Use Of Order Statistics Research Articles

Topological data analysis of human brain networks through order statistics.

Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significant topological difference between the male and female brain networks.

Determination of tolerance limits for fuel assembly fission gas release summary statistics

Instant release fraction is used in spent fuel final disposal studies to estimate the quickly released inventory from a spent fuel final disposal capsule. The instant release fraction has been correlated with fission gas release, which can be readily calculated with fuel performance codes. In spent fuel final disposal, individual rod fission gas releases are not important, as the fuel is treated in complete capsules containing multiple assemblies. Therefore assembly summary statistics are more suitable for this purpose.Summary statistics such as mean or maximum are useful in this application. However, the nominal values for the assembly mean fission gas release may be nonconservative estimates, whereas the assembly maximum fission gas release is a highly conservative assumption. This results from the “cutoff log-normal” distribution of fission gas release in an assembly and in a more general level, the reactor core. The tail of the distribution contains a small amount of rods with a high fission gas release, whereas a large number of rods typically have low fission gas releases.Compared to nominal summary statistics, a better method to show compliance with regulatory criteria is to determine the distribution of the assembly mean, taking into account the effects of manufacturing tolerances and uncertainty of the power history. The upper tolerance limit is straightforward to calculate with order statistics and with suitable parameters it is accepted by many regulatory authorities. In this work, the calculation of tolerance limits has been applied to mean fission gas release in complete fuel assemblies. A calculation system for such analyses has been developed at VTT, and by calculating each rod multiple times it can be used to determine the tolerance limits for complete nuclear reactor cores.In statistical analyses, typically a large number of simulations must be run. This increases the probability of failure of the simulation program due to nonconvergence of the calculation. This results in missing data, and this could prevent the use of order statistics which are based on the sorting of observations. With missing data, the real order of the observations is unknown. This work suggests a suitable data treatment method to overcome this problem.

Two stage adaptive cluster sampling based on ordered statistics

The estimation problem on sparsely distributed populations using adaptive cluster sampling (ACS) is discussed. In the first phase of ACS, two stage sampling is used in which primary and secondary sampling units are selected using simple random sampling without replacement. The idea of Thompson (1996) is introduced in order to choose an appropriate fixed value of pre-specified condition, which might represent the number of rare species, before conducting the survey by the use of order statistics. Different estimators of the population mean under the two possible schemes (open and closed boundaries of primary sampling units) are studied and the Rao-Blackwell theorem for improving these estimators is also used. Numerical illustrations, one on real life data and the other based on simulation study, are discussed for these two schemes. This design may be quite useful in environmental, forestry and other areas of research dealing with rare, endangered or threatened species.

A Framework for Acoustic Segmentation Using Order Statistic-Constant False Alarm Rate in Two Dimensions From Sidescan Sonar Data

This paper describes a framework for object segmentation from sidescan sonar acoustic data. The current techniques consume a great deal of computational resources to accurately carry out object segmentation. They also involve the tuning of many parameters to obtain good quality images. This is due to the handling of the large data volume generated by these devices and environmental fluctuations such as salinity, density, temperature, and others variations. The framework proposed uses a migration and adaptation of a technique widely used in radar technology for detecting moving objects. This radar technique is known as order statistic-constant false alarm rate (OS-CFAR) applied in 2-D. OS-CFAR 2-D rank orders the samples obtained from a sliding window to make a segmentation of the image. This segmentation is done into several types of regions: acoustic highlight, shadow, and different seafloor reverberation areas. OS-CFAR 2-D is less sensitive than other methods to the presence of the speckle noise due to the use of order statistics. This proposal was contrasted experimentally on real images. Likewise, an experimental comparison with the results obtained with the undecimated discrete wavelet transform, active contours, Markov random field, and accumulated cell averaging CFAR applied in two dimensions technique is also presented.

We are All Bayesian, Everyone is Not a Bayesian

Medical research makes intensive use of statistics in order to support its claims. In this paper we make explicit an epistemological tension between the conduct of clinical trials and their interpretation: statistical evidence is sometimes discarded on the basis of an (often) underlined Bayesian reasoning. We suggest that acknowledging the potentiality of Bayesian statistics might contribute to clarify and improve comprehension of medical research. Nevertheless, despite Bayesianism may provide a better account for scientific inference with respect to the standard frequentist approach, Bayesian statistics is rarely adopted in clinical research. The main reason lies in the supposed subjective elements characterizing this perspective. Hence, we discuss this objection presenting the so-called Reference analysis, a formal method which has been developed in the context of objective Bayesian statistics in order to define priors which have a minimal or null impact on posterior probabilities. Furthermore, according to this method only available data are relevant sources of information, so that it resists the most common criticisms against Bayesianism.

