Probability, random variables, and random processes theory and signal processing applications
Shynk, John J
2012-01-01
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several app
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)
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.
General Exact Solution to the Problem of the Probability Density for Sums of Random Variables
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.
Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables
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Andrew Rosalsky
2004-12-01
Full Text Available Let {X,Xn;nÃ¢Â‰Â¥1} be a sequence of real-valued i.i.d. random variables and let Sn=Ã¢ÂˆÂ‘i=1nXi, nÃ¢Â‰Â¥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/ÃÂ•(x=1, then for every t>0, limsupnÃ¢Â†Â’Ã¢ÂˆÂžP(|Sn|>tn1/p/(nÃÂ•(n=tpÃŽÂ±.
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
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.
Free probability and random matrices
Mingo, James A
2017-01-01
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Random phenomena fundamentals of probability and statistics for engineers
Ogunnaike, Babatunde A
2009-01-01
PreludeApproach PhilosophyFour Basic PrinciplesI FoundationsTwo Motivating ExamplesYield Improvement in a Chemical ProcessQuality Assurance in a Glass Sheet Manufacturing ProcessOutline of a Systematic ApproachRandom Phenomena, Variability, and UncertaintyTwo Extreme Idealizations of Natural PhenomenaRandom Mass PhenomenaIntroducing ProbabilityThe Probabilistic FrameworkII ProbabilityFundamentals of Probability TheoryBuilding BlocksOperationsProbabilityConditional ProbabilityIndependenceRandom Variables and DistributionsDistributionsMathematical ExpectationCharacterizing DistributionsSpecial Derived Probability FunctionsMultidimensional Random VariablesDistributions of Several Random VariablesDistributional Characteristics of Jointly Distributed Random VariablesRandom Variable TransformationsSingle Variable TransformationsBivariate TransformationsGeneral Multivariate TransformationsApplication Case Studies I: ProbabilityMendel and HeredityWorld War II Warship Tactical Response Under AttackIII DistributionsIde...
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
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
Fundamentals of applied probability and random processes
Ibe, Oliver
2014-01-01
The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability t
Probability of Failure in Random Vibration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
1988-01-01
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 out......-crossing. 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 thus for the first-passage probability...
Fundamentals of applied probability and random processes
Ibe, Oliver
2005-01-01
This book is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book''s clear writing style and homework problems make it ideal for the classroom or for self-study.* Good and solid introduction to probability theory and stochastic processes * Logically organized; writing is presented in a clear manner * Choice of topics is comprehensive within the area of probability * Ample homework problems are organized into chapter sections
Path probabilities of continuous time random walks
International Nuclear Information System (INIS)
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
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.
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
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Anwer Khurshid
2012-07-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE In this paper, it is shown that a complex multivariate random variable is a complex multivariate normal random variable of dimensionality if and only if all nondegenerate complex linear combinations of have a complex univariate normal distribution. The characteristic function of has been derived, and simpler forms of some theorems have been given using this characterization theorem without assuming that the variance-covariance matrix of the vector is Hermitian positive definite. Marginal distributions of have been given. In addition, a complex multivariate t-distribution has been defined and the density derived. A characterization of the complex multivariate t-distribution is given. A few possible uses of this distribution have been suggested.
Strong Decomposition of Random Variables
DEFF Research Database (Denmark)
Hoffmann-Jørgensen, Jørgen; Kagan, Abram M.; Pitt, Loren D.
2007-01-01
A random variable X is stongly decomposable if X=Y+Z where Y=Φ(X) and Z=X-Φ(X) are independent non-degenerated random variables (called the components). It is shown that at least one of the components is singular, and we derive a necessary and sufficient condition for strong decomposability...... of a discrete random variable....
Probability, random processes, and ergodic properties
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...
Contextuality is about identity of random variables
International Nuclear Information System (INIS)
Dzhafarov, Ehtibar N; Kujala, Janne V
2014-01-01
Contextual situations are those in which seemingly ‘the same’ random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is one and the same under different conditions leads to contradictions when one considers its joint distribution with other random variables (this is the essence of all Bell-type theorems). In our Contextuality-by-Default approach, instead of asking why or how the conditions force ‘one and the same’ random variable to change ‘its’ identity, any two random variables recorded under different conditions are considered different ‘automatically.’ They are never the same, nor are they jointly distributed, but one can always impose on them a joint distribution (probabilistic coupling). The special situations when there is a coupling in which these random variables are equal with probability 1 are considered noncontextual. Contextuality means that such couplings do not exist. We argue that the determination of the identity of random variables by conditions under which they are recorded is not a causal relationship and cannot violate laws of physics. (paper)
Contextuality in canonical systems of random variables
Dzhafarov, Ehtibar N.; Cervantes, Víctor H.; Kujala, Janne V.
2017-10-01
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables. This article is part of the themed issue `Second quantum revolution: foundational questions'.
Quantum interference of probabilities and hidden variable theories
International Nuclear Information System (INIS)
Srinivas, M.D.
1984-01-01
One of the fundamental contributions of Louis de Broglie, which does not get cited often, has been his analysis of the basic difference between the calculus of the probabilities as predicted by quantum theory and the usual calculus of probabilities - the one employed by most mathematicians, in its standard axiomatised version due to Kolmogorov. This paper is basically devoted to a discussion of the 'quantum interference of probabilities', discovered by de Broglie. In particular, it is shown that it is this feature of the quantum theoretic probabilities which leads to some serious constraints on the possible 'hidden-variable formulations' of quantum mechanics, including the celebrated theorem of Bell. (Auth.)
People's Intuitions about Randomness and Probability: An Empirical Study
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…
Separating the contributions of variability and parameter uncertainty in probability distributions
International Nuclear Information System (INIS)
Sankararaman, S.; Mahadevan, S.
2013-01-01
This paper proposes a computational methodology to quantify the individual contributions of variability and distribution parameter uncertainty to the overall uncertainty in a random variable. Even if the distribution type is assumed to be known, sparse or imprecise data leads to uncertainty about the distribution parameters. If uncertain distribution parameters are represented using probability distributions, then the random variable can be represented using a family of probability distributions. The family of distributions concept has been used to obtain qualitative, graphical inference of the contributions of natural variability and distribution parameter uncertainty. The proposed methodology provides quantitative estimates of the contributions of the two types of uncertainty. Using variance-based global sensitivity analysis, the contributions of variability and distribution parameter uncertainty to the overall uncertainty are computed. The proposed method is developed at two different levels; first, at the level of a variable whose distribution parameters are uncertain, and second, at the level of a model output whose inputs have uncertain distribution parameters
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.
Ordered random variables theory and applications
Shahbaz, Muhammad Qaiser; Hanif Shahbaz, Saman; Al-Zahrani, Bander M
2016-01-01
Ordered Random Variables have attracted several authors. The basic building block of Ordered Random Variables is Order Statistics which has several applications in extreme value theory and ordered estimation. The general model for ordered random variables, known as Generalized Order Statistics has been introduced relatively recently by Kamps (1995).
