Probability Issues in without Replacement Sampling

Science.gov (United States)

Joarder, A. H.; Al-Sabah, W. S.

2007-01-01

Sampling without replacement is an important aspect in teaching conditional probabilities in elementary statistics courses. Different methods proposed in different texts for calculating probabilities of events in this context are reviewed and their relative merits and limitations in applications are pinpointed. An alternative representation of…

Introduction to probability with R

CERN Document Server

Baclawski, Kenneth

2008-01-01

FOREWORD PREFACE Sets, Events, and Probability The Algebra of Sets The Bernoulli Sample Space The Algebra of Multisets The Concept of Probability Properties of Probability Measures Independent Events The Bernoulli Process The R Language Finite Processes The Basic Models Counting Rules Computing Factorials The Second Rule of Counting Computing Probabilities Discrete Random Variables The Bernoulli Process: Tossing a Coin The Bernoulli Process: Random Walk Independence and Joint Distributions Expectations The Inclusion-Exclusion Principle General Random Variable

The extinction probability in systems randomly varying in time

Directory of Open Access Journals (Sweden)

Imre Pázsit

2017-09-01

Full Text Available The extinction probability of a branching process (a neutron chain in a multiplying medium is calculated for a system randomly varying in time. The evolution of the first two moments of such a process was calculated previously by the authors in a system randomly shifting between two states of different multiplication properties. The same model is used here for the investigation of the extinction probability. It is seen that the determination of the extinction probability is significantly more complicated than that of the moments, and it can only be achieved by pure numerical methods. The numerical results indicate that for systems fluctuating between two subcritical or two supercritical states, the extinction probability behaves as expected, but for systems fluctuating between a supercritical and a subcritical state, there is a crucial and unexpected deviation from the predicted behaviour. The results bear some significance not only for neutron chains in a multiplying medium, but also for the evolution of biological populations in a time-varying environment.

Probability and stochastic modeling

CERN Document Server

Rotar, Vladimir I

2012-01-01

Basic NotionsSample Space and EventsProbabilitiesCounting TechniquesIndependence and Conditional ProbabilityIndependenceConditioningThe Borel-Cantelli TheoremDiscrete Random VariablesRandom Variables and VectorsExpected ValueVariance and Other Moments. Inequalities for DeviationsSome Basic DistributionsConvergence of Random Variables. The Law of Large NumbersConditional ExpectationGenerating Functions. Branching Processes. Random Walk RevisitedBranching Processes Generating Functions Branching Processes Revisited More on Random WalkMarkov ChainsDefinitions and Examples. Probability Distributions of Markov ChainsThe First Step Analysis. Passage TimesVariables Defined on a Markov ChainErgodicity and Stationary DistributionsA Classification of States and ErgodicityContinuous Random VariablesContinuous DistributionsSome Basic Distributions Continuous Multivariate Distributions Sums of Independent Random Variables Conditional Distributions and ExpectationsDistributions in the General Case. SimulationDistribution F...

Non-equilibrium random matrix theory. Transition probabilities

International Nuclear Information System (INIS)

Pedro, Francisco Gil; Westphal, Alexander

2016-06-01

In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.

Non-equilibrium random matrix theory. Transition probabilities

Energy Technology Data Exchange (ETDEWEB)

Pedro, Francisco Gil [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie

2016-06-15

In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.

Randomized branch sampling to estimatefruit production in Pecan trees cv. ‘Barton’

Directory of Open Access Journals (Sweden)

Filemom Manoel Mokochinski

Full Text Available ABSTRACT: Sampling techniques to quantify the production of fruits are still very scarce and create a gap in crop development research. This study was conducted in a rural property in the county of Cachoeira do Sul - RS to estimate the efficiency of randomized branch sampling (RBS in quantifying the production of pecan fruit at three different ages (5,7 and 10 years. Two selection techniques were tested: the probability proportional to the diameter (PPD and the uniform probability (UP techniques, which were performed on nine trees, three from each age and randomly chosen. The RBS underestimated fruit production for all ages, and its main drawback was the high sampling error (125.17% - PPD and 111.04% - UP. The UP was regarded as more efficient than the PPD, though both techniques estimated similar production and similar experimental errors. In conclusion, we reported that branch sampling was inaccurate for this case study, requiring new studies to produce estimates with smaller sampling error.

Random function representation of stationary stochastic vector processes for probability density evolution analysis of wind-induced structures

Science.gov (United States)

Liu, Zhangjun; Liu, Zenghui

2018-06-01

This paper develops a hybrid approach of spectral representation and random function for simulating stationary stochastic vector processes. In the proposed approach, the high-dimensional random variables, included in the original spectral representation (OSR) formula, could be effectively reduced to only two elementary random variables by introducing the random functions that serve as random constraints. Based on this, a satisfactory simulation accuracy can be guaranteed by selecting a small representative point set of the elementary random variables. The probability information of the stochastic excitations can be fully emerged through just several hundred of sample functions generated by the proposed approach. Therefore, combined with the probability density evolution method (PDEM), it could be able to implement dynamic response analysis and reliability assessment of engineering structures. For illustrative purposes, a stochastic turbulence wind velocity field acting on a frame-shear-wall structure is simulated by constructing three types of random functions to demonstrate the accuracy and efficiency of the proposed approach. Careful and in-depth studies concerning the probability density evolution analysis of the wind-induced structure have been conducted so as to better illustrate the application prospects of the proposed approach. Numerical examples also show that the proposed approach possesses a good robustness.

Predicting longitudinal trajectories of health probabilities with random-effects multinomial logit regression.

Science.gov (United States)

Liu, Xian; Engel, Charles C

2012-12-20

Researchers often encounter longitudinal health data characterized with three or more ordinal or nominal categories. Random-effects multinomial logit models are generally applied to account for potential lack of independence inherent in such clustered data. When parameter estimates are used to describe longitudinal processes, however, random effects, both between and within individuals, need to be retransformed for correctly predicting outcome probabilities. This study attempts to go beyond existing work by developing a retransformation method that derives longitudinal growth trajectories of unbiased health probabilities. We estimated variances of the predicted probabilities by using the delta method. Additionally, we transformed the covariates' regression coefficients on the multinomial logit function, not substantively meaningful, to the conditional effects on the predicted probabilities. The empirical illustration uses the longitudinal data from the Asset and Health Dynamics among the Oldest Old. Our analysis compared three sets of the predicted probabilities of three health states at six time points, obtained from, respectively, the retransformation method, the best linear unbiased prediction, and the fixed-effects approach. The results demonstrate that neglect of retransforming random errors in the random-effects multinomial logit model results in severely biased longitudinal trajectories of health probabilities as well as overestimated effects of covariates on the probabilities. Copyright © 2012 John Wiley & Sons, Ltd.

Age replacement policy based on imperfect repair with random probability

International Nuclear Information System (INIS)

Lim, J.H.; Qu, Jian; Zuo, Ming J.

2016-01-01

In most of literatures of age replacement policy, failures before planned replacement age can be either minimally repaired or perfectly repaired based on the types of failures, cost for repairs and so on. In this paper, we propose age replacement policy based on imperfect repair with random probability. The proposed policy incorporates the case that such intermittent failure can be either minimally repaired or perfectly repaired with random probabilities. The mathematical formulas of the expected cost rate per unit time are derived for both the infinite-horizon case and the one-replacement-cycle case. For each case, we show that the optimal replacement age exists and is finite. - Highlights: • We propose a new age replacement policy with random probability of perfect repair. • We develop the expected cost per unit time. • We discuss the optimal age for replacement minimizing the expected cost rate.

Data-driven probability concentration and sampling on manifold

Energy Technology Data Exchange (ETDEWEB)

Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)

2016-09-15

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation method for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.

People's Intuitions about Randomness and Probability: An Empirical Study

Science.gov (United States)

Lecoutre, Marie-Paule; Rovira, Katia; Lecoutre, Bruno; Poitevineau, Jacques

2006-01-01

What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

KAUST Repository

Migliorati, Giovanni; Nobile, Fabio; Tempone, Raul

2015-01-01

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability

Stationary Probability and First-Passage Time of Biased Random Walk

International Nuclear Information System (INIS)

Li Jing-Wen; Tang Shen-Li; Xu Xin-Ping

2016-01-01

In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively (0 ⩽ p, q ⩽ 1, p + q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F ∼ (N − 1) γ , where the exponent γ = 2 for N < |p − q| −1 and γ = 1 for N > |p − q| −1 . Our study sheds useful insights into the biased random-walk process. (paper)

BWIP-RANDOM-SAMPLING, Random Sample Generation for Nuclear Waste Disposal

International Nuclear Information System (INIS)

Sagar, B.

1989-01-01

1 - Description of program or function: Random samples for different distribution types are generated. Distribution types as required for performance assessment modeling of geologic nuclear waste disposal are provided. These are: - Uniform, - Log-uniform (base 10 or natural), - Normal, - Lognormal (base 10 or natural), - Exponential, - Bernoulli, - User defined continuous distribution. 2 - Method of solution: A linear congruential generator is used for uniform random numbers. A set of functions is used to transform the uniform distribution to the other distributions. Stratified, rather than random, sampling can be chosen. Truncated limits can be specified on many distributions, whose usual definition has an infinite support. 3 - Restrictions on the complexity of the problem: Generation of correlated random variables is not included

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

Science.gov (United States)

Yura, Harold T; Hanson, Steen G

2012-04-01

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.

Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game.

Science.gov (United States)

Krockow, Eva M; Colman, Andrew M; Pulford, Briony D

2018-03-01

Experimental games have previously been used to study principles of human interaction. Many such games are characterized by iterated or repeated designs that model dynamic relationships, including reciprocal cooperation. To enable the study of infinite game repetitions and to avoid endgame effects of lower cooperation toward the final game round, investigators have introduced random termination rules. This study extends previous research that has focused narrowly on repeated Prisoner's Dilemma games by conducting a controlled experiment of two-player, random termination Centipede games involving probabilistic reinforcement and characterized by the longest decision sequences reported in the empirical literature to date (24 decision nodes). Specifically, we assessed mean exit points and cooperation rates, and compared the effects of four different termination rules: no random game termination, random game termination with constant termination probability, random game termination with increasing termination probability, and random game termination with decreasing termination probability. We found that although mean exit points were lower for games with shorter expected game lengths, the subjects' cooperativeness was significantly reduced only in the most extreme condition with decreasing computer termination probability and an expected game length of two decision nodes. © 2018 Society for the Experimental Analysis of Behavior.

Positive random variables with a discrete probability mass at the origin: Parameter estimation for left-censored samples with application to air quality monitoring data

International Nuclear Information System (INIS)

Gogolak, C.V.

1986-11-01

The concentration of a contaminant measured in a particular medium might be distributed as a positive random variable when it is present, but it may not always be present. If there is a level below which the concentration cannot be distinguished from zero by the analytical apparatus, a sample from such a population will be censored on the left. The presence of both zeros and positive values in the censored portion of such samples complicates the problem of estimating the parameters of the underlying positive random variable and the probability of a zero observation. Using the method of maximum likelihood, it is shown that the solution to this estimation problem reduces largely to that of estimating the parameters of the distribution truncated at the point of censorship. The maximum likelihood estimate of the proportion of zero values follows directly. The derivation of the maximum likelihood estimates for a lognormal population with zeros is given in detail, and the asymptotic properties of the estimates are examined. The estimation method was used to fit several different distributions to a set of severely censored 85 Kr monitoring data from six locations at the Savannah River Plant chemical separations facilities

Probability Machines: Consistent Probability Estimation Using Nonparametric Learning Machines

Science.gov (United States)

Malley, J. D.; Kruppa, J.; Dasgupta, A.; Malley, K. G.; Ziegler, A.

2011-01-01

Summary Background Most machine learning approaches only provide a classification for binary responses. However, probabilities are required for risk estimation using individual patient characteristics. It has been shown recently that every statistical learning machine known to be consistent for a nonparametric regression problem is a probability machine that is provably consistent for this estimation problem. Objectives The aim of this paper is to show how random forests and nearest neighbors can be used for consistent estimation of individual probabilities. Methods Two random forest algorithms and two nearest neighbor algorithms are described in detail for estimation of individual probabilities. We discuss the consistency of random forests, nearest neighbors and other learning machines in detail. We conduct a simulation study to illustrate the validity of the methods. We exemplify the algorithms by analyzing two well-known data sets on the diagnosis of appendicitis and the diagnosis of diabetes in Pima Indians. Results Simulations demonstrate the validity of the method. With the real data application, we show the accuracy and practicality of this approach. We provide sample code from R packages in which the probability estimation is already available. This means that all calculations can be performed using existing software. Conclusions Random forest algorithms as well as nearest neighbor approaches are valid machine learning methods for estimating individual probabilities for binary responses. Freely available implementations are available in R and may be used for applications. PMID:21915433

Impact of controlling the sum of error probability in the sequential probability ratio test

Directory of Open Access Journals (Sweden)

Bijoy Kumarr Pradhan

2013-05-01

Full Text Available A generalized modified method is proposed to control the sum of error probabilities in sequential probability ratio test to minimize the weighted average of the two average sample numbers under a simple null hypothesis and a simple alternative hypothesis with the restriction that the sum of error probabilities is a pre-assigned constant to find the optimal sample size and finally a comparison is done with the optimal sample size found from fixed sample size procedure. The results are applied to the cases when the random variate follows a normal law as well as Bernoullian law.

Misrepresenting random sampling? A systematic review of research papers in the Journal of Advanced Nursing.

Science.gov (United States)

Williamson, Graham R

2003-11-01

This paper discusses the theoretical limitations of the use of random sampling and probability theory in the production of a significance level (or P-value) in nursing research. Potential alternatives, in the form of randomization tests, are proposed. Research papers in nursing, medicine and psychology frequently misrepresent their statistical findings, as the P-values reported assume random sampling. In this systematic review of studies published between January 1995 and June 2002 in the Journal of Advanced Nursing, 89 (68%) studies broke this assumption because they used convenience samples or entire populations. As a result, some of the findings may be questionable. The key ideas of random sampling and probability theory for statistical testing (for generating a P-value) are outlined. The result of a systematic review of research papers published in the Journal of Advanced Nursing is then presented, showing how frequently random sampling appears to have been misrepresented. Useful alternative techniques that might overcome these limitations are then discussed. REVIEW LIMITATIONS: This review is limited in scope because it is applied to one journal, and so the findings cannot be generalized to other nursing journals or to nursing research in general. However, it is possible that other nursing journals are also publishing research articles based on the misrepresentation of random sampling. The review is also limited because in several of the articles the sampling method was not completely clearly stated, and in this circumstance a judgment has been made as to the sampling method employed, based on the indications given by author(s). Quantitative researchers in nursing should be very careful that the statistical techniques they use are appropriate for the design and sampling methods of their studies. If the techniques they employ are not appropriate, they run the risk of misinterpreting findings by using inappropriate, unrepresentative and biased samples.

Learning Binomial Probability Concepts with Simulation, Random Numbers and a Spreadsheet

Science.gov (United States)

Rochowicz, John A., Jr.

2005-01-01

This paper introduces the reader to the concepts of binomial probability and simulation. A spreadsheet is used to illustrate these concepts. Random number generators are great technological tools for demonstrating the concepts of probability. Ideas of approximation, estimation, and mathematical usefulness provide numerous ways of learning…

Non-stationary random vibration analysis of a 3D train-bridge system using the probability density evolution method

Science.gov (United States)

Yu, Zhi-wu; Mao, Jian-feng; Guo, Feng-qi; Guo, Wei

2016-03-01

Rail irregularity is one of the main sources causing train-bridge random vibration. A new random vibration theory for the coupled train-bridge systems is proposed in this paper. First, number theory method (NTM) with 2N-dimensional vectors for the stochastic harmonic function (SHF) of rail irregularity power spectrum density was adopted to determine the representative points of spatial frequencies and phases to generate the random rail irregularity samples, and the non-stationary rail irregularity samples were modulated with the slowly varying function. Second, the probability density evolution method (PDEM) was employed to calculate the random dynamic vibration of the three-dimensional (3D) train-bridge system by a program compiled on the MATLAB® software platform. Eventually, the Newmark-β integration method and double edge difference method of total variation diminishing (TVD) format were adopted to obtain the mean value curve, the standard deviation curve and the time-history probability density information of responses. A case study was presented in which the ICE-3 train travels on a three-span simply-supported high-speed railway bridge with excitation of random rail irregularity. The results showed that compared to the Monte Carlo simulation, the PDEM has higher computational efficiency for the same accuracy, i.e., an improvement by 1-2 orders of magnitude. Additionally, the influences of rail irregularity and train speed on the random vibration of the coupled train-bridge system were discussed.

Probability, random processes, and ergodic properties

CERN Document Server

Gray, Robert M

1988-01-01

This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time random processes with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the suggestion to separate the material and split...

High throughput nonparametric probability density estimation.

Science.gov (United States)

Farmer, Jenny; Jacobs, Donald

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.

A Bayesian Justification for Random Sampling in Sample Survey

Directory of Open Access Journals (Sweden)

Glen Meeden

2012-07-01

Full Text Available In the usual Bayesian approach to survey sampling the sampling design, plays a minimal role, at best. Although a close relationship between exchangeable prior distributions and simple random sampling has been noted; how to formally integrate simple random sampling into the Bayesian paradigm is not clear. Recently it has been argued that the sampling design can be thought of as part of a Bayesian's prior distribution. We will show here that under this scenario simple random sample can be given a Bayesian justification in survey sampling.

Generation, combination and extension of random set approximations to coherent lower and upper probabilities

International Nuclear Information System (INIS)

Hall, Jim W.; Lawry, Jonathan

2004-01-01

Random set theory provides a convenient mechanism for representing uncertain knowledge including probabilistic and set-based information, and extending it through a function. This paper focuses upon the situation when the available information is in terms of coherent lower and upper probabilities, which are encountered, for example, when a probability distribution is specified by interval parameters. We propose an Iterative Rescaling Method (IRM) for constructing a random set with corresponding belief and plausibility measures that are a close outer approximation to the lower and upper probabilities. The approach is compared with the discrete approximation method of Williamson and Downs (sometimes referred to as the p-box), which generates a closer approximation to lower and upper cumulative probability distributions but in most cases a less accurate approximation to the lower and upper probabilities on the remainder of the power set. Four combination methods are compared by application to example random sets generated using the IRM

An unbiased estimator of the variance of simple random sampling using mixed random-systematic sampling

OpenAIRE

Padilla, Alberto

2009-01-01

Systematic sampling is a commonly used technique due to its simplicity and ease of implementation. The drawback of this simplicity is that it is not possible to estimate the design variance without bias. There are several ways to circumvent this problem. One method is to suppose that the variable of interest has a random order in the population, so the sample variance of simple random sampling without replacement is used. By means of a mixed random - systematic sample, an unbiased estimator o...

Sampling, Probability Models and Statistical Reasoning Statistical

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Sampling, Probability Models and Statistical Reasoning Statistical Inference. Mohan Delampady V R Padmawar. General Article Volume 1 Issue 5 May 1996 pp 49-58 ...

Problems in probability theory, mathematical statistics and theory of random functions

CERN Document Server

Sveshnikov, A A

1979-01-01

Problem solving is the main thrust of this excellent, well-organized workbook. Suitable for students at all levels in probability theory and statistics, the book presents over 1,000 problems and their solutions, illustrating fundamental theory and representative applications in the following fields: Random Events; Distribution Laws; Correlation Theory; Random Variables; Entropy & Information; Markov Processes; Systems of Random Variables; Limit Theorems; Data Processing; and more.The coverage of topics is both broad and deep, ranging from the most elementary combinatorial problems through lim

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

KAUST Repository

Migliorati, Giovanni

2015-08-28

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. The convergence estimates are given in mean-square sense with respect to the sampling measure. The noise may be correlated with the location of the evaluation and may have nonzero mean (offset). We consider both cases of bounded or square-integrable noise / offset. We prove conditions between the number of sampling points and the dimension of the underlying approximation space that ensure a stable and accurate approximation. Particular focus is on deriving estimates in probability within a given confidence level. We analyze how the best approximation error and the noise terms affect the convergence rate and the overall confidence level achieved by the convergence estimate. The proofs of our convergence estimates in probability use arguments from the theory of large deviations to bound the noise term. Finally we address the particular case of multivariate polynomial approximation spaces with any density in the beta family, including uniform and Chebyshev.

Random sampling of elementary flux modes in large-scale metabolic networks.

Science.gov (United States)

Machado, Daniel; Soons, Zita; Patil, Kiran Raosaheb; Ferreira, Eugénio C; Rocha, Isabel

2012-09-15

The description of a metabolic network in terms of elementary (flux) modes (EMs) provides an important framework for metabolic pathway analysis. However, their application to large networks has been hampered by the combinatorial explosion in the number of modes. In this work, we develop a method for generating random samples of EMs without computing the whole set. Our algorithm is an adaptation of the canonical basis approach, where we add an additional filtering step which, at each iteration, selects a random subset of the new combinations of modes. In order to obtain an unbiased sample, all candidates are assigned the same probability of getting selected. This approach avoids the exponential growth of the number of modes during computation, thus generating a random sample of the complete set of EMs within reasonable time. We generated samples of different sizes for a metabolic network of Escherichia coli, and observed that they preserve several properties of the full EM set. It is also shown that EM sampling can be used for rational strain design. A well distributed sample, that is representative of the complete set of EMs, should be suitable to most EM-based methods for analysis and optimization of metabolic networks. Source code for a cross-platform implementation in Python is freely available at http://code.google.com/p/emsampler. dmachado@deb.uminho.pt Supplementary data are available at Bioinformatics online.

Systematic versus random sampling in stereological studies.

Science.gov (United States)

West, Mark J

2012-12-01

The sampling that takes place at all levels of an experimental design must be random if the estimate is to be unbiased in a statistical sense. There are two fundamental ways by which one can make a random sample of the sections and positions to be probed on the sections. Using a card-sampling analogy, one can pick any card at all out of a deck of cards. This is referred to as independent random sampling because the sampling of any one card is made without reference to the position of the other cards. The other approach to obtaining a random sample would be to pick a card within a set number of cards and others at equal intervals within the deck. Systematic sampling along one axis of many biological structures is more efficient than random sampling, because most biological structures are not randomly organized. This article discusses the merits of systematic versus random sampling in stereological studies.

Accounting for randomness in measurement and sampling in studying cancer cell population dynamics.

Science.gov (United States)

Ghavami, Siavash; Wolkenhauer, Olaf; Lahouti, Farshad; Ullah, Mukhtar; Linnebacher, Michael

2014-10-01

Knowing the expected temporal evolution of the proportion of different cell types in sample tissues gives an indication about the progression of the disease and its possible response to drugs. Such systems have been modelled using Markov processes. We here consider an experimentally realistic scenario in which transition probabilities are estimated from noisy cell population size measurements. Using aggregated data of FACS measurements, we develop MMSE and ML estimators and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes. Our numerical results show that the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach for noisy measurements. This provides support for our argument that for the analysis of FACS data one should consider the observed state as a random variable. The second problem we address is about the consequences of estimating the probability of a cell being in a particular state from measurements of small population of cells. We show how the uncertainty arising from small sample sizes can be captured by a distribution for the state probability.

Generation and Analysis of Constrained Random Sampling Patterns

DEFF Research Database (Denmark)

Pierzchlewski, Jacek; Arildsen, Thomas

2016-01-01

Random sampling is a technique for signal acquisition which is gaining popularity in practical signal processing systems. Nowadays, event-driven analog-to-digital converters make random sampling feasible in practical applications. A process of random sampling is defined by a sampling pattern, which...... indicates signal sampling points in time. Practical random sampling patterns are constrained by ADC characteristics and application requirements. In this paper, we introduce statistical methods which evaluate random sampling pattern generators with emphasis on practical applications. Furthermore, we propose...... algorithm generates random sampling patterns dedicated for event-driven-ADCs better than existed sampling pattern generators. Finally, implementation issues of random sampling patterns are discussed....

An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems

International Nuclear Information System (INIS)

Zio, E.; Pedroni, N.

2010-01-01

The quantitative reliability assessment of a thermal-hydraulic (T-H) passive safety system of a nuclear power plant can be obtained by (i) Monte Carlo (MC) sampling the uncertainties of the system model and parameters, (ii) computing, for each sample, the system response by a mechanistic T-H code and (iii) comparing the system response with pre-established safety thresholds, which define the success or failure of the safety function. The computational effort involved can be prohibitive because of the large number of (typically long) T-H code simulations that must be performed (one for each sample) for the statistical estimation of the probability of success or failure. In this work, Line Sampling (LS) is adopted for efficient MC sampling. In the LS method, an 'important direction' pointing towards the failure domain of interest is determined and a number of conditional one-dimensional problems are solved along such direction; this allows for a significant reduction of the variance of the failure probability estimator, with respect, for example, to standard random sampling. Two issues are still open with respect to LS: first, the method relies on the determination of the 'important direction', which requires additional runs of the T-H code; second, although the method has been shown to improve the computational efficiency by reducing the variance of the failure probability estimator, no evidence has been given yet that accurate and precise failure probability estimates can be obtained with a number of samples reduced to below a few hundreds, which may be required in case of long-running models. The work presented in this paper addresses the first issue by (i) quantitatively comparing the efficiency of the methods proposed in the literature to determine the LS important direction; (ii) employing artificial neural network (ANN) regression models as fast-running surrogates of the original, long-running T-H code to reduce the computational cost associated to the

Secondary School Students' Reasoning about Conditional Probability, Samples, and Sampling Procedures

Science.gov (United States)

Prodromou, Theodosia

2016-01-01

In the Australian mathematics curriculum, Year 12 students (aged 16-17) are asked to solve conditional probability problems that involve the representation of the problem situation with two-way tables or three-dimensional diagrams and consider sampling procedures that result in different correct answers. In a small exploratory study, we…

Methodology Series Module 5: Sampling Strategies.

Science.gov (United States)

Setia, Maninder Singh

2016-01-01

Once the research question and the research design have been finalised, it is important to select the appropriate sample for the study. The method by which the researcher selects the sample is the ' Sampling Method'. There are essentially two types of sampling methods: 1) probability sampling - based on chance events (such as random numbers, flipping a coin etc.); and 2) non-probability sampling - based on researcher's choice, population that accessible & available. Some of the non-probability sampling methods are: purposive sampling, convenience sampling, or quota sampling. Random sampling method (such as simple random sample or stratified random sample) is a form of probability sampling. It is important to understand the different sampling methods used in clinical studies and mention this method clearly in the manuscript. The researcher should not misrepresent the sampling method in the manuscript (such as using the term ' random sample' when the researcher has used convenience sample). The sampling method will depend on the research question. For instance, the researcher may want to understand an issue in greater detail for one particular population rather than worry about the ' generalizability' of these results. In such a scenario, the researcher may want to use ' purposive sampling' for the study.

Methodology series module 5: Sampling strategies

Directory of Open Access Journals (Sweden)

Maninder Singh Setia

2016-01-01

Full Text Available Once the research question and the research design have been finalised, it is important to select the appropriate sample for the study. The method by which the researcher selects the sample is the 'Sampling Method'. There are essentially two types of sampling methods: 1 probability sampling – based on chance events (such as random numbers, flipping a coin etc.; and 2 non-probability sampling – based on researcher's choice, population that accessible & available. Some of the non-probability sampling methods are: purposive sampling, convenience sampling, or quota sampling. Random sampling method (such as simple random sample or stratified random sample is a form of probability sampling. It is important to understand the different sampling methods used in clinical studies and mention this method clearly in the manuscript. The researcher should not misrepresent the sampling method in the manuscript (such as using the term 'random sample' when the researcher has used convenience sample. The sampling method will depend on the research question. For instance, the researcher may want to understand an issue in greater detail for one particular population rather than worry about the 'generalizability' of these results. In such a scenario, the researcher may want to use 'purposive sampling' for the study.

Methodology Series Module 5: Sampling Strategies

Science.gov (United States)

Setia, Maninder Singh

2016-01-01

Once the research question and the research design have been finalised, it is important to select the appropriate sample for the study. The method by which the researcher selects the sample is the ‘ Sampling Method’. There are essentially two types of sampling methods: 1) probability sampling – based on chance events (such as random numbers, flipping a coin etc.); and 2) non-probability sampling – based on researcher's choice, population that accessible & available. Some of the non-probability sampling methods are: purposive sampling, convenience sampling, or quota sampling. Random sampling method (such as simple random sample or stratified random sample) is a form of probability sampling. It is important to understand the different sampling methods used in clinical studies and mention this method clearly in the manuscript. The researcher should not misrepresent the sampling method in the manuscript (such as using the term ‘ random sample’ when the researcher has used convenience sample). The sampling method will depend on the research question. For instance, the researcher may want to understand an issue in greater detail for one particular population rather than worry about the ‘ generalizability’ of these results. In such a scenario, the researcher may want to use ‘ purposive sampling’ for the study. PMID:27688438

Sample size estimation and sampling techniques for selecting a representative sample

Directory of Open Access Journals (Sweden)

Aamir Omair

2014-01-01

Full Text Available Introduction: The purpose of this article is to provide a general understanding of the concepts of sampling as applied to health-related research. Sample Size Estimation: It is important to select a representative sample in quantitative research in order to be able to generalize the results to the target population. The sample should be of the required sample size and must be selected using an appropriate probability sampling technique. There are many hidden biases which can adversely affect the outcome of the study. Important factors to consider for estimating the sample size include the size of the study population, confidence level, expected proportion of the outcome variable (for categorical variables/standard deviation of the outcome variable (for numerical variables, and the required precision (margin of accuracy from the study. The more the precision required, the greater is the required sample size. Sampling Techniques: The probability sampling techniques applied for health related research include simple random sampling, systematic random sampling, stratified random sampling, cluster sampling, and multistage sampling. These are more recommended than the nonprobability sampling techniques, because the results of the study can be generalized to the target population.

Sampling problems for randomly broken sticks

Energy Technology Data Exchange (ETDEWEB)

Huillet, Thierry [Laboratoire de Physique Theorique et Modelisation, CNRS-UMR 8089 et Universite de Cergy-Pontoise, 5 mail Gay-Lussac, 95031, Neuville sur Oise (France)

2003-04-11

Consider the random partitioning model of a population (represented by a stick of length 1) into n species (fragments) with identically distributed random weights (sizes). Upon ranking the fragments' weights according to ascending sizes, let S{sub m:n} be the size of the mth smallest fragment. Assume that some observer is sampling such populations as follows: drop at random k points (the sample size) onto this stick and record the corresponding numbers of visited fragments. We shall investigate the following sampling problems: (1) what is the sample size if the sampling is carried out until the first visit of the smallest fragment (size S{sub 1:n})? (2) For a given sample size, have all the fragments of the stick been visited at least once or not? This question is related to Feller's random coupon collector problem. (3) In what order are new fragments being discovered and what is the random number of samples separating the discovery of consecutive new fragments until exhaustion of the list? For this problem, the distribution of the size-biased permutation of the species' weights, as the sequence of their weights in their order of appearance is needed and studied.

Modern survey sampling

CERN Document Server

Chaudhuri, Arijit

2014-01-01

Exposure to SamplingAbstract Introduction Concepts of Population, Sample, and SamplingInitial RamificationsAbstract Introduction Sampling Design, Sampling SchemeRandom Numbers and Their Uses in Simple RandomSampling (SRS)Drawing Simple Random Samples with and withoutReplacementEstimation of Mean, Total, Ratio of Totals/Means:Variance and Variance EstimationDetermination of Sample SizesA.2 Appendix to Chapter 2 A.More on Equal Probability Sampling A.Horvitz-Thompson EstimatorA.SufficiencyA.LikelihoodA.Non-Existence Theorem More Intricacies Abstract Introduction Unequal Probability Sampling StrategiesPPS Sampling Exploring Improved WaysAbstract Introduction Stratified Sampling Cluster SamplingMulti-Stage SamplingMulti-Phase Sampling: Ratio and RegressionEstimationviiviii ContentsControlled SamplingModeling Introduction Super-Population ModelingPrediction Approach Model-Assisted Approach Bayesian Methods Spatial SmoothingSampling on Successive Occasions: Panel Rotation Non-Response and Not-at-Homes Weighting Adj...

What Are Probability Surveys used by the National Aquatic Resource Surveys?

Science.gov (United States)

The National Aquatic Resource Surveys (NARS) use probability-survey designs to assess the condition of the nation’s waters. In probability surveys (also known as sample-surveys or statistical surveys), sampling sites are selected randomly.

Effect of optimum stratification on sampling with varying probabilities under proportional allocation

Directory of Open Access Journals (Sweden)

Syed Ejaz Husain Rizvi

2007-10-01

Full Text Available The problem of optimum stratification on an auxiliary variable when the units from different strata are selected with probability proportional to the value of auxiliary variable (PPSWR was considered by Singh (1975 for univariate case. In this paper we have extended the same problem, for proportional allocation, when two variates are under study. A cum. 3 R3(x rule for obtaining approximately optimum strata boundaries has been provided. It has been shown theoretically as well as empirically that the use of stratification has inverse effect on the relative efficiency of PPSWR as compared to unstratified PPSWR method when proportional method of allocation is envisaged. Further comparison showed that with increase in number of strata the stratified simple random sampling is equally efficient as PPSWR.

Assessing representativeness of sampling methods for reaching men who have sex with men: a direct comparison of results obtained from convenience and probability samples.

Science.gov (United States)

Schwarcz, Sandra; Spindler, Hilary; Scheer, Susan; Valleroy, Linda; Lansky, Amy

2007-07-01

Convenience samples are used to determine HIV-related behaviors among men who have sex with men (MSM) without measuring the extent to which the results are representative of the broader MSM population. We compared results from a cross-sectional survey of MSM recruited from gay bars between June and October 2001 to a random digit dial telephone survey conducted between June 2002 and January 2003. The men in the probability sample were older, better educated, and had higher incomes than men in the convenience sample, the convenience sample enrolled more employed men and men of color. Substance use around the time of sex was higher in the convenience sample but other sexual behaviors were similar. HIV testing was common among men in both samples. Periodic validation, through comparison of data collected by different sampling methods, may be useful when relying on survey data for program and policy development.

Path integral methods for primordial density perturbations - sampling of constrained Gaussian random fields

International Nuclear Information System (INIS)

Bertschinger, E.

1987-01-01

Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a protovoid or supercluster at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario, and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume. 21 references

Bounds for Tail Probabilities of the Sample Variance

Directory of Open Access Journals (Sweden)

Van Zuijlen M

2009-01-01

Full Text Available We provide bounds for tail probabilities of the sample variance. The bounds are expressed in terms of Hoeffding functions and are the sharpest known. They are designed having in mind applications in auditing as well as in processing data related to environment.

Probability distribution for the Gaussian curvature of the zero level surface of a random function

Science.gov (United States)

Hannay, J. H.

2018-04-01

A rather natural construction for a smooth random surface in space is the level surface of value zero, or ‘nodal’ surface f(x,y,z)  =  0, of a (real) random function f; the interface between positive and negative regions of the function. A physically significant local attribute at a point of a curved surface is its Gaussian curvature (the product of its principal curvatures) because, when integrated over the surface it gives the Euler characteristic. Here the probability distribution for the Gaussian curvature at a random point on the nodal surface f  =  0 is calculated for a statistically homogeneous (‘stationary’) and isotropic zero mean Gaussian random function f. Capitalizing on the isotropy, a ‘fixer’ device for axes supplies the probability distribution directly as a multiple integral. Its evaluation yields an explicit algebraic function with a simple average. Indeed, this average Gaussian curvature has long been known. For a non-zero level surface instead of the nodal one, the probability distribution is not fully tractable, but is supplied as an integral expression.