Edge- and vertex-reinforced random walks with super-linear reinforcement on infinite graphs

In this paper we introduce a new simple but powerful general technique for the study of edge- and vertex-reinforced processes with super-linear reinforcement, based on the use of order statistics for the number of edge, respectively of vertex, traversals. The technique relies on upper bound estimates for the number of edge traversals, proved in a different context by Cotar and Limic [Ann. Appl. Probab. (2009)] for finite graphs with edge reinforcement. We apply our new method both to edge- and to vertex-reinforced random walks with super-linear reinforcement on arbitrary infinite connected graphs of bounded degree. We stress that, unlike all previous results for processes with super-linear reinforcement, we make no other assumption on the graphs. For edge-reinforced random walks, we complete the results of Limic and Tarr\`es [Ann. Probab. (2007)] and we settle a conjecture of Sellke [Technical Report 94-26, Purdue University (1994)] by showing that for any reciprocally summable reinforcement weight function w, the walk traverses a random attracting edge at all large times. For vertex-reinforced random walks, we extend results previously obtained on Z by Volkov [Ann. Probab. (2001)] and by Basdevant, Schapira and Singh [Ann. Probab. (2014)], and on complete graphs by Benaim, Raimond and Schapira [ALEA (2013)]. We show that on any infinite connected graph of bounded degree, with reinforcement weight function w taken from a general class of reciprocally summable reinforcement weight functions, the walk traverses two random neighbouring attracting vertices at all large times.

Are the Current Changes Good or Bad for Chemistry?

"… The key discoveries on which many commercial products are ultimately based are often the result of fundamental research performed with no (commercial) end-use even contemplated. It is remarkable that the idea of supporting truly fundamental research is under assault to varying degrees worldwide. Humankind will benefit from an environment where the emergence of completely new ideas is encouraged …" Read more in the Editorial by Ian Manners.

Use of Multivariate Statistics in Order to Understand the Flow of Acid Rock Drainage from an Abandoned Mining Site

Pathways for acid rock drainage from an abandoned mining site (sulphidic ore) were investigated by analysing ground, seepage and surface waters. It was found that in affected ground and seepage waters pH was lower (average pH 5.0); sulphate higher (average 350 mg/L) and trace element concentrations were significantly increased (4330 μg/L copper and 7700 μg/L zinc) compared to surrounding waters. Multivariate statistics (principal component analysis) were used on the data set. Obtained loading plot showed a clear negative correlation between pH and parameters found at high concentrations, indicating that these parameters are found at the source term (acid rock drainage). Lead was also found in close proximity to iron and turbidity indicating that lead might be associated with particles. The score plot presented almost all samples from high concentrations to low concentrations along the first principal component (explaining 63% of the variation in the data set) indicating that dilution was an important mechanism for the decrease in concentrations as opposed to immobilisation on surfaces along the flowpath. Decrease in fluoride and sulphate along one of the suspected flowpath coincided with an increase in calcium. Through geochemical calculations it was concluded that calcite (CaCO3) dissolved along the flowpath and thus induced precipitation of gypsum (CaSO4) and fluorite (CaF2). Through a combination of PCA and geochemical calculations the most likely flowpaths for contaminated water from the abandoned mining site were presented, making it possible to prevent further negative effects on the surface water.

Robust Parameter Estimations Using L-Moments, TL-Moments and the Order Statistics

Application of the method of moments for the parametric distribution is common in the construction of a suitable parametric distribution. However, moment method of parameter estimation does not produce good results. An alternative approach when constructing an appropriate parametric distribution for the considered data file is to use the so-called order statistics. This paper deals with the use of order statistics as the methods of L-moments and TL-moments of parameter estimation. L-moments have some theoretical advantages over conventional moments. L-moments have been introduced as a robust alternative to classical moments of probability distributions. However, L-moments and their estimations lack some robust features that belong to the TL-moments. TL-moments represent an alternative robust version of L-moments, which are called trimmed L-moments. This paper deals with the use of L-moments and TL-moments in the construction of models of wage distribution. Three-parametric lognormal curves represent the basic theoretical distribution whose parameters were simultaneously estimated by three methods of point parameter estimation and accuracy of these methods was then evaluated. There are method of TL-moments, method of L-moments and maximum likelihood method in combination with Cohen’s method. A total of 328 wage distribution has been the subject of research