Problems in probability theory, mathematical statistics and theory of random functions
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
Non-equilibrium random matrix theory. Transition probabilities
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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.
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.
Return probabilities for the reflected random walk on N_0
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
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...
The extinction probability in systems randomly varying in time
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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.
Sharp Bounds by Probability-Generating Functions and Variable Drift
DEFF Research Database (Denmark)
Doerr, Benjamin; Fouz, Mahmoud; Witt, Carsten
2011-01-01
We introduce to the runtime analysis of evolutionary algorithms two powerful techniques: probability-generating functions and variable drift analysis. They are shown to provide a clean framework for proving sharp upper and lower bounds. As an application, we improve the results by Doerr et al....... (GECCO 2010) in several respects. First, the upper bound on the expected running time of the most successful quasirandom evolutionary algorithm for the OneMax function is improved from 1.28nln n to 0.982nlnn, which breaks the barrier of nln n posed by coupon-collector processes. Compared to the classical...
A random number generator for continuous random variables
Guerra, V. M.; Tapia, R. A.; Thompson, J. R.
1972-01-01
A FORTRAN 4 routine is given which may be used to generate random observations of a continuous real valued random variable. Normal distribution of F(x), X, E(akimas), and E(linear) is presented in tabular form.
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
Designing neural networks that process mean values of random variables
International Nuclear Information System (INIS)
Barber, Michael J.; Clark, John W.
2014-01-01
We develop a class of neural networks derived from probabilistic models posed in the form of Bayesian networks. Making biologically and technically plausible assumptions about the nature of the probabilistic models to be represented in the networks, we derive neural networks exhibiting standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the relevant random variables, that can pool multiple sources of evidence, and that deal appropriately with ambivalent, inconsistent, or contradictory evidence. - Highlights: • High-level neural computations are specified by Bayesian belief networks of random variables. • Probability densities of random variables are encoded in activities of populations of neurons. • Top-down algorithm generates specific neural network implementation of given computation. • Resulting “neural belief networks” process mean values of random variables. • Such networks pool multiple sources of evidence and deal properly with inconsistent evidence
Designing neural networks that process mean values of random variables
Energy Technology Data Exchange (ETDEWEB)
Barber, Michael J. [AIT Austrian Institute of Technology, Innovation Systems Department, 1220 Vienna (Austria); Clark, John W. [Department of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, MO 63130 (United States); Centro de Ciências Matemáticas, Universidade de Madeira, 9000-390 Funchal (Portugal)
2014-06-13
We develop a class of neural networks derived from probabilistic models posed in the form of Bayesian networks. Making biologically and technically plausible assumptions about the nature of the probabilistic models to be represented in the networks, we derive neural networks exhibiting standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the relevant random variables, that can pool multiple sources of evidence, and that deal appropriately with ambivalent, inconsistent, or contradictory evidence. - Highlights: • High-level neural computations are specified by Bayesian belief networks of random variables. • Probability densities of random variables are encoded in activities of populations of neurons. • Top-down algorithm generates specific neural network implementation of given computation. • Resulting “neural belief networks” process mean values of random variables. • Such networks pool multiple sources of evidence and deal properly with inconsistent evidence.
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Inverse probability weighting for covariate adjustment in randomized studies.
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.
Brus, D.J.; Gruijter, de J.J.
2003-01-01
In estimating spatial means of environmental variables of a region from data collected by convenience or purposive sampling, validity of the results can be ensured by collecting additional data through probability sampling. The precision of the pi estimator that uses the probability sample can be
Generating variable and random schedules of reinforcement using Microsoft Excel macros.
Bancroft, Stacie L; Bourret, Jason C
2008-01-01
Variable reinforcement schedules are used to arrange the availability of reinforcement following varying response ratios or intervals of time. Random reinforcement schedules are subtypes of variable reinforcement schedules that can be used to arrange the availability of reinforcement at a constant probability across number of responses or time. Generating schedule values for variable and random reinforcement schedules can be difficult. The present article describes the steps necessary to write macros in Microsoft Excel that will generate variable-ratio, variable-interval, variable-time, random-ratio, random-interval, and random-time reinforcement schedule values.
Improved Variable Window Kernel Estimates of Probability Densities
Hall, Peter; Hu, Tien Chung; Marron, J. S.
1995-01-01
Variable window width kernel density estimators, with the width varying proportionally to the square root of the density, have been thought to have superior asymptotic properties. The rate of convergence has been claimed to be as good as those typical for higher-order kernels, which makes the variable width estimators more attractive because no adjustment is needed to handle the negativity usually entailed by the latter. However, in a recent paper, Terrell and Scott show that these results ca...
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
Benford's law and continuous dependent random variables
Becker, Thealexa; Burt, David; Corcoran, Taylor C.; Greaves-Tunnell, Alec; Iafrate, Joseph R.; Jing, Joy; Miller, Steven J.; Porfilio, Jaclyn D.; Ronan, Ryan; Samranvedhya, Jirapat; Strauch, Frederick W.; Talbut, Blaine
2018-01-01
Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11% of the time, as one would expect if all digits were equally likely, but rather 30%. This phenomenon is known as Benford's Law. Analyzing which datasets adhere to Benford's Law and how quickly Benford behavior sets in are the two most important problems in the field. Most previous work studied systems of independent random variables, and relied on the independence in their analyses. Inspired by natural processes such as particle decay, we study the dependent random variables that emerge from models of decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow, and give several conjectures for other fragmentation processes. The main difficulty is that the resulting random variables are dependent. We handle this by using tools from Fourier analysis and irrationality exponents to obtain quantified convergence rates as well as introducing and developing techniques to measure and control the dependencies. The construction of these tools is one of the major motivations of this work, as our approach can be applied to many other dependent systems. As an example, we show that the n ! entries in the determinant expansions of n × n matrices with entries independently drawn from nice random variables converges to Benford's Law.
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.
Probability on graphs random processes on graphs and lattices
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.
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...
Maximal Inequalities for Dependent Random Variables
DEFF Research Database (Denmark)
Hoffmann-Jorgensen, Jorgen
2016-01-01
Maximal inequalities play a crucial role in many probabilistic limit theorem; for instance, the law of large numbers, the law of the iterated logarithm, the martingale limit theorem and the central limit theorem. Let X-1, X-2,... be random variables with partial sums S-k = X-1 + ... + X-k. Then a......Maximal inequalities play a crucial role in many probabilistic limit theorem; for instance, the law of large numbers, the law of the iterated logarithm, the martingale limit theorem and the central limit theorem. Let X-1, X-2,... be random variables with partial sums S-k = X-1 + ... + X......-k. Then a maximal inequality gives conditions ensuring that the maximal partial sum M-n = max(1) (...