Optimal sample size for probability of detection curves

International Nuclear Information System (INIS)

Annis, Charles; Gandossi, Luca; Martin, Oliver

2013-01-01

Highlights: • We investigate sample size requirement to develop probability of detection curves. • We develop simulations to determine effective inspection target sizes, number and distribution. • We summarize these findings and provide guidelines for the NDE practitioner. -- Abstract: The use of probability of detection curves to quantify the reliability of non-destructive examination (NDE) systems is common in the aeronautical industry, but relatively less so in the nuclear industry, at least in European countries. Due to the nature of the components being inspected, sample sizes tend to be much lower. This makes the manufacturing of test pieces with representative flaws, in sufficient numbers, so to draw statistical conclusions on the reliability of the NDT system under investigation, quite costly. The European Network for Inspection and Qualification (ENIQ) has developed an inspection qualification methodology, referred to as the ENIQ Methodology. It has become widely used in many European countries and provides assurance on the reliability of NDE systems, but only qualitatively. The need to quantify the output of inspection qualification has become more important as structural reliability modelling and quantitative risk-informed in-service inspection methodologies become more widely used. A measure of the NDE reliability is necessary to quantify risk reduction after inspection and probability of detection (POD) curves provide such a metric. The Joint Research Centre, Petten, The Netherlands supported ENIQ by investigating the question of the sample size required to determine a reliable POD curve. As mentioned earlier manufacturing of test pieces with defects that are typically found in nuclear power plants (NPPs) is usually quite expensive. Thus there is a tendency to reduce sample sizes, which in turn increases the uncertainty associated with the resulting POD curve. The main question in conjunction with POS curves is the appropriate sample size. Not

Probability of coincidental similarity among the orbits of small bodies - I. Pairing

Science.gov (United States)

Jopek, Tadeusz Jan; Bronikowska, Małgorzata

2017-09-01

Probability of coincidental clustering among orbits of comets, asteroids and meteoroids depends on many factors like: the size of the orbital sample searched for clusters or the size of the identified group, it is different for groups of 2,3,4,… members. Probability of coincidental clustering is assessed by the numerical simulation, therefore, it depends also on the method used for the synthetic orbits generation. We have tested the impact of some of these factors. For a given size of the orbital sample we have assessed probability of random pairing among several orbital populations of different sizes. We have found how these probabilities vary with the size of the orbital samples. Finally, keeping fixed size of the orbital sample we have shown that the probability of random pairing can be significantly different for the orbital samples obtained by different observation techniques. Also for the user convenience we have obtained several formulae which, for given size of the orbital sample can be used to calculate the similarity threshold corresponding to the small value of the probability of coincidental similarity among two orbits.

Some Limit Properties of Random Transition Probability for Second-Order Nonhomogeneous Markov Chains Indexed by a Tree

Directory of Open Access Journals (Sweden)

Shi Zhiyan

2009-01-01

Full Text Available We study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain and a nonhomogeneous Markov chain indexed by a tree. As corollary, we obtain the property of the harmonic mean of random transition probability for a nonhomogeneous Markov chain.

Triangulation based inclusion probabilities: a design-unbiased sampling approach

OpenAIRE

Fehrmann, Lutz; Gregoire, Timothy; Kleinn, Christoph

2011-01-01

A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. ...

Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods

DEFF Research Database (Denmark)

Nielsen, Søren R.K.; Sørensen, John Dalsgaard

Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before...... passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response....... outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first...

Failure Probability Calculation Method Using Kriging Metamodel-based Importance Sampling Method

Energy Technology Data Exchange (ETDEWEB)

Lee, Seunggyu [Korea Aerospace Research Institue, Daejeon (Korea, Republic of); Kim, Jae Hoon [Chungnam Nat’l Univ., Daejeon (Korea, Republic of)

2017-05-15

The kernel density was determined based on sampling points obtained in a Markov chain simulation and was assumed to be an important sampling function. A Kriging metamodel was constructed in more detail in the vicinity of a limit state. The failure probability was calculated based on importance sampling, which was performed for the Kriging metamodel. A pre-existing method was modified to obtain more sampling points for a kernel density in the vicinity of a limit state. A stable numerical method was proposed to find a parameter of the kernel density. To assess the completeness of the Kriging metamodel, the possibility of changes in the calculated failure probability due to the uncertainty of the Kriging metamodel was calculated.

Evaluation of a Class of Simple and Effective Uncertainty Methods for Sparse Samples of Random Variables and Functions

Energy Technology Data Exchange (ETDEWEB)

Romero, Vicente [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bonney, Matthew [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Schroeder, Benjamin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Weirs, V. Gregory [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-11-01

When very few samples of a random quantity are available from a source distribution of unknown shape, it is usually not possible to accurately infer the exact distribution from which the data samples come. Under-estimation of important quantities such as response variance and failure probabilities can result. For many engineering purposes, including design and risk analysis, we attempt to avoid under-estimation with a strategy to conservatively estimate (bound) these types of quantities -- without being overly conservative -- when only a few samples of a random quantity are available from model predictions or replicate experiments. This report examines a class of related sparse-data uncertainty representation and inference approaches that are relatively simple, inexpensive, and effective. Tradeoffs between the methods' conservatism, reliability, and risk versus number of data samples (cost) are quantified with multi-attribute metrics use d to assess method performance for conservative estimation of two representative quantities: central 95% of response; and 10^-4 probability of exceeding a response threshold in a tail of the distribution. Each method's performance is characterized with 10,000 random trials on a large number of diverse and challenging distributions. The best method and number of samples to use in a given circumstance depends on the uncertainty quantity to be estimated, the PDF character, and the desired reliability of bounding the true value. On the basis of this large data base and study, a strategy is proposed for selecting the method and number of samples for attaining reasonable credibility levels in bounding these types of quantities when sparse samples of random variables or functions are available from experiments or simulations.

Fortran code for generating random probability vectors, unitaries, and quantum states

Directory of Open Access Journals (Sweden)

Jonas eMaziero

2016-03-01

Full Text Available The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards its betterment indicate that it will keep this status in the decades to come. In this article, we describe Fortran codes produced, or organized, for the generation of the following random objects: numbers, probability vectors, unitary matrices, and quantum state vectors and density matrices. Some matrix functions are also included and may be of independent interest.

Public Attitudes toward Stuttering in Turkey: Probability versus Convenience Sampling

Science.gov (United States)

Ozdemir, R. Sertan; St. Louis, Kenneth O.; Topbas, Seyhun

2011-01-01

Purpose: A Turkish translation of the "Public Opinion Survey of Human Attributes-Stuttering" ("POSHA-S") was used to compare probability versus convenience sampling to measure public attitudes toward stuttering. Method: A convenience sample of adults in Eskisehir, Turkey was compared with two replicates of a school-based,…

Sampling informative/complex a priori probability distributions using Gibbs sampling assisted by sequential simulation

DEFF Research Database (Denmark)

Hansen, Thomas Mejer; Mosegaard, Klaus; Cordua, Knud Skou

2010-01-01

Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample the solutions to non-linear inverse problems. In principle these methods allow incorporation of arbitrarily complex a priori information, but current methods allow only relatively simple...... this algorithm with the Metropolis algorithm to obtain an efficient method for sampling posterior probability densities for nonlinear inverse problems....

Probability Sampling Method for a Hidden Population Using Respondent-Driven Sampling: Simulation for Cancer Survivors.

Science.gov (United States)

Jung, Minsoo

2015-01-01

When there is no sampling frame within a certain group or the group is concerned that making its population public would bring social stigma, we say the population is hidden. It is difficult to approach this kind of population survey-methodologically because the response rate is low and its members are not quite honest with their responses when probability sampling is used. The only alternative known to address the problems caused by previous methods such as snowball sampling is respondent-driven sampling (RDS), which was developed by Heckathorn and his colleagues. RDS is based on a Markov chain, and uses the social network information of the respondent. This characteristic allows for probability sampling when we survey a hidden population. We verified through computer simulation whether RDS can be used on a hidden population of cancer survivors. According to the simulation results of this thesis, the chain-referral sampling of RDS tends to minimize as the sample gets bigger, and it becomes stabilized as the wave progresses. Therefore, it shows that the final sample information can be completely independent from the initial seeds if a certain level of sample size is secured even if the initial seeds were selected through convenient sampling. Thus, RDS can be considered as an alternative which can improve upon both key informant sampling and ethnographic surveys, and it needs to be utilized for various cases domestically as well.

Betting on Illusory Patterns: Probability Matching in Habitual Gamblers.

Science.gov (United States)

Gaissmaier, Wolfgang; Wilke, Andreas; Scheibehenne, Benjamin; McCanney, Paige; Barrett, H Clark

2016-03-01

Why do people gamble? A large body of research suggests that cognitive distortions play an important role in pathological gambling. Many of these distortions are specific cases of a more general misperception of randomness, specifically of an illusory perception of patterns in random sequences. In this article, we provide further evidence for the assumption that gamblers are particularly prone to perceiving illusory patterns. In particular, we compared habitual gamblers to a matched sample of community members with regard to how much they exhibit the choice anomaly 'probability matching'. Probability matching describes the tendency to match response proportions to outcome probabilities when predicting binary outcomes. It leads to a lower expected accuracy than the maximizing strategy of predicting the most likely event on each trial. Previous research has shown that an illusory perception of patterns in random sequences fuels probability matching. So does impulsivity, which is also reported to be higher in gamblers. We therefore hypothesized that gamblers will exhibit more probability matching than non-gamblers, which was confirmed in a controlled laboratory experiment. Additionally, gamblers scored much lower than community members on the cognitive reflection task, which indicates higher impulsivity. This difference could account for the difference in probability matching between the samples. These results suggest that gamblers are more willing to bet impulsively on perceived illusory patterns.

Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach.

Science.gov (United States)

Chandrasekar, A; Rakkiyappan, R; Cao, Jinde

2015-10-01

This paper studies the impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable. The aim of this paper is to obtain the synchronization criteria, which is suitable for both exactly known and partly unknown transition probabilities such that the coupled neural network is synchronized with mixed time-delay. The considered impulsive effects can be synchronized at partly unknown transition probabilities. Besides, a multiple integral approach is also proposed to strengthen the Markovian jumping randomly coupled neural networks with partly unknown transition probabilities. By making use of Kronecker product and some useful integral inequalities, a novel Lyapunov-Krasovskii functional was designed for handling the coupled neural network with mixed delay and then impulsive synchronization criteria are solvable in a set of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Bayesian Probability Theory

Science.gov (United States)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

Introduction to probability and statistics for science, engineering, and finance

CERN Document Server

Rosenkrantz, Walter A

2008-01-01

Data Analysis Orientation The Role and Scope of Statistics in Science and Engineering Types of Data: Examples from Engineering, Public Health, and Finance The Frequency Distribution of a Variable Defined on a Population Quantiles of a Distribution Measures of Location (Central Value) and Variability Covariance, Correlation, and Regression: Computing a Stock's Beta Mathematical Details and Derivations Large Data Sets Probability Theory Orientation Sample Space, Events, Axioms of Probability Theory Mathematical Models of Random Sampling Conditional Probability and Baye

Probability

CERN Document Server

Shiryaev, A N

1996-01-01

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter Many examples are discussed in detail, and there are a large number of exercises The book is accessible to advanced undergraduates and can be used as a text for self-study This new edition contains substantial revisions and updated references The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures Proofs for a number of some important results which were merely stated in the first edition have been added The author included new material on the probability of large deviations, and on the central limit theorem for sums of dependent random variables

Elements of probability and statistics an introduction to probability with De Finetti’s approach and to Bayesian statistics

CERN Document Server

Biagini, Francesca

2016-01-01

This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics.

A Combined Weighting Method Based on Hybrid of Interval Evidence Fusion and Random Sampling

Directory of Open Access Journals (Sweden)

Ying Yan

2017-01-01

Full Text Available Due to the complexity of system and lack of expertise, epistemic uncertainties may present in the experts’ judgment on the importance of certain indices during group decision-making. A novel combination weighting method is proposed to solve the index weighting problem when various uncertainties are present in expert comments. Based on the idea of evidence theory, various types of uncertain evaluation information are uniformly expressed through interval evidence structures. Similarity matrix between interval evidences is constructed, and expert’s information is fused. Comment grades are quantified using the interval number, and cumulative probability function for evaluating the importance of indices is constructed based on the fused information. Finally, index weights are obtained by Monte Carlo random sampling. The method can process expert’s information with varying degrees of uncertainties, which possesses good compatibility. Difficulty in effectively fusing high-conflict group decision-making information and large information loss after fusion is avertible. Original expert judgments are retained rather objectively throughout the processing procedure. Cumulative probability function constructing and random sampling processes do not require any human intervention or judgment. It can be implemented by computer programs easily, thus having an apparent advantage in evaluation practices of fairly huge index systems.

Visualization techniques for spatial probability density function data

Directory of Open Access Journals (Sweden)

Udeepta D Bordoloi

2006-01-01

Full Text Available Novel visualization methods are presented for spatial probability density function data. These are spatial datasets, where each pixel is a random variable, and has multiple samples which are the results of experiments on that random variable. We use clustering as a means to reduce the information contained in these datasets; and present two different ways of interpreting and clustering the data. The clustering methods are used on two datasets, and the results are discussed with the help of visualization techniques designed for the spatial probability data.

Sampling Methods in Cardiovascular Nursing Research: An Overview.

Science.gov (United States)

Kandola, Damanpreet; Banner, Davina; O'Keefe-McCarthy, Sheila; Jassal, Debbie

2014-01-01

Cardiovascular nursing research covers a wide array of topics from health services to psychosocial patient experiences. The selection of specific participant samples is an important part of the research design and process. The sampling strategy employed is of utmost importance to ensure that a representative sample of participants is chosen. There are two main categories of sampling methods: probability and non-probability. Probability sampling is the random selection of elements from the population, where each element of the population has an equal and independent chance of being included in the sample. There are five main types of probability sampling including simple random sampling, systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling. Non-probability sampling methods are those in which elements are chosen through non-random methods for inclusion into the research study and include convenience sampling, purposive sampling, and snowball sampling. Each approach offers distinct advantages and disadvantages and must be considered critically. In this research column, we provide an introduction to these key sampling techniques and draw on examples from the cardiovascular research. Understanding the differences in sampling techniques may aid nurses in effective appraisal of research literature and provide a reference pointfor nurses who engage in cardiovascular research.

Estimation of functional failure probability of passive systems based on adaptive importance sampling method

International Nuclear Information System (INIS)

Wang Baosheng; Wang Dongqing; Zhang Jianmin; Jiang Jing

2012-01-01

In order to estimate the functional failure probability of passive systems, an innovative adaptive importance sampling methodology is presented. In the proposed methodology, information of variables is extracted with some pre-sampling of points in the failure region. An important sampling density is then constructed from the sample distribution in the failure region. Taking the AP1000 passive residual heat removal system as an example, the uncertainties related to the model of a passive system and the numerical values of its input parameters are considered in this paper. And then the probability of functional failure is estimated with the combination of the response surface method and adaptive importance sampling method. The numerical results demonstrate the high computed efficiency and excellent computed accuracy of the methodology compared with traditional probability analysis methods. (authors)

A cellular automata model of traffic flow with variable probability of randomization

International Nuclear Information System (INIS)

Zheng Wei-Fan; Zhang Ji-Ye

2015-01-01

Research on the stochastic behavior of traffic flow is important to understand the intrinsic evolution rules of a traffic system. By introducing an interactional potential of vehicles into the randomization step, an improved cellular automata traffic flow model with variable probability of randomization is proposed in this paper. In the proposed model, the driver is affected by the interactional potential of vehicles before him, and his decision-making process is related to the interactional potential. Compared with the traditional cellular automata model, the modeling is more suitable for the driver’s random decision-making process based on the vehicle and traffic situations in front of him in actual traffic. From the improved model, the fundamental diagram (flow–density relationship) is obtained, and the detailed high-density traffic phenomenon is reproduced through numerical simulation. (paper)

Approximation of rejective sampling inclusion probabilities and application to high order correlations

NARCIS (Netherlands)

Boistard, H.; Lopuhää, H.P.; Ruiz-Gazen, A.

2012-01-01

This paper is devoted to rejective sampling. We provide an expansion of joint inclusion probabilities of any order in terms of the inclusion probabilities of order one, extending previous results by Hájek (1964) and Hájek (1981) and making the remainder term more precise. Following Hájek (1981), the

Probability theory and mathematical statistics for engineers

CERN Document Server

Pugachev, V S

1984-01-01

Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector

Sensitivity of probability-of-failure estimates with respect to probability of detection curve parameters

Energy Technology Data Exchange (ETDEWEB)

Garza, J. [University of Texas at San Antonio, Mechanical Engineering, 1 UTSA circle, EB 3.04.50, San Antonio, TX 78249 (United States); Millwater, H., E-mail: harry.millwater@utsa.edu [University of Texas at San Antonio, Mechanical Engineering, 1 UTSA circle, EB 3.04.50, San Antonio, TX 78249 (United States)

2012-04-15

A methodology has been developed and demonstrated that can be used to compute the sensitivity of the probability-of-failure (POF) with respect to the parameters of inspection processes that are simulated using probability of detection (POD) curves. The formulation is such that the probabilistic sensitivities can be obtained at negligible cost using sampling methods by reusing the samples used to compute the POF. As a result, the methodology can be implemented for negligible cost in a post-processing non-intrusive manner thereby facilitating implementation with existing or commercial codes. The formulation is generic and not limited to any specific random variables, fracture mechanics formulation, or any specific POD curve as long as the POD is modeled parametrically. Sensitivity estimates for the cases of different POD curves at multiple inspections, and the same POD curves at multiple inspections have been derived. Several numerical examples are presented and show excellent agreement with finite difference estimates with significant computational savings. - Highlights: Black-Right-Pointing-Pointer Sensitivity of the probability-of-failure with respect to the probability-of-detection curve. Black-Right-Pointing-Pointer The sensitivities are computed with negligible cost using Monte Carlo sampling. Black-Right-Pointing-Pointer The change in the POF due to a change in the POD curve parameters can be easily estimated.

Sensitivity of probability-of-failure estimates with respect to probability of detection curve parameters

International Nuclear Information System (INIS)

Garza, J.; Millwater, H.

2012-01-01

A methodology has been developed and demonstrated that can be used to compute the sensitivity of the probability-of-failure (POF) with respect to the parameters of inspection processes that are simulated using probability of detection (POD) curves. The formulation is such that the probabilistic sensitivities can be obtained at negligible cost using sampling methods by reusing the samples used to compute the POF. As a result, the methodology can be implemented for negligible cost in a post-processing non-intrusive manner thereby facilitating implementation with existing or commercial codes. The formulation is generic and not limited to any specific random variables, fracture mechanics formulation, or any specific POD curve as long as the POD is modeled parametrically. Sensitivity estimates for the cases of different POD curves at multiple inspections, and the same POD curves at multiple inspections have been derived. Several numerical examples are presented and show excellent agreement with finite difference estimates with significant computational savings. - Highlights: ► Sensitivity of the probability-of-failure with respect to the probability-of-detection curve. ►The sensitivities are computed with negligible cost using Monte Carlo sampling. ► The change in the POF due to a change in the POD curve parameters can be easily estimated.

Risk Probabilities

DEFF Research Database (Denmark)

Rojas-Nandayapa, Leonardo

Tail probabilities of sums of heavy-tailed random variables are of a major importance in various branches of Applied Probability, such as Risk Theory, Queueing Theory, Financial Management, and are subject to intense research nowadays. To understand their relevance one just needs to think...... analytic expression for the distribution function of a sum of random variables. The presence of heavy-tailed random variables complicates the problem even more. The objective of this dissertation is to provide better approximations by means of sharp asymptotic expressions and Monte Carlo estimators...

Probability an introduction

CERN Document Server

Grimmett, Geoffrey

2014-01-01

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit th...

A country-wide probability sample of public attitudes toward stuttering in Portugal.

Science.gov (United States)

Valente, Ana Rita S; St Louis, Kenneth O; Leahy, Margaret; Hall, Andreia; Jesus, Luis M T

2017-06-01

Negative public attitudes toward stuttering have been widely reported, although differences among countries and regions exist. Clear reasons for these differences remain obscure. Published research is unavailable on public attitudes toward stuttering in Portugal as well as a representative sample that explores stuttering attitudes in an entire country. This study sought to (a) determine the feasibility of a country-wide probability sampling scheme to measure public stuttering attitudes in Portugal using a standard instrument (the Public Opinion Survey of Human Attributes-Stuttering [POSHA-S]) and (b) identify demographic variables that predict Portuguese attitudes. The POSHA-S was translated to European Portuguese through a five-step process. Thereafter, a local administrative office-based, three-stage, cluster, probability sampling scheme was carried out to obtain 311 adult respondents who filled out the questionnaire. The Portuguese population held stuttering attitudes that were generally within the average range of those observed from numerous previous POSHA-S samples. Demographic variables that predicted more versus less positive stuttering attitudes were respondents' age, region of the country, years of school completed, working situation, and number of languages spoken. Non-predicting variables were respondents' sex, marital status, and parental status. A local administrative office-based, probability sampling scheme generated a respondent profile similar to census data and indicated that Portuguese attitudes are generally typical. Copyright © 2017 Elsevier Inc. All rights reserved.

Generalized Probability-Probability Plots

NARCIS (Netherlands)

Mushkudiani, N.A.; Einmahl, J.H.J.

2004-01-01

We introduce generalized Probability-Probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real valued data.These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P

An extended car-following model considering random safety distance with different probabilities

Science.gov (United States)

Wang, Jufeng; Sun, Fengxin; Cheng, Rongjun; Ge, Hongxia; Wei, Qi

2018-02-01

Because of the difference in vehicle type or driving skill, the driving strategy is not exactly the same. The driving speeds of the different vehicles may be different for the same headway. Since the optimal velocity function is just determined by the safety distance besides the maximum velocity and headway, an extended car-following model accounting for random safety distance with different probabilities is proposed in this paper. The linear stable condition for this extended traffic model is obtained by using linear stability theory. Numerical simulations are carried out to explore the complex phenomenon resulting from multiple safety distance in the optimal velocity function. The cases of multiple types of safety distances selected with different probabilities are presented. Numerical results show that the traffic flow with multiple safety distances with different probabilities will be more unstable than that with single type of safety distance, and will result in more stop-and-go phenomena.

Analytic results for asymmetric random walk with exponential transition probabilities

International Nuclear Information System (INIS)

Gutkowicz-Krusin, D.; Procaccia, I.; Ross, J.

1978-01-01

We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range

COVAL, Compound Probability Distribution for Function of Probability Distribution

International Nuclear Information System (INIS)

Astolfi, M.; Elbaz, J.

1979-01-01

1 - Nature of the physical problem solved: Computation of the probability distribution of a function of variables, given the probability distribution of the variables themselves. 'COVAL' has been applied to reliability analysis of a structure subject to random loads. 2 - Method of solution: Numerical transformation of probability distributions

Inverse probability weighting for covariate adjustment in randomized studies.

Science.gov (United States)

Shen, Changyu; Li, Xiaochun; Li, Lingling

2014-02-20

Covariate adjustment in randomized clinical trials has the potential benefit of precision gain. It also has the potential pitfall of reduced objectivity as it opens the possibility of selecting a 'favorable' model that yields strong treatment benefit estimate. Although there is a large volume of statistical literature targeting on the first aspect, realistic solutions to enforce objective inference and improve precision are rare. As a typical randomized trial needs to accommodate many implementation issues beyond statistical considerations, maintaining the objectivity is at least as important as precision gain if not more, particularly from the perspective of the regulatory agencies. In this article, we propose a two-stage estimation procedure based on inverse probability weighting to achieve better precision without compromising objectivity. The procedure is designed in a way such that the covariate adjustment is performed before seeing the outcome, effectively reducing the possibility of selecting a 'favorable' model that yields a strong intervention effect. Both theoretical and numerical properties of the estimation procedure are presented. Application of the proposed method to a real data example is presented. Copyright © 2013 John Wiley & Sons, Ltd.

Contribution to the neutronic theory of random stacks (diffusion coefficient and first-flight collision probabilities) with a general theorem on collision probabilities

International Nuclear Information System (INIS)

Dixmier, Marc.

1980-10-01

A general expression of the diffusion coefficient (d.c.) of neutrons was given, with stress being put on symmetries. A system of first-flight collision probabilities for the case of a random stack of any number of types of one- and two-zoned spherical pebbles, with an albedo at the frontiers of the elements or (either) consideration of the interstital medium, was built; to that end, the bases of collision probability theory were reviewed, and a wide generalisation of the reciprocity theorem for those probabilities was demonstrated. The migration area of neutrons was expressed for any random stack of convex, 'simple' and 'regular-contact' elements, taking into account the correlations between free-paths; the average cosinus of re-emission of neutrons by an element, in the case of a homogeneous spherical pebble and the transport approximation, was expressed; the superiority of the so-found result over Behrens' theory, for the type of media under consideration, was established. The 'fine structure current term' of the d.c. was also expressed, and it was shown that its 'polarisation term' is negligible. Numerical applications showed that the global heterogeneity effect on the d.c. of pebble-bed reactors is comparable with that for Graphite-moderated, Carbon gas-cooled, natural Uranium reactors. The code CARACOLE, which integrates all the results here obtained, was introduced [fr

Discrete probability models and methods probability on graphs and trees, Markov chains and random fields, entropy and coding

CERN Document Server

Brémaud, Pierre

2017-01-01

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book. .

Upgrading Probability via Fractions of Events

Directory of Open Access Journals (Sweden)

Frič Roman

2016-08-01

Full Text Available The influence of “Grundbegriffe” by A. N. Kolmogorov (published in 1933 on education in the area of probability and its impact on research in stochastics cannot be overestimated. We would like to point out three aspects of the classical probability theory “calling for” an upgrade: (i classical random events are black-and-white (Boolean; (ii classical random variables do not model quantum phenomena; (iii basic maps (probability measures and observables { dual maps to random variables have very different “mathematical nature”. Accordingly, we propose an upgraded probability theory based on Łukasiewicz operations (multivalued logic on events, elementary category theory, and covering the classical probability theory as a special case. The upgrade can be compared to replacing calculations with integers by calculations with rational (and real numbers. Namely, to avoid the three objections, we embed the classical (Boolean random events (represented by the f0; 1g-valued indicator functions of sets into upgraded random events (represented by measurable {0; 1}-valued functions, the minimal domain of probability containing “fractions” of classical random events, and we upgrade the notions of probability measure and random variable.

On the assessment of extremely low breakdown probabilities by an inverse sampling procedure [gaseous insulation

DEFF Research Database (Denmark)

Thyregod, Poul; Vibholm, Svend

1991-01-01

the flashover probability function and the corresponding distribution of first breakdown voltages under the inverse sampling procedure, and show how this relation may be utilized to assess the single-shot flashover probability corresponding to the observed average first breakdown voltage. Since the procedure......First breakdown voltages obtained under the inverse sampling procedure assuming a double exponential flashover probability function are discussed. An inverse sampling procedure commences the voltage application at a very low level, followed by applications at stepwise increased levels until...... is based on voltage applications in the neighbourhood of the quantile under investigation, the procedure is found to be insensitive to the underlying distributional assumptions...

Sampling in epidemiological research: issues, hazards and pitfalls

Science.gov (United States)

Tyrer, Stephen; Heyman, Bob

2016-01-01

Surveys of people's opinions are fraught with difficulties. It is easier to obtain information from those who respond to text messages or to emails than to attempt to obtain a representative sample. Samples of the population that are selected non-randomly in this way are termed convenience samples as they are easy to recruit. This introduces a sampling bias. Such non-probability samples have merit in many situations, but an epidemiological enquiry is of little value unless a random sample is obtained. If a sufficient number of those selected actually complete a survey, the results are likely to be representative of the population. This editorial describes probability and non-probability sampling methods and illustrates the difficulties and suggested solutions in performing accurate epidemiological research. PMID:27087985

Probability for human intake of an atom randomly released into ground, rivers, oceans and air

Energy Technology Data Exchange (ETDEWEB)

Cohen, B L

1984-08-01

Numerical estimates are developed for the probability of an atom randomly released in the top ground layers, in a river, or in the oceans to be ingested orally by a human, and for an atom emitted from an industrial source to be inhaled by a human. Estimates are obtained for both probability per year and for total eventual probability. Results vary considerably for different elements, but typical values for total probabilities are: ground, 3 X 10/sup -3/, oceans, 3 X 10/sup -4/; rivers, 1.7 x 10/sup -4/; and air, 5 X 10/sup -6/. Probabilities per year are typcially 1 X 10/sup -7/ for releases into the ground and 5 X 10/sup -8/ for releases into the oceans. These results indicate that for material with very long-lasting toxicity, it is important to include the pathways from the ground and from the oceans.

STADIC: a computer code for combining probability distributions

International Nuclear Information System (INIS)

Cairns, J.J.; Fleming, K.N.

1977-03-01

The STADIC computer code uses a Monte Carlo simulation technique for combining probability distributions. The specific function for combination of the input distribution is defined by the user by introducing the appropriate FORTRAN statements to the appropriate subroutine. The code generates a Monte Carlo sampling from each of the input distributions and combines these according to the user-supplied function to provide, in essence, a random sampling of the combined distribution. When the desired number of samples is obtained, the output routine calculates the mean, standard deviation, and confidence limits for the resultant distribution. This method of combining probability distributions is particularly useful in cases where analytical approaches are either too difficult or undefined

Estimating the joint survival probabilities of married individuals

NARCIS (Netherlands)

Sanders, Lisanne; Melenberg, Bertrand

We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squared

Eliciting and Developing Teachers' Conceptions of Random Processes in a Probability and Statistics Course

Science.gov (United States)

Smith, Toni M.; Hjalmarson, Margret A.

2013-01-01

The purpose of this study is to examine prospective mathematics specialists' engagement in an instructional sequence designed to elicit and develop their understandings of random processes. The study was conducted with two different sections of a probability and statistics course for K-8 teachers. Thirty-two teachers participated. Video analyses…

Efficient sampling of complex network with modified random walk strategies

Science.gov (United States)

Xie, Yunya; Chang, Shuhua; Zhang, Zhipeng; Zhang, Mi; Yang, Lei

2018-02-01

We present two novel random walk strategies, choosing seed node (CSN) random walk and no-retracing (NR) random walk. Different from the classical random walk sampling, the CSN and NR strategies focus on the influences of the seed node choice and path overlap, respectively. Three random walk samplings are applied in the Erdös-Rényi (ER), Barabási-Albert (BA), Watts-Strogatz (WS), and the weighted USAir networks, respectively. Then, the major properties of sampled subnets, such as sampling efficiency, degree distributions, average degree and average clustering coefficient, are studied. The similar conclusions can be reached with these three random walk strategies. Firstly, the networks with small scales and simple structures are conducive to the sampling. Secondly, the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps. And thirdly, all the degree distributions of the subnets are slightly biased to the high degree side. However, the NR strategy performs better for the average clustering coefficient of the subnet. In the real weighted USAir networks, some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies.

Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler function

Science.gov (United States)

Liang, Yingjie; Chen, Wen

2018-04-01

The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.

RandomSpot: A web-based tool for systematic random sampling of virtual slides.

Science.gov (United States)

Wright, Alexander I; Grabsch, Heike I; Treanor, Darren E

2015-01-01

This paper describes work presented at the Nordic Symposium on Digital Pathology 2014, Linköping, Sweden. Systematic random sampling (SRS) is a stereological tool, which provides a framework to quickly build an accurate estimation of the distribution of objects or classes within an image, whilst minimizing the number of observations required. RandomSpot is a web-based tool for SRS in stereology, which systematically places equidistant points within a given region of interest on a virtual slide. Each point can then be visually inspected by a pathologist in order to generate an unbiased sample of the distribution of classes within the tissue. Further measurements can then be derived from the distribution, such as the ratio of tumor to stroma. RandomSpot replicates the fundamental principle of traditional light microscope grid-shaped graticules, with the added benefits associated with virtual slides, such as facilitated collaboration and automated navigation between points. Once the sample points have been added to the region(s) of interest, users can download the annotations and view them locally using their virtual slide viewing software. Since its introduction, RandomSpot has been used extensively for international collaborative projects, clinical trials and independent research projects. So far, the system has been used to generate over 21,000 sample sets, and has been used to generate data for use in multiple publications, identifying significant new prognostic markers in colorectal, upper gastro-intestinal and breast cancer. Data generated using RandomSpot also has significant value for training image analysis algorithms using sample point coordinates and pathologist classifications.

On the Generation of Random Ensembles of Qubits and Qutrits Computing Separability Probabilities for Fixed Rank States

Directory of Open Access Journals (Sweden)

Khvedelidze Arsen

2018-01-01

Full Text Available The generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. In particular, we consider the generation of random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.

Probability of failure prediction for step-stress fatigue under sine or random stress

Science.gov (United States)

Lambert, R. G.

1979-01-01

A previously proposed cumulative fatigue damage law is extended to predict the probability of failure or fatigue life for structural materials with S-N fatigue curves represented as a scatterband of failure points. The proposed law applies to structures subjected to sinusoidal or random stresses and includes the effect of initial crack (i.e., flaw) sizes. The corrected cycle ratio damage function is shown to have physical significance.

Methodology Series Module 5: Sampling Strategies

OpenAIRE

Setia, Maninder Singh

2016-01-01

Once the research question and the research design have been finalised, it is important to select the appropriate sample for the study. The method by which the researcher selects the sample is the ? Sampling Method?. There are essentially two types of sampling methods: 1) probability sampling ? based on chance events (such as random numbers, flipping a coin etc.); and 2) non-probability sampling ? based on researcher's choice, population that accessible & available. Some of the non-probabilit...

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta‐analysis and group level studies

Science.gov (United States)

Bakbergenuly, Ilyas; Morgenthaler, Stephan

2016-01-01

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group‐level studies or in meta‐analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log‐odds and arcsine transformations of the estimated probability p^, both for single‐group studies and in combining results from several groups or studies in meta‐analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta‐analysis and result in abysmal coverage of the combined effect for large K. We also propose bias‐correction for the arcsine transformation. Our simulations demonstrate that this bias‐correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta‐analyses of prevalence. PMID:27192062

Nuclear data uncertainties: I, Basic concepts of probability

Energy Technology Data Exchange (ETDEWEB)

Smith, D.L.

1988-12-01

Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs.

Nuclear data uncertainties: I, Basic concepts of probability

International Nuclear Information System (INIS)

Smith, D.L.

1988-12-01

Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs

A random spatial sampling method in a rural developing nation

Science.gov (United States)

Michelle C. Kondo; Kent D.W. Bream; Frances K. Barg; Charles C. Branas

2014-01-01

Nonrandom sampling of populations in developing nations has limitations and can inaccurately estimate health phenomena, especially among hard-to-reach populations such as rural residents. However, random sampling of rural populations in developing nations can be challenged by incomplete enumeration of the base population. We describe a stratified random sampling method...

Calculation of parameter failure probability of thermodynamic system by response surface and importance sampling method

International Nuclear Information System (INIS)

Shang Yanlong; Cai Qi; Chen Lisheng; Zhang Yangwei

2012-01-01

In this paper, the combined method of response surface and importance sampling was applied for calculation of parameter failure probability of the thermodynamic system. The mathematics model was present for the parameter failure of physics process in the thermodynamic system, by which the combination arithmetic model of response surface and importance sampling was established, then the performance degradation model of the components and the simulation process of parameter failure in the physics process of thermodynamic system were also present. The parameter failure probability of the purification water system in nuclear reactor was obtained by the combination method. The results show that the combination method is an effective method for the calculation of the parameter failure probability of the thermodynamic system with high dimensionality and non-linear characteristics, because of the satisfactory precision with less computing time than the direct sampling method and the drawbacks of response surface method. (authors)

Normal probability plots with confidence.

Science.gov (United States)

Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank; Kiatsupaibul, Seksan; Hayter, Anthony J; Wan, Fang

2015-01-01

Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability 1-α. These simultaneous 1-α probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson-Darling and Shapiro-Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A probability measure for random surfaces of arbitrary genus and bosonic strings in 4 dimensions

International Nuclear Information System (INIS)

Albeverio, S.; Hoeegh-Krohn, R.; Paycha, S.; Scarlatti, S.

1989-01-01

We define a probability measure describing random surfaces in R D , 3≤D≤13, parametrized by compact Riemann surfaces of arbitrary genus. The measure involves the path space measure for scalar fields with exponential interaction in 2 space time dimensions. We show that it gives a mathematical realization of Polyakov's heuristic measure for bosonic strings. (orig.)

Random sampling of quantum states: a survey of methods and some issues regarding the Overparametrized Method

International Nuclear Information System (INIS)

Maziero, Jonas

2015-01-01

The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here, we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sampling of unbiased discrete probability distributions (DPD). Afterwards, the creation of random density matrices is addressed. In this context, we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence, the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general convenient for RQS generation. In the last part of the article, we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to create random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a simple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts of the elements of such general complex matrices. Subsequently, a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed. (author)

Gray bootstrap method for estimating frequency-varying random vibration signals with small samples

Directory of Open Access Journals (Sweden)

Wang Yanqing

2014-04-01

Full Text Available During environment testing, the estimation of random vibration signals (RVS is an important technique for the airborne platform safety and reliability. However, the available methods including extreme value envelope method (EVEM, statistical tolerances method (STM and improved statistical tolerance method (ISTM require large samples and typical probability distribution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method (GBM is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated interval, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method (BM and gray method (GM in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.

Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions

International Nuclear Information System (INIS)

Jumarie, Guy

2009-01-01

A probability distribution of fractional (or fractal) order is defined by the measure μ{dx} = p(x)(dx) α , 0 α (D x α h α )f(x) provided by the modified Riemann Liouville definition, one can expand a probability calculus parallel to the standard one. A Fourier's transform of fractional order using the Mittag-Leffler function is introduced, together with its inversion formula; and it provides a suitable generalization of the characteristic function of fractal random variables. It appears that the state moments of fractional order are more especially relevant. The main properties of this fractional probability calculus are outlined, it is shown that it provides a sound approach to Fokker-Planck equation which are fractional in both space and time, and it provides new results in the information theory of non-random functions.

Choosing a suitable sample size in descriptive sampling

International Nuclear Information System (INIS)

Lee, Yong Kyun; Choi, Dong Hoon; Cha, Kyung Joon

2010-01-01

Descriptive sampling (DS) is an alternative to crude Monte Carlo sampling (CMCS) in finding solutions to structural reliability problems. It is known to be an effective sampling method in approximating the distribution of a random variable because it uses the deterministic selection of sample values and their random permutation,. However, because this method is difficult to apply to complex simulations, the sample size is occasionally determined without thorough consideration. Input sample variability may cause the sample size to change between runs, leading to poor simulation results. This paper proposes a numerical method for choosing a suitable sample size for use in DS. Using this method, one can estimate a more accurate probability of failure in a reliability problem while running a minimal number of simulations. The method is then applied to several examples and compared with CMCS and conventional DS to validate its usefulness and efficiency

Blocked Randomization with Randomly Selected Block Sizes

Directory of Open Access Journals (Sweden)

Jimmy Efird

2010-12-01

Full Text Available When planning a randomized clinical trial, careful consideration must be given to how participants are selected for various arms of a study. Selection and accidental bias may occur when participants are not assigned to study groups with equal probability. A simple random allocation scheme is a process by which each participant has equal likelihood of being assigned to treatment versus referent groups. However, by chance an unequal number of individuals may be assigned to each arm of the study and thus decrease the power to detect statistically significant differences between groups. Block randomization is a commonly used technique in clinical trial design to reduce bias and achieve balance in the allocation of participants to treatment arms, especially when the sample size is small. This method increases the probability that each arm will contain an equal number of individuals by sequencing participant assignments by block. Yet still, the allocation process may be predictable, for example, when the investigator is not blind and the block size is fixed. This paper provides an overview of blocked randomization and illustrates how to avoid selection bias by using random block sizes.

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies.

Science.gov (United States)

Bakbergenuly, Ilyas; Kulinskaya, Elena; Morgenthaler, Stephan

2016-07-01

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probability p̂, both for single-group studies and in combining results from several groups or studies in meta-analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta-analysis and result in abysmal coverage of the combined effect for large K. We also propose bias-correction for the arcsine transformation. Our simulations demonstrate that this bias-correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta-analyses of prevalence. © 2016 The Authors. Biometrical Journal Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Introduction to probability theory with contemporary applications

CERN Document Server

Helms, Lester L

2010-01-01

This introduction to probability theory transforms a highly abstract subject into a series of coherent concepts. Its extensive discussions and clear examples, written in plain language, expose students to the rules and methods of probability. Suitable for an introductory probability course, this volume requires abstract and conceptual thinking skills and a background in calculus.Topics include classical probability, set theory, axioms, probability functions, random and independent random variables, expected values, and covariance and correlations. Additional subjects include stochastic process

Sampling little fish in big rivers: Larval fish detection probabilities in two Lake Erie tributaries and implications for sampling effort and abundance indices

Science.gov (United States)

Pritt, Jeremy J.; DuFour, Mark R.; Mayer, Christine M.; Roseman, Edward F.; DeBruyne, Robin L.

2014-01-01

Larval fish are frequently sampled in coastal tributaries to determine factors affecting recruitment, evaluate spawning success, and estimate production from spawning habitats. Imperfect detection of larvae is common, because larval fish are small and unevenly distributed in space and time, and coastal tributaries are often large and heterogeneous. We estimated detection probabilities of larval fish from several taxa in the Maumee and Detroit rivers, the two largest tributaries of Lake Erie. We then demonstrated how accounting for imperfect detection influenced (1) the probability of observing taxa as present relative to sampling effort and (2) abundance indices for larval fish of two Detroit River species. We found that detection probabilities ranged from 0.09 to 0.91 but were always less than 1.0, indicating that imperfect detection is common among taxa and between systems. In general, taxa with high fecundities, small larval length at hatching, and no nesting behaviors had the highest detection probabilities. Also, detection probabilities were higher in the Maumee River than in the Detroit River. Accounting for imperfect detection produced up to fourfold increases in abundance indices for Lake Whitefish Coregonus clupeaformis and Gizzard Shad Dorosoma cepedianum. The effect of accounting for imperfect detection in abundance indices was greatest during periods of low abundance for both species. Detection information can be used to determine the appropriate level of sampling effort for larval fishes and may improve management and conservation decisions based on larval fish data.

Bayesian optimization for computationally extensive probability distributions.

Science.gov (United States)

Tamura, Ryo; Hukushima, Koji

2018-01-01

An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.

Multipartite nonlocality and random measurements

Science.gov (United States)

de Rosier, Anna; Gruca, Jacek; Parisio, Fernando; Vértesi, Tamás; Laskowski, Wiesław

2017-07-01

We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness of genuine multipartite entanglement.

Concepts of probability theory

CERN Document Server

Pfeiffer, Paul E

1979-01-01

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

SOME SYSTEMATIC SAMPLING STRATEGIES USING MULTIPLE RANDOM STARTS

OpenAIRE

Sampath Sundaram; Ammani Sivaraman

2010-01-01

In this paper an attempt is made to extend linear systematic sampling using multiple random starts due to Gautschi(1957)for various types of systematic sampling schemes available in literature, namely(i)  Balanced Systematic Sampling (BSS) of  Sethi (1965) and (ii) Modified Systematic Sampling (MSS) of Singh, Jindal, and Garg  (1968). Further, the proposed methods were compared with Yates corrected estimator developed with reference to Gautschi’s Linear systematic samplin...

RANdom SAmple Consensus (RANSAC) algorithm for material-informatics: application to photovoltaic solar cells.

Science.gov (United States)

Kaspi, Omer; Yosipof, Abraham; Senderowitz, Hanoch

2017-06-06

An important aspect of chemoinformatics and material-informatics is the usage of machine learning algorithms to build Quantitative Structure Activity Relationship (QSAR) models. The RANdom SAmple Consensus (RANSAC) algorithm is a predictive modeling tool widely used in the image processing field for cleaning datasets from noise. RANSAC could be used as a "one stop shop" algorithm for developing and validating QSAR models, performing outlier removal, descriptors selection, model development and predictions for test set samples using applicability domain. For "future" predictions (i.e., for samples not included in the original test set) RANSAC provides a statistical estimate for the probability of obtaining reliable predictions, i.e., predictions within a pre-defined number of standard deviations from the true values. In this work we describe the first application of RNASAC in material informatics, focusing on the analysis of solar cells. We demonstrate that for three datasets representing different metal oxide (MO) based solar cell libraries RANSAC-derived models select descriptors previously shown to correlate with key photovoltaic properties and lead to good predictive statistics for these properties. These models were subsequently used to predict the properties of virtual solar cells libraries highlighting interesting dependencies of PV properties on MO compositions.

Spencer-Brown vs. Probability and Statistics: Entropy’s Testimony on Subjective and Objective Randomness

Directory of Open Access Journals (Sweden)

Julio Michael Stern

2011-04-01

Full Text Available This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

Probability elements of the mathematical theory

CERN Document Server

Heathcote, C R

2000-01-01

Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.

Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral

International Nuclear Information System (INIS)

Lin, T.L.; Wang, R.; Bi, W.P.; El Kaabouchi, A.; Pujos, C.; Calvayrac, F.; Wang, Q.A.

2013-01-01

We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model of simulation is a one-dimensional particle subject to conservative force and Gaussian random displacement. The probability that a sample path between two fixed points is taken is computed from the number of particles moving along this path, an output of the simulation, divided by the total number of particles arriving at the final point. It is found that the path probability decays exponentially with increasing action of the sample paths. The decay rate increases with decreasing randomness. This result supports the existence of a classical analog of the Feynman factor in the path integral formulation of quantum mechanics for Hamiltonian systems

Optimal Sample Size for Probability of Detection Curves

International Nuclear Information System (INIS)

Annis, Charles; Gandossi, Luca; Martin, Oliver

2012-01-01

The use of Probability of Detection (POD) curves to quantify NDT reliability is common in the aeronautical industry, but relatively less so in the nuclear industry. The European Network for Inspection Qualification's (ENIQ) Inspection Qualification Methodology is based on the concept of Technical Justification, a document assembling all the evidence to assure that the NDT system in focus is indeed capable of finding the flaws for which it was designed. This methodology has become widely used in many countries, but the assurance it provides is usually of qualitative nature. The need to quantify the output of inspection qualification has become more important, especially as structural reliability modelling and quantitative risk-informed in-service inspection methodologies become more widely used. To credit the inspections in structural reliability evaluations, a measure of the NDT reliability is necessary. A POD curve provides such metric. In 2010 ENIQ developed a technical report on POD curves, reviewing the statistical models used to quantify inspection reliability. Further work was subsequently carried out to investigate the issue of optimal sample size for deriving a POD curve, so that adequate guidance could be given to the practitioners of inspection reliability. Manufacturing of test pieces with cracks that are representative of real defects found in nuclear power plants (NPP) can be very expensive. Thus there is a tendency to reduce sample sizes and in turn reduce the conservatism associated with the POD curve derived. Not much guidance on the correct sample size can be found in the published literature, where often qualitative statements are given with no further justification. The aim of this paper is to summarise the findings of such work. (author)

Models for probability and statistical inference theory and applications

CERN Document Server

Stapleton, James H

2007-01-01

This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readersModels for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses mo...

Health plan auditing: 100-percent-of-claims vs. random-sample audits.

Science.gov (United States)

Sillup, George P; Klimberg, Ronald K

2011-01-01

The objective of this study was to examine the relative efficacy of two different methodologies for auditing self-funded medical claim expenses: 100-percent-of-claims auditing versus random-sampling auditing. Multiple data sets of claim errors or 'exceptions' from two Fortune-100 corporations were analysed and compared to 100 simulated audits of 300- and 400-claim random samples. Random-sample simulations failed to identify a significant number and amount of the errors that ranged from $200,000 to $750,000. These results suggest that health plan expenses of corporations could be significantly reduced if they audited 100% of claims and embraced a zero-defect approach.

Choice Probability Generating Functions

DEFF Research Database (Denmark)

Fosgerau, Mogens; McFadden, Daniel L; Bierlaire, Michel

This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications....

Fixation probability in a two-locus intersexual selection model.

Science.gov (United States)

Durand, Guillermo; Lessard, Sabin

2016-06-01

We study a two-locus model of intersexual selection in a finite haploid population reproducing according to a discrete-time Moran model with a trait locus expressed in males and a preference locus expressed in females. We show that the probability of ultimate fixation of a single mutant allele for a male ornament introduced at random at the trait locus given any initial frequency state at the preference locus is increased by weak intersexual selection and recombination, weak or strong. Moreover, this probability exceeds the initial frequency of the mutant allele even in the case of a costly male ornament if intersexual selection is not too weak. On the other hand, the probability of ultimate fixation of a single mutant allele for a female preference towards a male ornament introduced at random at the preference locus is increased by weak intersexual selection and weak recombination if the female preference is not costly, and is strong enough in the case of a costly male ornament. The analysis relies on an extension of the ancestral recombination-selection graph for samples of haplotypes to take into account events of intersexual selection, while the symbolic calculation of the fixation probabilities is made possible in a reasonable time by an optimizing algorithm. Copyright © 2016 Elsevier Inc. All rights reserved.

A methodology for more efficient tail area sampling with discrete probability distribution

International Nuclear Information System (INIS)

Park, Sang Ryeol; Lee, Byung Ho; Kim, Tae Woon

1988-01-01

Monte Carlo Method is commonly used to observe the overall distribution and to determine the lower or upper bound value in statistical approach when direct analytical calculation is unavailable. However, this method would not be efficient if the tail area of a distribution is concerned. A new method entitled 'Two Step Tail Area Sampling' is developed, which uses the assumption of discrete probability distribution and samples only the tail area without distorting the overall distribution. This method uses two step sampling procedure. First, sampling at points separated by large intervals is done and second, sampling at points separated by small intervals is done with some check points determined at first step sampling. Comparison with Monte Carlo Method shows that the results obtained from the new method converge to analytic value faster than Monte Carlo Method if the numbers of calculation of both methods are the same. This new method is applied to DNBR (Departure from Nucleate Boiling Ratio) prediction problem in design of the pressurized light water nuclear reactor

Sample size methodology

CERN Document Server

Desu, M M

2012-01-01

One of the most important problems in designing an experiment or a survey is sample size determination and this book presents the currently available methodology. It includes both random sampling from standard probability distributions and from finite populations. Also discussed is sample size determination for estimating parameters in a Bayesian setting by considering the posterior distribution of the parameter and specifying the necessary requirements. The determination of the sample size is considered for ranking and selection problems as well as for the design of clinical trials. Appropria

Method for Evaluation of Outage Probability on Random Access Channel in Mobile Communication Systems

Science.gov (United States)

Kollár, Martin

2012-05-01

In order to access the cell in all mobile communication technologies a so called random-access procedure is used. For example in GSM this is represented by sending the CHANNEL REQUEST message from Mobile Station (MS) to Base Transceiver Station (BTS) which is consequently forwarded as an CHANNEL REQUIRED message to the Base Station Controller (BSC). If the BTS decodes some noise on the Random Access Channel (RACH) as random access by mistake (so- called ‘phantom RACH') then it is a question of pure coincidence which èstablishment cause’ the BTS thinks to have recognized. A typical invalid channel access request or phantom RACH is characterized by an IMMEDIATE ASSIGNMENT procedure (assignment of an SDCCH or TCH) which is not followed by sending an ESTABLISH INDICATION from MS to BTS. In this paper a mathematical model for evaluation of the Power RACH Busy Threshold (RACHBT) in order to guaranty in advance determined outage probability on RACH is described and discussed as well. It focuses on Global System for Mobile Communications (GSM) however the obtained results can be generalized on remaining mobile technologies (ie WCDMA and LTE).

The quantum probability calculus

International Nuclear Information System (INIS)

Jauch, J.M.

1976-01-01

The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)

Choice probability generating functions

DEFF Research Database (Denmark)

Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel

2013-01-01

This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended...

Revisiting sample size: are big trials the answer?

Science.gov (United States)

Lurati Buse, Giovanna A L; Botto, Fernando; Devereaux, P J

2012-07-18

The superiority of the evidence generated in randomized controlled trials over observational data is not only conditional to randomization. Randomized controlled trials require proper design and implementation to provide a reliable effect estimate. Adequate random sequence generation, allocation implementation, analyses based on the intention-to-treat principle, and sufficient power are crucial to the quality of a randomized controlled trial. Power, or the probability of the trial to detect a difference when a real difference between treatments exists, strongly depends on sample size. The quality of orthopaedic randomized controlled trials is frequently threatened by a limited sample size. This paper reviews basic concepts and pitfalls in sample-size estimation and focuses on the importance of large trials in the generation of valid evidence.

Optimal random search for a single hidden target.

Science.gov (United States)

Snider, Joseph

2011-01-01

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the minimum number of trials. Here it will be shown that if the searcher must get very close to the target to find it, then the best search distribution is proportional to the square root of the target distribution regardless of dimension. For a Gaussian target distribution, the optimum search distribution is approximately a Gaussian with a standard deviation that varies inversely with how close the searcher must be to the target to find it. For a network where the searcher randomly samples nodes and looks for the fixed target along edges, the optimum is either to sample a node with probability proportional to the square root of the out-degree plus 1 or not to do so at all.

Probability an introduction

CERN Document Server

Goldberg, Samuel

1960-01-01

Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, more. Includes 360 problems with answers for half.

[Biometric bases: basic concepts of probability calculation].

Science.gov (United States)

Dinya, E

1998-04-26

The author gives or outline of the basic concepts of probability theory. The bases of the event algebra, definition of the probability, the classical probability model and the random variable are presented.

Probability densities and the radon variable transformation theorem

International Nuclear Information System (INIS)

Ramshaw, J.D.

1985-01-01

D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation

Coordination of Conditional Poisson Samples

Directory of Open Access Journals (Sweden)

Grafström Anton

2015-12-01

Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.

Estimates of Inequality Indices Based on Simple Random, Ranked Set, and Systematic Sampling

OpenAIRE

Bansal, Pooja; Arora, Sangeeta; Mahajan, Kalpana K.

2013-01-01

Gini index, Bonferroni index, and Absolute Lorenz index are some popular indices of inequality showing different features of inequality measurement. In general simple random sampling procedure is commonly used to estimate the inequality indices and their related inference. The key condition that the samples must be drawn via simple random sampling procedure though makes calculations much simpler but this assumption is often violated in practice as the data does not always yield simple random ...

Probability-1

CERN Document Server

Shiryaev, Albert N

2016-01-01

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for independent study. To accommodate the greatly expanded material in the third edition of Probability, the book is now divided into two volumes. This first volume contains updated references and substantial revisions of the first three chapters of the second edition. In particular, new material has been added on generating functions, the inclusion-exclusion principle, theorems on monotonic classes (relying on a detailed treatment of “π-λ” systems), and the fundamental theorems of mathematical statistics.

An alternative procedure for estimating the population mean in simple random sampling

Directory of Open Access Journals (Sweden)

Housila P. Singh

2012-03-01

Full Text Available This paper deals with the problem of estimating the finite population mean using auxiliary information in simple random sampling. Firstly we have suggested a correction to the mean squared error of the estimator proposed by Gupta and Shabbir [On improvement in estimating the population mean in simple random sampling. Jour. Appl. Statist. 35(5 (2008, pp. 559-566]. Later we have proposed a ratio type estimator and its properties are studied in simple random sampling. Numerically we have shown that the proposed class of estimators is more efficient than different known estimators including Gupta and Shabbir (2008 estimator.

Systematic random sampling of the comet assay.

Science.gov (United States)

McArt, Darragh G; Wasson, Gillian R; McKerr, George; Saetzler, Kurt; Reed, Matt; Howard, C Vyvyan

2009-07-01

The comet assay is a technique used to quantify DNA damage and repair at a cellular level. In the assay, cells are embedded in agarose and the cellular content is stripped away leaving only the DNA trapped in an agarose cavity which can then be electrophoresed. The damaged DNA can enter the agarose and migrate while the undamaged DNA cannot and is retained. DNA damage is measured as the proportion of the migratory 'tail' DNA compared to the total DNA in the cell. The fundamental basis of these arbitrary values is obtained in the comet acquisition phase using fluorescence microscopy with a stoichiometric stain in tandem with image analysis software. Current methods deployed in such an acquisition are expected to be both objectively and randomly obtained. In this paper we examine the 'randomness' of the acquisition phase and suggest an alternative method that offers both objective and unbiased comet selection. In order to achieve this, we have adopted a survey sampling approach widely used in stereology, which offers a method of systematic random sampling (SRS). This is desirable as it offers an impartial and reproducible method of comet analysis that can be used both manually or automated. By making use of an unbiased sampling frame and using microscope verniers, we are able to increase the precision of estimates of DNA damage. Results obtained from a multiple-user pooled variation experiment showed that the SRS technique attained a lower variability than that of the traditional approach. The analysis of a single user with repetition experiment showed greater individual variances while not being detrimental to overall averages. This would suggest that the SRS method offers a better reflection of DNA damage for a given slide and also offers better user reproducibility.

Correlated random sampling for multivariate normal and log-normal distributions

International Nuclear Information System (INIS)

Žerovnik, Gašper; Trkov, Andrej; Kodeli, Ivan A.

2012-01-01

A method for correlated random sampling is presented. Representative samples for multivariate normal or log-normal distribution can be produced. Furthermore, any combination of normally and log-normally distributed correlated variables may be sampled to any requested accuracy. Possible applications of the method include sampling of resonance parameters which are used for reactor calculations.

General Exact Solution to the Problem of the Probability Density for Sums of Random Variables

Science.gov (United States)

Tribelsky, Michael I.

2002-07-01

The exact explicit expression for the probability density pN(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of pN(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.

Probability Theory Plus Noise: Descriptive Estimation and Inferential Judgment.

Science.gov (United States)

Costello, Fintan; Watts, Paul

2018-01-01

We describe a computational model of two central aspects of people's probabilistic reasoning: descriptive probability estimation and inferential probability judgment. This model assumes that people's reasoning follows standard frequentist probability theory, but it is subject to random noise. This random noise has a regressive effect in descriptive probability estimation, moving probability estimates away from normative probabilities and toward the center of the probability scale. This random noise has an anti-regressive effect in inferential judgement, however. These regressive and anti-regressive effects explain various reliable and systematic biases seen in people's descriptive probability estimation and inferential probability judgment. This model predicts that these contrary effects will tend to cancel out in tasks that involve both descriptive estimation and inferential judgement, leading to unbiased responses in those tasks. We test this model by applying it to one such task, described by Gallistel et al. ). Participants' median responses in this task were unbiased, agreeing with normative probability theory over the full range of responses. Our model captures the pattern of unbiased responses in this task, while simultaneously explaining systematic biases away from normatively correct probabilities seen in other tasks. Copyright © 2018 Cognitive Science Society, Inc.

Sampling Random Bioinformatics Puzzles using Adaptive Probability Distributions

DEFF Research Database (Denmark)

Have, Christian Theil; Appel, Emil Vincent; Bork-Jensen, Jette

2016-01-01

We present a probabilistic logic program to generate an educational puzzle that introduces the basic principles of next generation sequencing, gene finding and the translation of genes to proteins following the central dogma in biology. In the puzzle, a secret "protein word" must be found by asse...

Jenis Sample: Keuntungan dan Kerugiannya

OpenAIRE

Suprapto, Agus

1994-01-01

Sample is a part of a population that are used in a study for purposes of making estimation about the nature of the total population that is obtained with sampling technic. Sampling technic is more adventagous than cencus because it can reduce cost, time, and it can gather deeper information and more accurate data. It is useful to distinguish two major types of sampling technics. First, Prob bility sampling i.e. simple random sampling. Second, Non Probability sampling i.e. systematic sam­plin...

Non-Archimedean Probability

NARCIS (Netherlands)

Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia

We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned

Romantic Relationship Characteristics and Adolescent Relationship Abuse in a Probability-Based Sample of Youth.

Science.gov (United States)

Taylor, Bruce; Joseph, Hannah; Mumford, Elizabeth

2017-09-01

This study examines the longitudinal association between baseline adolescent romantic relationship characteristics and later adolescent relationship abuse (ARA). Data are from the first two waves of the National Survey on Teen Relationships and Intimate Violence (STRiV). Girls and boys ages 10 to 18 were recruited randomly from the children of adults participating in a larger national household probability sample panel. About three quarters of the sample identified as White, non-Hispanic. Controlling behavior by a romantic partner consistently predicted later ARA. Higher levels of controlling behavior in the relationship was associated with higher rates of sexual and/or physical ARA victimization and higher rates for similar acts of perpetration. More controlling behavior by the partner was also associated with higher rates of psychological ARA victimization (and higher rates for psychological ARA perpetration). Our results suggest that ARA prevention programs should have explicit discussions of the deleterious effects of controlling behavior with adolescents. Respondents reporting higher feelings of passionate love were also at higher risk of experiencing sexual and/or physical ARA victimization. This finding will need to be considered by clinicians and prevention specialist in their work with youth as a potential risk marker for ARA. Baseline reports of at least one form of ARA were predictive of 1-year follow-up rates of ARA in all of our models, underscoring a long line of research that past aggressive or violent behavior is one of the strongest predictors of current aggressive or violent behavior. We also observed that female respondents were twice as likely to be perpetrators of physical and/or sexual ARA as male respondents. Prevention messaging often is focused on girls as ARA victims and our results imply that messaging should also be directed toward girls as perpetrators.

On the pertinence to Physics of random walks induced by random dynamical systems: a survey

International Nuclear Information System (INIS)

Petritis, Dimitri

2016-01-01

Let be an abstract space and a denumerable (finite or infinite) alphabet. Suppose that is a family of functions such that for all we have and a family of transformations . The pair (( S_a)_a , ( p_a)_a ) is termed an iterated function system with place dependent probabilities. Such systems can be thought as generalisations of random dynamical systems. As a matter of fact, suppose we start from a given ; we pick then randomly, with probability p_a (x) , the transformation S_a and evolve to S_a (x) . We are interested in the behaviour of the system when the iteration continues indefinitely. Random walks of the above type are omnipresent in both classical and quantum Physics. To give a small sample of occurrences we mention: random walks on the affine group, random walks on Penrose lattices, random walks on partially directed lattices, evolution of density matrices induced by repeated quantum measurements, quantum channels, quantum random walks, etc. In this article, we review some basic properties of such systems and provide with a pathfinder in the extensive bibliography (both on mathematical and physical sides) where the main results have been originally published. (paper)

Random sampling of evolution time space and Fourier transform processing

International Nuclear Information System (INIS)

Kazimierczuk, Krzysztof; Zawadzka, Anna; Kozminski, Wiktor; Zhukov, Igor

2006-01-01

Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments. The experimental examples include 3D HNCA, HNCACB and 15 N-edited NOESY-HSQC spectra of 13 C 15 N labeled ubiquitin sample. Obtained results revealed general applicability of proposed method and the significant improvement of resolution in comparison with conventional spectra recorded in the same time

Sampling from the normal and exponential distributions

International Nuclear Information System (INIS)

Chaplin, K.R.; Wills, C.A.

1982-01-01

Methods for generating random numbers from the normal and exponential distributions are described. These involve dividing each function into subregions, and for each of these developing a method of sampling usually based on an acceptance rejection technique. When sampling from the normal or exponential distribution, each subregion provides the required random value with probability equal to the ratio of its area to the total area. Procedures written in FORTRAN for the CYBER 175/CDC 6600 system are provided to implement the two algorithms

A random sampling procedure for anisotropic distributions

International Nuclear Information System (INIS)

Nagrajan, P.S.; Sethulakshmi, P.; Raghavendran, C.P.; Bhatia, D.P.

1975-01-01

A procedure is described for sampling the scattering angle of neutrons as per specified angular distribution data. The cosine of the scattering angle is written as a double Legendre expansion in the incident neutron energy and a random number. The coefficients of the expansion are given for C, N, O, Si, Ca, Fe and Pb and these elements are of interest in dosimetry and shielding. (author)

Characteristics of the probability function for three random-walk models of reaction--diffusion processes

International Nuclear Information System (INIS)

Musho, M.K.; Kozak, J.J.

1984-01-01

A method is presented for calculating exactly the relative width (sigma 2 )/sup 1/2// , the skewness γ 1 , and the kurtosis γ 2 characterizing the probability distribution function for three random-walk models of diffusion-controlled processes. For processes in which a diffusing coreactant A reacts irreversibly with a target molecule B situated at a reaction center, three models are considered. The first is the traditional one of an unbiased, nearest-neighbor random walk on a d-dimensional periodic/confining lattice with traps; the second involves the consideration of unbiased, non-nearest-neigh bor (i.e., variable-step length) walks on the same d-dimensional lattice; and, the third deals with the case of a biased, nearest-neighbor walk on a d-dimensional lattice (wherein a walker experiences a potential centered at the deep trap site of the lattice). Our method, which has been described in detail elsewhere [P.A. Politowicz and J. J. Kozak, Phys. Rev. B 28, 5549 (1983)] is based on the use of group theoretic arguments within the framework of the theory of finite Markov processes

Probability and statistics for particle physics

CERN Document Server

Mana, Carlos

2017-01-01

This book comprehensively presents the basic concepts of probability and Bayesian inference with sufficient generality to make them applicable to current problems in scientific research. The first chapter provides the fundamentals of probability theory that are essential for the analysis of random phenomena. The second chapter includes a full and pragmatic review of the Bayesian methods that constitute a natural and coherent framework with enough freedom to analyze all the information available from experimental data in a conceptually simple manner. The third chapter presents the basic Monte Carlo techniques used in scientific research, allowing a large variety of problems to be handled difficult to tackle by other procedures. The author also introduces a basic algorithm, which enables readers to simulate samples from simple distribution, and describes useful cases for researchers in particle physics.The final chapter is devoted to the basic ideas of Information Theory, which are important in the Bayesian me...

Sampling the stream landscape: Improving the applicability of an ecoregion-level capture probability model for stream fishes

Science.gov (United States)

Mollenhauer, Robert; Mouser, Joshua B.; Brewer, Shannon K.

2018-01-01

Temporal and spatial variability in streams result in heterogeneous gear capture probability (i.e., the proportion of available individuals identified) that confounds interpretation of data used to monitor fish abundance. We modeled tow-barge electrofishing capture probability at multiple spatial scales for nine Ozark Highland stream fishes. In addition to fish size, we identified seven reach-scale environmental characteristics associated with variable capture probability: stream discharge, water depth, conductivity, water clarity, emergent vegetation, wetted width–depth ratio, and proportion of riffle habitat. The magnitude of the relationship between capture probability and both discharge and depth varied among stream fishes. We also identified lithological characteristics among stream segments as a coarse-scale source of variable capture probability. The resulting capture probability model can be used to adjust catch data and derive reach-scale absolute abundance estimates across a wide range of sampling conditions with similar effort as used in more traditional fisheries surveys (i.e., catch per unit effort). Adjusting catch data based on variable capture probability improves the comparability of data sets, thus promoting both well-informed conservation and management decisions and advances in stream-fish ecology.

Probabilistic finite element stiffness of a laterally loaded monopile based on an improved asymptotic sampling method

DEFF Research Database (Denmark)

Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard

2015-01-01

shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates......The mechanical responses of an offshore monopile foundation mounted in over-consolidated clay are calculated by employing a stochastic approach where a nonlinear p–y curve is incorporated with a finite element scheme. The random field theory is applied to represent a spatial variation for undrained...... an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation....

47 CFR 1.1623 - Probability calculation.

Science.gov (United States)

2010-10-01

... 47 Telecommunication 1 2010-10-01 2010-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a) All calculations shall be...

Prediction and probability in sciences

International Nuclear Information System (INIS)

Klein, E.; Sacquin, Y.

1998-01-01

This book reports the 7 presentations made at the third meeting 'physics and fundamental questions' whose theme was probability and prediction. The concept of probability that was invented to apprehend random phenomena has become an important branch of mathematics and its application range spreads from radioactivity to species evolution via cosmology or the management of very weak risks. The notion of probability is the basis of quantum mechanics and then is bound to the very nature of matter. The 7 topics are: - radioactivity and probability, - statistical and quantum fluctuations, - quantum mechanics as a generalized probability theory, - probability and the irrational efficiency of mathematics, - can we foresee the future of the universe?, - chance, eventuality and necessity in biology, - how to manage weak risks? (A.C.)

Probability of assertive behaviour, interpersonal anxiety and self-efficacy of South African registered dietitians.

Science.gov (United States)

Paterson, Marie; Green, J M; Basson, C J; Ross, F

2002-02-01

There is little information on the probability of assertive behaviour, interpersonal anxiety and self-efficacy in the literature regarding dietitians. The objective of this study was to establish baseline information of these attributes and the factors affecting them. Questionnaires collecting biographical information and self-assessment psychometric scales measuring levels of probability of assertiveness, interpersonal anxiety and self-efficacy were mailed to 350 subjects, who comprised a random sample of dietitians registered with the Health Professions Council of South Africa. Forty-one per cent (n=145) of the sample responded. Self-assessment inventory results were compared to test levels of probability of assertive behaviour, interpersonal anxiety and self-efficacy. The inventory results were compared with the biographical findings to establish statistical relationships between the variables. The hypotheses were formulated before data collection. Dietitians had acceptable levels of probability of assertive behaviour and interpersonal anxiety. The probability of assertive behaviour was significantly lower than the level noted in the literature and was negatively related to interpersonal anxiety and positively related to self-efficacy.

Fast egg collection method greatly improves randomness of egg sampling in Drosophila melanogaster

DEFF Research Database (Denmark)

Schou, Mads Fristrup

2013-01-01

When obtaining samples for population genetic studies, it is essential that the sampling is random. For Drosophila, one of the crucial steps in sampling experimental flies is the collection of eggs. Here an egg collection method is presented, which randomizes the eggs in a water column...... and diminishes environmental variance. This method was compared with a traditional egg collection method where eggs are collected directly from the medium. Within each method the observed and expected standard deviations of egg-to-adult viability were compared, whereby the difference in the randomness...... and to obtain a representative collection of genotypes, the method presented here is strongly recommended when collecting eggs from Drosophila....

A Markov random field approach for microstructure synthesis

International Nuclear Information System (INIS)

Kumar, A; Nguyen, L; DeGraef, M; Sundararaghavan, V

2016-01-01

We test the notion that many microstructures have an underlying stationary probability distribution. The stationary probability distribution is ubiquitous: we know that different windows taken from a polycrystalline microstructure are generally ‘statistically similar’. To enable computation of such a probability distribution, microstructures are represented in the form of undirected probabilistic graphs called Markov Random Fields (MRFs). In the model, pixels take up integer or vector states and interact with multiple neighbors over a window. Using this lattice structure, algorithms are developed to sample the conditional probability density for the state of each pixel given the known states of its neighboring pixels. The sampling is performed using reference experimental images. 2D microstructures are artificially synthesized using the sampled probabilities. Statistical features such as grain size distribution and autocorrelation functions closely match with those of the experimental images. The mechanical properties of the synthesized microstructures were computed using the finite element method and were also found to match the experimental values. (paper)

The influence of initial beliefs on judgments of probability.

Science.gov (United States)

Yu, Erica C; Lagnado, David A

2012-01-01

This study aims to investigate whether experimentally induced prior beliefs affect processing of evidence including the updating of beliefs under uncertainty about the unknown probabilities of outcomes and the structural, outcome-generating nature of the environment. Participants played a gambling task in the form of computer-simulated slot machines and were given information about the slot machines' possible outcomes without their associated probabilities. One group was induced with a prior belief about the outcome space that matched the space of actual outcomes to be sampled; the other group was induced with a skewed prior belief that included the actual outcomes and also fictional higher outcomes. In reality, however, all participants sampled evidence from the same underlying outcome distribution, regardless of priors given. Before and during sampling, participants expressed their beliefs about the outcome distribution (values and probabilities). Evaluation of those subjective probability distributions suggests that all participants' judgments converged toward the observed outcome distribution. However, despite observing no supporting evidence for fictional outcomes, a significant proportion of participants in the skewed priors condition expected them in the future. A probe of the participants' understanding of the underlying outcome-generating processes indicated that participants' judgments were based on the information given in the induced priors and consequently, a significant proportion of participants in the skewed condition believed the slot machines were not games of chance while participants in the control condition believed the machines generated outcomes at random. Beyond Bayesian or heuristic belief updating, priors not only contribute to belief revision but also affect one's deeper understanding of the environment.

STATISTICAL LANDMARKS AND PRACTICAL ISSUES REGARDING THE USE OF SIMPLE RANDOM SAMPLING IN MARKET RESEARCHES

Directory of Open Access Journals (Sweden)

CODRUŢA DURA

2010-01-01

Full Text Available The sample represents a particular segment of the statistical populationchosen to represent it as a whole. The representativeness of the sample determines the accuracyfor estimations made on the basis of calculating the research indicators and the inferentialstatistics. The method of random sampling is part of probabilistic methods which can be usedwithin marketing research and it is characterized by the fact that it imposes the requirementthat each unit belonging to the statistical population should have an equal chance of beingselected for the sampling process. When the simple random sampling is meant to be rigorouslyput into practice, it is recommended to use the technique of random number tables in order toconfigure the sample which will provide information that the marketer needs. The paper alsodetails the practical procedure implemented in order to create a sample for a marketingresearch by generating random numbers using the facilities offered by Microsoft Excel.

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

Science.gov (United States)

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2013-04-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling , or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.

CAN'T MISS--conquer any number task by making important statistics simple. Part 2. Probability, populations, samples, and normal distributions.

Science.gov (United States)

Hansen, John P

2003-01-01

Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.

Random magnetism

International Nuclear Information System (INIS)

Tahir-Kheli, R.A.