“Anti-Bayesian” parametric pattern classification using order statistics criteria for some members of the exponential family

This paper submits a comprehensive report of the use of order statistics (OS) for parametric pattern recognition (PR) for various distributions within the exponential family. Although the field of parametric PR has been thoroughly studied for over five decades, the use of the OS of the distributions to achieve this has not been reported. The pioneering work on using OS for classification was presented earlier for the uniform distribution and for some members of the exponential family, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean. Apart from the results for the Gaussian and doubly exponential which are merely cited here, our new results include the Rayleigh, Gamma and certain Beta distributions. The new scheme, referred to as classification by moments of order statistics (CMOS), has an accuracy that attains Bayes' bound for symmetric distributions, and is, otherwise, very close to the optimal Bayes' bound, as has been shown both theoretically and by rigorous experimental testing. The results here also give a theoretical foundation for the families of border identification (BI) algorithms reported in the literature.

Rank normalization of impact factors will resolve Vanclay’s dilemma with TRIF

The ThomsonReuters impact factor is a viable, widely used and informative measure of journal visibility and frequency of use. It is accurate, transparent and easy to use. It is a live and evolving system, that can broaden its scope and implement new features and methods. Some of Vanclay's suggestions, like wider use of order statistics, or our suggestion of rank normalization might be implemented by JCR in the future.

Reply

Abstract This reply addresses the use of order statistics in extreme value analysis. The author has previously proposed in this journal that the distribution-dependent estimators of plotting position in extreme value analysis should be abandoned and replaced by the Weibull formula. It was also demonstrated that the use of the wrong plotting positions has resulted in underestimation of the probability of extreme-weather events. Cook’s comments challenge these developments and defend the previously presented plotting methods. In this reply it is outlined that the Weibull formula provides the exact probability PI of nonexceedance in order-ranked data. Hence, there is no sampling error related to PI. This renders Cook’s primary arguments invalid. The specific critical comments by Cook are also replied to and are shown to be unfounded.

Two Nonparametric Predictive Control Charts

Abstract Control charts based on distributional assumptions may be unsatisfactory if the assumptions are violated, as the average run length (ARL) might deviate from its anticipated value. Control limits for such charts are based on estimates of parameters, which might cause biased ARL. We introduced extrema charts based on nonparametric predictive inference (NPI) (Arts, Coolen and van der Laan, 2004), which do not suffer from these problems. Such charts use a reference set, and resulting inferences are exactly calibrated (Lawless and Fredette, 2005). It was shown that extrema charts perform well when compared to X charts, and they can quickly detect medium to large shifts. In this paper, we explore two alternative charts based on NPI, focussing on their data requirement and performance in detecting smaller shifts. We consider charts that use other order statistics than the extrema, and charts that use subsequent samples rather than single samples. The main conclusions are that the use of order statistics...

Resampling‐based analyses of the effects of combinations of HIV genetic mutations on drug susceptibility

Viral genotype data aid in understanding the development of antiretroviral drug resistance and in identifying appropriate treatments. Using HIV-1 protease sequences and measures of in vitro sensitivity to the drug amprenavir, we develop a novel statistical approach that can be used to investigate combinations of mutations that alter drug susceptibility. Our method is based on the use of order statistics whose null distributions are estimated through resampling and used for formal hypothesis testing. We present a step-down testing method that preserves the overall family-wise error rate in finite samples via an application of the monotonicity condition of Romano and Wolf. Simulations demonstrate that the power of this new approach is comparable to a traditional resampling method; however, this approach can also be used as a visual diagnostic that may be informative even when specified hypotheses are not rejected, for example, in suggesting candidate regression models. Analysis of the data from the Stanford HIV database shows that while M46I/L mutations are associated with drug resistance, addition of the L88D/S mutation leads to hypersusceptible virus. Further addition of T90M/L mutations results in highly resistant virus. Use of this order statistics method allows the investigation of how mutations act in the presence of others and may suggest mechanisms by which resistance occurs or is reversed through the accumulation of mutations.