Probability theory and mathematical statistics for engineers
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
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
Generation of correlated finite alphabet waveforms using gaussian random variables
Jardak, Seifallah
2014-09-01
Correlated waveforms have a number of applications in different fields, such as radar and communication. It is very easy to generate correlated waveforms using infinite alphabets, but for some of the applications, it is very challenging to use them in practice. Moreover, to generate infinite alphabet constant envelope correlated waveforms, the available research uses iterative algorithms, which are computationally very expensive. In this work, we propose simple novel methods to generate correlated waveforms using finite alphabet constant and non-constant-envelope symbols. To generate finite alphabet waveforms, the proposed method map the Gaussian random variables onto the phase-shift-keying, pulse-amplitude, and quadrature-amplitude modulation schemes. For such mapping, the probability-density-function of Gaussian random variables is divided into M regions, where M is the number of alphabets in the corresponding modulation scheme. By exploiting the mapping function, the relationship between the cross-correlation of Gaussian and finite alphabet symbols is derived. To generate equiprobable symbols, the area of each region is kept same. If the requirement is to have each symbol with its own unique probability, the proposed scheme allows us that as well. Although, the proposed scheme is general, the main focus of this paper is to generate finite alphabet waveforms for multiple-input multiple-output radar, where correlated waveforms are used to achieve desired beampatterns. © 2014 IEEE.
Selection for altruism through random drift in variable size populations
Directory of Open Access Journals (Sweden)
Houchmandzadeh Bahram
2012-05-01
Full Text Available Abstract Background Altruistic behavior is defined as helping others at a cost to oneself and a lowered fitness. The lower fitness implies that altruists should be selected against, which is in contradiction with their widespread presence is nature. Present models of selection for altruism (kin or multilevel show that altruistic behaviors can have ‘hidden’ advantages if the ‘common good’ produced by altruists is restricted to some related or unrelated groups. These models are mostly deterministic, or assume a frequency dependent fitness. Results Evolutionary dynamics is a competition between deterministic selection pressure and stochastic events due to random sampling from one generation to the next. We show here that an altruistic allele extending the carrying capacity of the habitat can win by increasing the random drift of “selfish” alleles. In other terms, the fixation probability of altruistic genes can be higher than those of a selfish ones, even though altruists have a smaller fitness. Moreover when populations are geographically structured, the altruists advantage can be highly amplified and the fixation probability of selfish genes can tend toward zero. The above results are obtained both by numerical and analytical calculations. Analytical results are obtained in the limit of large populations. Conclusions The theory we present does not involve kin or multilevel selection, but is based on the existence of random drift in variable size populations. The model is a generalization of the original Fisher-Wright and Moran models where the carrying capacity depends on the number of altruists.
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. .
Learning Binomial Probability Concepts with Simulation, Random Numbers and a Spreadsheet
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…
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.
Generating Variable and Random Schedules of Reinforcement Using Microsoft Excel Macros
Bancroft, Stacie L.; Bourret, Jason C.
2008-01-01
Variable reinforcement schedules are used to arrange the availability of reinforcement following varying response ratios or intervals of time. Random reinforcement schedules are subtypes of variable reinforcement schedules that can be used to arrange the availability of reinforcement at a constant probability across number of responses or time.…
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
Concepts of probability theory
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.
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.
Probability and stochastic modeling
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...
Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game.
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.
Effects of variability in probable maximum precipitation patterns on flood losses
Zischg, Andreas Paul; Felder, Guido; Weingartner, Rolf; Quinn, Niall; Coxon, Gemma; Neal, Jeffrey; Freer, Jim; Bates, Paul
2018-05-01
The assessment of the impacts of extreme floods is important for dealing with residual risk, particularly for critical infrastructure management and for insurance purposes. Thus, modelling of the probable maximum flood (PMF) from probable maximum precipitation (PMP) by coupling hydrological and hydraulic models has gained interest in recent years. Herein, we examine whether variability in precipitation patterns exceeds or is below selected uncertainty factors in flood loss estimation and if the flood losses within a river basin are related to the probable maximum discharge at the basin outlet. We developed a model experiment with an ensemble of probable maximum precipitation scenarios created by Monte Carlo simulations. For each rainfall pattern, we computed the flood losses with a model chain and benchmarked the effects of variability in rainfall distribution with other model uncertainties. The results show that flood losses vary considerably within the river basin and depend on the timing and superimposition of the flood peaks from the basin's sub-catchments. In addition to the flood hazard component, the other components of flood risk, exposure, and vulnerability contribute remarkably to the overall variability. This leads to the conclusion that the estimation of the probable maximum expectable flood losses in a river basin should not be based exclusively on the PMF. Consequently, the basin-specific sensitivities to different precipitation patterns and the spatial organization of the settlements within the river basin need to be considered in the analyses of probable maximum flood losses.
Influences of variables on ship collision probability in a Bayesian belief network model
International Nuclear Information System (INIS)
Hänninen, Maria; Kujala, Pentti
2012-01-01
The influences of the variables in a Bayesian belief network model for estimating the role of human factors on ship collision probability in the Gulf of Finland are studied for discovering the variables with the largest influences and for examining the validity of the network. The change in the so-called causation probability is examined while observing each state of the network variables and by utilizing sensitivity and mutual information analyses. Changing course in an encounter situation is the most influential variable in the model, followed by variables such as the Officer of the Watch's action, situation assessment, danger detection, personal condition and incapacitation. The least influential variables are the other distractions on bridge, the bridge view, maintenance routines and the officer's fatigue. In general, the methods are found to agree on the order of the model variables although some disagreements arise due to slightly dissimilar approaches to the concept of variable influence. The relative values and the ranking of variables based on the values are discovered to be more valuable than the actual numerical values themselves. Although the most influential variables seem to be plausible, there are some discrepancies between the indicated influences in the model and literature. Thus, improvements are suggested to the network.
Hidden measurements, hidden variables and the volume representation of transition probabilities
Oliynyk, Todd A.
2005-01-01
We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions $n \\geq 3$. We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and th...
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.
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...
Introduction to probability with R
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
Introduction to probability with Mathematica
Hastings, Kevin J
2009-01-01
Discrete ProbabilityThe Cast of Characters Properties of Probability Simulation Random SamplingConditional ProbabilityIndependenceDiscrete DistributionsDiscrete Random Variables, Distributions, and ExpectationsBernoulli and Binomial Random VariablesGeometric and Negative Binomial Random Variables Poisson DistributionJoint, Marginal, and Conditional Distributions More on ExpectationContinuous ProbabilityFrom the Finite to the (Very) Infinite Continuous Random Variables and DistributionsContinuous ExpectationContinuous DistributionsThe Normal Distribution Bivariate Normal DistributionNew Random Variables from OldOrder Statistics Gamma DistributionsChi-Square, Student's t, and F-DistributionsTransformations of Normal Random VariablesAsymptotic TheoryStrong and Weak Laws of Large Numbers Central Limit TheoremStochastic Processes and ApplicationsMarkov ChainsPoisson Processes QueuesBrownian MotionFinancial MathematicsAppendixIntroduction to Mathematica Glossary of Mathematica Commands for Probability Short Answers...