1975-01-01

A few simple problems relating to random magnetic systems are presented. Translational symmetry, only on the macroscopic scale, is assumed for these systems. A random set of parameters, on the microscopic scale, for the various regions of these systems is also assumed. A probability distribution for randomness is obeyed. Knowledge of the form of these probability distributions, is assumed in all cases [pt

Characterization of electron microscopes with binary pseudo-random multilayer test samples

Science.gov (United States)

Yashchuk, Valeriy V.; Conley, Raymond; Anderson, Erik H.; Barber, Samuel K.; Bouet, Nathalie; McKinney, Wayne R.; Takacs, Peter Z.; Voronov, Dmitriy L.

2011-09-01

Verification of the reliability of metrology data from high quality X-ray optics requires that adequate methods for test and calibration of the instruments be developed. For such verification for optical surface profilometers in the spatial frequency domain, a modulation transfer function (MTF) calibration method based on binary pseudo-random (BPR) gratings and arrays has been suggested [1,2] and proven to be an effective calibration method for a number of interferometric microscopes, a phase shifting Fizeau interferometer, and a scatterometer [5]. Here we describe the details of development of binary pseudo-random multilayer (BPRML) test samples suitable for characterization of scanning (SEM) and transmission (TEM) electron microscopes. We discuss the results of TEM measurements with the BPRML test samples fabricated from a WiSi 2/Si multilayer coating with pseudo-randomly distributed layers. In particular, we demonstrate that significant information about the metrological reliability of the TEM measurements can be extracted even when the fundamental frequency of the BPRML sample is smaller than the Nyquist frequency of the measurements. The measurements demonstrate a number of problems related to the interpretation of the SEM and TEM data. Note that similar BPRML test samples can be used to characterize X-ray microscopes. Corresponding work with X-ray microscopes is in progress.

Characterization of electron microscopes with binary pseudo-random multilayer test samples

International Nuclear Information System (INIS)

Yashchuk, Valeriy V.; Conley, Raymond; Anderson, Erik H.; Barber, Samuel K.; Bouet, Nathalie; McKinney, Wayne R.; Takacs, Peter Z.; Voronov, Dmitriy L.

2011-01-01

Verification of the reliability of metrology data from high quality X-ray optics requires that adequate methods for test and calibration of the instruments be developed. For such verification for optical surface profilometers in the spatial frequency domain, a modulation transfer function (MTF) calibration method based on binary pseudo-random (BPR) gratings and arrays has been suggested and proven to be an effective calibration method for a number of interferometric microscopes, a phase shifting Fizeau interferometer, and a scatterometer [5]. Here we describe the details of development of binary pseudo-random multilayer (BPRML) test samples suitable for characterization of scanning (SEM) and transmission (TEM) electron microscopes. We discuss the results of TEM measurements with the BPRML test samples fabricated from a WiSi 2 /Si multilayer coating with pseudo-randomly distributed layers. In particular, we demonstrate that significant information about the metrological reliability of the TEM measurements can be extracted even when the fundamental frequency of the BPRML sample is smaller than the Nyquist frequency of the measurements. The measurements demonstrate a number of problems related to the interpretation of the SEM and TEM data. Note that similar BPRML test samples can be used to characterize X-ray microscopes. Corresponding work with X-ray microscopes is in progress.

LOD score exclusion analyses for candidate genes using random population samples.

Science.gov (United States)

Deng, H W; Li, J; Recker, R R

2001-05-01

While extensive analyses have been conducted to test for, no formal analyses have been conducted to test against, the importance of candidate genes with random population samples. We develop a LOD score approach for exclusion analyses of candidate genes with random population samples. Under this approach, specific genetic effects and inheritance models at candidate genes can be analysed and if a LOD score is < or = - 2.0, the locus can be excluded from having an effect larger than that specified. Computer simulations show that, with sample sizes often employed in association studies, this approach has high power to exclude a gene from having moderate genetic effects. In contrast to regular association analyses, population admixture will not affect the robustness of our analyses; in fact, it renders our analyses more conservative and thus any significant exclusion result is robust. Our exclusion analysis complements association analysis for candidate genes in random population samples and is parallel to the exclusion mapping analyses that may be conducted in linkage analyses with pedigrees or relative pairs. The usefulness of the approach is demonstrated by an application to test the importance of vitamin D receptor and estrogen receptor genes underlying the differential risk to osteoporotic fractures.

Estimating the probability that the sample mean is within a desired fraction of the standard deviation of the true mean.

Science.gov (United States)

Schillaci, Michael A; Schillaci, Mario E

2009-02-01

The use of small sample sizes in human and primate evolutionary research is commonplace. Estimating how well small samples represent the underlying population, however, is not commonplace. Because the accuracy of determinations of taxonomy, phylogeny, and evolutionary process are dependant upon how well the study sample represents the population of interest, characterizing the uncertainty, or potential error, associated with analyses of small sample sizes is essential. We present a method for estimating the probability that the sample mean is within a desired fraction of the standard deviation of the true mean using small (nresearchers to determine post hoc the probability that their sample is a meaningful approximation of the population parameter. We tested the method using a large craniometric data set commonly used by researchers in the field. Given our results, we suggest that sample estimates of the population mean can be reasonable and meaningful even when based on small, and perhaps even very small, sample sizes.

The mean distance to the nth neighbour in a uniform distribution of random points: an application of probability theory

International Nuclear Information System (INIS)

Bhattacharyya, Pratip; Chakrabarti, Bikas K

2008-01-01

We study different ways of determining the mean distance (r n ) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating (r n ). Next, we describe two alternative means of deriving the exact expression of (r n ): we review the method using absolute probability and develop an alternative method using conditional probability. Finally, we obtain an approximation to (r n ) from the mean volume between the reference point and its nth neighbour and compare it with the heuristic and exact results

Probability with applications and R

CERN Document Server

Dobrow, Robert P

2013-01-01

An introduction to probability at the undergraduate level Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability. With real-life examples and thoughtful exercises from fields as diverse as biology, computer science, cryptology, ecology, public health, and sports, the book is accessible for a variety of readers. The book's emphasis on simulation through the use of the popular R software language c

Generating Random Samples of a Given Size Using Social Security Numbers.

Science.gov (United States)

Erickson, Richard C.; Brauchle, Paul E.

1984-01-01

The purposes of this article are (1) to present a method by which social security numbers may be used to draw cluster samples of a predetermined size and (2) to describe procedures used to validate this method of drawing random samples. (JOW)

Probably not future prediction using probability and statistical inference

CERN Document Server

Dworsky, Lawrence N

2008-01-01

An engaging, entertaining, and informative introduction to probability and prediction in our everyday lives Although Probably Not deals with probability and statistics, it is not heavily mathematical and is not filled with complex derivations, proofs, and theoretical problem sets. This book unveils the world of statistics through questions such as what is known based upon the information at hand and what can be expected to happen. While learning essential concepts including "the confidence factor" and "random walks," readers will be entertained and intrigued as they move from chapter to chapter. Moreover, the author provides a foundation of basic principles to guide decision making in almost all facets of life including playing games, developing winning business strategies, and managing personal finances. Much of the book is organized around easy-to-follow examples that address common, everyday issues such as: How travel time is affected by congestion, driving speed, and traffic lights Why different gambling ...

A flexible method for multi-level sample size determination

International Nuclear Information System (INIS)

Lu, Ming-Shih; Sanborn, J.B.; Teichmann, T.

1997-01-01

This paper gives a flexible method to determine sample sizes for both systematic and random error models (this pertains to sampling problems in nuclear safeguard questions). In addition, the method allows different attribute rejection limits. The new method could assist achieving a higher detection probability and enhance inspection effectiveness

Random On-Board Pixel Sampling (ROPS) X-Ray Camera

Energy Technology Data Exchange (ETDEWEB)

Wang, Zhehui [Los Alamos; Iaroshenko, O. [Los Alamos; Li, S. [Los Alamos; Liu, T. [Fermilab; Parab, N. [Argonne (main); Chen, W. W. [Purdue U.; Chu, P. [Los Alamos; Kenyon, G. [Los Alamos; Lipton, R. [Fermilab; Sun, K.-X. [Nevada U., Las Vegas

2017-09-25

Recent advances in compressed sensing theory and algorithms offer new possibilities for high-speed X-ray camera design. In many CMOS cameras, each pixel has an independent on-board circuit that includes an amplifier, noise rejection, signal shaper, an analog-to-digital converter (ADC), and optional in-pixel storage. When X-ray images are sparse, i.e., when one of the following cases is true: (a.) The number of pixels with true X-ray hits is much smaller than the total number of pixels; (b.) The X-ray information is redundant; or (c.) Some prior knowledge about the X-ray images exists, sparse sampling may be allowed. Here we first illustrate the feasibility of random on-board pixel sampling (ROPS) using an existing set of X-ray images, followed by a discussion about signal to noise as a function of pixel size. Next, we describe a possible circuit architecture to achieve random pixel access and in-pixel storage. The combination of a multilayer architecture, sparse on-chip sampling, and computational image techniques, is expected to facilitate the development and applications of high-speed X-ray camera technology.

Probability on graphs random processes on graphs and lattices

CERN Document Server

Grimmett, Geoffrey

2018-01-01

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

Simulations of Probabilities for Quantum Computing

Science.gov (United States)

Zak, M.

1996-01-01

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

Probability and Statistics The Science of Uncertainty (Revised Edition)

CERN Document Server

Tabak, John

2011-01-01

Probability and Statistics, Revised Edition deals with the history of probability, describing the modern concept of randomness and examining "pre-probabilistic" ideas of what most people today would characterize as randomness. This revised book documents some historically important early uses of probability to illustrate some very important probabilistic questions. It goes on to explore statistics and the generations of mathematicians and non-mathematicians who began to address problems in statistical analysis, including the statistical structure of data sets as well as the theory of

Introduction to probability with statistical applications

CERN Document Server

Schay, Géza

2016-01-01

Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises

Choice probability generating functions

DEFF Research Database (Denmark)

Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel

2010-01-01

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice...... probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications....... The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to competing risk survival models....

Risk and protective factors of dissocial behavior in a probability sample.

Science.gov (United States)

Moral de la Rubia, José; Ortiz Morales, Humberto

2012-07-01

The aims of this study were to know risk and protective factors for dissocial behavior keeping in mind that the self-report of dissocial behavior is biased by the impression management. A probability sample of adolescents that lived in two neighborhoods with high indexes of gangs and offenses (112 male and 86 women) was collected. The 27-item Dissocial Behavior Scale (ECODI27; Pacheco & Moral, 2010), Balanced Inventory of Desirable Responding, version 6 (BIDR-6; Paulhus, 1991), Sensation Seeking Scale, form V (SSS-V; Zuckerman, Eysenck, & Eysenck, 1978), Parent-Adolescent Communication Scale (PACS; Barnes & Olson, 1982), 30-item Rathus Assertiveness Schedule (RAS; Rathus, 1973), Interpersonal Reactivity Index (IRI; Davis, 1983) and a social relationship questionnaire (SRQ) were applied. Binary logistic regression was used for the data analysis. A third of the participants showed dissocial behavior. Belonging to a gang in the school (schooled adolescents) or to a gang out of school and job (total sample) and desinhibition were risk factors; being woman, perspective taking and open communication with the father were protective factors. School-leaving was a differential aspect. We insisted on the need of intervention on these variables.

A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models

International Nuclear Information System (INIS)

Echard, B.; Gayton, N.; Lemaire, M.; Relun, N.

2013-01-01

Applying reliability methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable method called AK-IS for active learning and Kriging-based Importance Sampling. This new method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the method is, first, proved on two academic applications. It is then conducted for assessing the reliability of a challenging aerospace case study submitted to fatigue.

Gambling problems in the family – A stratified probability sample study of prevalence and reported consequences

Directory of Open Access Journals (Sweden)

Øren Anita

2008-12-01

Full Text Available Abstract Background Prior studies on the impact of problem gambling in the family mainly include help-seeking populations with small numbers of participants. The objective of the present stratified probability sample study was to explore the epidemiology of problem gambling in the family in the general population. Methods Men and women 16–74 years-old randomly selected from the Norwegian national population database received an invitation to participate in this postal questionnaire study. The response rate was 36.1% (3,483/9,638. Given the lack of validated criteria, two survey questions ("Have you ever noticed that a close relative spent more and more money on gambling?" and "Have you ever experienced that a close relative lied to you about how much he/she gambles?" were extrapolated from the Lie/Bet Screen for pathological gambling. Respondents answering "yes" to both questions were defined as Concerned Significant Others (CSOs. Results Overall, 2.0% of the study population was defined as CSOs. Young age, female gender, and divorced marital status were factors positively associated with being a CSO. CSOs often reported to have experienced conflicts in the family related to gambling, worsening of the family's financial situation, and impaired mental and physical health. Conclusion Problematic gambling behaviour not only affects the gambling individual but also has a strong impact on the quality of life of family members.

Estimating rare events in biochemical systems using conditional sampling

Science.gov (United States)

Sundar, V. S.

2017-01-01

The paper focuses on development of variance reduction strategies to estimate rare events in biochemical systems. Obtaining this probability using brute force Monte Carlo simulations in conjunction with the stochastic simulation algorithm (Gillespie's method) is computationally prohibitive. To circumvent this, important sampling tools such as the weighted stochastic simulation algorithm and the doubly weighted stochastic simulation algorithm have been proposed. However, these strategies require an additional step of determining the important region to sample from, which is not straightforward for most of the problems. In this paper, we apply the subset simulation method, developed as a variance reduction tool in the context of structural engineering, to the problem of rare event estimation in biochemical systems. The main idea is that the rare event probability is expressed as a product of more frequent conditional probabilities. These conditional probabilities are estimated with high accuracy using Monte Carlo simulations, specifically the Markov chain Monte Carlo method with the modified Metropolis-Hastings algorithm. Generating sample realizations of the state vector using the stochastic simulation algorithm is viewed as mapping the discrete-state continuous-time random process to the standard normal random variable vector. This viewpoint opens up the possibility of applying more sophisticated and efficient sampling schemes developed elsewhere to problems in stochastic chemical kinetics. The results obtained using the subset simulation method are compared with existing variance reduction strategies for a few benchmark problems, and a satisfactory improvement in computational time is demonstrated.

Smoothing the redshift distributions of random samples for the baryon acoustic oscillations: applications to the SDSS-III BOSS DR12 and QPM mock samples

Science.gov (United States)

Wang, Shao-Jiang; Guo, Qi; Cai, Rong-Gen

2017-12-01

We investigate the impact of different redshift distributions of random samples on the baryon acoustic oscillations (BAO) measurements of D_V(z)r_d^fid/r_d from the two-point correlation functions of galaxies in the Data Release 12 of the Baryon Oscillation Spectroscopic Survey (BOSS). Big surveys, such as BOSS, usually assign redshifts to the random samples by randomly drawing values from the measured redshift distributions of the data, which would necessarily introduce fiducial signals of fluctuations into the random samples, weakening the signals of BAO, if the cosmic variance cannot be ignored. We propose a smooth function of redshift distribution that fits the data well to populate the random galaxy samples. The resulting cosmological parameters match the input parameters of the mock catalogue very well. The significance of BAO signals has been improved by 0.33σ for a low-redshift sample and by 0.03σ for a constant-stellar-mass sample, though the absolute values do not change significantly. Given the precision of the measurements of current cosmological parameters, it would be appreciated for the future improvements on the measurements of galaxy clustering.

Applied probability and stochastic processes

CERN Document Server

Sumita, Ushio

1999-01-01

Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...

USING THE WEB-SERVICES WOLFRAM|ALPHA TO SOLVE PROBLEMS IN PROBABILITY THEORY

Directory of Open Access Journals (Sweden)

Taras Kobylnyk

2015-10-01

Full Text Available The trend towards the use of remote network resources on the Internet clearly delineated. Traditional training combined with increasingly networked, remote technologies become popular cloud computing. Research methods of probability theory are used in various fields. Of particular note is the use of methods of probability theory in psychological and educational research in statistical analysis of experimental data. Conducting such research is impossible without the use of modern information technology. Given the advantages of web-based software, the article describes web-service Wolfram|Alpha. Detailed analysis of the possibilities of using web-service Wolfram|Alpha for solving problems of probability theory. In the case studies described the results of queries for solving of probability theory, in particular the sections random events and random variables. Considered and analyzed the problem of the number of occurrences of event A in n independent trials using Wolfram|Alpha, detailed analysis of the possibilities of using the service Wolfram|Alpha for the study of continuous random variable that has a normal and uniform probability distribution, including calculating the probability of getting the value of a random variable in a given interval. The problem in applying the binomial and hypergeometric probability distribution of a discrete random variable and demonstrates the possibility of using the service Wolfram|Alpha for solving it.

Joint probabilities and quantum cognition

International Nuclear Information System (INIS)

Acacio de Barros, J.

2012-01-01

In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.

Joint probabilities and quantum cognition

Energy Technology Data Exchange (ETDEWEB)

Acacio de Barros, J. [Liberal Studies, 1600 Holloway Ave., San Francisco State University, San Francisco, CA 94132 (United States)

2012-12-18

In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.

Verbal versus Numerical Probabilities: Does Format Presentation of Probabilistic Information regarding Breast Cancer Screening Affect Women's Comprehension?

Science.gov (United States)

Vahabi, Mandana

2010-01-01

Objective: To test whether the format in which women receive probabilistic information about breast cancer and mammography affects their comprehension. Methods: A convenience sample of 180 women received pre-assembled randomized packages containing a breast health information brochure, with probabilities presented in either verbal or numeric…

Convergence analysis for Latin-hypercube lattice-sample selection strategies for 3D correlated random hydraulic-conductivity fields

OpenAIRE

Simuta-Champo, R.; Herrera-Zamarrón, G. S.

2010-01-01

The Monte Carlo technique provides a natural method for evaluating uncertainties. The uncertainty is represented by a probability distribution or by related quantities such as statistical moments. When the groundwater flow and transport governing equations are solved and the hydraulic conductivity field is treated as a random spatial function, the hydraulic head, velocities and concentrations also become random spatial functions. When that is the case, for the stochastic simulation of groundw...

Sampling guidelines for oral fluid-based surveys of group-housed animals.

Science.gov (United States)

Rotolo, Marisa L; Sun, Yaxuan; Wang, Chong; Giménez-Lirola, Luis; Baum, David H; Gauger, Phillip C; Harmon, Karen M; Hoogland, Marlin; Main, Rodger; Zimmerman, Jeffrey J

2017-09-01

Formulas and software for calculating sample size for surveys based on individual animal samples are readily available. However, sample size formulas are not available for oral fluids and other aggregate samples that are increasingly used in production settings. Therefore, the objective of this study was to develop sampling guidelines for oral fluid-based porcine reproductive and respiratory syndrome virus (PRRSV) surveys in commercial swine farms. Oral fluid samples were collected in 9 weekly samplings from all pens in 3 barns on one production site beginning shortly after placement of weaned pigs. Samples (n=972) were tested by real-time reverse-transcription PCR (RT-rtPCR) and the binary results analyzed using a piecewise exponential survival model for interval-censored, time-to-event data with misclassification. Thereafter, simulation studies were used to study the barn-level probability of PRRSV detection as a function of sample size, sample allocation (simple random sampling vs fixed spatial sampling), assay diagnostic sensitivity and specificity, and pen-level prevalence. These studies provided estimates of the probability of detection by sample size and within-barn prevalence. Detection using fixed spatial sampling was as good as, or better than, simple random sampling. Sampling multiple barns on a site increased the probability of detection with the number of barns sampled. These results are relevant to PRRSV control or elimination projects at the herd, regional, or national levels, but the results are also broadly applicable to contagious pathogens of swine for which oral fluid tests of equivalent performance are available. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

Zero field reversal probability in thermally assisted magnetization reversal

Science.gov (United States)

Prasetya, E. B.; Utari; Purnama, B.

2017-11-01

This paper discussed about zero field reversal probability in thermally assisted magnetization reversal (TAMR). Appearance of reversal probability in zero field investigated through micromagnetic simulation by solving stochastic Landau-Lifshitz-Gibert (LLG). The perpendicularly anisotropy magnetic dot of 50×50×20 nm3 is considered as single cell magnetic storage of magnetic random acces memory (MRAM). Thermally assisted magnetization reversal was performed by cooling writing process from near/almost Curie point to room temperature on 20 times runs for different randomly magnetized state. The results show that the probability reversal under zero magnetic field decreased with the increase of the energy barrier. The zero-field probability switching of 55% attained for energy barrier of 60 k B T and the reversal probability become zero noted at energy barrier of 2348 k B T. The higest zero-field switching probability of 55% attained for energy barrier of 60 k B T which corespond to magnetif field of 150 Oe for switching.

40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.

Science.gov (United States)

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Sample selection by random number... § 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional square... area created in accordance with paragraph (a) of this section, select two random numbers: one each for...

Correcting Classifiers for Sample Selection Bias in Two-Phase Case-Control Studies

Science.gov (United States)

Theis, Fabian J.

2017-01-01

Epidemiological studies often utilize stratified data in which rare outcomes or exposures are artificially enriched. This design can increase precision in association tests but distorts predictions when applying classifiers on nonstratified data. Several methods correct for this so-called sample selection bias, but their performance remains unclear especially for machine learning classifiers. With an emphasis on two-phase case-control studies, we aim to assess which corrections to perform in which setting and to obtain methods suitable for machine learning techniques, especially the random forest. We propose two new resampling-based methods to resemble the original data and covariance structure: stochastic inverse-probability oversampling and parametric inverse-probability bagging. We compare all techniques for the random forest and other classifiers, both theoretically and on simulated and real data. Empirical results show that the random forest profits from only the parametric inverse-probability bagging proposed by us. For other classifiers, correction is mostly advantageous, and methods perform uniformly. We discuss consequences of inappropriate distribution assumptions and reason for different behaviors between the random forest and other classifiers. In conclusion, we provide guidance for choosing correction methods when training classifiers on biased samples. For random forests, our method outperforms state-of-the-art procedures if distribution assumptions are roughly fulfilled. We provide our implementation in the R package sambia. PMID:29312464

The pleasures of probability

CERN Document Server

Isaac, Richard

1995-01-01

The ideas of probability are all around us. Lotteries, casino gambling, the al­ most non-stop polling which seems to mold public policy more and more­ these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re­ moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac­ ing quantum mechanics, has a world view that is at its core probabilistic in nature, contrary to the deterministic one of classical physics. In addition to all this muscular evidence of the importance of probability ideas it should also be said that probability can be lots of fun. It is a subject where you can start thinking about amusing, interesting, and often difficult problems with very little mathematical background. In this book, I wanted to introduce a reader with at least a fairl...

School and conference on probability theory

International Nuclear Information System (INIS)

Lawler, G.F.

2004-01-01

This volume includes expanded lecture notes from the School and Conference in Probability Theory held at ICTP in May, 2001. Probability theory is a very large area, too large for a single school and conference. The organizers, G. Lawler, C. Newman, and S. Varadhan chose to focus on a number of active research areas that have their roots in statistical physics. The pervasive theme in these lectures is trying to find the large time or large space behaviour of models defined on discrete lattices. Usually the definition of the model is relatively simple: either assigning a particular weight to each possible configuration (equilibrium statistical mechanics) or specifying the rules under which the system evolves (nonequilibrium statistical mechanics). Interacting particle systems is the area of probability that studies the evolution of particles (either finite or infinite in number) under random motions. The evolution of particles depends on the positions of the other particles; often one assumes that it depends only on the particles that are close to the particular particle. Thomas Liggett's lectures give an introduction to this very large area. Claudio Landim's follows up by discussing hydrodynamic limits of particle systems. The goal of this area is to describe the long time, large system size dynamics in terms of partial differential equations. The area of random media is concerned with the properties of materials or environments that are not homogeneous. Percolation theory studies one of the simplest stated models for impurities - taking a lattice and removing some of the vertices or bonds. Luiz Renato G. Fontes and Vladas Sidoravicius give a detailed introduction to this area. Random walk in random environment combines two sources of randomness - a particle performing stochastic motion in which the transition probabilities depend on position and have been chosen from some probability distribution. Alain-Sol Sznitman gives a survey of recent developments in this

An introduction to probability and stochastic processes

CERN Document Server

Melsa, James L

2013-01-01

Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

Random Numbers and Monte Carlo Methods

Science.gov (United States)

Scherer, Philipp O. J.

Many-body problems often involve the calculation of integrals of very high dimension which cannot be treated by standard methods. For the calculation of thermodynamic averages Monte Carlo methods are very useful which sample the integration volume at randomly chosen points. After summarizing some basic statistics, we discuss algorithms for the generation of pseudo-random numbers with given probability distribution which are essential for all Monte Carlo methods. We show how the efficiency of Monte Carlo integration can be improved by sampling preferentially the important configurations. Finally the famous Metropolis algorithm is applied to classical many-particle systems. Computer experiments visualize the central limit theorem and apply the Metropolis method to the traveling salesman problem.

Ensemble based system for whole-slide prostate cancer probability mapping using color texture features.

LENUS (Irish Health Repository)

DiFranco, Matthew D

2011-01-01

We present a tile-based approach for producing clinically relevant probability maps of prostatic carcinoma in histological sections from radical prostatectomy. Our methodology incorporates ensemble learning for feature selection and classification on expert-annotated images. Random forest feature selection performed over varying training sets provides a subset of generalized CIEL*a*b* co-occurrence texture features, while sample selection strategies with minimal constraints reduce training data requirements to achieve reliable results. Ensembles of classifiers are built using expert-annotated tiles from training images, and scores for the probability of cancer presence are calculated from the responses of each classifier in the ensemble. Spatial filtering of tile-based texture features prior to classification results in increased heat-map coherence as well as AUC values of 95% using ensembles of either random forests or support vector machines. Our approach is designed for adaptation to different imaging modalities, image features, and histological decision domains.

Monitoring oil persistence on beaches : SCAT versus stratified random sampling designs

International Nuclear Information System (INIS)

Short, J.W.; Lindeberg, M.R.; Harris, P.M.; Maselko, J.M.; Pella, J.J.; Rice, S.D.

2003-01-01

In the event of a coastal oil spill, shoreline clean-up assessment teams (SCAT) commonly rely on visual inspection of the entire affected area to monitor the persistence of the oil on beaches. Occasionally, pits are excavated to evaluate the persistence of subsurface oil. This approach is practical for directing clean-up efforts directly following a spill. However, sampling of the 1989 Exxon Valdez oil spill in Prince William Sound 12 years later has shown that visual inspection combined with pit excavation does not offer estimates of contaminated beach area of stranded oil volumes. This information is needed to statistically evaluate the significance of change with time. Assumptions regarding the correlation of visually-evident surface oil and cryptic subsurface oil are usually not evaluated as part of the SCAT mandate. Stratified random sampling can avoid such problems and could produce precise estimates of oiled area and volume that allow for statistical assessment of major temporal trends and the extent of the impact. The 2001 sampling of the shoreline of Prince William Sound showed that 15 per cent of surface oil occurrences were associated with subsurface oil. This study demonstrates the usefulness of the stratified random sampling method and shows how sampling design parameters impact statistical outcome. Power analysis based on the study results, indicate that optimum power is derived when unnecessary stratification is avoided. It was emphasized that sampling effort should be balanced between choosing sufficient beaches for sampling and the intensity of sampling

Surprisingly rational: probability theory plus noise explains biases in judgment.

Science.gov (United States)

Costello, Fintan; Watts, Paul

2014-07-01

The systematic biases seen in people's probability judgments are typically taken as evidence that people do not use the rules of probability theory when reasoning about probability but instead use heuristics, which sometimes yield reasonable judgments and sometimes yield systematic biases. This view has had a major impact in economics, law, medicine, and other fields; indeed, the idea that people cannot reason with probabilities has become a truism. We present a simple alternative to this view, where people reason about probability according to probability theory but are subject to random variation or noise in the reasoning process. In this account the effect of noise is canceled for some probabilistic expressions. Analyzing data from 2 experiments, we find that, for these expressions, people's probability judgments are strikingly close to those required by probability theory. For other expressions, this account produces systematic deviations in probability estimates. These deviations explain 4 reliable biases in human probabilistic reasoning (conservatism, subadditivity, conjunction, and disjunction fallacies). These results suggest that people's probability judgments embody the rules of probability theory and that biases in those judgments are due to the effects of random noise. (c) 2014 APA, all rights reserved.

Log-concave Probability Distributions: Theory and Statistical Testing

DEFF Research Database (Denmark)

An, Mark Yuing

1996-01-01

This paper studies the broad class of log-concave probability distributions that arise in economics of uncertainty and information. For univariate, continuous, and log-concave random variables we prove useful properties without imposing the differentiability of density functions. Discrete...... and multivariate distributions are also discussed. We propose simple non-parametric testing procedures for log-concavity. The test statistics are constructed to test one of the two implicati ons of log-concavity: increasing hazard rates and new-is-better-than-used (NBU) property. The test for increasing hazard...... rates are based on normalized spacing of the sample order statistics. The tests for NBU property fall into the category of Hoeffding's U-statistics...

Entanglement probabilities of polymers: a white noise functional approach

International Nuclear Information System (INIS)

Bernido, Christopher C; Carpio-Bernido, M Victoria

2003-01-01

The entanglement probabilities for a highly flexible polymer to wind n times around a straight polymer are evaluated using white noise analysis. To introduce the white noise functional approach, the one-dimensional random walk problem is taken as an example. The polymer entanglement scenario, viewed as a random walk on a plane, is then treated and the entanglement probabilities are obtained for a magnetic flux confined along the straight polymer, and a case where an entangled polymer is subjected to the potential V = f-dot(s)θ. In the absence of the magnetic flux and the potential V, the entanglement probabilities reduce to a result obtained by Wiegel

Are most samples of animals systematically biased? Consistent individual trait differences bias samples despite random sampling.

Science.gov (United States)

Biro, Peter A

2013-02-01

Sampling animals from the wild for study is something nearly every biologist has done, but despite our best efforts to obtain random samples of animals, 'hidden' trait biases may still exist. For example, consistent behavioral traits can affect trappability/catchability, independent of obvious factors such as size and gender, and these traits are often correlated with other repeatable physiological and/or life history traits. If so, systematic sampling bias may exist for any of these traits. The extent to which this is a problem, of course, depends on the magnitude of bias, which is presently unknown because the underlying trait distributions in populations are usually unknown, or unknowable. Indeed, our present knowledge about sampling bias comes from samples (not complete population censuses), which can possess bias to begin with. I had the unique opportunity to create naturalized populations of fish by seeding each of four small fishless lakes with equal densities of slow-, intermediate-, and fast-growing fish. Using sampling methods that are not size-selective, I observed that fast-growing fish were up to two-times more likely to be sampled than slower-growing fish. This indicates substantial and systematic bias with respect to an important life history trait (growth rate). If correlations between behavioral, physiological and life-history traits are as widespread as the literature suggests, then many animal samples may be systematically biased with respect to these traits (e.g., when collecting animals for laboratory use), and affect our inferences about population structure and abundance. I conclude with a discussion on ways to minimize sampling bias for particular physiological/behavioral/life-history types within animal populations.

Orthogonal Algorithm of Logic Probability and Syndrome-Testable Analysis

Institute of Scientific and Technical Information of China (English)

无

1990-01-01

A new method,orthogonal algoritm,is presented to compute the logic probabilities(i.e.signal probabilities)accurately,The transfer properties of logic probabilities are studied first,which are useful for the calculation of logic probability of the circuit with random independent inputs.Then the orthogonal algoritm is described to compute the logic probability of Boolean function realized by a combinational circuit.This algorithm can make Boolean function “ORTHOGONAL”so that the logic probabilities can be easily calculated by summing up the logic probabilities of all orthogonal terms of the Booleam function.

Robust estimation of the expected survival probabilities from high-dimensional Cox models with biomarker-by-treatment interactions in randomized clinical trials

Directory of Open Access Journals (Sweden)

Nils Ternès

2017-05-01

Full Text Available Abstract Background Thanks to the advances in genomics and targeted treatments, more and more prediction models based on biomarkers are being developed to predict potential benefit from treatments in a randomized clinical trial. Despite the methodological framework for the development and validation of prediction models in a high-dimensional setting is getting more and more established, no clear guidance exists yet on how to estimate expected survival probabilities in a penalized model with biomarker-by-treatment interactions. Methods Based on a parsimonious biomarker selection in a penalized high-dimensional Cox model (lasso or adaptive lasso, we propose a unified framework to: estimate internally the predictive accuracy metrics of the developed model (using double cross-validation; estimate the individual survival probabilities at a given timepoint; construct confidence intervals thereof (analytical or bootstrap; and visualize them graphically (pointwise or smoothed with spline. We compared these strategies through a simulation study covering scenarios with or without biomarker effects. We applied the strategies to a large randomized phase III clinical trial that evaluated the effect of adding trastuzumab to chemotherapy in 1574 early breast cancer patients, for which the expression of 462 genes was measured. Results In our simulations, penalized regression models using the adaptive lasso estimated the survival probability of new patients with low bias and standard error; bootstrapped confidence intervals had empirical coverage probability close to the nominal level across very different scenarios. The double cross-validation performed on the training data set closely mimicked the predictive accuracy of the selected models in external validation data. We also propose a useful visual representation of the expected survival probabilities using splines. In the breast cancer trial, the adaptive lasso penalty selected a prediction model with 4

Reliability of structures by using probability and fatigue theories

International Nuclear Information System (INIS)

Lee, Ouk Sub; Kim, Dong Hyeok; Park, Yeon Chang

2008-01-01

Methodologies to calculate failure probability and to estimate the reliability of fatigue loaded structures are developed. The applicability of the methodologies is evaluated with the help of the fatigue crack growth models suggested by Paris and Walker. The probability theories such as the FORM (first order reliability method), the SORM (second order reliability method) and the MCS (Monte Carlo simulation) are utilized. It is found that the failure probability decreases with the increase of the design fatigue life and the applied minimum stress, the decrease of the initial edge crack size, the applied maximum stress and the slope of Paris equation. Furthermore, according to the sensitivity analysis of random variables, the slope of Pairs equation affects the failure probability dominantly among other random variables in the Paris and the Walker models

Men who have sex with men in Great Britain: comparing methods and estimates from probability and convenience sample surveys

Science.gov (United States)

Prah, Philip; Hickson, Ford; Bonell, Chris; McDaid, Lisa M; Johnson, Anne M; Wayal, Sonali; Clifton, Soazig; Sonnenberg, Pam; Nardone, Anthony; Erens, Bob; Copas, Andrew J; Riddell, Julie; Weatherburn, Peter; Mercer, Catherine H

2016-01-01

Objective To examine sociodemographic and behavioural differences between men who have sex with men (MSM) participating in recent UK convenience surveys and a national probability sample survey. Methods We compared 148 MSM aged 18–64 years interviewed for Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3) undertaken in 2010–2012, with men in the same age range participating in contemporaneous convenience surveys of MSM: 15 500 British resident men in the European MSM Internet Survey (EMIS); 797 in the London Gay Men's Sexual Health Survey; and 1234 in Scotland's Gay Men's Sexual Health Survey. Analyses compared men reporting at least one male sexual partner (past year) on similarly worded questions and multivariable analyses accounted for sociodemographic differences between the surveys. Results MSM in convenience surveys were younger and better educated than MSM in Natsal-3, and a larger proportion identified as gay (85%–95% vs 62%). Partner numbers were higher and same-sex anal sex more common in convenience surveys. Unprotected anal intercourse was more commonly reported in EMIS. Compared with Natsal-3, MSM in convenience surveys were more likely to report gonorrhoea diagnoses and HIV testing (both past year). Differences between the samples were reduced when restricting analysis to gay-identifying MSM. Conclusions National probability surveys better reflect the population of MSM but are limited by their smaller samples of MSM. Convenience surveys recruit larger samples of MSM but tend to over-represent MSM identifying as gay and reporting more sexual risk behaviours. Because both sampling strategies have strengths and weaknesses, methods are needed to triangulate data from probability and convenience surveys. PMID:26965869

Classical probability model for Bell inequality

International Nuclear Information System (INIS)

Khrennikov, Andrei

2014-01-01

We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction 'Kolmogorovization' of contextuality. This construction of common probability space is applied to Bell's inequality. It is well known that its violation is a consequence of collecting statistical data in a few incompatible experiments. In experiments performed in quantum optics contexts are determined by selections of pairs of angles (θ i ,θ ' j ) fixing orientations of polarization beam splitters. Opposite to the common opinion, we show that statistical data corresponding to measurements of polarizations of photons in the singlet state, e.g., in the form of correlations, can be described in the classical probabilistic framework. The crucial point is that in constructing the common probability space one has to take into account not only randomness of the source (as Bell did), but also randomness of context-realizations (in particular, realizations of pairs of angles (θ i , θ ' j )). One may (but need not) say that randomness of 'free will' has to be accounted for.

