974 ◽  
Vol 28 ◽  
pp. 1-6
Author(s):  
James W. Mueller
Keyword(s):  
Survey Methods ◽  
Theoretical Framework ◽  
Archaeological Survey ◽  
General Outline ◽  
Sampling Fraction

A general outline of, and justification for, this study, as well as a discussion of the major related concepts, are presented in this chapter.Carl Lloyd supervised an archaeological survey of the area adjacent to the Ackmen pueblo in southwestern Colorado in 1937 in order to supplement the data recovered from the excavation of this famous site. Sixty-six quarter-sections (each equivalent to a ¼ sq mi area) measuring ½ mi on each side, were intensively surveyed by a large crew. Members of the crew were stationed 100 ft apart along the ½-mi width of the quarter-section, and the entire crew walked across the ½-mi length of the quarter-section.From each section consisting of 4 quarter-sections, 2 diagonal quarter-sections were selected for investigation. Lloyd assumed that 66 surveyed quarter-sections would reflect adequately, at least, on a 33-sq mi area near the rim. This assumption was based on the rather large (50%) sampling fraction that he employed. He was not certain that his survey methods would produce a contribution to the archaeology of the area and stated the uncertainty as follows: “Given a discontinous intensive archaeological survey of a region, what contributions can be made to the archaeology of that region by means of an analysis of the data thus obtained?” (Lloyd 1938:282). He did not explicitly answer that question during the course of his report. However, I believe that his answer was implicitly positive, that is, the kind of survey he performed did produce a meaningful contribution to the archaeology of the Ackmen-Lowry region.

scholarly journals A Metric Fractionator for Estimation of Total Cell Number in Paraffin-Embedded Flat or Hollow Organs

2020 ◽  
Vol 48 (6) ◽  
pp. 784-790
Author(s):  
Rosanna Mirabile ◽  
Rogely Waite Boyce ◽  
Hans Jørgen G. Gundersen
Keyword(s):  
Cell Number ◽  
Total Cell ◽  
Total Cell Number ◽  
Organ Volume ◽  
Final Sample ◽  
Sampling Fraction ◽  
Tissue Shrinkage ◽  
Final Fraction ◽  
The Individual ◽  
Physical Disector

The physical fractionator is a convenient and practical solution for estimation of total cell number in a regulatory toxicology setting because it is insensitive to shrinkage allowing for paraffin processing/embedding and does not require measurement of the reference or organ volume. The principle involves sampling a known fraction of an organ in one or more steps and counting the total number of cells present in the final sample, physical disector section pairs. The total cell number in the organ is estimated by multiplying the cell count in the final fraction by the inverse of the sampling fraction(s). The key feature of the design is that tissue shrinkage due to paraffin processing occurs before the organ is uniformly sampled. Another requirement is that thermal expansion or contraction is avoided during the preparation of disector sections from the individual embedded subsamples, which ensures that the disector sections represent a known constant fraction. This vertical physical fractionator with subsampling is a simple and fast estimator to obtain precise and robust estimates of total cell number in large flat or hollow organs that do not prolong routine necropsy procedures. It is compatible with paraffin processing, avoids exhaustive sectioning, and allows for the collection of routine histopathology sections.

RE-IDENTIFYING REGISTER DATA BY SURVEY DATA USING CLUSTER ANALYSIS: AN EMPIRICAL STUDY

2002 ◽  
Vol 10 (05) ◽  
pp. 589-607 ◽  
Author(s):  
JOHANN BACHER ◽  
RUTH BRAND ◽  
STEFAN BENDER
Keyword(s):  
Cluster Analysis ◽  
Survey Data ◽  
Empirical Studies ◽  
Register Data ◽  
Special Groups ◽  
The Social ◽  
Sampling Fraction ◽  
Statistical Agencies ◽  
Life History Study ◽  
Sample Fraction

More and more empirical researchers from universities or research centres like to use register or survey data collected by statistical agencies or the social security system, since these data can by used for several empirical studies, e.g. the analysis of special groups or quantitative effects of economic or social policies. Most of the data required have to be (factually) anonymised before they are disseminated to preserve confidentiality. In the area of statistics on households and individuals this path has been pursued in Germany for several years. The transmission of de facto anonymised datafiles has proved to be a good form of co-operation between scientists and statisticians. Factual anonymity of the data depends on the costs and benefits of a potential re-identification. The paper assumes that the intruder only accepts low costs. Therefore he uses a cluster analysis module that is available in a standards statistical software package to re-identify persons. After a description of the method different factors influencing the re-identification risk are studied using German employment statistics (register data) and the German Life History Study (survey data). The factors are: sample fraction and number of (irrelevant) variables. The results show, that the number of identifiable persons is remarkable high. Furthermore it can be confirmed with the cluster analysis that the number of re-identifiable records increases with increasing sampling fraction and that irrelevant variables reduce this number.

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