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.)
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…
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)
On the product and ratio of Bessel random variables
Directory of Open Access Journals (Sweden)
Saralees Nadarajah
2005-01-01
Full Text Available The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.
Hoeffding’s Inequality for Sums of Dependent Random Variables
Czech Academy of Sciences Publication Activity Database
Pelekis, Christos; Ramon, J.
2017-01-01
Roč. 14, č. 6 (2017), č. článku 243. ISSN 1660-5446 Institutional support: RVO:67985807 Keywords : dependent random variables * Hoeffding’s inequality * k-wise independent random variables * martingale differences Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.868, year: 2016
New Results On the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza
2015-01-01
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented.
New Results on the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza
2016-01-06
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented [1].
New Results on the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza; Alouini, Mohamed-Slim
2016-01-01
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented [1].
PaCAL: A Python Package for Arithmetic Computations with Random Variables
Directory of Open Access Journals (Sweden)
Marcin Korze?
2014-05-01
Full Text Available In this paper we present PaCAL, a Python package for arithmetical computations on random variables. The package is capable of performing the four arithmetic operations: addition, subtraction, multiplication and division, as well as computing many standard functions of random variables. Summary statistics, random number generation, plots, and histograms of the resulting distributions can easily be obtained and distribution parameter ?tting is also available. The operations are performed numerically and their results interpolated allowing for arbitrary arithmetic operations on random variables following practically any probability distribution encountered in practice. The package is easy to use, as operations on random variables are performed just as they are on standard Python variables. Independence of random variables is, by default, assumed on each step but some computations on dependent random variables are also possible. We demonstrate on several examples that the results are very accurate, often close to machine precision. Practical applications include statistics, physical measurements or estimation of error distributions in scienti?c computations.
Statistics for Ratios of Rayleigh, Rician, Nakagami-m, and Weibull Distributed Random Variables
Directory of Open Access Journals (Sweden)
Dragana Č. Pavlović
2013-01-01
Full Text Available The distributions of ratios of random variables are of interest in many areas of the sciences. In this brief paper, we present the joint probability density function (PDF and PDF of maximum of ratios μ1=R1/r1 and μ2=R2/r2 for the cases where R1, R2, r1, and r2 are Rayleigh, Rician, Nakagami-m, and Weibull distributed random variables. Random variables R1 and R2, as well as random variables r1 and r2, are correlated. Ascertaining on the suitability of the Weibull distribution to describe fading in both indoor and outdoor environments, special attention is dedicated to the case of Weibull random variables. For this case, analytical expressions for the joint PDF, PDF of maximum, PDF of minimum, and product moments of arbitrary number of ratios μi=Ri/ri, i=1,…,L are obtained. Random variables in numerator, Ri, as well as random variables in denominator, ri, are exponentially correlated. To the best of the authors' knowledge, analytical expressions for the PDF of minimum and product moments of {μi}i=1L are novel in the open technical literature. The proposed mathematical analysis is complemented by various numerical results. An application of presented theoretical results is illustrated with respect to performance assessment of wireless systems.
Probability distribution for the Gaussian curvature of the zero level surface of a random function
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.
Analysis of blocking probability for OFDM-based variable bandwidth optical network
Gong, Lei; Zhang, Jie; Zhao, Yongli; Lin, Xuefeng; Wu, Yuyao; Gu, Wanyi
2011-12-01
Orthogonal Frequency Division Multiplexing (OFDM) has recently been proposed as a modulation technique. For optical networks, because of its good spectral efficiency, flexibility, and tolerance to impairments, optical OFDM is much more flexible compared to traditional WDM systems, enabling elastic bandwidth transmissions, and optical networking is the future trend of development. In OFDM-based optical network the research of blocking rate has very important significance for network assessment. Current research for WDM network is basically based on a fixed bandwidth, in order to accommodate the future business and the fast-changing development of optical network, our study is based on variable bandwidth OFDM-based optical networks. We apply the mathematical analysis and theoretical derivation, based on the existing theory and algorithms, research blocking probability of the variable bandwidth of optical network, and then we will build a model for blocking probability.
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.
Probability of failure prediction for step-stress fatigue under sine or random stress
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.
An extended car-following model considering random safety distance with different probabilities
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.
On the fluctuations of sums of independent random variables.
Feller, W
1969-07-01
If X(1), X(2),... are independent random variables with zero expectation and finite variances, the cumulative sums S(n) are, on the average, of the order of magnitude S(n), where S(n) (2) = E(S(n) (2)). The occasional maxima of the ratios S(n)/S(n) are surprisingly large and the problem is to estimate the extent of their probable fluctuations.Specifically, let S(n) (*) = (S(n) - b(n))/a(n), where {a(n)} and {b(n)}, two numerical sequences. For any interval I, denote by p(I) the probability that the event S(n) (*) epsilon I occurs for infinitely many n. Under mild conditions on {a(n)} and {b(n)}, it is shown that p(I) equals 0 or 1 according as a certain series converges or diverges. To obtain the upper limit of S(n)/a(n), one has to set b(n) = +/- epsilon a(n), but finer results are obtained with smaller b(n). No assumptions concerning the under-lying distributions are made; the criteria explain structurally which features of {X(n)} affect the fluctuations, but for concrete results something about P{S(n)>a(n)} must be known. For example, a complete solution is possible when the X(n) are normal, replacing the classical law of the iterated logarithm. Further concrete estimates may be obtained by combining the new criteria with some recently developed limit theorems.
Polynomial chaos expansion with random and fuzzy variables
Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.
2016-06-01
A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.
Exponential Inequalities for Positively Associated Random Variables and Applications
Directory of Open Access Journals (Sweden)
Yang Shanchao
2008-01-01
Full Text Available Abstract We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005. By one of the inequalities, we obtain the convergence rate for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under the Hartman-Wintner law of the iterated logarithm and improves the convergence rate derived by Oliveira (2005 for the above case.
[Biometric bases: basic concepts of probability calculation].
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.
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.
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
Couso, Inés; Sánchez, Luciano
2014-01-01
This short book provides a unified view of the history and theory of random sets and fuzzy random variables, with special emphasis on its use for representing higher-order non-statistical uncertainty about statistical experiments. The authors lay bare the existence of two streams of works using the same mathematical ground, but differing form their use of sets, according to whether they represent objects of interest naturally taking the form of sets, or imprecise knowledge about such objects. Random (fuzzy) sets can be used in many fields ranging from mathematical morphology, economics, artificial intelligence, information processing and statistics per se, especially in areas where the outcomes of random experiments cannot be observed with full precision. This book also emphasizes the link between random sets and fuzzy sets with some techniques related to the theory of imprecise probabilities. This small book is intended for graduate and doctoral students in mathematics or engineering, but also provides an i...