A simple and efficient alternative to implementing systematic random sampling in stereological designs without a motorized microscope stage.

Science.gov (United States)

Melvin, Neal R; Poda, Daniel; Sutherland, Robert J

2007-10-01

When properly applied, stereology is a very robust and efficient method to quantify a variety of parameters from biological material. A common sampling strategy in stereology is systematic random sampling, which involves choosing a random sampling [corrected] start point outside the structure of interest, and sampling relevant objects at [corrected] sites that are placed at pre-determined, equidistant intervals. This has proven to be a very efficient sampling strategy, and is used widely in stereological designs. At the microscopic level, this is most often achieved through the use of a motorized stage that facilitates the systematic random stepping across the structure of interest. Here, we report a simple, precise and cost-effective software-based alternative to accomplishing systematic random sampling under the microscope. We believe that this approach will facilitate the use of stereological designs that employ systematic random sampling in laboratories that lack the resources to acquire costly, fully automated systems.

Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

Science.gov (United States)

Sztepanacz, Jacqueline L; Blows, Mark W

2017-07-01

The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.

Application of binomial and multinomial probability statistics to the sampling design process of a global grain tracing and recall system

Science.gov (United States)

Small, coded, pill-sized tracers embedded in grain are proposed as a method for grain traceability. A sampling process for a grain traceability system was designed and investigated by applying probability statistics using a science-based sampling approach to collect an adequate number of tracers fo...

Computing Confidence Bounds for Power and Sample Size of the General Linear Univariate Model

OpenAIRE

Taylor, Douglas J.; Muller, Keith E.

1995-01-01

The power of a test, the probability of rejecting the null hypothesis in favor of an alternative, may be computed using estimates of one or more distributional parameters. Statisticians frequently fix mean values and calculate power or sample size using a variance estimate from an existing study. Hence computed power becomes a random variable for a fixed sample size. Likewise, the sample size necessary to achieve a fixed power varies randomly. Standard statistical practice requires reporting ...

Effect of drain current on appearance probability and amplitude of random telegraph noise in low-noise CMOS image sensors

Science.gov (United States)

Ichino, Shinya; Mawaki, Takezo; Teramoto, Akinobu; Kuroda, Rihito; Park, Hyeonwoo; Wakashima, Shunichi; Goto, Tetsuya; Suwa, Tomoyuki; Sugawa, Shigetoshi

2018-04-01

Random telegraph noise (RTN), which occurs in in-pixel source follower (SF) transistors, has become one of the most critical problems in high-sensitivity CMOS image sensors (CIS) because it is a limiting factor of dark random noise. In this paper, the behaviors of RTN toward changes in SF drain current conditions were analyzed using a low-noise array test circuit measurement system with a floor noise of 35 µV rms. In addition to statistical analysis by measuring a large number of transistors (18048 transistors), we also analyzed the behaviors of RTN parameters such as amplitude and time constants in the individual transistors. It is demonstrated that the appearance probability of RTN becomes small under a small drain current condition, although large-amplitude RTN tends to appear in a very small number of cells.

Two-slit experiment: quantum and classical probabilities

International Nuclear Information System (INIS)

Khrennikov, Andrei

2015-01-01

Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum–classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane). (paper)

Importance Sampling for Failure Probabilities in Computing and Data Transmission

DEFF Research Database (Denmark)

Asmussen, Søren

We study efficient simulation algorithms for estimating P(Χ > χ), where Χ is the total time of a job with ideal time T that needs to be restarted after a failure. The main tool is importance sampling where one tries to identify a good importance distribution via an asymptotic description...... of the conditional distribution of T given Χ > χ. If T ≡ t is constant, the problem reduces to the efficient simulation of geometric sums, and a standard algorithm involving a Cramér type root  γ(t) is available. However, we also discuss  an algorithm avoiding the rootfinding. If T is random, particular attention...... is given to T having either a gamma-like tail or a regularly varying tail, and to failures at Poisson times. Different type of conditional limits occur, in particular exponentially tilted Gumbel distributions and Pareto distributions. The algorithms based upon importance distributions for T using...

Importance sampling for failure probabilities in computing and data transmission

DEFF Research Database (Denmark)

Asmussen, Søren

2009-01-01

In this paper we study efficient simulation algorithms for estimating P(X›x), where X is the total time of a job with ideal time $T$ that needs to be restarted after a failure. The main tool is importance sampling, where a good importance distribution is identified via an asymptotic description...... of the conditional distribution of T given X›x. If T≡t is constant, the problem reduces to the efficient simulation of geometric sums, and a standard algorithm involving a Cramér-type root, γ(t), is available. However, we also discuss an algorithm that avoids finding the root. If T is random, particular attention...... is given to T having either a gamma-like tail or a regularly varying tail, and to failures at Poisson times. Different types of conditional limit occur, in particular exponentially tilted Gumbel distributions and Pareto distributions. The algorithms based upon importance distributions for T using...

A random sampling approach for robust estimation of tissue-to-plasma ratio from extremely sparse data.

Science.gov (United States)

Chu, Hui-May; Ette, Ene I

2005-09-02

his study was performed to develop a new nonparametric approach for the estimation of robust tissue-to-plasma ratio from extremely sparsely sampled paired data (ie, one sample each from plasma and tissue per subject). Tissue-to-plasma ratio was estimated from paired/unpaired experimental data using independent time points approach, area under the curve (AUC) values calculated with the naïve data averaging approach, and AUC values calculated using sampling based approaches (eg, the pseudoprofile-based bootstrap [PpbB] approach and the random sampling approach [our proposed approach]). The random sampling approach involves the use of a 2-phase algorithm. The convergence of the sampling/resampling approaches was investigated, as well as the robustness of the estimates produced by different approaches. To evaluate the latter, new data sets were generated by introducing outlier(s) into the real data set. One to 2 concentration values were inflated by 10% to 40% from their original values to produce the outliers. Tissue-to-plasma ratios computed using the independent time points approach varied between 0 and 50 across time points. The ratio obtained from AUC values acquired using the naive data averaging approach was not associated with any measure of uncertainty or variability. Calculating the ratio without regard to pairing yielded poorer estimates. The random sampling and pseudoprofile-based bootstrap approaches yielded tissue-to-plasma ratios with uncertainty and variability. However, the random sampling approach, because of the 2-phase nature of its algorithm, yielded more robust estimates and required fewer replications. Therefore, a 2-phase random sampling approach is proposed for the robust estimation of tissue-to-plasma ratio from extremely sparsely sampled data.

The Influence of Mark-Recapture Sampling Effort on Estimates of Rock Lobster Survival.

Directory of Open Access Journals (Sweden)

Ziya Kordjazi

Full Text Available Five annual capture-mark-recapture surveys on Jasus edwardsii were used to evaluate the effect of sample size and fishing effort on the precision of estimated survival probability. Datasets of different numbers of individual lobsters (ranging from 200 to 1,000 lobsters were created by random subsampling from each annual survey. This process of random subsampling was also used to create 12 datasets of different levels of effort based on three levels of the number of traps (15, 30 and 50 traps per day and four levels of the number of sampling-days (2, 4, 6 and 7 days. The most parsimonious Cormack-Jolly-Seber (CJS model for estimating survival probability shifted from a constant model towards sex-dependent models with increasing sample size and effort. A sample of 500 lobsters or 50 traps used on four consecutive sampling-days was required for obtaining precise survival estimations for males and females, separately. Reduced sampling effort of 30 traps over four sampling days was sufficient if a survival estimate for both sexes combined was sufficient for management of the fishery.

The Influence of Mark-Recapture Sampling Effort on Estimates of Rock Lobster Survival

Science.gov (United States)

Kordjazi, Ziya; Frusher, Stewart; Buxton, Colin; Gardner, Caleb; Bird, Tomas

2016-01-01

Five annual capture-mark-recapture surveys on Jasus edwardsii were used to evaluate the effect of sample size and fishing effort on the precision of estimated survival probability. Datasets of different numbers of individual lobsters (ranging from 200 to 1,000 lobsters) were created by random subsampling from each annual survey. This process of random subsampling was also used to create 12 datasets of different levels of effort based on three levels of the number of traps (15, 30 and 50 traps per day) and four levels of the number of sampling-days (2, 4, 6 and 7 days). The most parsimonious Cormack-Jolly-Seber (CJS) model for estimating survival probability shifted from a constant model towards sex-dependent models with increasing sample size and effort. A sample of 500 lobsters or 50 traps used on four consecutive sampling-days was required for obtaining precise survival estimations for males and females, separately. Reduced sampling effort of 30 traps over four sampling days was sufficient if a survival estimate for both sexes combined was sufficient for management of the fishery. PMID:26990561

Reduction of the Random Variables of the Turbulent Wind Field

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.

2012-01-01

.e. Importance Sampling (IS) or Subset Simulation (SS), will be deteriorated on problems with many random variables. The problem with PDEM is that a multidimensional integral has to be carried out over the space defined by the random variables of the system. The numerical procedure requires discretization......Applicability of the Probability Density Evolution Method (PDEM) for realizing evolution of the probability density for the wind turbines has rather strict bounds on the basic number of the random variables involved in the model. The efficiency of most of the Advanced Monte Carlo (AMC) methods, i...... of the integral domain; this becomes increasingly difficult as the dimensions of the integral domain increase. On the other hand efficiency of the AMC methods is closely dependent on the design points of the problem. Presence of many random variables may increase the number of the design points, hence affects...

Media Use and Source Trust among Muslims in Seven Countries: Results of a Large Random Sample Survey

Directory of Open Access Journals (Sweden)

Steven R. Corman

2013-12-01

Full Text Available Despite the perceived importance of media in the spread of and resistance against Islamist extremism, little is known about how Muslims use different kinds of media to get information about religious issues, and what sources they trust when doing so. This paper reports the results of a large, random sample survey among Muslims in seven countries Southeast Asia, West Africa and Western Europe, which helps fill this gap. Results show a diverse set of profiles of media use and source trust that differ by country, with overall low trust in mediated sources of information. Based on these findings, we conclude that mass media is still the most common source of religious information for Muslims, but that trust in mediated information is low overall. This suggests that media are probably best used to persuade opinion leaders, who will then carry anti-extremist messages through more personal means.

Men who have sex with men in Great Britain: comparing methods and estimates from probability and convenience sample surveys.

Science.gov (United States)

Prah, Philip; Hickson, Ford; Bonell, Chris; McDaid, Lisa M; Johnson, Anne M; Wayal, Sonali; Clifton, Soazig; Sonnenberg, Pam; Nardone, Anthony; Erens, Bob; Copas, Andrew J; Riddell, Julie; Weatherburn, Peter; Mercer, Catherine H

2016-09-01

To examine sociodemographic and behavioural differences between men who have sex with men (MSM) participating in recent UK convenience surveys and a national probability sample survey. We compared 148 MSM aged 18-64 years interviewed for Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3) undertaken in 2010-2012, with men in the same age range participating in contemporaneous convenience surveys of MSM: 15 500 British resident men in the European MSM Internet Survey (EMIS); 797 in the London Gay Men's Sexual Health Survey; and 1234 in Scotland's Gay Men's Sexual Health Survey. Analyses compared men reporting at least one male sexual partner (past year) on similarly worded questions and multivariable analyses accounted for sociodemographic differences between the surveys. MSM in convenience surveys were younger and better educated than MSM in Natsal-3, and a larger proportion identified as gay (85%-95% vs 62%). Partner numbers were higher and same-sex anal sex more common in convenience surveys. Unprotected anal intercourse was more commonly reported in EMIS. Compared with Natsal-3, MSM in convenience surveys were more likely to report gonorrhoea diagnoses and HIV testing (both past year). Differences between the samples were reduced when restricting analysis to gay-identifying MSM. National probability surveys better reflect the population of MSM but are limited by their smaller samples of MSM. Convenience surveys recruit larger samples of MSM but tend to over-represent MSM identifying as gay and reporting more sexual risk behaviours. Because both sampling strategies have strengths and weaknesses, methods are needed to triangulate data from probability and convenience surveys. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Random Walks on Directed Networks: Inference and Respondent-Driven Sampling

Directory of Open Access Journals (Sweden)

Malmros Jens

2016-06-01

Full Text Available Respondent-driven sampling (RDS is often used to estimate population properties (e.g., sexual risk behavior in hard-to-reach populations. In RDS, already sampled individuals recruit population members to the sample from their social contacts in an efficient snowball-like sampling procedure. By assuming a Markov model for the recruitment of individuals, asymptotically unbiased estimates of population characteristics can be obtained. Current RDS estimation methodology assumes that the social network is undirected, that is, all edges are reciprocal. However, empirical social networks in general also include a substantial number of nonreciprocal edges. In this article, we develop an estimation method for RDS in populations connected by social networks that include reciprocal and nonreciprocal edges. We derive estimators of the selection probabilities of individuals as a function of the number of outgoing edges of sampled individuals. The proposed estimators are evaluated on artificial and empirical networks and are shown to generally perform better than existing estimators. This is the case in particular when the fraction of directed edges in the network is large.

Random Sampling of Correlated Parameters – a Consistent Solution for Unfavourable Conditions

Energy Technology Data Exchange (ETDEWEB)

Žerovnik, G., E-mail: gasper.zerovnik@ijs.si [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Trkov, A. [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); International Atomic Energy Agency, PO Box 100, A-1400 Vienna (Austria); Kodeli, I.A. [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Capote, R. [International Atomic Energy Agency, PO Box 100, A-1400 Vienna (Austria); Smith, D.L. [Argonne National Laboratory, 1710 Avenida del Mundo, Coronado, CA 92118-3073 (United States)

2015-01-15

Two methods for random sampling according to a multivariate lognormal distribution – the correlated sampling method and the method of transformation of correlation coefficients – are briefly presented. The methods are mathematically exact and enable consistent sampling of correlated inherently positive parameters with given information on the first two distribution moments. Furthermore, a weighted sampling method to accelerate the convergence of parameters with extremely large relative uncertainties is described. However, the method is efficient only for a limited number of correlated parameters.

The Bootstrap, the Jackknife, and the Randomization Test: A Sampling Taxonomy.

Science.gov (United States)

Rodgers, J L

1999-10-01

A simple sampling taxonomy is defined that shows the differences between and relationships among the bootstrap, the jackknife, and the randomization test. Each method has as its goal the creation of an empirical sampling distribution that can be used to test statistical hypotheses, estimate standard errors, and/or create confidence intervals. Distinctions between the methods can be made based on the sampling approach (with replacement versus without replacement) and the sample size (replacing the whole original sample versus replacing a subset of the original sample). The taxonomy is useful for teaching the goals and purposes of resampling schemes. An extension of the taxonomy implies other possible resampling approaches that have not previously been considered. Univariate and multivariate examples are presented.

Radiation Transport in Random Media With Large Fluctuations

Science.gov (United States)

Olson, Aaron; Prinja, Anil; Franke, Brian

2017-09-01

Neutral particle transport in media exhibiting large and complex material property spatial variation is modeled by representing cross sections as lognormal random functions of space and generated through a nonlinear memory-less transformation of a Gaussian process with covariance uniquely determined by the covariance of the cross section. A Karhunen-Loève decomposition of the Gaussian process is implemented to effciently generate realizations of the random cross sections and Woodcock Monte Carlo used to transport particles on each realization and generate benchmark solutions for the mean and variance of the particle flux as well as probability densities of the particle reflectance and transmittance. A computationally effcient stochastic collocation method is implemented to directly compute the statistical moments such as the mean and variance, while a polynomial chaos expansion in conjunction with stochastic collocation provides a convenient surrogate model that also produces probability densities of output quantities of interest. Extensive numerical testing demonstrates that use of stochastic reduced-order modeling provides an accurate and cost-effective alternative to random sampling for particle transport in random media.

Survey research with a random digit dial national mobile phone sample in Ghana: Methods and sample quality

Science.gov (United States)

Sefa, Eunice; Adimazoya, Edward Akolgo; Yartey, Emmanuel; Lenzi, Rachel; Tarpo, Cindy; Heward-Mills, Nii Lante; Lew, Katherine; Ampeh, Yvonne

2018-01-01

Introduction Generating a nationally representative sample in low and middle income countries typically requires resource-intensive household level sampling with door-to-door data collection. High mobile phone penetration rates in developing countries provide new opportunities for alternative sampling and data collection methods, but there is limited information about response rates and sample biases in coverage and nonresponse using these methods. We utilized data from an interactive voice response, random-digit dial, national mobile phone survey in Ghana to calculate standardized response rates and assess representativeness of the obtained sample. Materials and methods The survey methodology was piloted in two rounds of data collection. The final survey included 18 demographic, media exposure, and health behavior questions. Call outcomes and response rates were calculated according to the American Association of Public Opinion Research guidelines. Sample characteristics, productivity, and costs per interview were calculated. Representativeness was assessed by comparing data to the Ghana Demographic and Health Survey and the National Population and Housing Census. Results The survey was fielded during a 27-day period in February-March 2017. There were 9,469 completed interviews and 3,547 partial interviews. Response, cooperation, refusal, and contact rates were 31%, 81%, 7%, and 39% respectively. Twenty-three calls were dialed to produce an eligible contact: nonresponse was substantial due to the automated calling system and dialing of many unassigned or non-working numbers. Younger, urban, better educated, and male respondents were overrepresented in the sample. Conclusions The innovative mobile phone data collection methodology yielded a large sample in a relatively short period. Response rates were comparable to other surveys, although substantial coverage bias resulted from fewer women, rural, and older residents completing the mobile phone survey in

Survey research with a random digit dial national mobile phone sample in Ghana: Methods and sample quality.

Science.gov (United States)

L'Engle, Kelly; Sefa, Eunice; Adimazoya, Edward Akolgo; Yartey, Emmanuel; Lenzi, Rachel; Tarpo, Cindy; Heward-Mills, Nii Lante; Lew, Katherine; Ampeh, Yvonne

2018-01-01

Generating a nationally representative sample in low and middle income countries typically requires resource-intensive household level sampling with door-to-door data collection. High mobile phone penetration rates in developing countries provide new opportunities for alternative sampling and data collection methods, but there is limited information about response rates and sample biases in coverage and nonresponse using these methods. We utilized data from an interactive voice response, random-digit dial, national mobile phone survey in Ghana to calculate standardized response rates and assess representativeness of the obtained sample. The survey methodology was piloted in two rounds of data collection. The final survey included 18 demographic, media exposure, and health behavior questions. Call outcomes and response rates were calculated according to the American Association of Public Opinion Research guidelines. Sample characteristics, productivity, and costs per interview were calculated. Representativeness was assessed by comparing data to the Ghana Demographic and Health Survey and the National Population and Housing Census. The survey was fielded during a 27-day period in February-March 2017. There were 9,469 completed interviews and 3,547 partial interviews. Response, cooperation, refusal, and contact rates were 31%, 81%, 7%, and 39% respectively. Twenty-three calls were dialed to produce an eligible contact: nonresponse was substantial due to the automated calling system and dialing of many unassigned or non-working numbers. Younger, urban, better educated, and male respondents were overrepresented in the sample. The innovative mobile phone data collection methodology yielded a large sample in a relatively short period. Response rates were comparable to other surveys, although substantial coverage bias resulted from fewer women, rural, and older residents completing the mobile phone survey in comparison to household surveys. Random digit dialing of mobile

Survey research with a random digit dial national mobile phone sample in Ghana: Methods and sample quality.

Directory of Open Access Journals (Sweden)

Kelly L'Engle

Full Text Available Generating a nationally representative sample in low and middle income countries typically requires resource-intensive household level sampling with door-to-door data collection. High mobile phone penetration rates in developing countries provide new opportunities for alternative sampling and data collection methods, but there is limited information about response rates and sample biases in coverage and nonresponse using these methods. We utilized data from an interactive voice response, random-digit dial, national mobile phone survey in Ghana to calculate standardized response rates and assess representativeness of the obtained sample.The survey methodology was piloted in two rounds of data collection. The final survey included 18 demographic, media exposure, and health behavior questions. Call outcomes and response rates were calculated according to the American Association of Public Opinion Research guidelines. Sample characteristics, productivity, and costs per interview were calculated. Representativeness was assessed by comparing data to the Ghana Demographic and Health Survey and the National Population and Housing Census.The survey was fielded during a 27-day period in February-March 2017. There were 9,469 completed interviews and 3,547 partial interviews. Response, cooperation, refusal, and contact rates were 31%, 81%, 7%, and 39% respectively. Twenty-three calls were dialed to produce an eligible contact: nonresponse was substantial due to the automated calling system and dialing of many unassigned or non-working numbers. Younger, urban, better educated, and male respondents were overrepresented in the sample.The innovative mobile phone data collection methodology yielded a large sample in a relatively short period. Response rates were comparable to other surveys, although substantial coverage bias resulted from fewer women, rural, and older residents completing the mobile phone survey in comparison to household surveys. Random digit

Evaluation of probability and hazard in nuclear energy

International Nuclear Information System (INIS)

Novikov, V.Ya.; Romanov, N.L.

1979-01-01

Various methods of evaluation of accident probability on NPP are proposed because of NPP security statistic evaluation unreliability. The conception of subjective probability for quantitative analysis of security and hazard are described. Intrepretation of probability as real faith of an expert is assumed as a basis of the conception. It is suggested to study the event uncertainty in the framework of subjective probability theory which not only permits but demands to take into account expert opinions when evaluating the probability. These subjective expert evaluations effect to a certain extent the calculation of the usual mathematical event probability. The above technique is advantageous to use for consideration of a separate experiment or random event

Testing for variation in taxonomic extinction probabilities: a suggested methodology and some results

Science.gov (United States)

Conroy, M.J.; Nichols, J.D.

1984-01-01

Several important questions in evolutionary biology and paleobiology involve sources of variation in extinction rates. In all cases of which we are aware, extinction rates have been estimated from data in which the probability that an observation (e.g., a fossil taxon) will occur is related both to extinction rates and to what we term encounter probabilities. Any statistical method for analyzing fossil data should at a minimum permit separate inferences on these two components. We develop a method for estimating taxonomic extinction rates from stratigraphic range data and for testing hypotheses about variability in these rates. We use this method to estimate extinction rates and to test the hypothesis of constant extinction rates for several sets of stratigraphic range data. The results of our tests support the hypothesis that extinction rates varied over the geologic time periods examined. We also present a test that can be used to identify periods of high or low extinction probabilities and provide an example using Phanerozoic invertebrate data. Extinction rates should be analyzed using stochastic models, in which it is recognized that stratigraphic samples are random varlates and that sampling is imperfect

A Randomized Central Limit Theorem

International Nuclear Information System (INIS)

Eliazar, Iddo; Klafter, Joseph

2010-01-01

The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.

Random Photon Absorption Model Elucidates How Early Gain Control in Fly Photoreceptors Arises from Quantal Sampling

Science.gov (United States)

Song, Zhuoyi; Zhou, Yu; Juusola, Mikko

2016-01-01

Many diurnal photoreceptors encode vast real-world light changes effectively, but how this performance originates from photon sampling is unclear. A 4-module biophysically-realistic fly photoreceptor model, in which information capture is limited by the number of its sampling units (microvilli) and their photon-hit recovery time (refractoriness), can accurately simulate real recordings and their information content. However, sublinear summation in quantum bump production (quantum-gain-nonlinearity) may also cause adaptation by reducing the bump/photon gain when multiple photons hit the same microvillus simultaneously. Here, we use a Random Photon Absorption Model (RandPAM), which is the 1st module of the 4-module fly photoreceptor model, to quantify the contribution of quantum-gain-nonlinearity in light adaptation. We show how quantum-gain-nonlinearity already results from photon sampling alone. In the extreme case, when two or more simultaneous photon-hits reduce to a single sublinear value, quantum-gain-nonlinearity is preset before the phototransduction reactions adapt the quantum bump waveform. However, the contribution of quantum-gain-nonlinearity in light adaptation depends upon the likelihood of multi-photon-hits, which is strictly determined by the number of microvilli and light intensity. Specifically, its contribution to light-adaptation is marginal (≤ 1%) in fly photoreceptors with many thousands of microvilli, because the probability of simultaneous multi-photon-hits on any one microvillus is low even during daylight conditions. However, in cells with fewer sampling units, the impact of quantum-gain-nonlinearity increases with brightening light. PMID:27445779

Honest Importance Sampling with Multiple Markov Chains.

Science.gov (United States)

Tan, Aixin; Doss, Hani; Hobert, James P

2015-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable

Occupational position and its relation to mental distress in a random sample of Danish residents

DEFF Research Database (Denmark)

Rugulies, Reiner Ernst; Madsen, Ida E H; Nielsen, Maj Britt D

2010-01-01

PURPOSE: To analyze the distribution of depressive, anxiety, and somatization symptoms across different occupational positions in a random sample of Danish residents. METHODS: The study sample consisted of 591 Danish residents (50% women), aged 20-65, drawn from an age- and gender-stratified random...... sample of the Danish population. Participants filled out a survey that included the 92 item version of the Hopkins Symptom Checklist (SCL-92). We categorized occupational position into seven groups: high- and low-grade non-manual workers, skilled and unskilled manual workers, high- and low-grade self...

Estimation of Sensitive Proportion by Randomized Response Data in Successive Sampling

Directory of Open Access Journals (Sweden)

Bo Yu

2015-01-01

Full Text Available This paper considers the problem of estimation for binomial proportions of sensitive or stigmatizing attributes in the population of interest. Randomized response techniques are suggested for protecting the privacy of respondents and reducing the response bias while eliciting information on sensitive attributes. In many sensitive question surveys, the same population is often sampled repeatedly on each occasion. In this paper, we apply successive sampling scheme to improve the estimation of the sensitive proportion on current occasion.

Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables

Directory of Open Access Journals (Sweden)

Andrew Rosalsky

2004-12-01

Full Text Available Let {X,Xn;n≥1} be a sequence of real-valued i.i.d. random variables and let Sn=∑i=1nXi, n≥1. In this paper, we study the probabilities of large deviations of the form P(Sn>tn1/p, P(Sntn1/p, where t>0 and 0x1/p/ϕ(x=1, then for every t>0, limsupn→∞P(|Sn|>tn1/p/(nϕ(n=tpα.

Risk Attitudes, Sample Selection and Attrition in a Longitudinal Field Experiment

DEFF Research Database (Denmark)

Harrison, Glenn W.; Lau, Morten Igel

with respect to risk attitudes. Our design builds in explicit randomization on the incentives for participation. We show that there are significant sample selection effects on inferences about the extent of risk aversion, but that the effects of subsequent sample attrition are minimal. Ignoring sample...... selection leads to inferences that subjects in the population are more risk averse than they actually are. Correcting for sample selection and attrition affects utility curvature, but does not affect inferences about probability weighting. Properly accounting for sample selection and attrition effects leads...... to findings of temporal stability in overall risk aversion. However, that stability is around different levels of risk aversion than one might naively infer without the controls for sample selection and attrition we are able to implement. This evidence of “randomization bias” from sample selection...

Collocation methods for uncertainty quanti cation in PDE models with random data

KAUST Repository

Nobile, Fabio

2014-01-06

In this talk we consider Partial Differential Equations (PDEs) whose input data are modeled as random fields to account for their intrinsic variability or our lack of knowledge. After parametrizing the input random fields by finitely many independent random variables, we exploit the high regularity of the solution of the PDE as a function of the input random variables and consider sparse polynomial approximations in probability (Polynomial Chaos expansion) by collocation methods. We first address interpolatory approximations where the PDE is solved on a sparse grid of Gauss points in the probability space and the solutions thus obtained interpolated by multivariate polynomials. We present recent results on optimized sparse grids in which the selection of points is based on a knapsack approach and relies on sharp estimates of the decay of the coefficients of the polynomial chaos expansion of the solution. Secondly, we consider regression approaches where the PDE is evaluated on randomly chosen points in the probability space and a polynomial approximation constructed by the least square method. We present recent theoretical results on the stability and optimality of the approximation under suitable conditions between the number of sampling points and the dimension of the polynomial space. In particular, we show that for uniform random variables, the number of sampling point has to scale quadratically with the dimension of the polynomial space to maintain the stability and optimality of the approximation. Numerical results show that such condition is sharp in the monovariate case but seems to be over-constraining in higher dimensions. The regression technique seems therefore to be attractive in higher dimensions.

Determination of the influence of dispersion pattern of pesticide-resistant individuals on the reliability of resistance estimates using different sampling plans.

Science.gov (United States)

Shah, R; Worner, S P; Chapman, R B

2012-10-01

Pesticide resistance monitoring includes resistance detection and subsequent documentation/ measurement. Resistance detection would require at least one (≥1) resistant individual(s) to be present in a sample to initiate management strategies. Resistance documentation, on the other hand, would attempt to get an estimate of the entire population (≥90%) of the resistant individuals. A computer simulation model was used to compare the efficiency of simple random and systematic sampling plans to detect resistant individuals and to document their frequencies when the resistant individuals were randomly or patchily distributed. A patchy dispersion pattern of resistant individuals influenced the sampling efficiency of systematic sampling plans while the efficiency of random sampling was independent of such patchiness. When resistant individuals were randomly distributed, sample sizes required to detect at least one resistant individual (resistance detection) with a probability of 0.95 were 300 (1%) and 50 (10% and 20%); whereas, when resistant individuals were patchily distributed, using systematic sampling, sample sizes required for such detection were 6000 (1%), 600 (10%) and 300 (20%). Sample sizes of 900 and 400 would be required to detect ≥90% of resistant individuals (resistance documentation) with a probability of 0.95 when resistant individuals were randomly dispersed and present at a frequency of 10% and 20%, respectively; whereas, when resistant individuals were patchily distributed, using systematic sampling, a sample size of 3000 and 1500, respectively, was necessary. Small sample sizes either underestimated or overestimated the resistance frequency. A simple random sampling plan is, therefore, recommended for insecticide resistance detection and subsequent documentation.

Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian

2011-01-01

The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has consid...... dimensional reliability problems in structural dynamics.......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...

Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal

International Nuclear Information System (INIS)

Helton, J.C.

1996-03-01

A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S st , S st , p st ) for stochastic uncertainty, a probability space (S su , S su , p su ) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S st , S st , p st ) and (S su , S su , p su ). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the U.S. Environmental Protection Agency's standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems

Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal

International Nuclear Information System (INIS)

Helton, J.C.

1996-01-01

A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S st , L st , P st ) for stochastic uncertainty, a probability space (S su , L su , P su ) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S st , L st , P st ) and (S su , L su , P su ). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the US Environmental Protection Agency's standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems

Introduction to probability and stochastic processes with applications

CERN Document Server

Castañ, Blanco; Arunachalam, Viswanathan; Dharmaraja, Selvamuthu

2012-01-01

An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic t

Adaptive importance sampling of random walks on continuous state spaces

International Nuclear Information System (INIS)

Baggerly, K.; Cox, D.; Picard, R.

1998-01-01

The authors consider adaptive importance sampling for a random walk with scoring in a general state space. Conditions under which exponential convergence occurs to the zero-variance solution are reviewed. These results generalize previous work for finite, discrete state spaces in Kollman (1993) and in Kollman, Baggerly, Cox, and Picard (1996). This paper is intended for nonstatisticians and includes considerable explanatory material

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

Science.gov (United States)

Frahm, Klaus M.; Shepelyansky, Dima L.

2014-04-01

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.

The randomly renewed general item and the randomly inspected item with exponential life distribution

International Nuclear Information System (INIS)

Schneeweiss, W.G.

1979-01-01

For a randomly renewed item the probability distributions of the time to failure and of the duration of down time and the expectations of these random variables are determined. Moreover, it is shown that the same theory applies to randomly checked items with exponential probability distribution of life such as electronic items. The case of periodic renewals is treated as an example. (orig.) [de

Model uncertainty and probability

International Nuclear Information System (INIS)

Parry, G.W.

1994-01-01

This paper discusses the issue of model uncertainty. The use of probability as a measure of an analyst's uncertainty as well as a means of describing random processes has caused some confusion, even though the two uses are representing different types of uncertainty with respect to modeling a system. The importance of maintaining the distinction between the two types is illustrated with a simple example

Precision of systematic and random sampling in clustered populations: habitat patches and aggregating organisms.

Science.gov (United States)

McGarvey, Richard; Burch, Paul; Matthews, Janet M

2016-01-01

Natural populations of plants and animals spatially cluster because (1) suitable habitat is patchy, and (2) within suitable habitat, individuals aggregate further into clusters of higher density. We compare the precision of random and systematic field sampling survey designs under these two processes of species clustering. Second, we evaluate the performance of 13 estimators for the variance of the sample mean from a systematic survey. Replicated simulated surveys, as counts from 100 transects, allocated either randomly or systematically within the study region, were used to estimate population density in six spatial point populations including habitat patches and Matérn circular clustered aggregations of organisms, together and in combination. The standard one-start aligned systematic survey design, a uniform 10 x 10 grid of transects, was much more precise. Variances of the 10 000 replicated systematic survey mean densities were one-third to one-fifth of those from randomly allocated transects, implying transect sample sizes giving equivalent precision by random survey would need to be three to five times larger. Organisms being restricted to patches of habitat was alone sufficient to yield this precision advantage for the systematic design. But this improved precision for systematic sampling in clustered populations is underestimated by standard variance estimators used to compute confidence intervals. True variance for the survey sample mean was computed from the variance of 10 000 simulated survey mean estimates. Testing 10 published and three newly proposed variance estimators, the two variance estimators (v) that corrected for inter-transect correlation (ν₈ and ν(W)) were the most accurate and also the most precise in clustered populations. These greatly outperformed the two "post-stratification" variance estimators (ν₂ and ν₃) that are now more commonly applied in systematic surveys. Similar variance estimator performance rankings were found with

Daniel Courgeau: Probability and social science: methodological relationships between the two approaches [Review of: . Probability and social science: methodological relationships between the two approaches

NARCIS (Netherlands)

Willekens, F.J.C.

2013-01-01

Throughout history, humans engaged in games in which randomness plays a role. In the 17th century, scientists started to approach chance scientifically and to develop a theory of probability. Courgeau describes how the relationship between probability theory and social sciences emerged and evolved

On the universality of knot probability ratios

Energy Technology Data Exchange (ETDEWEB)

Janse van Rensburg, E J [Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3 (Canada); Rechnitzer, A, E-mail: rensburg@yorku.ca, E-mail: andrewr@math.ubc.ca [Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2 (Canada)

2011-04-22

Let p{sub n} denote the number of self-avoiding polygons of length n on a regular three-dimensional lattice, and let p{sub n}(K) be the number which have knot type K. The probability that a random polygon of length n has knot type K is p{sub n}(K)/p{sub n} and is known to decay exponentially with length (Sumners and Whittington 1988 J. Phys. A: Math. Gen. 21 1689-94, Pippenger 1989 Discrete Appl. Math. 25 273-8). Little is known rigorously about the asymptotics of p{sub n}(K), but there is substantial numerical evidence. It is believed that the entropic exponent, {alpha}, is universal, while the exponential growth rate is independent of the knot type but varies with the lattice. The amplitude, C{sub K}, depends on both the lattice and the knot type. The above asymptotic form implies that the relative probability of a random polygon of length n having prime knot type K over prime knot type L. In the thermodynamic limit this probability ratio becomes an amplitude ratio; it should be universal and depend only on the knot types K and L. In this communication we examine the universality of these probability ratios for polygons in the simple cubic, face-centred cubic and body-centred cubic lattices. Our results support the hypothesis that these are universal quantities. For example, we estimate that a long random polygon is approximately 28 times more likely to be a trefoil than be a figure-eight, independent of the underlying lattice, giving an estimate of the intrinsic entropy associated with knot types in closed curves. (fast track communication)

Monte Carlo simulation of the sequential probability ratio test for radiation monitoring

International Nuclear Information System (INIS)

Coop, K.L.