Analyzing Forced Unfolding of Protein Tandems by Ordered Variates, 2: Dependent Unfolding Times

Statistical analyses of forced unfolding data for protein tandems, i.e., unfolding forces (force-ramp) and unfolding times (force-clamp), used in single-molecule dynamic force spectroscopy rely on the assumption that the unfolding transitions of individual protein domains are independent (uncorrelated) and characterized, respectively, by identically distributed unfolding forces and unfolding times. In our previous work, we showed that in the experimentally accessible piconewton force range, this assumption, which holds at a lower constant force, may break at an elevated force level, i.e., the unfolding transitions may become correlated when force is increased. In this work, we develop much needed statistical tests for assessing the independence of the unobserved forced unfolding times for individual protein domains in the tandem and equality of their parent distributions, which are based solely on the observed ordered unfolding times. The use and performance of these tests are illustrated through the analysis of unfolding times for computer models of protein tandems. The proposed tests can be used in force-clamp atomic force microscopy experiments to obtain accurate information on protein forced unfolding and to probe data on the presence of interdomain interactions. The order statistics-based formalism is extended to cover the analysis of correlated unfolding transitions. The use of order statistics leads naturally to the development of new kinetic models, which describe the probabilities of ordered unfolding transitions rather than the populations of chemical species.

Contribution of the mathematical modelling of knowledge to the evaluation of uncertainty margins of a LBLOCA transient (LOFT-L2-5)

This work is devoted to some recent developments in uncertainty analysis of the computer code responses used for accident management procedures in nuclear industry. The classical probabilistic approach to evaluate uncertainties is recalled. In this case, the statistical treatment of the code responses is based on the use of order statistics. It provides direct estimations of relevant statistical measures for safety studies. However, the lack of knowledge about uncertainty sources can deteriorate the decision-making. To respect the real state of knowledge, a second model, based on the Dempster–Shafer theory is introduced. It allows to mix the probabilistic approach with the possibility theory that is more appropriate when few information is available. An application of both methodologies to the uncertainty analysis of a LBLOCA transient (LOFT-L2-5) is given.

A non-parametric estimator for setting reservation prices in procurement auctions

Electronic auction markets collect large amounts of auction field data. This enables a structural estimation of the bid distributions and the possibility to derive optimal reservation prices. In this paper we propose a new approach to setting reservation prices. In contrast to traditional auction theory we use the buyer's risk statement for getting a winning bid as a key criterion to set an optimal reservation price. The reservation price for a given probability can then be derived from the distribution function of the observed drop-out bids. In order to get an accurate model of this function, we propose a nonparametric technique based on kernel distribution function estimators and the use of order statistics. We improve our estimator by additional information, which can be observed about bidders and qualitative differences of goods in past auctions rounds (e.g. different delivery times). This makes the technique applicable to RFQs and multi-attribute auctions, with qualitatively differentiated offers.

Blind source separation using order statistics

This paper shows the possibility to blindly separate instantaneous mixtures of sources by means of a criterion exploiting order statistics. Properties of higher order statistics and second-order methods are first underlined. Then a brief description of the order statistics shows that they gather all these properties and a new criterion is proposed. Next an iterative algorithm able to simultaneously extract all the sources is developed. The last part is comparison of this algorithm with well-known methods (JADE and SOBI). The most striking result is the possibility to exploit together independence and correlation through the use of order statistics.

Rank‐normalized impact factor: A way to compare journal performance across subject categories

AbstractIt is well known that uninformed science administrators often use ISI's journal impact factors without taking into account the inherent citation characteristics of individual scientific disciplines. A rank normalized impact factor (rnlF) is proposed which involves use of order statistics for the complete set of journals within each JCR category. We believe the normalization procedure provides reliable and easily interpretable values. For any journal j, its rnlF is designated as rnlF1and equals (K–R1+ 1)/K, where R1 is the descending rank of journal j in its JCR category and K is the number of journals in the category. Note: JCR impact factor listings are published in descending order. The proposed rnlF is compared with normalized impact factors proposed by earlier authors. The efficacy of the rnlF is illustrated in the cases of seven highly‐cited scientists, one each from seven different fields.

Performance metrics for embedded parallel pipelines

A statistical approach to performance prediction is applied to a system development methodology for pipelines comprised of independent parallel stages. The methodology is aimed at distributed memory machines employing medium-grained parallelization. The target applications are continuous-flow embedded systems. The use of order statistics on this type of system is compared to previous practical usage which appears largely confined to traditional Non-Uniform Memory Access (NUMA) machines for loop parallelization. A range of suitable performance metrics which give upper bounds or estimates for task durations are discussed. The metrics have a practical role when included in prediction equations in checking fidelity to an application performance specification. An empirical study applies the mathematical findings to the performance of a multicomputer for a synchronous pipeline stage. The results of a simulation are given for larger numbers of processors. In a further simulation, the results are extended to take account of waiting-time distributions while data are buffered between stages of an asynchronous pipeline. Order statistics are also employed to estimate the degradation due to an output ordering constraint. Practical illustrations in the image communication and vision application domains are included.