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.
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Hideki Katagiri
2017-10-01
Full Text Available This paper considers linear programming problems (LPPs where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables. New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.
Method for Evaluation of Outage Probability on Random Access Channel in Mobile Communication Systems
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).
Compound Poisson Approximations for Sums of Random Variables
Serfozo, Richard F.
1986-01-01
We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of...
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.
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
Randomized trial of intermittent or continuous amnioinfusion for variable decelerations.
Rinehart, B K; Terrone, D A; Barrow, J H; Isler, C M; Barrilleaux, P S; Roberts, W E
2000-10-01
To determine whether continuous or intermittent bolus amnioinfusion is more effective in relieving variable decelerations. Patients with repetitive variable decelerations were randomized to an intermittent bolus or continuous amnioinfusion. The intermittent bolus infusion group received boluses of 500 mL of normal saline, each over 30 minutes, with boluses repeated if variable decelerations recurred. The continuous infusion group received a bolus infusion of 500 mL of normal saline over 30 minutes and then 3 mL per minute until delivery occurred. The ability of the amnioinfusion to abolish variable decelerations was analyzed, as were maternal demographic and pregnancy outcome variables. Power analysis indicated that 64 patients would be required. Thirty-five patients were randomized to intermittent infusion and 30 to continuous infusion. There were no differences between groups in terms of maternal demographics, gestational age, delivery mode, neonatal outcome, median time to resolution of variable decelerations, or the number of times variable decelerations recurred. The median volume infused in the intermittent infusion group (500 mL) was significantly less than that in the continuous infusion group (905 mL, P =.003). Intermittent bolus amnioinfusion is as effective as continuous infusion in relieving variable decelerations in labor. Further investigation is necessary to determine whether either of these techniques is associated with increased occurrence of rare complications such as cord prolapse or uterine rupture.
How a dependent's variable non-randomness affects taper equation ...
African Journals Online (AJOL)
In order to apply the least squares method in regression analysis, the values of the dependent variable Y should be random. In an example of regression analysis linear and nonlinear taper equations, which estimate the diameter of the tree dhi at any height of the tree hi, were compared. For each tree the diameter at the ...
An infinite-dimensional weak KAM theory via random variables
Gomes, Diogo A.; Nurbekyan, Levon
2016-01-01
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
An infinite-dimensional weak KAM theory via random variables
Gomes, Diogo A.
2016-08-31
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables\\' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
Extensions of von Neumann's method for generating random variables
International Nuclear Information System (INIS)
Monahan, J.F.
1979-01-01
Von Neumann's method of generating random variables with the exponential distribution and Forsythe's method for obtaining distributions with densities of the form e/sup -G//sup( x/) are generalized to apply to certain power series representations. The flexibility of the power series methods is illustrated by algorithms for the Cauchy and geometric distributions
Yampolsky, M; Salafia, C M; Shlakhter, O
2013-06-01
While the mean shape of human placenta is round with centrally inserted umbilical cord, significant deviations from this ideal are fairly common, and may be clinically meaningful. Traditionally, they are explained by trophotropism. We have proposed a hypothesis explaining typical variations in placental shape by randomly determined fluctuations in the growth process of the vascular tree. It has been recently reported that umbilical cord displacement in a birth cohort has a log-normal probability distribution, which indicates that the displacement between an initial point of origin and the centroid of the mature shape is a result of accumulation of random fluctuations of the dynamic growth of the placenta. To confirm this, we investigate statistical distributions of other features of placental morphology. In a cohort of 1023 births at term digital photographs of placentas were recorded at delivery. Excluding cases with velamentous cord insertion, or missing clinical data left 1001 (97.8%) for which placental surface morphology features were measured. Best-fit statistical distributions for them were obtained using EasyFit. The best-fit distributions of umbilical cord displacement, placental disk diameter, area, perimeter, and maximal radius calculated from the cord insertion point are of heavy-tailed type, similar in shape to log-normal distributions. This is consistent with a stochastic origin of deviations of placental shape from normal. Deviations of placental shape descriptors from average have heavy-tailed distributions similar in shape to log-normal. This evidence points away from trophotropism, and towards a spontaneous stochastic evolution of the variants of placental surface shape features. Copyright © 2013 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
A. Stankovic
2012-12-01
Full Text Available The distributions of random variables are of interest in many areas of science. In this paper, ascertaining on the importance of multi-hop transmission in contemporary wireless communications systems operating over fading channels in the presence of cochannel interference, the probability density functions (PDFs of minimum of arbitrary number of ratios of Rayleigh, Rician, Nakagami-m, Weibull and α-µ random variables are derived. These expressions can be used to study the outage probability as an important multi-hop system performance measure. Various numerical results complement the proposed mathematical analysis.
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...
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).
A review of instrumental variable estimators for Mendelian randomization.
Burgess, Stephen; Small, Dylan S; Thompson, Simon G
2017-10-01
Instrumental variable analysis is an approach for obtaining causal inferences on the effect of an exposure (risk factor) on an outcome from observational data. It has gained in popularity over the past decade with the use of genetic variants as instrumental variables, known as Mendelian randomization. An instrumental variable is associated with the exposure, but not associated with any confounder of the exposure-outcome association, nor is there any causal pathway from the instrumental variable to the outcome other than via the exposure. Under the assumption that a single instrumental variable or a set of instrumental variables for the exposure is available, the causal effect of the exposure on the outcome can be estimated. There are several methods available for instrumental variable estimation; we consider the ratio method, two-stage methods, likelihood-based methods, and semi-parametric methods. Techniques for obtaining statistical inferences and confidence intervals are presented. The statistical properties of estimates from these methods are compared, and practical advice is given about choosing a suitable analysis method. In particular, bias and coverage properties of estimators are considered, especially with weak instruments. Settings particularly relevant to Mendelian randomization are prioritized in the paper, notably the scenario of a continuous exposure and a continuous or binary outcome.
Probability elements of the mathematical theory
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.
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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.
Characteristics of quantum open systems: free random variables approach
International Nuclear Information System (INIS)
Gudowska-Nowak, E.; Papp, G.; Brickmann, J.
1998-01-01
Random Matrix Theory provides an interesting tool for modelling a number of phenomena where noises (fluctuations) play a prominent role. Various applications range from the theory of mesoscopic systems in nuclear and atomic physics to biophysical models, like Hopfield-type models of neural networks and protein folding. Random Matrix Theory is also used to study dissipative systems with broken time-reversal invariance providing a setup for analysis of dynamic processes in condensed, disordered media. In the paper we use the Random Matrix Theory (RMT) within the formalism of Free Random Variables (alias Blue's functions), which allows to characterize spectral properties of non-Hermitean ''Hamiltonians''. The relevance of using the Blue's function method is discussed in connection with application of non-Hermitean operators in various problems of physical chemistry. (author)
International Nuclear Information System (INIS)
Bakosi, Jozsef; Ristorcelli, Raymond J.