1984-01-01

A computer program simulates the Sequential Probability Ratio Test (SPRT) using Monte Carlo techniques. The program, SEQTEST, performs random-number sampling of either a Poisson or normal distribution to simulate radiation monitoring data. The results are in terms of the detection probabilities and the average time required for a trial. The computed SPRT results can be compared with tabulated single interval test (SIT) values to determine the better statistical test for particular monitoring applications. Use of the SPRT in a hand-and-foot alpha monitor shows that the SPRT provides better detection probabilities while generally requiring less counting time. Calculations are also performed for a monitor where the SPRT is not permitted to the take longer than the single interval test. Although the performance of the SPRT is degraded by this restriction, the detection probabilities are still similar to the SIT values, and average counting times are always less than 75% of the SIT time. Some optimal conditions for use of the SPRT are described. The SPRT should be the test of choice in many radiation monitoring situations. 6 references, 8 figures, 1 table

(I Can't Get No) Saturation: A simulation and guidelines for sample sizes in qualitative research.

Science.gov (United States)

van Rijnsoever, Frank J

2017-01-01

I explore the sample size in qualitative research that is required to reach theoretical saturation. I conceptualize a population as consisting of sub-populations that contain different types of information sources that hold a number of codes. Theoretical saturation is reached after all the codes in the population have been observed once in the sample. I delineate three different scenarios to sample information sources: "random chance," which is based on probability sampling, "minimal information," which yields at least one new code per sampling step, and "maximum information," which yields the largest number of new codes per sampling step. Next, I use simulations to assess the minimum sample size for each scenario for systematically varying hypothetical populations. I show that theoretical saturation is more dependent on the mean probability of observing codes than on the number of codes in a population. Moreover, the minimal and maximal information scenarios are significantly more efficient than random chance, but yield fewer repetitions per code to validate the findings. I formulate guidelines for purposive sampling and recommend that researchers follow a minimum information scenario.

Internal Medicine residents use heuristics to estimate disease probability

OpenAIRE

Phang, Sen Han; Ravani, Pietro; Schaefer, Jeffrey; Wright, Bruce; McLaughlin, Kevin

2015-01-01

Background: Training in Bayesian reasoning may have limited impact on accuracy of probability estimates. In this study, our goal was to explore whether residents previously exposed to Bayesian reasoning use heuristics rather than Bayesian reasoning to estimate disease probabilities. We predicted that if residents use heuristics then post-test probability estimates would be increased by non-discriminating clinical features or a high anchor for a target condition. Method: We randomized 55 In...

On estimating probability of presence from use-availability or presence-background data.

Science.gov (United States)

Phillips, Steven J; Elith, Jane

2013-06-01

A fundamental ecological modeling task is to estimate the probability that a species is present in (or uses) a site, conditional on environmental variables. For many species, available data consist of "presence" data (locations where the species [or evidence of it] has been observed), together with "background" data, a random sample of available environmental conditions. Recently published papers disagree on whether probability of presence is identifiable from such presence-background data alone. This paper aims to resolve the disagreement, demonstrating that additional information is required. We defined seven simulated species representing various simple shapes of response to environmental variables (constant, linear, convex, unimodal, S-shaped) and ran five logistic model-fitting methods using 1000 presence samples and 10 000 background samples; the simulations were repeated 100 times. The experiment revealed a stark contrast between two groups of methods: those based on a strong assumption that species' true probability of presence exactly matches a given parametric form had highly variable predictions and much larger RMS error than methods that take population prevalence (the fraction of sites in which the species is present) as an additional parameter. For six species, the former group grossly under- or overestimated probability of presence. The cause was not model structure or choice of link function, because all methods were logistic with linear and, where necessary, quadratic terms. Rather, the experiment demonstrates that an estimate of prevalence is not just helpful, but is necessary (except in special cases) for identifying probability of presence. We therefore advise against use of methods that rely on the strong assumption, due to Lele and Keim (recently advocated by Royle et al.) and Lancaster and Imbens. The methods are fragile, and their strong assumption is unlikely to be true in practice. We emphasize, however, that we are not arguing against

Return probabilities for the reflected random walk on N_0

NARCIS (Netherlands)

Essifi, R.; Peigné, M.

2015-01-01

Let \\((Y_n)\\) be a sequence of i.i.d. \\(\\mathbb{Z }\\)-valued random variables with law \\(\\mu \\). The reflected random walk \\((X_n)\\) is defined recursively by \\(X_0=x \\in \\mathbb{N }_0, X_{n+1}=\\vert X_n+Y_{n+1}\\vert \\). Under mild hypotheses on the law \\(\\mu \\), it is proved that, for any \\( y \\in

A Table-Based Random Sampling Simulation for Bioluminescence Tomography

Directory of Open Access Journals (Sweden)

Xiaomeng Zhang

2006-01-01

Full Text Available As a popular simulation of photon propagation in turbid media, the main problem of Monte Carlo (MC method is its cumbersome computation. In this work a table-based random sampling simulation (TBRS is proposed. The key idea of TBRS is to simplify multisteps of scattering to a single-step process, through randomly table querying, thus greatly reducing the computing complexity of the conventional MC algorithm and expediting the computation. The TBRS simulation is a fast algorithm of the conventional MC simulation of photon propagation. It retained the merits of flexibility and accuracy of conventional MC method and adapted well to complex geometric media and various source shapes. Both MC simulations were conducted in a homogeneous medium in our work. Also, we present a reconstructing approach to estimate the position of the fluorescent source based on the trial-and-error theory as a validation of the TBRS algorithm. Good agreement is found between the conventional MC simulation and the TBRS simulation.

The Work Sample Verification and the Calculation of the Statistical, Mathematical and Economical Probability for the Risks of the Direct Procurement

Directory of Open Access Journals (Sweden)

Lazăr Cristiana Daniela

2017-01-01

Full Text Available Each organization has among its multiple secondary endpoints subordinated to a centralobjective that one of avoiding the contingencies. The direct procurement is carried out on themarket in SEAP (Electronic System of Public Procurement, and a performing management in apublic institution has as sub-base and risk management. The risks may be investigated byeconometric simulation, which is calculated by the use of calculus of probability and the sample fordetermining the relevance of these probabilities.

Some results on convergence rates for probabilities of moderate deviations for sums of random variables

Directory of Open Access Journals (Sweden)

Deli Li

1992-01-01

Full Text Available Let X, Xn, n≥1 be a sequence of iid real random variables, and Sn=∑k=1nXk, n≥1. Convergence rates of moderate deviations are derived, i.e., the rate of convergence to zero of certain tail probabilities of the partial sums are determined. For example, we obtain equivalent conditions for the convergence of series ∑n≥1(ψ2(n/nP(|Sn|≥nφ(n only under the assumptions convergence that EX=0 and EX2=1, where φ and ψ are taken from a broad class of functions. These results generalize and improve some recent results of Li (1991 and Gafurov (1982 and some previous work of Davis (1968. For b∈[0,1] and ϵ>0, letλϵ,b=∑n≥3((loglognb/nI(|Sn|≥(2+ϵnloglogn.The behaviour of Eλϵ,b as ϵ↓0 is also studied.

40 CFR 761.306 - Sampling 1 meter square surfaces by random selection of halves.

Science.gov (United States)

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Sampling 1 meter square surfaces by...(b)(3) § 761.306 Sampling 1 meter square surfaces by random selection of halves. (a) Divide each 1 meter square portion where it is necessary to collect a surface wipe test sample into two equal (or as...

A Nationwide Random Sampling Survey of Potential Complicated Grief in Japan

Science.gov (United States)

Mizuno, Yasunao; Kishimoto, Junji; Asukai, Nozomu

2012-01-01

To investigate the prevalence of significant loss, potential complicated grief (CG), and its contributing factors, we conducted a nationwide random sampling survey of Japanese adults aged 18 or older (N = 1,343) using a self-rating Japanese-language version of the Complicated Grief Brief Screen. Among them, 37.0% experienced their most significant…

Reinforcing Sampling Distributions through a Randomization-Based Activity for Introducing ANOVA

Science.gov (United States)

Taylor, Laura; Doehler, Kirsten

2015-01-01

This paper examines the use of a randomization-based activity to introduce the ANOVA F-test to students. The two main goals of this activity are to successfully teach students to comprehend ANOVA F-tests and to increase student comprehension of sampling distributions. Four sections of students in an advanced introductory statistics course…

Lay understanding of forensic statistics: Evaluation of random match probabilities, likelihood ratios, and verbal equivalents.

Science.gov (United States)

Thompson, William C; Newman, Eryn J

2015-08-01

Forensic scientists have come under increasing pressure to quantify the strength of their evidence, but it is not clear which of several possible formats for presenting quantitative conclusions will be easiest for lay people, such as jurors, to understand. This experiment examined the way that people recruited from Amazon's Mechanical Turk (n = 541) responded to 2 types of forensic evidence--a DNA comparison and a shoeprint comparison--when an expert explained the strength of this evidence 3 different ways: using random match probabilities (RMPs), likelihood ratios (LRs), or verbal equivalents of likelihood ratios (VEs). We found that verdicts were sensitive to the strength of DNA evidence regardless of how the expert explained it, but verdicts were sensitive to the strength of shoeprint evidence only when the expert used RMPs. The weight given to DNA evidence was consistent with the predictions of a Bayesian network model that incorporated the perceived risk of a false match from 3 causes (coincidence, a laboratory error, and a frame-up), but shoeprint evidence was undervalued relative to the same Bayesian model. Fallacious interpretations of the expert's testimony (consistent with the source probability error and the defense attorney's fallacy) were common and were associated with the weight given to the evidence and verdicts. The findings indicate that perceptions of forensic science evidence are shaped by prior beliefs and expectations as well as expert testimony and consequently that the best way to characterize and explain forensic evidence may vary across forensic disciplines. (c) 2015 APA, all rights reserved).

Randomization tests

CERN Document Server

Edgington, Eugene

2007-01-01

Statistical Tests That Do Not Require Random Sampling Randomization Tests Numerical Examples Randomization Tests and Nonrandom Samples The Prevalence of Nonrandom Samples in Experiments The Irrelevance of Random Samples for the Typical Experiment Generalizing from Nonrandom Samples Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References Randomized Experiments Unique Benefits of Experiments Experimentation without Mani

Network Sampling with Memory: A proposal for more efficient sampling from social networks

Science.gov (United States)

Mouw, Ted; Verdery, Ashton M.

2013-01-01

Techniques for sampling from networks have grown into an important area of research across several fields. For sociologists, the possibility of sampling from a network is appealing for two reasons: (1) A network sample can yield substantively interesting data about network structures and social interactions, and (2) it is useful in situations where study populations are difficult or impossible to survey with traditional sampling approaches because of the lack of a sampling frame. Despite its appeal, methodological concerns about the precision and accuracy of network-based sampling methods remain. In particular, recent research has shown that sampling from a network using a random walk based approach such as Respondent Driven Sampling (RDS) can result in high design effects (DE)—the ratio of the sampling variance to the sampling variance of simple random sampling (SRS). A high design effect means that more cases must be collected to achieve the same level of precision as SRS. In this paper we propose an alternative strategy, Network Sampling with Memory (NSM), which collects network data from respondents in order to reduce design effects and, correspondingly, the number of interviews needed to achieve a given level of statistical power. NSM combines a “List” mode, where all individuals on the revealed network list are sampled with the same cumulative probability, with a “Search” mode, which gives priority to bridge nodes connecting the current sample to unexplored parts of the network. We test the relative efficiency of NSM compared to RDS and SRS on 162 school and university networks from Add Health and Facebook that range in size from 110 to 16,278 nodes. The results show that the average design effect for NSM on these 162 networks is 1.16, which is very close to the efficiency of a simple random sample (DE=1), and 98.5% lower than the average DE we observed for RDS. PMID:24159246

An analytical calculation of neighbourhood order probabilities for high dimensional Poissonian processes and mean field models

International Nuclear Information System (INIS)

Tercariol, Cesar Augusto Sangaletti; Kiipper, Felipe de Moura; Martinez, Alexandre Souto

2007-01-01

Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability P (d,N) m,n that an arbitrary point is the mth nearest neighbour to its own nth nearest neighbour (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we propose a simpler derivation of Cox probabilities, where we stress the role played by the system dimensionality d. In the limit d → ∞, the distances between pair of points become independent (random link model) and closed analytical forms for the neighbourhood probabilities are obtained both for the thermodynamic limit and finite-size system. Breaking the distance symmetry constraint drives us to the random map model, for which the Cox probabilities are obtained for two cases: whether a point is its own nearest neighbour or not

LOD score exclusion analyses for candidate QTLs using random population samples.

Science.gov (United States)

Deng, Hong-Wen

2003-11-01

While extensive analyses have been conducted to test for, no formal analyses have been conducted to test against, the importance of candidate genes as putative QTLs using random population samples. Previously, we developed an LOD score exclusion mapping approach for candidate genes for complex diseases. Here, we extend this LOD score approach for exclusion analyses of candidate genes for quantitative traits. Under this approach, specific genetic effects (as reflected by heritability) and inheritance models at candidate QTLs can be analyzed and if an LOD score is < or = -2.0, the locus can be excluded from having a heritability larger than that specified. Simulations show that this approach has high power to exclude a candidate gene from having moderate genetic effects if it is not a QTL and is robust to population admixture. Our exclusion analysis complements association analysis for candidate genes as putative QTLs in random population samples. The approach is applied to test the importance of Vitamin D receptor (VDR) gene as a potential QTL underlying the variation of bone mass, an important determinant of osteoporosis.

The study of combining Latin Hypercube Sampling method and LU decomposition method (LULHS method) for constructing spatial random field

Science.gov (United States)

WANG, P. T.

2015-12-01

Groundwater modeling requires to assign hydrogeological properties to every numerical grid. Due to the lack of detailed information and the inherent spatial heterogeneity, geological properties can be treated as random variables. Hydrogeological property is assumed to be a multivariate distribution with spatial correlations. By sampling random numbers from a given statistical distribution and assigning a value to each grid, a random field for modeling can be completed. Therefore, statistics sampling plays an important role in the efficiency of modeling procedure. Latin Hypercube Sampling (LHS) is a stratified random sampling procedure that provides an efficient way to sample variables from their multivariate distributions. This study combines the the stratified random procedure from LHS and the simulation by using LU decomposition to form LULHS. Both conditional and unconditional simulations of LULHS were develpoed. The simulation efficiency and spatial correlation of LULHS are compared to the other three different simulation methods. The results show that for the conditional simulation and unconditional simulation, LULHS method is more efficient in terms of computational effort. Less realizations are required to achieve the required statistical accuracy and spatial correlation.

Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal

Energy Technology Data Exchange (ETDEWEB)

Helton, J.C. [Arizona State Univ., Tempe, AZ (United States)

1996-03-01

A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S{sub st}, S{sub st}, p{sub st}) for stochastic uncertainty, a probability space (S{sub su}, S{sub su}, p{sub su}) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S{sub st}, S{sub st}, p{sub st}) and (S{sub su}, S{sub su}, p{sub su}). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the U.S. Environmental Protection Agency`s standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems.

The Dirichet-Multinomial model for multivariate randomized response data and small samples

NARCIS (Netherlands)

Avetisyan, Marianna; Fox, Gerardus J.A.

2012-01-01

In survey sampling the randomized response (RR) technique can be used to obtain truthful answers to sensitive questions. Although the individual answers are masked due to the RR technique, individual (sensitive) response rates can be estimated when observing multivariate response data. The

Failure probability under parameter uncertainty.

Science.gov (United States)

Gerrard, R; Tsanakas, A

2011-05-01

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications. © 2010 Society for Risk Analysis.

Predicting binary choices from probability phrase meanings.

Science.gov (United States)

Wallsten, Thomas S; Jang, Yoonhee

2008-08-01

The issues of how individuals decide which of two events is more likely and of how they understand probability phrases both involve judging relative likelihoods. In this study, we investigated whether derived scales representing probability phrase meanings could be used within a choice model to predict independently observed binary choices. If they can, this simultaneously provides support for our model and suggests that the phrase meanings are measured meaningfully. The model assumes that, when deciding which of two events is more likely, judges take a single sample from memory regarding each event and respond accordingly. The model predicts choice probabilities by using the scaled meanings of individually selected probability phrases as proxies for confidence distributions associated with sampling from memory. Predictions are sustained for 34 of 41 participants but, nevertheless, are biased slightly low. Sequential sampling models improve the fit. The results have both theoretical and applied implications.

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

KAUST Repository

Migliorati, Giovanni; Nobile, Fabio; von Schwerin, Erik; Tempone, Raul

2014-01-01

We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is uncertainty quantification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the univariate case, when the observation points are sampled in a bounded domain from a probability density function bounded away from zero and bounded from above, provided the number of samples scales quadratically with the dimension of the polynomial space. Optimality is meant in the sense that the weighted L2 norm of the error committed by the random discrete projection is bounded with high probability from above by the best L∞ error achievable in the given polynomial space, up to logarithmic factors. Several numerical tests are presented in both the univariate and multivariate cases, confirming our theoretical estimates. The numerical tests also clarify how the convergence rate depends on the number of sampling points, on the polynomial degree, and on the smoothness of the target function. © 2014 SFoCM.

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

KAUST Repository

Migliorati, Giovanni

2014-03-05

We analyze the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is uncertainty quantification for computational models. We prove an optimal convergence estimate, up to a logarithmic factor, in the univariate case, when the observation points are sampled in a bounded domain from a probability density function bounded away from zero and bounded from above, provided the number of samples scales quadratically with the dimension of the polynomial space. Optimality is meant in the sense that the weighted L2 norm of the error committed by the random discrete projection is bounded with high probability from above by the best L∞ error achievable in the given polynomial space, up to logarithmic factors. Several numerical tests are presented in both the univariate and multivariate cases, confirming our theoretical estimates. The numerical tests also clarify how the convergence rate depends on the number of sampling points, on the polynomial degree, and on the smoothness of the target function. © 2014 SFoCM.

Visualizing and Understanding Probability and Statistics: Graphical Simulations Using Excel

Science.gov (United States)

Gordon, Sheldon P.; Gordon, Florence S.

2009-01-01

The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…

Electrofishing capture probability of smallmouth bass in streams

Science.gov (United States)

Dauwalter, D.C.; Fisher, W.L.

2007-01-01

Abundance estimation is an integral part of understanding the ecology and advancing the management of fish populations and communities. Mark-recapture and removal methods are commonly used to estimate the abundance of stream fishes. Alternatively, abundance can be estimated by dividing the number of individuals sampled by the probability of capture. We conducted a mark-recapture study and used multiple repeated-measures logistic regression to determine the influence of fish size, sampling procedures, and stream habitat variables on the cumulative capture probability for smallmouth bass Micropterus dolomieu in two eastern Oklahoma streams. The predicted capture probability was used to adjust the number of individuals sampled to obtain abundance estimates. The observed capture probabilities were higher for larger fish and decreased with successive electrofishing passes for larger fish only. Model selection suggested that the number of electrofishing passes, fish length, and mean thalweg depth affected capture probabilities the most; there was little evidence for any effect of electrofishing power density and woody debris density on capture probability. Leave-one-out cross validation showed that the cumulative capture probability model predicts smallmouth abundance accurately. ?? Copyright by the American Fisheries Society 2007.

Random phenomena; Phenomenes aleatoires

Energy Technology Data Exchange (ETDEWEB)

Bonnet, G. [Commissariat a l' energie atomique et aux energies alternatives - CEA, C.E.N.G., Service d' Electronique, Section d' Electronique, Grenoble (France)

1963-07-01

This document gathers a set of conferences presented in 1962. A first one proposes a mathematical introduction to the analysis of random phenomena. The second one presents an axiomatic of probability calculation. The third one proposes an overview of one-dimensional random variables. The fourth one addresses random pairs, and presents basic theorems regarding the algebra of mathematical expectations. The fifth conference discusses some probability laws: binomial distribution, the Poisson distribution, and the Laplace-Gauss distribution. The last one deals with the issues of stochastic convergence and asymptotic distributions.

Propagating Mixed Uncertainties in Cyber Attacker Payoffs: Exploration of Two-Phase Monte Carlo Sampling and Probability Bounds Analysis

Energy Technology Data Exchange (ETDEWEB)

Chatterjee, Samrat; Tipireddy, Ramakrishna; Oster, Matthew R.; Halappanavar, Mahantesh

2016-09-16

Securing cyber-systems on a continual basis against a multitude of adverse events is a challenging undertaking. Game-theoretic approaches, that model actions of strategic decision-makers, are increasingly being applied to address cybersecurity resource allocation challenges. Such game-based models account for multiple player actions and represent cyber attacker payoffs mostly as point utility estimates. Since a cyber-attacker’s payoff generation mechanism is largely unknown, appropriate representation and propagation of uncertainty is a critical task. In this paper we expand on prior work and focus on operationalizing the probabilistic uncertainty quantification framework, for a notional cyber system, through: 1) representation of uncertain attacker and system-related modeling variables as probability distributions and mathematical intervals, and 2) exploration of uncertainty propagation techniques including two-phase Monte Carlo sampling and probability bounds analysis.

Additive non-uniform random sampling in superimposed fiber Bragg grating strain gauge

Science.gov (United States)

Ma, Y. C.; Liu, H. Y.; Yan, S. B.; Yang, Y. H.; Yang, M. W.; Li, J. M.; Tang, J.

2013-05-01

This paper demonstrates an additive non-uniform random sampling and interrogation method for dynamic and/or static strain gauge using a reflection spectrum from two superimposed fiber Bragg gratings (FBGs). The superimposed FBGs are designed to generate non-equidistant space of a sensing pulse train in the time domain during dynamic strain gauge. By combining centroid finding with smooth filtering methods, both the interrogation speed and accuracy are improved. A 1.9 kHz dynamic strain is measured by generating an additive non-uniform randomly distributed 2 kHz optical sensing pulse train from a mean 500 Hz triangular periodically changing scanning frequency.

Perceptions of randomized security schedules.

Science.gov (United States)

Scurich, Nicholas; John, Richard S

2014-04-01

Security of infrastructure is a major concern. Traditional security schedules are unable to provide omnipresent coverage; consequently, adversaries can exploit predictable vulnerabilities to their advantage. Randomized security schedules, which randomly deploy security measures, overcome these limitations, but public perceptions of such schedules have not been examined. In this experiment, participants were asked to make a choice between attending a venue that employed a traditional (i.e., search everyone) or a random (i.e., a probability of being searched) security schedule. The absolute probability of detecting contraband was manipulated (i.e., 1/10, 1/4, 1/2) but equivalent between the two schedule types. In general, participants were indifferent to either security schedule, regardless of the probability of detection. The randomized schedule was deemed more convenient, but the traditional schedule was considered fairer and safer. There were no differences between traditional and random schedule in terms of perceived effectiveness or deterrence. Policy implications for the implementation and utilization of randomized schedules are discussed. © 2013 Society for Risk Analysis.

Baysian estimation of P(X > x) from a small sample of Gaussian data

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager

2017-01-01

The classical statistical uncertainty problem of estimation of upper tail probabilities on the basis of a small sample of observations of a Gaussian random variable is considered. Predictive posterior estimation is discussed, adopting the standard statistical model with diffuse priors of the two...

An efficient method of randomly sampling the coherent angular scatter distribution

International Nuclear Information System (INIS)

Williamson, J.F.; Morin, R.L.

1983-01-01

Monte Carlo simulations of photon transport phenomena require random selection of an interaction process at each collision site along the photon track. Possible choices are usually limited to photoelectric absorption and incoherent scatter as approximated by the Klein-Nishina distribution. A technique is described for sampling the coherent angular scatter distribution, for the benefit of workers in medical physics. (U.K.)

(I Can’t Get No) Saturation: A simulation and guidelines for sample sizes in qualitative research

Science.gov (United States)

2017-01-01

I explore the sample size in qualitative research that is required to reach theoretical saturation. I conceptualize a population as consisting of sub-populations that contain different types of information sources that hold a number of codes. Theoretical saturation is reached after all the codes in the population have been observed once in the sample. I delineate three different scenarios to sample information sources: “random chance,” which is based on probability sampling, “minimal information,” which yields at least one new code per sampling step, and “maximum information,” which yields the largest number of new codes per sampling step. Next, I use simulations to assess the minimum sample size for each scenario for systematically varying hypothetical populations. I show that theoretical saturation is more dependent on the mean probability of observing codes than on the number of codes in a population. Moreover, the minimal and maximal information scenarios are significantly more efficient than random chance, but yield fewer repetitions per code to validate the findings. I formulate guidelines for purposive sampling and recommend that researchers follow a minimum information scenario. PMID:28746358

"I Don't Really Understand Probability at All": Final Year Pre-Service Teachers' Understanding of Probability

Science.gov (United States)

Maher, Nicole; Muir, Tracey

2014-01-01

This paper reports on one aspect of a wider study that investigated a selection of final year pre-service primary teachers' responses to four probability tasks. The tasks focused on foundational ideas of probability including sample space, independence, variation and expectation. Responses suggested that strongly held intuitions appeared to…

ON THE ESTIMATION OF RANDOM UNCERTAINTIES OF STAR FORMATION HISTORIES

Energy Technology Data Exchange (ETDEWEB)

Dolphin, Andrew E., E-mail: adolphin@raytheon.com [Raytheon Company, Tucson, AZ, 85734 (United States)

2013-09-20

The standard technique for measurement of random uncertainties of star formation histories (SFHs) is the bootstrap Monte Carlo, in which the color-magnitude diagram (CMD) is repeatedly resampled. The variation in SFHs measured from the resampled CMDs is assumed to represent the random uncertainty in the SFH measured from the original data. However, this technique systematically and significantly underestimates the uncertainties for times in which the measured star formation rate is low or zero, leading to overly (and incorrectly) high confidence in that measurement. This study proposes an alternative technique, the Markov Chain Monte Carlo (MCMC), which samples the probability distribution of the parameters used in the original solution to directly estimate confidence intervals. While the most commonly used MCMC algorithms are incapable of adequately sampling a probability distribution that can involve thousands of highly correlated dimensions, the Hybrid Monte Carlo algorithm is shown to be extremely effective and efficient for this particular task. Several implementation details, such as the handling of implicit priors created by parameterization of the SFH, are discussed in detail.

ON THE ESTIMATION OF RANDOM UNCERTAINTIES OF STAR FORMATION HISTORIES

International Nuclear Information System (INIS)

Dolphin, Andrew E.

2013-01-01

The standard technique for measurement of random uncertainties of star formation histories (SFHs) is the bootstrap Monte Carlo, in which the color-magnitude diagram (CMD) is repeatedly resampled. The variation in SFHs measured from the resampled CMDs is assumed to represent the random uncertainty in the SFH measured from the original data. However, this technique systematically and significantly underestimates the uncertainties for times in which the measured star formation rate is low or zero, leading to overly (and incorrectly) high confidence in that measurement. This study proposes an alternative technique, the Markov Chain Monte Carlo (MCMC), which samples the probability distribution of the parameters used in the original solution to directly estimate confidence intervals. While the most commonly used MCMC algorithms are incapable of adequately sampling a probability distribution that can involve thousands of highly correlated dimensions, the Hybrid Monte Carlo algorithm is shown to be extremely effective and efficient for this particular task. Several implementation details, such as the handling of implicit priors created by parameterization of the SFH, are discussed in detail

What's Missing in Teaching Probability and Statistics: Building Cognitive Schema for Understanding Random Phenomena

Science.gov (United States)

Kuzmak, Sylvia

2016-01-01

Teaching probability and statistics is more than teaching the mathematics itself. Historically, the mathematics of probability and statistics was first developed through analyzing games of chance such as the rolling of dice. This article makes the case that the understanding of probability and statistics is dependent upon building a…

Random vs. systematic sampling from administrative databases involving human subjects.

Science.gov (United States)

Hagino, C; Lo, R J

1998-09-01

Two sampling techniques, simple random sampling (SRS) and systematic sampling (SS), were compared to determine whether they yield similar and accurate distributions for the following four factors: age, gender, geographic location and years in practice. Any point estimate within 7 yr or 7 percentage points of its reference standard (SRS or the entire data set, i.e., the target population) was considered "acceptably similar" to the reference standard. The sampling frame was from the entire membership database of the Canadian Chiropractic Association. The two sampling methods were tested using eight different sample sizes of n (50, 100, 150, 200, 250, 300, 500, 800). From the profile/characteristics, summaries of four known factors [gender, average age, number (%) of chiropractors in each province and years in practice], between- and within-methods chi 2 tests and unpaired t tests were performed to determine whether any of the differences [descriptively greater than 7% or 7 yr] were also statistically significant. The strengths of the agreements between the provincial distributions were quantified by calculating the percent agreements for each (provincial pairwise-comparison methods). Any percent agreement less than 70% was judged to be unacceptable. Our assessments of the two sampling methods (SRS and SS) for the different sample sizes tested suggest that SRS and SS yielded acceptably similar results. Both methods started to yield "correct" sample profiles at approximately the same sample size (n > 200). SS is not only convenient, it can be recommended for sampling from large databases in which the data are listed without any inherent order biases other than alphabetical listing by surname.

Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

Science.gov (United States)

Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy

2006-01-01

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…

Eliciting Subjective Probabilities with Binary Lotteries

DEFF Research Database (Denmark)

Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd

objective probabilities. Drawing a sample from the same subject population, we find evidence that the binary lottery procedure induces linear utility in a subjective probability elicitation task using the Quadratic Scoring Rule. We also show that the binary lottery procedure can induce direct revelation...

Probability Judgements in Multi-Stage Problems : Experimental Evidence of Systematic Biases

NARCIS (Netherlands)

Gneezy, U.

1996-01-01

We report empirical evidence that in problems of random walk with positive drift, bounded rationality leads individuals to under-estimate the probability of success in the long run.In particular, individuals who were given the stage by stage probability distribution failed to aggregate this

Fast Outage Probability Simulation for FSO Links with a Generalized Pointing Error Model

KAUST Repository

Ben Issaid, Chaouki

2017-02-07

Over the past few years, free-space optical (FSO) communication has gained significant attention. In fact, FSO can provide cost-effective and unlicensed links, with high-bandwidth capacity and low error rate, making it an exciting alternative to traditional wireless radio-frequency communication systems. However, the system performance is affected not only by the presence of atmospheric turbulences, which occur due to random fluctuations in the air refractive index but also by the existence of pointing errors. Metrics, such as the outage probability which quantifies the probability that the instantaneous signal-to-noise ratio is smaller than a given threshold, can be used to analyze the performance of this system. In this work, we consider weak and strong turbulence regimes, and we study the outage probability of an FSO communication system under a generalized pointing error model with both a nonzero boresight component and different horizontal and vertical jitter effects. More specifically, we use an importance sampling approach which is based on the exponential twisting technique to offer fast and accurate results.

Concurrency meets probability: theory and practice (abstract)

NARCIS (Netherlands)

Katoen, Joost P.

Treating random phenomena in concurrency theory has a long tradition. Petri nets [18, 10] and process algebras [14] have been extended with probabilities. The same applies to behavioural semantics such as strong and weak (bi)simulation [1], and testing pre-orders [5]. Beautiful connections between

Prestack inversion based on anisotropic Markov random field-maximum posterior probability inversion and its application to identify shale gas sweet spots

Science.gov (United States)

Wang, Kang-Ning; Sun, Zan-Dong; Dong, Ning

2015-12-01

Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young's modulus and Poisson's ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation-maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

Random broadcast on random geometric graphs

Energy Technology Data Exchange (ETDEWEB)

Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY

2009-01-01

In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.

Ruin probability with claims modeled by a stationary ergodic stable process

NARCIS (Netherlands)

Mikosch, T.; Samorodnitsky, G.

2000-01-01

For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin

Additive non-uniform random sampling in superimposed fiber Bragg grating strain gauge

International Nuclear Information System (INIS)

Ma, Y C; Liu, H Y; Yan, S B; Li, J M; Tang, J; Yang, Y H; Yang, M W

2013-01-01

This paper demonstrates an additive non-uniform random sampling and interrogation method for dynamic and/or static strain gauge using a reflection spectrum from two superimposed fiber Bragg gratings (FBGs). The superimposed FBGs are designed to generate non-equidistant space of a sensing pulse train in the time domain during dynamic strain gauge. By combining centroid finding with smooth filtering methods, both the interrogation speed and accuracy are improved. A 1.9 kHz dynamic strain is measured by generating an additive non-uniform randomly distributed 2 kHz optical sensing pulse train from a mean 500 Hz triangular periodically changing scanning frequency. (paper)

The Dirichlet-Multinomial Model for Multivariate Randomized Response Data and Small Samples

Science.gov (United States)

Avetisyan, Marianna; Fox, Jean-Paul

2012-01-01

In survey sampling the randomized response (RR) technique can be used to obtain truthful answers to sensitive questions. Although the individual answers are masked due to the RR technique, individual (sensitive) response rates can be estimated when observing multivariate response data. The beta-binomial model for binary RR data will be generalized…

Estimation of Extreme Response and Failure Probability of Wind Turbines under Normal Operation using Probability Density Evolution Method

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Liu, W. F.

2013-01-01

Estimation of extreme response and failure probability of structures subjected to ultimate design loads is essential for structural design of wind turbines according to the new standard IEC61400-1. This task is focused on in the present paper in virtue of probability density evolution method (PDEM......), which underlies the schemes of random vibration analysis and structural reliability assessment. The short-term rare failure probability of 5-mega-watt wind turbines, for illustrative purposes, in case of given mean wind speeds and turbulence levels is investigated through the scheme of extreme value...... distribution instead of any other approximate schemes of fitted distribution currently used in statistical extrapolation techniques. Besides, the comparative studies against the classical fitted distributions and the standard Monte Carlo techniques are carried out. Numerical results indicate that PDEM exhibits...

Absolute transition probabilities for 559 strong lines of neutral cerium

Energy Technology Data Exchange (ETDEWEB)

Curry, J J, E-mail: jjcurry@nist.go [National Institute of Standards and Technology, Gaithersburg, MD 20899-8422 (United States)

2009-07-07

Absolute radiative transition probabilities are reported for 559 strong lines of neutral cerium covering the wavelength range 340-880 nm. These transition probabilities are obtained by scaling published relative line intensities (Meggers et al 1975 Tables of Spectral Line Intensities (National Bureau of Standards Monograph 145)) with a smaller set of published absolute transition probabilities (Bisson et al 1991 J. Opt. Soc. Am. B 8 1545). All 559 new values are for lines for which transition probabilities have not previously been available. The estimated relative random uncertainty of the new data is +-35% for nearly all lines.

Randomized random walk on a random walk

International Nuclear Information System (INIS)

Lee, P.A.

1983-06-01

This paper discusses generalizations of the model introduced by Kehr and Kunter of the random walk of a particle on a one-dimensional chain which in turn has been constructed by a random walk procedure. The superimposed random walk is randomised in time according to the occurrences of a stochastic point process. The probability of finding the particle in a particular position at a certain instant is obtained explicitly in the transform domain. It is found that the asymptotic behaviour for large time of the mean-square displacement of the particle depends critically on the assumed structure of the basic random walk, giving a diffusion-like term for an asymmetric walk or a square root law if the walk is symmetric. Many results are obtained in closed form for the Poisson process case, and these agree with those given previously by Kehr and Kunter. (author)

Comparison of pure and 'Latinized' centroidal Voronoi tessellation against various other statistical sampling methods

International Nuclear Information System (INIS)

Romero, Vicente J.; Burkardt, John V.; Gunzburger, Max D.; Peterson, Janet S.

2006-01-01

A recently developed centroidal Voronoi tessellation (CVT) sampling method is investigated here to assess its suitability for use in statistical sampling applications. CVT efficiently generates a highly uniform distribution of sample points over arbitrarily shaped M-dimensional parameter spaces. On several 2-D test problems CVT has recently been found to provide exceedingly effective and efficient point distributions for response surface generation. Additionally, for statistical function integration and estimation of response statistics associated with uniformly distributed random-variable inputs (uncorrelated), CVT has been found in initial investigations to provide superior points sets when compared against latin-hypercube and simple-random Monte Carlo methods and Halton and Hammersley quasi-random sequence methods. In this paper, the performance of all these sampling methods and a new variant ('Latinized' CVT) are further compared for non-uniform input distributions. Specifically, given uncorrelated normal inputs in a 2-D test problem, statistical sampling efficiencies are compared for resolving various statistics of response: mean, variance, and exceedence probabilities

Use of probability tables for propagating uncertainties in neutronics

International Nuclear Information System (INIS)

Coste-Delclaux, M.; Diop, C.M.; Lahaye, S.

2017-01-01

Highlights: • Moment-based probability table formalism is described. • Representation by probability tables of any uncertainty distribution is established. • Multiband equations for two kinds of uncertainty propagation problems are solved. • Numerical examples are provided and validated against Monte Carlo simulations. - Abstract: Probability tables are a generic tool that allows representing any random variable whose probability density function is known. In the field of nuclear reactor physics, this tool is currently used to represent the variation of cross-sections versus energy (neutron transport codes TRIPOLI4®, MCNP, APOLLO2, APOLLO3®, ECCO/ERANOS…). In the present article we show how we can propagate uncertainties, thanks to a probability table representation, through two simple physical problems: an eigenvalue problem (neutron multiplication factor) and a depletion problem.

A Monte Carlo study of adsorption of random copolymers on random surfaces

CERN Document Server

Moghaddam, M S

2003-01-01

We study the adsorption problem of a random copolymer on a random surface in which a self-avoiding walk in three dimensions interacts with a plane defining a half-space to which the walk is confined. Each vertex of the walk is randomly labelled A with probability p sub p or B with probability 1 - p sub p , and only vertices labelled A are attracted to the surface plane. Each lattice site on the plane is also labelled either A with probability p sub s or B with probability 1 - p sub s , and only lattice sites labelled A interact with the walk. We study two variations of this model: in the first case the A-vertices of the walk interact only with the A-sites on the surface. In the second case the constraint of selective binding is removed; that is, any contact between the walk and the surface that involves an A-labelling, either from the surface or from the walk, is counted as a visit to the surface. The system is quenched in both cases, i.e. the labellings of the walk and of the surface are fixed as thermodynam...

On the Determinants of the Conjunction Fallacy: Probability versus Inductive Confirmation

Science.gov (United States)

Tentori, Katya; Crupi, Vincenzo; Russo, Selena

2013-01-01

Major recent interpretations of the conjunction fallacy postulate that people assess the probability of a conjunction according to (non-normative) averaging rules as applied to the constituents' probabilities or represent the conjunction fallacy as an effect of random error in the judgment process. In the present contribution, we contrast such…

Landslide Susceptibility Assessment Using Frequency Ratio Technique with Iterative Random Sampling

Directory of Open Access Journals (Sweden)

Hyun-Joo Oh

2017-01-01

Full Text Available This paper assesses the performance of the landslide susceptibility analysis using frequency ratio (FR with an iterative random sampling. A pair of before-and-after digital aerial photographs with 50 cm spatial resolution was used to detect landslide occurrences in Yongin area, Korea. Iterative random sampling was run ten times in total and each time it was applied to the training and validation datasets. Thirteen landslide causative factors were derived from the topographic, soil, forest, and geological maps. The FR scores were calculated from the causative factors and training occurrences repeatedly ten times. The ten landslide susceptibility maps were obtained from the integration of causative factors that assigned FR scores. The landslide susceptibility maps were validated by using each validation dataset. The FR method achieved susceptibility accuracies from 89.48% to 93.21%. And the landslide susceptibility accuracy of the FR method is higher than 89%. Moreover, the ten times iterative FR modeling may contribute to a better understanding of a regularized relationship between the causative factors and landslide susceptibility. This makes it possible to incorporate knowledge-driven considerations of the causative factors into the landslide susceptibility analysis and also be extensively used to other areas.

Probabilistic sensitivity analysis on Markov models with uncertain transition probabilities: an application in evaluating treatment decisions for type 2 diabetes.

Science.gov (United States)

Zhang, Yuanhui; Wu, Haipeng; Denton, Brian T; Wilson, James R; Lobo, Jennifer M

2017-10-27

Markov models are commonly used for decision-making studies in many application domains; however, there are no widely adopted methods for performing sensitivity analysis on such models with uncertain transition probability matrices (TPMs). This article describes two simulation-based approaches for conducting probabilistic sensitivity analysis on a given discrete-time, finite-horizon, finite-state Markov model using TPMs that are sampled over a specified uncertainty set according to a relevant probability distribution. The first approach assumes no prior knowledge of the probability distribution, and each row of a TPM is independently sampled from the uniform distribution on the row's uncertainty set. The second approach involves random sampling from the (truncated) multivariate normal distribution of the TPM's maximum likelihood estimators for its rows subject to the condition that each row has nonnegative elements and sums to one. The two sampling methods are easily implemented and have reasonable computation times. A case study illustrates the application of these methods to a medical decision-making problem involving the evaluation of treatment guidelines for glycemic control of patients with type 2 diabetes, where natural variation in a patient's glycated hemoglobin (HbA1c) is modeled as a Markov chain, and the associated TPMs are subject to uncertainty.

Probability problems in seismic risk analysis and load combinations for nuclear power plants

International Nuclear Information System (INIS)

George, L.L.

1983-01-01

This workshop describes some probability problems in power plant reliability and maintenance analysis. The problems are seismic risk analysis, loss of load probability, load combinations, and load sharing. The seismic risk problem is to compute power plant reliability given an earthquake and the resulting risk. Component survival occurs if its peak random response to the earthquake does not exceed its strength. Power plant survival is a complicated Boolean function of component failures and survivals. The responses and strengths of components are dependent random processes, and the peak responses are maxima of random processes. The resulting risk is the expected cost of power plant failure

Probability an introduction with statistical applications

CERN Document Server

Kinney, John J

2014-01-01

Praise for the First Edition""This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory.""  - The StatisticianThoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, h

Economic Intervention and Parenting: A Randomized Experiment of Statewide Child Development Accounts

Science.gov (United States)

Nam, Yunju; Wikoff, Nora; Sherraden, Michael

2016-01-01

Objective: We examine the effects of Child Development Accounts (CDAs) on parenting stress and practices. Methods: We use data from the SEED for Oklahoma Kids (SEED OK) experiment. SEED OK selected caregivers of infants from Oklahoma birth certificates using a probability sampling method, randomly assigned caregivers to the treatment (n = 1,132)…

Quantifying predictability through information theory: small sample estimation in a non-Gaussian framework

International Nuclear Information System (INIS)

Haven, Kyle; Majda, Andrew; Abramov, Rafail

2005-01-01

Many situations in complex systems require quantitative estimates of the lack of information in one probability distribution relative to another. In short term climate and weather prediction, examples of these issues might involve the lack of information in the historical climate record compared with an ensemble prediction, or the lack of information in a particular Gaussian ensemble prediction strategy involving the first and second moments compared with the non-Gaussian ensemble itself. The relative entropy is a natural way to quantify the predictive utility in this information, and recently a systematic computationally feasible hierarchical framework has been developed. In practical systems with many degrees of freedom, computational overhead limits ensemble predictions to relatively small sample sizes. Here the notion of predictive utility, in a relative entropy framework, is extended to small random samples by the definition of a sample utility, a measure of the unlikeliness that a random sample was produced by a given prediction strategy. The sample utility is the minimum predictability, with a statistical level of confidence, which is implied by the data. Two practical algorithms for measuring such a sample utility are developed here. The first technique is based on the statistical method of null-hypothesis testing, while the second is based upon a central limit theorem for the relative entropy of moment-based probability densities. These techniques are tested on known probability densities with parameterized bimodality and skewness, and then applied to the Lorenz '96 model, a recently developed 'toy' climate model with chaotic dynamics mimicking the atmosphere. The results show a detection of non-Gaussian tendencies of prediction densities at small ensemble sizes with between 50 and 100 members, with a 95% confidence level

Fatigue Reliability under Random Loads

DEFF Research Database (Denmark)

Talreja, R.

1979-01-01

We consider the problem of estimating the probability of survival (non-failure) and the probability of safe operation (strength greater than a limiting value) of structures subjected to random loads. These probabilities are formulated in terms of the probability distributions of the loads...... propagation stage. The consequences of this behaviour on the fatigue reliability are discussed....

Sampled-Data Consensus of Linear Multi-agent Systems With Packet Losses.

Science.gov (United States)

Zhang, Wenbing; Tang, Yang; Huang, Tingwen; Kurths, Jurgen

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function

Decomposition of conditional probability for high-order symbolic Markov chains

Science.gov (United States)

Melnik, S. S.; Usatenko, O. V.

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Weak randomness in device independent quantum key distribution and the advantage of using high dimensional entanglement

OpenAIRE

Huber, Marcus; Pawlowski, Marcin

2013-01-01

We show that in device independent quantum key distribution protocols the privacy of randomness is of crucial importance. For sublinear test sample sizes even the slightest guessing probability by an eavesdropper will completely compromise security. We show that a combined attack exploiting test sample and measurement choices compromises the security even with a linear size test sample and otherwise device independent security considerations. We explicitly derive the sample size needed to ret...

Impact of target point deviations on control and complication probabilities in stereotactic radiosurgery of AVMs and metastases

International Nuclear Information System (INIS)

Treuer, Harald; Kocher, Martin; Hoevels, Moritz; Hunsche, Stefan; Luyken, Klaus; Maarouf, Mohammad; Voges, Juergen; Mueller, Rolf-Peter; Sturm, Volker

2006-01-01

Objective: Determination of the impact of inaccuracies in the determination and setup of the target point in stereotactic radiosurgery (SRS) on the expectable complication and control probabilities. Methods: Two randomized samples of patients with arteriovenous malformation (AVM) (n = 20) and with brain metastases (n = 20) treated with SRS were formed, and the probability for complete obliteration (COP) or complete remission (CRP), the size of the 10 Gy-volume in the brain tissue (VOI10), and the probability for radiation necrosis (NTCP) were calculated. The dose-effect relations for COP and CRP were fitted to clinical data. Target point deviations were simulated through random vectors and the resulting probabilities and volumes were calculated and compared with the values of the treatment plan. Results: The decrease of the relative value of the control probabilities at 1 mm target point deviation was up to 4% for AVMs and up to 10% for metastases. At 2 mm the median decrease was 5% for AVMs and 9% for metastases. The value for the target point deviation, at which COP and CRP decreased about 0.05 in 90% of the cases, was 1.3 mm. The increase of NTCP was maximally 0.0025 per mm target point deviation for AVMs and 0.0035/mm for metastases. The maximal increase of VOI10 was 0.7 cm 3 /mm target point deviation in both patient groups. Conclusions: The upper limit for tolerable target point deviations is at 1.3 mm. If this value cannot be achieved during the system test, a supplementary safety margin should be applied for the definition of the target volume. A better accuracy level is desirable, in order to ensure optimal chances for the success of the treatment. The target point precision is less important for the minimization of the probability of radiation necroses

A simple sample size formula for analysis of covariance in cluster randomized trials.

NARCIS (Netherlands)

Teerenstra, S.; Eldridge, S.; Graff, M.J.; Hoop, E. de; Borm, G.F.

2012-01-01

For cluster randomized trials with a continuous outcome, the sample size is often calculated as if an analysis of the outcomes at the end of the treatment period (follow-up scores) would be performed. However, often a baseline measurement of the outcome is available or feasible to obtain. An

Probability Sampling - A Guideline for Quantitative Health Care ...

African Journals Online (AJOL)

A more direct definition is the method used for selecting a given ... description of the chosen population, the sampling procedure giving ... target population, precision, and stratification. The ... survey estimates, it is recommended that researchers first analyze a .... The optimum sample size has a relation to the type of planned ...

Probability theory and statistical applications a profound treatise for self-study

CERN Document Server

Zörnig, Peter

2016-01-01

This accessible and easy-to-read book provides many examples to illustrate diverse topics in probability and statistics, from initial concepts up to advanced calculations. Special attention is devoted e.g. to independency of events, inequalities in probability and functions of random variables. The book is directed to students of mathematics, statistics, engineering, and other quantitative sciences.

Application of a stratified random sampling technique to the estimation and minimization of respirable quartz exposure to underground miners

International Nuclear Information System (INIS)

Makepeace, C.E.; Horvath, F.J.; Stocker, H.

1981-11-01

The aim of a stratified random sampling plan is to provide the best estimate (in the absence of full-shift personal gravimetric sampling) of personal exposure to respirable quartz among underground miners. One also gains information of the exposure distribution of all the miners at the same time. Three variables (or strata) are considered in the present scheme: locations, occupations and times of sampling. Random sampling within each stratum ensures that each location, occupation and time of sampling has equal opportunity of being selected without bias. Following implementation of the plan and analysis of collected data, one can determine the individual exposures and the mean. This information can then be used to identify those groups whose exposure contributes significantly to the collective exposure. In turn, this identification, along with other considerations, allows the mine operator to carry out a cost-benefit optimization and eventual implementation of engineering controls for these groups. This optimization and engineering control procedure, together with the random sampling plan, can then be used in an iterative manner to minimize the mean value of the distribution and collective exposures

SCRAED - Simple and Complex Random Assignment in Experimental Designs

OpenAIRE

Alferes, Valentim R.

2009-01-01

SCRAED is a package of 37 self-contained SPSS syntax files that performs simple and complex random assignment in experimental designs. For between-subjects designs, SCRAED includes simple random assignment (no restrictions, forced equal sizes, forced unequal sizes, and unequal probabilities), block random assignment (simple and generalized blocks), and stratified random assignment (no restrictions, forced equal sizes, forced unequal sizes, and unequal probabilities). For within-subject...

Event-triggered synchronization for reaction-diffusion complex networks via random sampling

Science.gov (United States)

Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng

2018-04-01

In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.

HIV-related risk behaviours and the correlates among rickshaw pullers of Kamrangirchar, Dhaka, Bangladesh: a cross-sectional study using probability sampling

Directory of Open Access Journals (Sweden)

Ravari Shahrzad

2009-03-01

Full Text Available Abstract Background National HIV serological and behavioural surveillance of Bangladesh repeatedly demonstrated a very high proportion of rickshaw pullers in Dhaka city, having sex with female sex workers (FSWs and using illicit substances. However, no study has been conducted to identify the correlates of having sex with FSWs among this population. This study aimed to describe behavioural profile of rickshaw pullers in Dhaka city using probability samples and to identify the correlates for having sex with FSWs in order to focus HIV prevention intervention. Methods Six hundred rickshaw pullers were randomly selected from rickshaw garages in the Kamrangirchar area, the single largest slum cluster of Dhaka, Bangladesh, during March–April 2008 using the Proportion Probability to Size method. Participants were interviewed, with a response rate of 99.2% (n = 595, using a structured questionnaire and asked about illicit substance use, sexual behaviour and risk perception for HIV and sexually transmitted diseases. Independent predictors of having sex with FSWs were analysed by multivariate analysis. A qualitative study was subsequently conducted with 30 rickshaw pullers to supplement the findings of the initial survey. Results The proportion of survey respondents who had sex with FSWs and those who used illicit substances in the previous 12 months period were 7.9% and 24.9%, respectively, much lower than the results achieved in the 2003–04 behavioural surveillance (72.8% and 89.9%, respectively. Multivariate analysis revealed the characteristics of younger age, being never married, living alone with family remaining in other districts and using illicit substances in the previous 12 months were significantly associated with having sex with FSWs. Conclusion HIV-related risk behaviour of our study population of the rickshaw pullers was lower than what has been suggested by the results of behavioural surveillance. While this discrepancy should be

Digital dice computational solutions to practical probability problems

CERN Document Server

Nahin, Paul J

2013-01-01

Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the

Uncertainty relation and probability. Numerical illustration

International Nuclear Information System (INIS)

Fujikawa, Kazuo; Umetsu, Koichiro

2011-01-01

The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty product of suitably sampled events with a very small probability. We have shown elsewhere that some examples of the evasion of the uncertainty relation noted in the past are in fact understood in this way. We here numerically illustrate that a very small uncertainty product is realized if one performs a suitable sampling of measured data that occur with a very small probability. We introduce a notion of cyclic measurements. It is also shown that our analysis is consistent with the Landau-Pollak-type uncertainty relation. It is suggested that the present analysis may help reconcile the contradicting views about the 'standard quantum limit' in the detection of gravitational waves. (author)

Influence of random setup error on dose distribution

International Nuclear Information System (INIS)

Zhai Zhenyu

2008-01-01

Objective: To investigate the influence of random setup error on dose distribution in radiotherapy and determine the margin from ITV to PTV. Methods: A random sample approach was used to simulate the fields position in target coordinate system. Cumulative effect of random setup error was the sum of dose distributions of all individual treatment fractions. Study of 100 cumulative effects might get shift sizes of 90% dose point position. Margins from ITV to PTV caused by random setup error were chosen by 95% probability. Spearman's correlation was used to analyze the influence of each factor. Results: The average shift sizes of 90% dose point position was 0.62, 1.84, 3.13, 4.78, 6.34 and 8.03 mm if random setup error was 1,2,3,4,5 and 6 mm,respectively. Univariate analysis showed the size of margin was associated only by the size of random setup error. Conclusions: Margin of ITV to PTV is 1.2 times random setup error for head-and-neck cancer and 1.5 times for thoracic and abdominal cancer. Field size, energy and target depth, unlike random setup error, have no relation with the size of the margin. (authors)

Measuring public opinion on alcohol policy: a factor analytic study of a US probability sample.

Science.gov (United States)

Latimer, William W; Harwood, Eileen M; Newcomb, Michael D; Wagenaar, Alexander C

2003-03-01

Public opinion has been one factor affecting change in policies designed to reduce underage alcohol use. Extant research, however, has been criticized for using single survey items of unknown reliability to define adult attitudes on alcohol policy issues. The present investigation addresses a critical gap in the literature by deriving scales on public attitudes, knowledge, and concerns pertinent to alcohol policies designed to reduce underage drinking using a US probability sample survey of 7021 adults. Five attitudinal scales were derived from exploratory and confirmatory factor analyses addressing policies to: (1) regulate alcohol marketing, (2) regulate alcohol consumption in public places, (3) regulate alcohol distribution, (4) increase alcohol taxes, and (5) regulate youth access. The scales exhibited acceptable psychometric properties and were largely consistent with a rational framework which guided the survey construction.

Sample design effects in landscape genetics

Science.gov (United States)

Oyler-McCance, Sara J.; Fedy, Bradley C.; Landguth, Erin L.

2012-01-01

An important research gap in landscape genetics is the impact of different field sampling designs on the ability to detect the effects of landscape pattern on gene flow. We evaluated how five different sampling regimes (random, linear, systematic, cluster, and single study site) affected the probability of correctly identifying the generating landscape process of population structure. Sampling regimes were chosen to represent a suite of designs common in field studies. We used genetic data generated from a spatially-explicit, individual-based program and simulated gene flow in a continuous population across a landscape with gradual spatial changes in resistance to movement. Additionally, we evaluated the sampling regimes using realistic and obtainable number of loci (10 and 20), number of alleles per locus (5 and 10), number of individuals sampled (10-300), and generational time after the landscape was introduced (20 and 400). For a simulated continuously distributed species, we found that random, linear, and systematic sampling regimes performed well with high sample sizes (>200), levels of polymorphism (10 alleles per locus), and number of molecular markers (20). The cluster and single study site sampling regimes were not able to correctly identify the generating process under any conditions and thus, are not advisable strategies for scenarios similar to our simulations. Our research emphasizes the importance of sampling data at ecologically appropriate spatial and temporal scales and suggests careful consideration for sampling near landscape components that are likely to most influence the genetic structure of the species. In addition, simulating sampling designs a priori could help guide filed data collection efforts.

Sampling designs matching species biology produce accurate and affordable abundance indices

Directory of Open Access Journals (Sweden)

Grant Harris

2013-12-01

Full Text Available Wildlife biologists often use grid-based designs to sample animals and generate abundance estimates. Although sampling in grids is theoretically sound, in application, the method can be logistically difficult and expensive when sampling elusive species inhabiting extensive areas. These factors make it challenging to sample animals and meet the statistical assumption of all individuals having an equal probability of capture. Violating this assumption biases results. Does an alternative exist? Perhaps by sampling only where resources attract animals (i.e., targeted sampling, it would provide accurate abundance estimates more efficiently and affordably. However, biases from this approach would also arise if individuals have an unequal probability of capture, especially if some failed to visit the sampling area. Since most biological programs are resource limited, and acquiring abundance data drives many conservation and management applications, it becomes imperative to identify economical and informative sampling designs. Therefore, we evaluated abundance estimates generated from grid and targeted sampling designs using simulations based on geographic positioning system (GPS data from 42 Alaskan brown bears (Ursus arctos. Migratory salmon drew brown bears from the wider landscape, concentrating them at anadromous streams. This provided a scenario for testing the targeted approach. Grid and targeted sampling varied by trap amount, location (traps placed randomly, systematically or by expert opinion, and traps stationary or moved between capture sessions. We began by identifying when to sample, and if bears had equal probability of capture. We compared abundance estimates against seven criteria: bias, precision, accuracy, effort, plus encounter rates, and probabilities of capture and recapture. One grid (49 km2 cells and one targeted configuration provided the most accurate results. Both placed traps by expert opinion and moved traps between capture

Sampling designs matching species biology produce accurate and affordable abundance indices.

Science.gov (United States)

Harris, Grant; Farley, Sean; Russell, Gareth J; Butler, Matthew J; Selinger, Jeff

2013-01-01

Wildlife biologists often use grid-based designs to sample animals and generate abundance estimates. Although sampling in grids is theoretically sound, in application, the method can be logistically difficult and expensive when sampling elusive species inhabiting extensive areas. These factors make it challenging to sample animals and meet the statistical assumption of all individuals having an equal probability of capture. Violating this assumption biases results. Does an alternative exist? Perhaps by sampling only where resources attract animals (i.e., targeted sampling), it would provide accurate abundance estimates more efficiently and affordably. However, biases from this approach would also arise if individuals have an unequal probability of capture, especially if some failed to visit the sampling area. Since most biological programs are resource limited, and acquiring abundance data drives many conservation and management applications, it becomes imperative to identify economical and informative sampling designs. Therefore, we evaluated abundance estimates generated from grid and targeted sampling designs using simulations based on geographic positioning system (GPS) data from 42 Alaskan brown bears (Ursus arctos). Migratory salmon drew brown bears from the wider landscape, concentrating them at anadromous streams. This provided a scenario for testing the targeted approach. Grid and targeted sampling varied by trap amount, location (traps placed randomly, systematically or by expert opinion), and traps stationary or moved between capture sessions. We began by identifying when to sample, and if bears had equal probability of capture. We compared abundance estimates against seven criteria: bias, precision, accuracy, effort, plus encounter rates, and probabilities of capture and recapture. One grid (49 km(2) cells) and one targeted configuration provided the most accurate results. Both placed traps by expert opinion and moved traps between capture sessions

Sampling designs matching species biology produce accurate and affordable abundance indices

Science.gov (United States)

Farley, Sean; Russell, Gareth J.; Butler, Matthew J.; Selinger, Jeff

2013-01-01

Wildlife biologists often use grid-based designs to sample animals and generate abundance estimates. Although sampling in grids is theoretically sound, in application, the method can be logistically difficult and expensive when sampling elusive species inhabiting extensive areas. These factors make it challenging to sample animals and meet the statistical assumption of all individuals having an equal probability of capture. Violating this assumption biases results. Does an alternative exist? Perhaps by sampling only where resources attract animals (i.e., targeted sampling), it would provide accurate abundance estimates more efficiently and affordably. However, biases from this approach would also arise if individuals have an unequal probability of capture, especially if some failed to visit the sampling area. Since most biological programs are resource limited, and acquiring abundance data drives many conservation and management applications, it becomes imperative to identify economical and informative sampling designs. Therefore, we evaluated abundance estimates generated from grid and targeted sampling designs using simulations based on geographic positioning system (GPS) data from 42 Alaskan brown bears (Ursus arctos). Migratory salmon drew brown bears from the wider landscape, concentrating them at anadromous streams. This provided a scenario for testing the targeted approach. Grid and targeted sampling varied by trap amount, location (traps placed randomly, systematically or by expert opinion), and traps stationary or moved between capture sessions. We began by identifying when to sample, and if bears had equal probability of capture. We compared abundance estimates against seven criteria: bias, precision, accuracy, effort, plus encounter rates, and probabilities of capture and recapture. One grid (49 km2 cells) and one targeted configuration provided the most accurate results. Both placed traps by expert opinion and moved traps between capture sessions, which

Fifty challenging problems in probability with solutions

CERN Document Server

Mosteller, Frederick

1987-01-01

Can you solve the problem of ""The Unfair Subway""? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to chall

Theory of sampling and its application in tissue based diagnosis

Directory of Open Access Journals (Sweden)

Kayser Gian

2009-02-01

Full Text Available Abstract Background A general theory of sampling and its application in tissue based diagnosis is presented. Sampling is defined as extraction of information from certain limited spaces and its transformation into a statement or measure that is valid for the entire (reference space. The procedure should be reproducible in time and space, i.e. give the same results when applied under similar circumstances. Sampling includes two different aspects, the procedure of sample selection and the efficiency of its performance. The practical performance of sample selection focuses on search for localization of specific compartments within the basic space, and search for presence of specific compartments. Methods When a sampling procedure is applied in diagnostic processes two different procedures can be distinguished: I the evaluation of a diagnostic significance of a certain object, which is the probability that the object can be grouped into a certain diagnosis, and II the probability to detect these basic units. Sampling can be performed without or with external knowledge, such as size of searched objects, neighbourhood conditions, spatial distribution of objects, etc. If the sample size is much larger than the object size, the application of a translation invariant transformation results in Kriege's formula, which is widely used in search for ores. Usually, sampling is performed in a series of area (space selections of identical size. The size can be defined in relation to the reference space or according to interspatial relationship. The first method is called random sampling, the second stratified sampling. Results Random sampling does not require knowledge about the reference space, and is used to estimate the number and size of objects. Estimated features include area (volume fraction, numerical, boundary and surface densities. Stratified sampling requires the knowledge of objects (and their features and evaluates spatial features in relation to

Information-theoretic methods for estimating of complicated probability distributions

CERN Document Server

Zong, Zhi

2006-01-01

Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neur

A probable risk factor of female breast cancer: study on benign and malignant breast tissue samples.

Science.gov (United States)

Rehman, Sohaila; Husnain, Syed M

2014-01-01

The study reports enhanced Fe, Cu, and Zn contents in breast tissues, a probable risk factor of breast cancer in females. Forty-one formalin-fixed breast tissues were analyzed using atomic absorption spectrophotometry. Twenty malignant, six adjacent to malignant and 15 benign tissues samples were investigated. The malignant tissues samples were of grade 11 and type invasive ductal carcinoma. The quantitative comparison between the elemental levels measured in the two types of specimen (benign and malignant) tissues (removed after surgery) suggests significant elevation of these metals (Fe, Cu, and Zn) in the malignant tissue. The specimens were collected just after mastectomy of women aged 19 to 59 years from the hospitals of Islamabad and Rawalpindi, Pakistan. Most of the patients belong to urban areas of Pakistan. Findings of study depict that these elements have a promising role in the initiation and development of carcinoma as consistent pattern of elevation for Fe, Cu, and Zn was observed. The results showed the excessive accumulation of Fe (229 ± 121 mg/L) in malignant breast tissue samples of patients (p factor of breast cancer. In order to validate our method of analysis, certified reference material muscle tissue lyophilized (IAEA) MA-M-2/TM was analyzed for metal studied. Determined concentrations were quite in good agreement with certified levels. Asymmetric concentration distribution for Fe, Cu, and Zn was observed in both malignant and benign tissue samples.

Linking of uniform random polygons in confined spaces

International Nuclear Information System (INIS)

Arsuaga, J; Blackstone, T; Diao, Y; Karadayi, E; Saito, M

2007-01-01

In this paper, we study the topological entanglement of uniform random polygons in a confined space. We derive the formula for the mean squared linking number of such polygons. For a fixed simple closed curve in the confined space, we rigorously show that the linking probability between this curve and a uniform random polygon of n vertices is at least 1-O(1/√n). Our numerical study also indicates that the linking probability between two uniform random polygons (in a confined space), of m and n vertices respectively, is bounded below by 1-O(1/√(mn)). In particular, the linking probability between two uniform random polygons, both of n vertices, is bounded below by 1-O(1/n)

Probabilistic generation of random networks taking into account information on motifs occurrence.

Science.gov (United States)

Bois, Frederic Y; Gayraud, Ghislaine

2015-01-01

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate realistic graphs with several hundred nodes mimicking a gene transcription interaction network in Escherichia coli.

Quantum Zeno and anti-Zeno effects measured by transition probabilities

Energy Technology Data Exchange (ETDEWEB)

Zhang, Wenxian, E-mail: wxzhang@whu.edu.cn [School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072 (China); Department of Optical Science and Engineering, Fudan University, Shanghai 200433 (China); CEMS, RIKEN, Saitama 351-0198 (Japan); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Kofman, A.G. [CEMS, RIKEN, Saitama 351-0198 (Japan); Department of Physics, The University of Michigan, Ann Arbor, MI 48109-1040 (United States); Zhuang, Jun [Department of Optical Science and Engineering, Fudan University, Shanghai 200433 (China); You, J.Q. [Beijing Computational Science Research Center, Beijing 10084 (China); Department of Physics, Fudan University, Shanghai 200433 (China); CEMS, RIKEN, Saitama 351-0198 (Japan); Nori, Franco [CEMS, RIKEN, Saitama 351-0198 (Japan); Department of Physics, The University of Michigan, Ann Arbor, MI 48109-1040 (United States)

2013-10-30

Using numerical calculations, we compare the transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For various distribution functions, we find the transition probability under frequent modulations is suppressed most if the pulse delay is short and the evolution time is larger than a critical value. Furthermore, decay freezing occurs only under frequent modulations as the pulse delay approaches zero. In the large pulse-delay region, however, the transition probabilities under frequent modulations are highest among the three control methods.

Men who have sex with men in Great Britain: comparing methods and estimates from probability and convenience sample surveys

OpenAIRE

Prah, Philip; Hickson, Ford; Bonell, Chris; McDaid, Lisa M; Johnson, Anne M; Wayal, Sonali; Clifton, Soazig; Sonnenberg, Pam; Nardone, Anthony; Erens, Bob; Copas, Andrew J; Riddell, Julie; Weatherburn, Peter; Mercer, Catherine H

2016-01-01

Objective: To examine sociodemographic and behavioural differences between men whohave sex with men (MSM) participating in recent UK convenience surveys and a national probability sample survey.\\ud Methods: We compared 148 MSM aged 18–64 years interviewed for Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3) undertaken in 2010–2012, with men inthe same age range participating in contemporaneous convenience surveys of MSM: 15 500 British resident men in the European...

Integrated sampling vs ion chromatography: Mathematical considerations

International Nuclear Information System (INIS)

Sundberg, L.L.

1992-01-01

This paper presents some general purpose considerations that can be utilized when comparisons are made between the results of integrated sampling over several hours or days, and ion chromatography where sample collection times are measured in minutes. The discussion is geared toward the measurement of soluble transition metal ions in BWR feedwater. Under steady-state conditions, the concentrations reported by both techniques should be in reasonable agreement. Transient operations effect both types of measurements. A simplistic model, applicable to both sampling techniques, is presented that demonstrates the effect of transients which occur during the acquisition of a steady-state sample. For a common set of conditions, the integrated concentration is proportional to the concentration and duration of the transient, and inversely proportional to the sample collection time. The adjustment of the collection period during a known transient allows an estimation of peak transient concentration. Though the probability of sampling a random transient with the integrated sampling technique is very high, the magnitude is severely diluted with long integration times. Transient concentrations are magnified with ion chromatography, but the probability of sampling a transient is significantly lower using normal ion chromatography operations. Various data averaging techniques are discussed for integrated sampling and IC determinations. The use of time-weighted averages appears to offer more advantages over arithmetic and geometric means for integrated sampling when the collection period is variable. For replicate steady-state ion chromatography determinations which bracket a transient sample, it may be advantageous to ignore the calculation of averages, and report the data as trending information only

Modelling the Probability of Landslides Impacting Road Networks

Science.gov (United States)

Taylor, F. E.; Malamud, B. D.

2012-04-01

During a landslide triggering event, the threat of landslides blocking roads poses a risk to logistics, rescue efforts and communities dependant on those road networks. Here we present preliminary results of a stochastic model we have developed to evaluate the probability of landslides intersecting a simple road network during a landslide triggering event and apply simple network indices to measure the state of the road network in the affected region. A 4000 x 4000 cell array with a 5 m x 5 m resolution was used, with a pre-defined simple road network laid onto it, and landslides 'randomly' dropped onto it. Landslide areas (AL) were randomly selected from a three-parameter inverse gamma probability density function, consisting of a power-law decay of about -2.4 for medium and large values of AL and an exponential rollover for small values of AL; the rollover (maximum probability) occurs at about AL = 400 m2 This statistical distribution was chosen based on three substantially complete triggered landslide inventories recorded in existing literature. The number of landslide areas (NL) selected for each triggered event iteration was chosen to have an average density of 1 landslide km-2, i.e. NL = 400 landslide areas chosen randomly for each iteration, and was based on several existing triggered landslide event inventories. A simple road network was chosen, in a 'T' shape configuration, with one road 1 x 4000 cells (5 m x 20 km) in a 'T' formation with another road 1 x 2000 cells (5 m x 10 km). The landslide areas were then randomly 'dropped' over the road array and indices such as the location, size (ABL) and number of road blockages (NBL) recorded. This process was performed 500 times (iterations) in a Monte-Carlo type simulation. Initial results show that for a landslide triggering event with 400 landslides over a 400 km2 region, the number of road blocks per iteration, NBL,ranges from 0 to 7. The average blockage area for the 500 iterations (A¯ BL) is about 3000 m

Random walk generated by random permutations of {1, 2, 3, ..., n + 1}

International Nuclear Information System (INIS)

Oshanin, G; Voituriez, R

2004-01-01

We study properties of a non-Markovian random walk X (n) l , l = 0, 1, 2, ..., n, evolving in discrete time l on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the rise-and-descent sequences characterizing random permutations π of [n + 1] = {1, 2, 3, ..., n + 1}. We determine exactly the probability of finding the end-point X n = X (n) n of the trajectory of such a permutation-generated random walk (PGRW) at site X, and show that in the limit n → ∞ it converges to a normal distribution with a smaller, compared to the conventional Polya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identical to the distribution of the intermediate points X (n) l , l < n, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of 'turns' of the PGRW trajectories

Estimating HIES Data through Ratio and Regression Methods for Different Sampling Designs

Directory of Open Access Journals (Sweden)

Faqir Muhammad

2007-01-01

Full Text Available In this study, comparison has been made for different sampling designs, using the HIES data of North West Frontier Province (NWFP for 2001-02 and 1998-99 collected from the Federal Bureau of Statistics, Statistical Division, Government of Pakistan, Islamabad. The performance of the estimators has also been considered using bootstrap and Jacknife. A two-stage stratified random sample design is adopted by HIES. In the first stage, enumeration blocks and villages are treated as the first stage Primary Sampling Units (PSU. The sample PSU’s are selected with probability proportional to size. Secondary Sampling Units (SSU i.e., households are selected by systematic sampling with a random start. They have used a single study variable. We have compared the HIES technique with some other designs, which are: Stratified Simple Random Sampling. Stratified Systematic Sampling. Stratified Ranked Set Sampling. Stratified Two Phase Sampling. Ratio and Regression methods were applied with two study variables, which are: Income (y and Household sizes (x. Jacknife and Bootstrap are used for variance replication. Simple Random Sampling with sample size (462 to 561 gave moderate variances both by Jacknife and Bootstrap. By applying Systematic Sampling, we received moderate variance with sample size (467. In Jacknife with Systematic Sampling, we obtained variance of regression estimator greater than that of ratio estimator for a sample size (467 to 631. At a sample size (952 variance of ratio estimator gets greater than that of regression estimator. The most efficient design comes out to be Ranked set sampling compared with other designs. The Ranked set sampling with jackknife and bootstrap, gives minimum variance even with the smallest sample size (467. Two Phase sampling gave poor performance. Multi-stage sampling applied by HIES gave large variances especially if used with a single study variable.

Probability theory plus noise: Replies to Crupi and Tentori (2016) and to Nilsson, Juslin, and Winman (2016).

Science.gov (United States)

Costello, Fintan; Watts, Paul

2016-01-01

A standard assumption in much of current psychology is that people do not reason about probability using the rules of probability theory but instead use various heuristics or "rules of thumb," which can produce systematic reasoning biases. In Costello and Watts (2014), we showed that a number of these biases can be explained by a model where people reason according to probability theory but are subject to random noise. More importantly, that model also predicted agreement with probability theory for certain expressions that cancel the effects of random noise: Experimental results strongly confirmed this prediction, showing that probabilistic reasoning is simultaneously systematically biased and "surprisingly rational." In their commentaries on that paper, both Crupi and Tentori (2016) and Nilsson, Juslin, and Winman (2016) point to various experimental results that, they suggest, our model cannot explain. In this reply, we show that our probability theory plus noise model can in fact explain every one of the results identified by these authors. This gives a degree of additional support to the view that people's probability judgments embody the rational rules of probability theory and that biases in those judgments can be explained as simply effects of random noise. (c) 2015 APA, all rights reserved).