2010-01-01
Probability density function (PDF) methods are extended to variable-density pressure-gradient-driven turbulence. We apply the new method to compute the joint PDF of density and velocity in a non-premixed binary mixture of different-density molecularly mixing fluids under gravity. The full time-evolution of the joint PDF is captured in the highly non-equilibrium flow: starting from a quiescent state, transitioning to fully developed turbulence and finally dissipated by molecular diffusion. High-Atwood-number effects (as distinguished from the Boussinesq case) are accounted for: both hydrodynamic turbulence and material mixing are treated at arbitrary density ratios, with the specific volume, mass flux and all their correlations in closed form. An extension of the generalized Langevin model, originally developed for the Lagrangian fluid particle velocity in constant-density shear-driven turbulence, is constructed for variable-density pressure-gradient-driven flows. The persistent small-scale anisotropy, a fundamentally 'non-Kolmogorovian' feature of flows under external acceleration forces, is captured by a tensorial diffusion term based on the external body force. The material mixing model for the fluid density, an active scalar, is developed based on the beta distribution. The beta-PDF is shown to be capable of capturing the mixing asymmetry and that it can accurately represent the density through transition, in fully developed turbulence and in the decay process. The joint model for hydrodynamics and active material mixing yields a time-accurate evolution of the turbulent kinetic energy and Reynolds stress anisotropy without resorting to gradient diffusion hypotheses, and represents the mixing state by the density PDF itself, eliminating the need for dubious mixing measures. Direct numerical simulations of the homogeneous Rayleigh-Taylor instability are used for model validation.
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)
Ironside, Kirsten E.; Mattson, David J.; Choate, David; Stoner, David; Arundel, Terry; Hansen, Jered R.; Theimer, Tad; Holton, Brandon; Jansen, Brian; Sexton, Joseph O.; Longshore, Kathleen M.; Edwards, Thomas C.; Peters, Michael
2017-01-01
Studies using global positioning system (GPS) telemetry rarely result in 100% fix success rates (FSR), which may bias datasets because data loss is systematic rather than a random process. Previous spatially explicit models developed to correct for sampling bias have been limited to small study areas, a small range of data loss, or were study-area specific. We modeled environmental effects on FSR from desert to alpine biomes, investigated the full range of potential data loss (0–100% FSR), and evaluated whether animal body position can contribute to lower FSR because of changes in antenna orientation based on GPS detection rates for 4 focal species: cougars (Puma concolor), desert bighorn sheep (Ovis canadensis nelsoni), Rocky Mountain elk (Cervus elaphus nelsoni), and mule deer (Odocoileus hemionus). Terrain exposure and height of over story vegetation were the most influential factors affecting FSR. Model evaluation showed a strong correlation (0.88) between observed and predicted FSR and no significant differences between predicted and observed FSRs using 2 independent validation datasets. We found that cougars and canyon-dwelling bighorn sheep may select for environmental features that influence their detectability by GPS technology, mule deer may select against these features, and elk appear to be nonselective. We observed temporal patterns in missed fixes only for cougars. We provide a model for cougars, predicting fix success by time of day that is likely due to circadian changes in collar orientation and selection of daybed sites. We also provide a model predicting the probability of GPS fix acquisitions given environmental conditions, which had a strong relationship (r 2 = 0.82) with deployed collar FSRs across species.
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
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid
2016-01-13
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Variable Selection in Time Series Forecasting Using Random Forests
Directory of Open Access Journals (Sweden)
Hristos Tyralis
2017-10-01
Full Text Available Time series forecasting using machine learning algorithms has gained popularity recently. Random forest is a machine learning algorithm implemented in time series forecasting; however, most of its forecasting properties have remained unexplored. Here we focus on assessing the performance of random forests in one-step forecasting using two large datasets of short time series with the aim to suggest an optimal set of predictor variables. Furthermore, we compare its performance to benchmarking methods. The first dataset is composed by 16,000 simulated time series from a variety of Autoregressive Fractionally Integrated Moving Average (ARFIMA models. The second dataset consists of 135 mean annual temperature time series. The highest predictive performance of RF is observed when using a low number of recent lagged predictor variables. This outcome could be useful in relevant future applications, with the prospect to achieve higher predictive accuracy.
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid; Alouini, Mohamed-Slim; Jardak, Seifallah
2016-01-01
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Problems of variance reduction in the simulation of random variables
International Nuclear Information System (INIS)
Lessi, O.
1987-01-01
The definition of the uniform linear generator is given and some of the mostly used tests to evaluate the uniformity and the independence of the obtained determinations are listed. The problem of calculating, through simulation, some moment W of a random variable function is taken into account. The Monte Carlo method enables the moment W to be estimated and the estimator variance to be obtained. Some techniques for the construction of other estimators of W with a reduced variance are introduced
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…
Haller, Bernhard; Ulm, Kurt
2018-02-20
To individualize treatment decisions based on patient characteristics, identification of an interaction between a biomarker and treatment is necessary. Often such potential interactions are analysed using data from randomized clinical trials intended for comparison of two treatments. Tests of interactions are often lacking statistical power and we investigated if and how a consideration of further prognostic variables can improve power and decrease the bias of estimated biomarker-treatment interactions in randomized clinical trials with time-to-event outcomes. A simulation study was performed to assess how prognostic factors affect the estimate of the biomarker-treatment interaction for a time-to-event outcome, when different approaches, like ignoring other prognostic factors, including all available covariates or using variable selection strategies, are applied. Different scenarios regarding the proportion of censored observations, the correlation structure between the covariate of interest and further potential prognostic variables, and the strength of the interaction were considered. The simulation study revealed that in a regression model for estimating a biomarker-treatment interaction, the probability of detecting a biomarker-treatment interaction can be increased by including prognostic variables that are associated with the outcome, and that the interaction estimate is biased when relevant prognostic variables are not considered. However, the probability of a false-positive finding increases if too many potential predictors are included or if variable selection is performed inadequately. We recommend undertaking an adequate literature search before data analysis to derive information about potential prognostic variables and to gain power for detecting true interaction effects and pre-specifying analyses to avoid selective reporting and increased false-positive rates.
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.
International Nuclear Information System (INIS)
Todinov, M.T.
2004-01-01
A new reliability measure is proposed and equations are derived which determine the probability of existence of a specified set of minimum gaps between random variables following a homogeneous Poisson process in a finite interval. Using the derived equations, a method is proposed for specifying the upper bound of the random variables' number density which guarantees that the probability of clustering of two or more random variables in a finite interval remains below a maximum acceptable level. It is demonstrated that even for moderate number densities the probability of clustering is substantial and should not be neglected in reliability calculations. In the important special case where the random variables are failure times, models have been proposed for determining the upper bound of the hazard rate which guarantees a set of minimum failure-free operating intervals before the random failures, with a specified probability. A model has also been proposed for determining the upper bound of the hazard rate which guarantees a minimum availability target. Using the models proposed, a new strategy, models and reliability tools have been developed for setting quantitative reliability requirements which consist of determining the intersection of the hazard rate envelopes (hazard rate upper bounds) which deliver a minimum failure-free operating period before random failures, a risk of premature failure below a maximum acceptable level and a minimum required availability. It is demonstrated that setting reliability requirements solely based on an availability target does not necessarily mean a low risk of premature failure. Even at a high availability level, the probability of premature failure can be substantial. For industries characterised by a high cost of failure, the reliability requirements should involve a hazard rate envelope limiting the risk of failure below a maximum acceptable level
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
Introduction to probability theory with contemporary applications
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
Effects of population variability on the accuracy of detection probability estimates
DEFF Research Database (Denmark)
Ordonez Gloria, Alejandro
2011-01-01
Observing a constant fraction of the population over time, locations, or species is virtually impossible. Hence, quantifying this proportion (i.e. detection probability) is an important task in quantitative population ecology. In this study we determined, via computer simulations, the ef- fect of...
Analysis of Secret Key Randomness Exploiting the Radio Channel Variability
Directory of Open Access Journals (Sweden)
Taghrid Mazloum
2015-01-01
Full Text Available A few years ago, physical layer based techniques have started to be considered as a way to improve security in wireless communications. A well known problem is the management of ciphering keys, both regarding the generation and distribution of these keys. A way to alleviate such difficulties is to use a common source of randomness for the legitimate terminals, not accessible to an eavesdropper. This is the case of the fading propagation channel, when exact or approximate reciprocity applies. Although this principle has been known for long, not so many works have evaluated the effect of radio channel properties in practical environments on the degree of randomness of the generated keys. To this end, we here investigate indoor radio channel measurements in different environments and settings at either 2.4625 GHz or 5.4 GHz band, of particular interest for WIFI related standards. Key bits are extracted by quantizing the complex channel coefficients and their randomness is evaluated using the NIST test suite. We then look at the impact of the carrier frequency, the channel variability in the space, time, and frequency degrees of freedom used to construct a long secret key, in relation to the nature of the radio environment such as the LOS/NLOS character.
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.
Extended q -Gaussian and q -exponential distributions from gamma random variables
Budini, Adrián A.
2015-05-01
The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.
Fox, Eric W; Hill, Ryan A; Leibowitz, Scott G; Olsen, Anthony R; Thornbrugh, Darren J; Weber, Marc H
2017-07-01
Random forest (RF) modeling has emerged as an important statistical learning method in ecology due to its exceptional predictive performance. However, for large and complex ecological data sets, there is limited guidance on variable selection methods for RF modeling. Typically, either a preselected set of predictor variables are used or stepwise procedures are employed which iteratively remove variables according to their importance measures. This paper investigates the application of variable selection methods to RF models for predicting probable biological stream condition. Our motivating data set consists of the good/poor condition of n = 1365 stream survey sites from the 2008/2009 National Rivers and Stream Assessment, and a large set (p = 212) of landscape features from the StreamCat data set as potential predictors. We compare two types of RF models: a full variable set model with all 212 predictors and a reduced variable set model selected using a backward elimination approach. We assess model accuracy using RF's internal out-of-bag estimate, and a cross-validation procedure with validation folds external to the variable selection process. We also assess the stability of the spatial predictions generated by the RF models to changes in the number of predictors and argue that model selection needs to consider both accuracy and stability. The results suggest that RF modeling is robust to the inclusion of many variables of moderate to low importance. We found no substantial improvement in cross-validated accuracy as a result of variable reduction. Moreover, the backward elimination procedure tended to select too few variables and exhibited numerous issues such as upwardly biased out-of-bag accuracy estimates and instabilities in the spatial predictions. We use simulations to further support and generalize results from the analysis of real data. A main purpose of this work is to elucidate issues of model selection bias and instability to ecologists interested in
Pritikin, Joshua N; Brick, Timothy R; Neale, Michael C
2018-04-01
A novel method for the maximum likelihood estimation of structural equation models (SEM) with both ordinal and continuous indicators is introduced using a flexible multivariate probit model for the ordinal indicators. A full information approach ensures unbiased estimates for data missing at random. Exceeding the capability of prior methods, up to 13 ordinal variables can be included before integration time increases beyond 1 s per row. The method relies on the axiom of conditional probability to split apart the distribution of continuous and ordinal variables. Due to the symmetry of the axiom, two similar methods are available. A simulation study provides evidence that the two similar approaches offer equal accuracy. A further simulation is used to develop a heuristic to automatically select the most computationally efficient approach. Joint ordinal continuous SEM is implemented in OpenMx, free and open-source software.
Generating Correlated QPSK Waveforms By Exploiting Real Gaussian Random Variables
Jardak, Seifallah
2012-11-01
The design of waveforms with specified auto- and cross-correlation properties has a number of applications in multiple-input multiple-output (MIMO) radar, one of them is the desired transmit beampattern design. In this work, an algorithm is proposed to generate quadrature phase shift- keying (QPSK) waveforms with required cross-correlation properties using real Gaussian random-variables (RV’s). This work can be considered as the extension of what was presented in [1] to generate BPSK waveforms. This work will be extended for the generation of correlated higher-order phase shift-keying (PSK) and quadrature amplitude modulation (QAM) schemes that can better approximate the desired beampattern.
Generating Correlated QPSK Waveforms By Exploiting Real Gaussian Random Variables
Jardak, Seifallah; Ahmed, Sajid; Alouini, Mohamed-Slim
2012-01-01
The design of waveforms with specified auto- and cross-correlation properties has a number of applications in multiple-input multiple-output (MIMO) radar, one of them is the desired transmit beampattern design. In this work, an algorithm is proposed to generate quadrature phase shift- keying (QPSK) waveforms with required cross-correlation properties using real Gaussian random-variables (RV’s). This work can be considered as the extension of what was presented in [1] to generate BPSK waveforms. This work will be extended for the generation of correlated higher-order phase shift-keying (PSK) and quadrature amplitude modulation (QAM) schemes that can better approximate the desired beampattern.
Spectral shaping of a randomized PWM DC-DC converter using maximum entropy probability distributions
CSIR Research Space (South Africa)
Dove, Albert
2017-01-01
Full Text Available maintaining constraints in a DC-DC converter is investigated. A probability distribution whose aim is to ensure maximal harmonic spreading and yet mainaint constraints is presented. The PDFs are determined from a direct application of the method of Maximum...