Flipping Out: Calculating Probability with a Coin Game

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Degner, Kate

2015-01-01

In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…

The Use of Conditional Probability Integral Transformation Method for Testing Accelerated Failure Time Models

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Abdalla Ahmed Abdel-Ghaly

2016-06-01

Full Text Available This paper suggests the use of the conditional probability integral transformation (CPIT method as a goodness of fit (GOF technique in the field of accelerated life testing (ALT, specifically for validating the underlying distributional assumption in accelerated failure time (AFT model. The method is based on transforming the data into independent and identically distributed (i.i.d Uniform (0, 1 random variables and then applying the modified Watson statistic to test the uniformity of the transformed random variables. This technique is used to validate each of the exponential, Weibull and lognormal distributions' assumptions in AFT model under constant stress and complete sampling. The performance of the CPIT method is investigated via a simulation study. It is concluded that this method performs well in case of exponential and lognormal distributions. Finally, a real life example is provided to illustrate the application of the proposed procedure.

Making Heads or Tails of Probability: An Experiment with Random Generators

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Morsanyi, Kinga; Handley, Simon J.; Serpell, Sylvie

2013-01-01

Background: The equiprobability bias is a tendency for individuals to think of probabilistic events as "equiprobable" by nature, and to judge outcomes that occur with different probabilities as equally likely. The equiprobability bias has been repeatedly found to be related to formal education in statistics, and it is claimed to be based…

Randomization of grab-sampling strategies for estimating the annual exposure of U miners to Rn daughters.

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Borak, T B

1986-04-01

Periodic grab sampling in combination with time-of-occupancy surveys has been the accepted procedure for estimating the annual exposure of underground U miners to Rn daughters. Temporal variations in the concentration of potential alpha energy in the mine generate uncertainties in this process. A system to randomize the selection of locations for measurement is described which can reduce uncertainties and eliminate systematic biases in the data. In general, a sample frequency of 50 measurements per year is sufficient to satisfy the criteria that the annual exposure be determined in working level months to within +/- 50% of the true value with a 95% level of confidence. Suggestions for implementing this randomization scheme are presented.

A systematic examination of a random sampling strategy for source apportionment calculations.

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Andersson, August

2011-12-15

Estimating the relative contributions from multiple potential sources of a specific component in a mixed environmental matrix is a general challenge in diverse fields such as atmospheric, environmental and earth sciences. Perhaps the most common strategy for tackling such problems is by setting up a system of linear equations for the fractional influence of different sources. Even though an algebraic solution of this approach is possible for the common situation with N+1 sources and N source markers, such methodology introduces a bias, since it is implicitly assumed that the calculated fractions and the corresponding uncertainties are independent of the variability of the source distributions. Here, a random sampling (RS) strategy for accounting for such statistical bias is examined by investigating rationally designed synthetic data sets. This random sampling methodology is found to be robust and accurate with respect to reproducibility and predictability. This method is also compared to a numerical integration solution for a two-source situation where source variability also is included. A general observation from this examination is that the variability of the source profiles not only affects the calculated precision but also the mean/median source contributions. Copyright © 2011 Elsevier B.V. All rights reserved.

Prevalence of probable Attention-Deficit/Hyperactivity Disorder symptoms: result from a Spanish sample of children.

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Cerrillo-Urbina, Alberto José; García-Hermoso, Antonio; Martínez-Vizcaíno, Vicente; Pardo-Guijarro, María Jesús; Ruiz-Hermosa, Abel; Sánchez-López, Mairena

2018-03-15

The aims of our study were to: (i) determine the prevalence of children aged 4 to 6 years with probable Attention-Deficit/Hyperactivity Disorder (ADHD) symptoms in the Spanish population; and (ii) analyse the association of probable ADHD symptoms with sex, age, type of school, origin (native or foreign) and socio-economic status in these children. This cross-sectional study included 1189 children (4 to 6 years-old) from 21 primary schools in 19 towns from the Ciudad Real and Cuenca provinces, Castilla-La Mancha region, Spain. The ADHD Rating Scales IV for parents and teachers was administered to determine the probability of ADHD. The 90th percentile cut-off was used to establish the prevalence of inattention, hyperactivity/impulsivity and combined subtype. The prevalence of children with probable ADHD symptoms was 5.4% (2.6% inattention subtype symptoms, 1.5% hyperactivity/impulsivity subtype symptoms, and 1.3% combined subtype symptoms). Children aged 4 to 5 years showed a higher prevalence of probable ADHD in the inattention subtype symptoms and in total of all subtypes than children aged 6 years, and children with low socio-economic status reported a higher prevalence of probable ADHD symptoms (each subtype and total of all of them) than those with medium and high socio-economic status. Early diagnosis and an understanding of the predictors of being probable ADHD are needed to direct appropriate identification and intervention efforts. These screening efforts should be especially addressed to vulnerable groups, particularly low socio-economic status families and younger children.

The proportionator: unbiased stereological estimation using biased automatic image analysis and non-uniform probability proportional to size sampling

DEFF Research Database (Denmark)

Gardi, Jonathan Eyal; Nyengaard, Jens Randel; Gundersen, Hans Jørgen Gottlieb

2008-01-01

examined, which in turn leads to any of the known stereological estimates, including size distributions and spatial distributions. The unbiasedness is not a function of the assumed relation between the weight and the structure, which is in practice always a biased relation from a stereological (integral......, the desired number of fields are sampled automatically with probability proportional to the weight and presented to the expert observer. Using any known stereological probe and estimator, the correct count in these fields leads to a simple, unbiased estimate of the total amount of structure in the sections...... geometric) point of view. The efficiency of the proportionator depends, however, directly on this relation to be positive. The sampling and estimation procedure is simulated in sections with characteristics and various kinds of noises in possibly realistic ranges. In all cases examined, the proportionator...

A Systematic Review of Surgical Randomized Controlled Trials: Part 2. Funding Source, Conflict of Interest, and Sample Size in Plastic Surgery.

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Voineskos, Sophocles H; Coroneos, Christopher J; Ziolkowski, Natalia I; Kaur, Manraj N; Banfield, Laura; Meade, Maureen O; Chung, Kevin C; Thoma, Achilleas; Bhandari, Mohit

2016-02-01

The authors examined industry support, conflict of interest, and sample size in plastic surgery randomized controlled trials that compared surgical interventions. They hypothesized that industry-funded trials demonstrate statistically significant outcomes more often, and randomized controlled trials with small sample sizes report statistically significant results more frequently. An electronic search identified randomized controlled trials published between 2000 and 2013. Independent reviewers assessed manuscripts and performed data extraction. Funding source, conflict of interest, primary outcome direction, and sample size were examined. Chi-squared and independent-samples t tests were used in the analysis. The search identified 173 randomized controlled trials, of which 100 (58 percent) did not acknowledge funding status. A relationship between funding source and trial outcome direction was not observed. Both funding status and conflict of interest reporting improved over time. Only 24 percent (six of 25) of industry-funded randomized controlled trials reported authors to have independent control of data and manuscript contents. The mean number of patients randomized was 73 per trial (median, 43, minimum, 3, maximum, 936). Small trials were not found to be positive more often than large trials (p = 0.87). Randomized controlled trials with small sample size were common; however, this provides great opportunity for the field to engage in further collaboration and produce larger, more definitive trials. Reporting of trial funding and conflict of interest is historically poor, but it greatly improved over the study period. Underreporting at author and journal levels remains a limitation when assessing the relationship between funding source and trial outcomes. Improved reporting and manuscript control should be goals that both authors and journals can actively achieve.

Generation of pseudo-random numbers

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Howell, L. W.; Rheinfurth, M. H.

1982-01-01

Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.

Linking of uniform random polygons in confined spaces

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Arsuaga, J.; Blackstone, T.; Diao, Y.; Karadayi, E.; Saito, M.

2007-03-01

In this paper, we study the topological entanglement of uniform random polygons in a confined space. We derive the formula for the mean squared linking number of such polygons. For a fixed simple closed curve in the confined space, we rigorously show that the linking probability between this curve and a uniform random polygon of n vertices is at least 1-O\\big(\\frac{1}{\\sqrt{n}}\\big) . Our numerical study also indicates that the linking probability between two uniform random polygons (in a confined space), of m and n vertices respectively, is bounded below by 1-O\\big(\\frac{1}{\\sqrt{mn}}\\big) . In particular, the linking probability between two uniform random polygons, both of n vertices, is bounded below by 1-O\\big(\\frac{1}{n}\\big) .

Response and reliability analysis of nonlinear uncertain dynamical structures by the probability density evolution method

DEFF Research Database (Denmark)

Nielsen, Søren R. K.; Peng, Yongbo; Sichani, Mahdi Teimouri

2016-01-01

The paper deals with the response and reliability analysis of hysteretic or geometric nonlinear uncertain dynamical systems of arbitrary dimensionality driven by stochastic processes. The approach is based on the probability density evolution method proposed by Li and Chen (Stochastic dynamics...... of structures, 1st edn. Wiley, London, 2009; Probab Eng Mech 20(1):33–44, 2005), which circumvents the dimensional curse of traditional methods for the determination of non-stationary probability densities based on Markov process assumptions and the numerical solution of the related Fokker–Planck and Kolmogorov......–Feller equations. The main obstacle of the method is that a multi-dimensional convolution integral needs to be carried out over the sample space of a set of basic random variables, for which reason the number of these need to be relatively low. In order to handle this problem an approach is suggested, which...

Epidemiology of undiagnosed trichomoniasis in a probability sample of urban young adults.

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Susan M Rogers

Full Text Available T. vaginalis infection (trichomoniasis is the most common curable sexually transmitted infection (STI in the U.S. It is associated with increased HIV risk and adverse pregnancy outcomes. Trichomoniasis surveillance data do not exist for either national or local populations. The Monitoring STIs Survey Program (MSSP collected survey data and specimens which were tested using nucleic acid amplification tests to monitor trichomoniasis and other STIs in 2006-09 among a probability sample of young adults (N = 2,936 in Baltimore, Maryland--an urban area with high rates of reported STIs. The estimated prevalence of trichomoniasis was 7.5% (95% CI 6.3, 9.1 in the overall population and 16.1% (95% CI 13.0, 19.8 among Black women. The overwhelming majority of infected men (98.5% and women (73.3% were asymptomatic. Infections were more common in both women (OR = 3.6, 95% CI 1.6, 8.2 and men (OR = 9.0, 95% CI 1.8, 44.3 with concurrent chlamydial infection. Trichomoniasis did not vary significantly by age for either men or women. Women with two or more partners in the past year and women with a history of personal or partner incarceration were more likely to have an infection. Overall, these results suggest that routine T vaginalis screening in populations at elevated risk of infection should be considered.

Distributed fiber sparse-wideband vibration sensing by sub-Nyquist additive random sampling

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Zhang, Jingdong; Zheng, Hua; Zhu, Tao; Yin, Guolu; Liu, Min; Bai, Yongzhong; Qu, Dingrong; Qiu, Feng; Huang, Xianbing

2018-05-01

The round trip time of the light pulse limits the maximum detectable vibration frequency response range of phase-sensitive optical time domain reflectometry ({\\phi}-OTDR). Unlike the uniform laser pulse interval in conventional {\\phi}-OTDR, we randomly modulate the pulse interval, so that an equivalent sub-Nyquist additive random sampling (sNARS) is realized for every sensing point of the long interrogation fiber. For an {\\phi}-OTDR system with 10 km sensing length, the sNARS method is optimized by theoretical analysis and Monte Carlo simulation, and the experimental results verify that a wide-band spars signal can be identified and reconstructed. Such a method can broaden the vibration frequency response range of {\\phi}-OTDR, which is of great significance in sparse-wideband-frequency vibration signal detection, such as rail track monitoring and metal defect detection.

Efficiency of analytical and sampling-based uncertainty propagation in intensity-modulated proton therapy

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Wahl, N.; Hennig, P.; Wieser, H. P.; Bangert, M.

2017-07-01

The sensitivity of intensity-modulated proton therapy (IMPT) treatment plans to uncertainties can be quantified and mitigated with robust/min-max and stochastic/probabilistic treatment analysis and optimization techniques. Those methods usually rely on sparse random, importance, or worst-case sampling. Inevitably, this imposes a trade-off between computational speed and accuracy of the uncertainty propagation. Here, we investigate analytical probabilistic modeling (APM) as an alternative for uncertainty propagation and minimization in IMPT that does not rely on scenario sampling. APM propagates probability distributions over range and setup uncertainties via a Gaussian pencil-beam approximation into moments of the probability distributions over the resulting dose in closed form. It supports arbitrary correlation models and allows for efficient incorporation of fractionation effects regarding random and systematic errors. We evaluate the trade-off between run-time and accuracy of APM uncertainty computations on three patient datasets. Results are compared against reference computations facilitating importance and random sampling. Two approximation techniques to accelerate uncertainty propagation and minimization based on probabilistic treatment plan optimization are presented. Runtimes are measured on CPU and GPU platforms, dosimetric accuracy is quantified in comparison to a sampling-based benchmark (5000 random samples). APM accurately propagates range and setup uncertainties into dose uncertainties at competitive run-times (GPU ≤slant {5} min). The resulting standard deviation (expectation value) of dose show average global γ{3% / {3}~mm} pass rates between 94.2% and 99.9% (98.4% and 100.0%). All investigated importance sampling strategies provided less accuracy at higher run-times considering only a single fraction. Considering fractionation, APM uncertainty propagation and treatment plan optimization was proven to be possible at constant time complexity

Design-based Sample and Probability Law-Assumed Sample: Their Role in Scientific Investigation.

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Ojeda, Mario Miguel; Sahai, Hardeo

2002-01-01

Discusses some key statistical concepts in probabilistic and non-probabilistic sampling to provide an overview for understanding the inference process. Suggests a statistical model constituting the basis of statistical inference and provides a brief review of the finite population descriptive inference and a quota sampling inferential theory.…

Risk estimation using probability machines

Science.gov (United States)

2014-01-01

Background Logistic regression has been the de facto, and often the only, model used in the description and analysis of relationships between a binary outcome and observed features. It is widely used to obtain the conditional probabilities of the outcome given predictors, as well as predictor effect size estimates using conditional odds ratios. Results We show how statistical learning machines for binary outcomes, provably consistent for the nonparametric regression problem, can be used to provide both consistent conditional probability estimation and conditional effect size estimates. Effect size estimates from learning machines leverage our understanding of counterfactual arguments central to the interpretation of such estimates. We show that, if the data generating model is logistic, we can recover accurate probability predictions and effect size estimates with nearly the same efficiency as a correct logistic model, both for main effects and interactions. We also propose a method using learning machines to scan for possible interaction effects quickly and efficiently. Simulations using random forest probability machines are presented. Conclusions The models we propose make no assumptions about the data structure, and capture the patterns in the data by just specifying the predictors involved and not any particular model structure. So they do not run the same risks of model mis-specification and the resultant estimation biases as a logistic model. This methodology, which we call a “risk machine”, will share properties from the statistical machine that it is derived from. PMID:24581306

Free random variables

CERN Document Server

Voiculescu, Dan; Nica, Alexandru

1992-01-01

This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.

Sensitivity of the probability of failure to probability of detection curve regions

International Nuclear Information System (INIS)

Garza, J.; Millwater, H.

2016-01-01

Non-destructive inspection (NDI) techniques have been shown to play a vital role in fracture control plans, structural health monitoring, and ensuring availability and reliability of piping, pressure vessels, mechanical and aerospace equipment. Probabilistic fatigue simulations are often used in order to determine the efficacy of an inspection procedure with the NDI method modeled as a probability of detection (POD) curve. These simulations can be used to determine the most advantageous NDI method for a given application. As an aid to this process, a first order sensitivity method of the probability-of-failure (POF) with respect to regions of the POD curve (lower tail, middle region, right tail) is developed and presented here. The sensitivity method computes the partial derivative of the POF with respect to a change in each region of a POD or multiple POD curves. The sensitivities are computed at no cost by reusing the samples from an existing Monte Carlo (MC) analysis. A numerical example is presented considering single and multiple inspections. - Highlights: • Sensitivities of probability-of-failure to a region of probability-of-detection curve. • The sensitivities are computed with negligible cost. • Sensitivities identify the important region of a POD curve. • Sensitivities can be used as a guide to selecting the optimal POD curve.

Theory of random sets

CERN Document Server

Molchanov, Ilya

2017-01-01

This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integ...

Predicting the probability of mortality of gastric cancer patients using decision tree.

Science.gov (United States)

Mohammadzadeh, F; Noorkojuri, H; Pourhoseingholi, M A; Saadat, S; Baghestani, A R

2015-06-01

Gastric cancer is the fourth most common cancer worldwide. This reason motivated us to investigate and introduce gastric cancer risk factors utilizing statistical methods. The aim of this study was to identify the most important factors influencing the mortality of patients who suffer from gastric cancer disease and to introduce a classification approach according to decision tree model for predicting the probability of mortality from this disease. Data on 216 patients with gastric cancer, who were registered in Taleghani hospital in Tehran,Iran, were analyzed. At first, patients were divided into two groups: the dead and alive. Then, to fit decision tree model to our data, we randomly selected 20% of dataset to the test sample and remaining dataset considered as the training sample. Finally, the validity of the model examined with sensitivity, specificity, diagnosis accuracy and the area under the receiver operating characteristic curve. The CART version 6.0 and SPSS version 19.0 softwares were used for the analysis of the data. Diabetes, ethnicity, tobacco, tumor size, surgery, pathologic stage, age at diagnosis, exposure to chemical weapons and alcohol consumption were determined as effective factors on mortality of gastric cancer. The sensitivity, specificity and accuracy of decision tree were 0.72, 0.75 and 0.74 respectively. The indices of sensitivity, specificity and accuracy represented that the decision tree model has acceptable accuracy to prediction the probability of mortality in gastric cancer patients. So a simple decision tree consisted of factors affecting on mortality of gastric cancer may help clinicians as a reliable and practical tool to predict the probability of mortality in these patients.

Survival probability in a one-dimensional quantum walk on a trapped lattice

International Nuclear Information System (INIS)

Goenuelol, Meltem; Aydiner, Ekrem; Shikano, Yutaka; Muestecaplioglu, Oezguer E

2011-01-01

The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps is investigated. The survival probability of quantum walkers is compared with that of classical walkers. It is shown that the time dependence of the survival probability of quantum walkers has a piecewise stretched exponential character depending on the density of traps in numerical and analytical observations. The crossover between the quantum analogues of the Rosenstock and Donsker-Varadhan behavior is identified.

Theory of overdispersion in counting statistics caused by fluctuating probabilities

International Nuclear Information System (INIS)

Semkow, Thomas M.

1999-01-01

It is shown that the random Lexis fluctuations of probabilities such as probability of decay or detection cause the counting statistics to be overdispersed with respect to the classical binomial, Poisson, or Gaussian distributions. The generating and the distribution functions for the overdispersed counting statistics are derived. Applications to radioactive decay with detection and more complex experiments are given, as well as distinguishing between the source and background, in the presence of overdispersion. Monte-Carlo verifications are provided

BMR in a Brazilian adult probability sample: the Nutrition, Physical Activity and Health Survey.

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Anjos, Luiz A; Wahrlich, Vivian; Vasconcellos, Mauricio Tl

2014-04-01

To measure BMR in a probability sample of adults from an urban city of Brazil and to compare indirectly measured BMR (BMRi) with BMR predicted from different equations. BMR data were obtained by indirect calorimetry and estimated by different predictive equations (Schofield; Harris and Benedict; Henry and Rees). Anthropometric and body composition measures were also obtained. The Nutrition, Physical Activity and Health Survey (PNAFS), a household survey conducted in Niterói, Rio de Janeiro state, Brazil. Representative sample of 529 adults (aged ≥20 years; 339 females) living in Niterói, Rio de Janeiro state, Brazil. Mean BMRi values were 5839.7 (se 73.9) kJ/d and 4758.1 (se 39.5) kJ/d for men and women, respectively. Predicted BMR by all equations was significantly higher (difference between means and 95% CI did not include zero) than BMRi in both men and women of all ages. Overall bias in BMR (predicted BMR minus BMRi) using the Schofield equations (overestimation of about 20%) was higher than when using the Henry and Rees equations (13% and 16% overestimation for males and females, respectively). The percentage of individuals whose BMR predicted by the Schofield equations fell within 10% of BMRi was very low (7.8% and 14.1% of males nd females, respectively). Current available predictive equations of BMR are not adequate to estimate BMR in Brazilians living in Niterói, Rio de Janeiro, Brazil.

Randomized central limit theorems: A unified theory.

Science.gov (United States)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Effect of randomness on multi-frequency aeroelastic responses resolved by Unsteady Adaptive Stochastic Finite Elements

International Nuclear Information System (INIS)

Witteveen, Jeroen A.S.; Bijl, Hester

2009-01-01

The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions.

Sensitivity analysis of limit state functions for probability-based plastic design

Science.gov (United States)

Frangopol, D. M.

1984-01-01

The evaluation of the total probability of a plastic collapse failure P sub f for a highly redundant structure of random interdependent plastic moments acted on by random interdepedent loads is a difficult and computationally very costly process. The evaluation of reasonable bounds to this probability requires the use of second moment algebra which involves man statistical parameters. A computer program which selects the best strategy for minimizing the interval between upper and lower bounds of P sub f is now in its final stage of development. The relative importance of various uncertainties involved in the computational process on the resulting bounds of P sub f, sensitivity is analyzed. Response sensitivities for both mode and system reliability of an ideal plastic portal frame are shown.

Quantum Probabilities as Behavioral Probabilities

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Vyacheslav I. Yukalov

2017-03-01

Full Text Available We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans do not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.

Pseudo-random number generator based on asymptotic deterministic randomness

Science.gov (United States)

Wang, Kai; Pei, Wenjiang; Xia, Haishan; Cheung, Yiu-ming

2008-06-01

A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.

Pseudo-random number generator based on asymptotic deterministic randomness

International Nuclear Information System (INIS)

Wang Kai; Pei Wenjiang; Xia Haishan; Cheung Yiuming

2008-01-01

A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks

A random walk rule for phase I clinical trials.

Science.gov (United States)

Durham, S D; Flournoy, N; Rosenberger, W F

1997-06-01

We describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose-response study, or phase I clinical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, which may be determined by ethical considerations as well as the patient's response. It is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest. Estimation of the quantile is discussed; the maximum likelihood estimator and its variance are derived under a two-parameter logistic distribution, and the maximum likelihood estimator is compared with other nonparametric estimators. Random walk rules have clear advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random walk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design. The small sample properties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.

Probability Aggregates in Probability Answer Set Programming

OpenAIRE

Saad, Emad

2013-01-01

Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of p...

Probability theory a comprehensive course

CERN Document Server

Klenke, Achim

2014-01-01

This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms.   To address these concepts, the title covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as:   • limit theorems for sums of random variables • martingales • percolation • Markov chains and electrical networks • construction of stochastic processes • Poisson point process and infinite divisibility • large deviation principles and statistical physics • Brownian motion • stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the c...

Estimating Model Probabilities using Thermodynamic Markov Chain Monte Carlo Methods

Science.gov (United States)

Ye, M.; Liu, P.; Beerli, P.; Lu, D.; Hill, M. C.

2014-12-01

Markov chain Monte Carlo (MCMC) methods are widely used to evaluate model probability for quantifying model uncertainty. In a general procedure, MCMC simulations are first conducted for each individual model, and MCMC parameter samples are then used to approximate marginal likelihood of the model by calculating the geometric mean of the joint likelihood of the model and its parameters. It has been found the method of evaluating geometric mean suffers from the numerical problem of low convergence rate. A simple test case shows that even millions of MCMC samples are insufficient to yield accurate estimation of the marginal likelihood. To resolve this problem, a thermodynamic method is used to have multiple MCMC runs with different values of a heating coefficient between zero and one. When the heating coefficient is zero, the MCMC run is equivalent to a random walk MC in the prior parameter space; when the heating coefficient is one, the MCMC run is the conventional one. For a simple case with analytical form of the marginal likelihood, the thermodynamic method yields more accurate estimate than the method of using geometric mean. This is also demonstrated for a case of groundwater modeling with consideration of four alternative models postulated based on different conceptualization of a confining layer. This groundwater example shows that model probabilities estimated using the thermodynamic method are more reasonable than those obtained using the geometric method. The thermodynamic method is general, and can be used for a wide range of environmental problem for model uncertainty quantification.

Hitting probabilities for nonlinear systems of stochastic waves

CERN Document Server

Dalang, Robert C

2015-01-01

The authors consider a d-dimensional random field u = \\{u(t,x)\\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \\in \\{1,2,3\\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \\beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \\mathbb{R}^d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap

Tobacco smoking surveillance: is quota sampling an efficient tool for monitoring national trends? A comparison with a random cross-sectional survey.

Directory of Open Access Journals (Sweden)

Romain Guignard

Full Text Available OBJECTIVES: It is crucial for policy makers to monitor the evolution of tobacco smoking prevalence. In France, this monitoring is based on a series of cross-sectional general population surveys, the Health Barometers, conducted every five years and based on random samples. A methodological study has been carried out to assess the reliability of a monitoring system based on regular quota sampling surveys for smoking prevalence. DESIGN / OUTCOME MEASURES: In 2010, current and daily tobacco smoking prevalences obtained in a quota survey on 8,018 people were compared with those of the 2010 Health Barometer carried out on 27,653 people. Prevalences were assessed separately according to the telephone equipment of the interviewee (landline phone owner vs "mobile-only", and logistic regressions were conducted in the pooled database to assess the impact of the telephone equipment and of the survey mode on the prevalences found. Finally, logistic regressions adjusted for sociodemographic characteristics were conducted in the random sample in order to determine the impact of the needed number of calls to interwiew "hard-to-reach" people on the prevalence found. RESULTS: Current and daily prevalences were higher in the random sample (respectively 33.9% and 27.5% in 15-75 years-old than in the quota sample (respectively 30.2% and 25.3%. In both surveys, current and daily prevalences were lower among landline phone owners (respectively 31.8% and 25.5% in the random sample and 28.9% and 24.0% in the quota survey. The required number of calls was slightly related to the smoking status after adjustment for sociodemographic characteristics. CONCLUSION: Random sampling appears to be more effective than quota sampling, mainly by making it possible to interview hard-to-reach populations.

A procedure for estimation of pipe break probabilities due to IGSCC

International Nuclear Information System (INIS)

Bergman, M.; Brickstad, B.; Nilsson, F.

1998-06-01

A procedure has been developed for estimation of the failure probability of welds joints in nuclear piping susceptible to intergranular stress corrosion cracking. The procedure aims at a robust and rapid estimate of the failure probability for a specific weld with known stress state. Random properties are taken into account of the crack initiation rate, the initial crack length, the in-service inspection efficiency and the leak rate. A computer realization of the procedure has been developed for user friendly applications by design engineers. Some examples are considered to investigate the sensitivity of the failure probability to different input quantities. (au)

Probability of inadvertent operation of electrical components in harsh environments

International Nuclear Information System (INIS)

Knoll, A.

1989-01-01

Harsh environment, which means humidity and high temperature, may and will affect unsealed electrical components by causing leakage ground currents in ungrounded direct current systems. The concern in a nuclear power plant is that such harsh environment conditions could cause inadvertent operation of normally deenergized components, which may have a safety-related isolation function. Harsh environment is a common cause failure, and one way to approach the problem is to assume that all the unsealed electrical components will simultaneously and inadvertently energize as a result of the environmental common cause failure. This assumption is unrealistically conservative. Test results indicated that insulating resistences of any terminal block in harsh environments have a random distribution in the range of 1 to 270 kΩ, with a mean value ∼59 kΩ. The objective of this paper is to evaluate a realistic conditional failure probability for inadvertent operation of electrical components in harsh environments. This value will be used thereafter in probabilistic safety evaluations of harsh environment events and will replace both the overconservative common cause probability of 1 and the random failure probability used for mild environments

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

International Nuclear Information System (INIS)

Stanek, Jan; Kozminski, Wiktor

2010-01-01

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D 15 N- and 13 C-edited NOESY-HSQC spectra of human ubiquitin.

Random isotropic one-dimensional XY-model

Science.gov (United States)

Gonçalves, L. L.; Vieira, A. P.

1998-01-01

The 1D isotropic s = ½XY-model ( N sites), with random exchange interaction in a transverse random field is considered. The random variables satisfy bimodal quenched distributions. The solution is obtained by using the Jordan-Wigner fermionization and a canonical transformation, reducing the problem to diagonalizing an N × N matrix, corresponding to a system of N noninteracting fermions. The calculations are performed numerically for N = 1000, and the field-induced magnetization at T = 0 is obtained by averaging the results for the different samples. For the dilute case, in the uniform field limit, the magnetization exhibits various discontinuities, which are the consequence of the existence of disconnected finite clusters distributed along the chain. Also in this limit, for finite exchange constants J A and J B, as the probability of J A varies from one to zero, the saturation field is seen to vary from Γ A to Γ B, where Γ A(Γ B) is the value of the saturation field for the pure case with exchange constant equal to J A(J B) .

Transgender Population Size in the United States: a Meta-Regression of Population-Based Probability Samples

Science.gov (United States)

Sevelius, Jae M.

2017-01-01

Background. Transgender individuals have a gender identity that differs from the sex they were assigned at birth. The population size of transgender individuals in the United States is not well-known, in part because official records, including the US Census, do not include data on gender identity. Population surveys today more often collect transgender-inclusive gender-identity data, and secular trends in culture and the media have created a somewhat more favorable environment for transgender people. Objectives. To estimate the current population size of transgender individuals in the United States and evaluate any trend over time. Search methods. In June and July 2016, we searched PubMed, Cumulative Index to Nursing and Allied Health Literature, and Web of Science for national surveys, as well as “gray” literature, through an Internet search. We limited the search to 2006 through 2016. Selection criteria. We selected population-based surveys that used probability sampling and included self-reported transgender-identity data. Data collection and analysis. We used random-effects meta-analysis to pool eligible surveys and used meta-regression to address our hypothesis that the transgender population size estimate would increase over time. We used subsample and leave-one-out analysis to assess for bias. Main results. Our meta-regression model, based on 12 surveys covering 2007 to 2015, explained 62.5% of model heterogeneity, with a significant effect for each unit increase in survey year (F = 17.122; df = 1,10; b = 0.026%; P = .002). Extrapolating these results to 2016 suggested a current US population size of 390 adults per 100 000, or almost 1 million adults nationally. This estimate may be more indicative for younger adults, who represented more than 50% of the respondents in our analysis. Authors’ conclusions. Future national surveys are likely to observe higher numbers of transgender people. The large variety in questions used to ask

Interpretation of the results of statistical measurements. [search for basic probability model

Science.gov (United States)

Olshevskiy, V. V.

1973-01-01

For random processes, the calculated probability characteristic, and the measured statistical estimate are used in a quality functional, which defines the difference between the two functions. Based on the assumption that the statistical measurement procedure is organized so that the parameters for a selected model are optimized, it is shown that the interpretation of experimental research is a search for a basic probability model.

Nonlinear Spatial Inversion Without Monte Carlo Sampling

Science.gov (United States)

Curtis, A.; Nawaz, A.

2017-12-01

High-dimensional, nonlinear inverse or inference problems usually have non-unique solutions. The distribution of solutions are described by probability distributions, and these are usually found using Monte Carlo (MC) sampling methods. These take pseudo-random samples of models in parameter space, calculate the probability of each sample given available data and other information, and thus map out high or low probability values of model parameters. However, such methods would converge to the solution only as the number of samples tends to infinity; in practice, MC is found to be slow to converge, convergence is not guaranteed to be achieved in finite time, and detection of convergence requires the use of subjective criteria. We propose a method for Bayesian inversion of categorical variables such as geological facies or rock types in spatial problems, which requires no sampling at all. The method uses a 2-D Hidden Markov Model over a grid of cells, where observations represent localized data constraining the model in each cell. The data in our example application are seismic properties such as P- and S-wave impedances or rock density; our model parameters are the hidden states and represent the geological rock types in each cell. The observations at each location are assumed to depend on the facies at that location only - an assumption referred to as `localized likelihoods'. However, the facies at a location cannot be determined solely by the observation at that location as it also depends on prior information concerning its correlation with the spatial distribution of facies elsewhere. Such prior information is included in the inversion in the form of a training image which represents a conceptual depiction of the distribution of local geologies that might be expected, but other forms of prior information can be used in the method as desired. The method provides direct (pseudo-analytic) estimates of posterior marginal probability distributions over each variable

Determination of bounds on failure probability in the presence of ...

Indian Academy of Sciences (India)

In particular, fuzzy set theory provides a more rational framework for ..... indicating that the random variations inT andO2 do not affect failure probability significantly. ... The upper-bound for PF shown in figure 6 can be used in decision-making.

Negative probability in the framework of combined probability

OpenAIRE

Burgin, Mark

2013-01-01

Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of conventional probability. So, it is natural that negative probability also has different axiomatic frameworks. In the previous publications (Burgin, 2009; 2010), negative probability was mathematically formalized and rigorously interpreted in the context of extende...

On the Distribution of Random Geometric Graphs

DEFF Research Database (Denmark)

Badiu, Mihai Alin; Coon, Justin P.

2018-01-01

as a measure of the graph’s topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution......Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy...... of the n(n − 1)/2 distances between n nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in R 2. This enables the calculation of the probability distribution...

Computer code ENDSAM for random sampling and validation of the resonance parameters covariance matrices of some major nuclear data libraries

International Nuclear Information System (INIS)

Plevnik, Lucijan; Žerovnik, Gašper

2016-01-01

Highlights: • Methods for random sampling of correlated parameters. • Link to open-source code for sampling of resonance parameters in ENDF-6 format. • Validation of the code on realistic and artificial data. • Validation of covariances in three major contemporary nuclear data libraries. - Abstract: Methods for random sampling of correlated parameters are presented. The methods are implemented for sampling of resonance parameters in ENDF-6 format and a link to the open-source code ENDSAM is given. The code has been validated on realistic data. Additionally, consistency of covariances of resonance parameters of three major contemporary nuclear data libraries (JEFF-3.2, ENDF/B-VII.1 and JENDL-4.0u2) has been checked.

Probability mapping of contaminants

International Nuclear Information System (INIS)

Rautman, C.A.; Kaplan, P.G.; McGraw, M.A.; Istok, J.D.; Sigda, J.M.

1994-01-01

Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. The probability mapping approach illustrated in this paper appears to offer site operators a reasonable, quantitative methodology for many environmental remediation decisions and allows evaluation of the risk associated with those decisions. For example, output from this approach can be used in quantitative, cost-based decision models for evaluating possible site characterization and/or remediation plans, resulting in selection of the risk-adjusted, least-cost alternative. The methodology is completely general, and the techniques are applicable to a wide variety of environmental restoration projects. The probability-mapping approach is illustrated by application to a contaminated site at the former DOE Feed Materials Production Center near Fernald, Ohio. Soil geochemical data, collected as part of the Uranium-in-Soils Integrated Demonstration Project, have been used to construct a number of geostatistical simulations of potential contamination for parcels approximately the size of a selective remediation unit (the 3-m width of a bulldozer blade). Each such simulation accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination (potential clean-up or personnel-hazard thresholds)

Probability mapping of contaminants

Energy Technology Data Exchange (ETDEWEB)

Rautman, C.A.; Kaplan, P.G. [Sandia National Labs., Albuquerque, NM (United States); McGraw, M.A. [Univ. of California, Berkeley, CA (United States); Istok, J.D. [Oregon State Univ., Corvallis, OR (United States); Sigda, J.M. [New Mexico Inst. of Mining and Technology, Socorro, NM (United States)

1994-04-01

Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. The probability mapping approach illustrated in this paper appears to offer site operators a reasonable, quantitative methodology for many environmental remediation decisions and allows evaluation of the risk associated with those decisions. For example, output from this approach can be used in quantitative, cost-based decision models for evaluating possible site characterization and/or remediation plans, resulting in selection of the risk-adjusted, least-cost alternative. The methodology is completely general, and the techniques are applicable to a wide variety of environmental restoration projects. The probability-mapping approach is illustrated by application to a contaminated site at the former DOE Feed Materials Production Center near Fernald, Ohio. Soil geochemical data, collected as part of the Uranium-in-Soils Integrated Demonstration Project, have been used to construct a number of geostatistical simulations of potential contamination for parcels approximately the size of a selective remediation unit (the 3-m width of a bulldozer blade). Each such simulation accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination (potential clean-up or personnel-hazard thresholds).

An empirical probability model of detecting species at low densities.

Science.gov (United States)