Making Heads or Tails of Probability: An Experiment with Random Generators
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…
DEFF Research Database (Denmark)
Falk, Anne Katrine Vinther; Gryning, Sven-Erik
1997-01-01
In this model for atmospheric dispersion particles are simulated by the Langevin Equation, which is a stochastic differential equation. It uses the probability density function (PDF) of the vertical velocity fluctuations as input. The PDF is constructed as an expansion after Hermite polynomials...
International Nuclear Information System (INIS)
Alili, Smail; Rugh, Hans Henrik
2008-01-01
We consider a supercritical branching process in time-dependent environment ξ. We assume that the offspring distributions depend regularly (C k or real-analytically) on real parameters λ. We show that the extinction probability q λ (ξ), given the environment ξ 'inherits' this regularity whenever the offspring distributions satisfy a condition of contraction-type. Our proof makes use of the Poincaré metric on the complex unit disc and a real-analytic implicit function theorem
Wang, Kezhi; Wang, Tian; Chen, Yunfei; Alouini, Mohamed-Slim
2014-01-01
The sum of ratios of products of independent 2642 2642α-μ random variables (RVs) is approximated by using the Generalized Gamma ratio approximation (GGRA) with Gamma ratio approximation (GRA) as a special case. The proposed approximation is used to calculate the outage probability of the equal gain combining (EGC) or maximum ratio combining (MRC) receivers for wireless multihop relaying or multiple scattering systems considering interferences. Numerical results show that the newly derived approximation works very well verified by the simulation, while GRA has a slightly worse performance than GGRA when outage probability is below 0.1 but with a more simplified form.
Wang, Kezhi
2014-09-01
The sum of ratios of products of independent 2642 2642α-μ random variables (RVs) is approximated by using the Generalized Gamma ratio approximation (GGRA) with Gamma ratio approximation (GRA) as a special case. The proposed approximation is used to calculate the outage probability of the equal gain combining (EGC) or maximum ratio combining (MRC) receivers for wireless multihop relaying or multiple scattering systems considering interferences. Numerical results show that the newly derived approximation works very well verified by the simulation, while GRA has a slightly worse performance than GGRA when outage probability is below 0.1 but with a more simplified form.
Wang, Fuming; Hunsche, Stefan; Anunciado, Roy; Corradi, Antonio; Tien, Hung Yu; Tang, Peng; Wei, Junwei; Wang, Yongjun; Fang, Wei; Wong, Patrick; van Oosten, Anton; van Ingen Schenau, Koen; Slachter, Bram
2018-03-01
We present an experimental study of pattern variability and defectivity, based on a large data set with more than 112 million SEM measurements from an HMI high-throughput e-beam tool. The test case is a 10nm node SRAM via array patterned with a DUV immersion LELE process, where we see a variation in mean size and litho sensitivities between different unique via patterns that leads to a seemingly qualitative differences in defectivity. The large available data volume enables further analysis to reliably distinguish global and local CDU variations, including a breakdown into local systematics and stochastics. A closer inspection of the tail end of the distributions and estimation of defect probabilities concludes that there is a common defect mechanism and defect threshold despite the observed differences of specific pattern characteristics. We expect that the analysis methodology can be applied for defect probability modeling as well as general process qualification in the future.
Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?
Directory of Open Access Journals (Sweden)
Andrei Khrennikov
2008-03-01
Full Text Available The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space. These investigations were started hundred of years ago by J. Boole (who invented Boolean algebras. The complete solution of the problem was obtained by Soviet mathematician Vorobjev in 60th. Surprisingly probabilists and statisticians obtained inequalities for probabilities and correlations among which one can find the famous BellÃ¢Â€Â™s inequality and its generalizations. Such inequalities appeared simply as constraints for probabilistic compatibility. In this framework one can not see a priori any link to such problems as nonlocality and Ã¢Â€Âœdeath of realityÃ¢Â€Â which are typically linked to BellÃ¢Â€Â™s type inequalities in physical literature. We analyze the difference between positions of mathematicians and quantum physicists. In particular, we found that one of the most reasonable explanations of probabilistic incompatibility is mixing in BellÃ¢Â€Â™s type inequalities statistical data from a number of experiments performed under different experimental contexts.
Automatic Probabilistic Program Verification through Random Variable Abstraction
Directory of Open Access Journals (Sweden)
Damián Barsotti
2010-06-01
Full Text Available The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any denumerable state space using iterative backwards fixed point calculation in the general framework of abstract interpretation. In order to accomplish this task we present the technique of random variable abstraction (RVA and we also postulate a sufficient condition to achieve exact fixed point computation in the abstract domain. The feasibility of our approach is shown with two examples, one obtaining the expected running time of a probabilistic program, and the other the expected gain of a gambling strategy. Our method works on general guarded probabilistic and nondeterministic transition systems instead of plain pGCL programs, allowing us to easily model a wide range of systems including distributed ones and unstructured programs. We present the operational and weakest precondition semantics for this programs and prove its equivalence.
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
Gonzalo, David Cárdenas
2016-09-01
Stress at work and in the family is a very common issue in our society that generates many health-related problems. During recent years, numerous studies have sought to define the term stress, raising many contradictions that various authors have studied. Other authors have attempted to establish some criteria, in subjective and not very quantitative ways, in an attempt to reduce and even to eliminate stressors and their effects at work and in the family context. The purpose of this study was to quantify so-called cushioning variables, such as control, social support, home/work life conciliation, and even sports and leisure activities, with the purpose of, as much as possible, reducing the negative effects of stress, which seriously affects the health of workers. The study employs data from the Fifth European Working Conditions Survey, in which nearly 44,000 interviewees from 34 countries in the European Union participated. We constructed a probabilistic model based on a Bayesian network, using variables from both the workplace and the family, the aforementioned cushioning variables, as well as the variable stress. If action is taken on the above variables, then the probabilities of suffering high levels of stress may be reduced. Such action may improve the quality of life of people at work and in the family.
Directory of Open Access Journals (Sweden)
David Cárdenas Gonzalo
2016-09-01
Full Text Available Stress at work and in the family is a very common issue in our society that generates many health-related problems. During recent years, numerous studies have sought to define the term stress, raising many contradictions that various authors have studied. Other authors have attempted to establish some criteria, in subjective and not very quantitative ways, in an attempt to reduce and even to eliminate stressors and their effects at work and in the family context. The purpose of this study was to quantify so-called cushioning variables, such as control, social support, home/work life conciliation, and even sports and leisure activities, with the purpose of, as much as possible, reducing the negative effects of stress, which seriously affects the health of workers. The study employs data from the Fifth European Working Conditions Survey, in which nearly 44,000 interviewees from 34 countries in the European Union participated. We constructed a probabilistic model based on a Bayesian network, using variables from both the workplace and the family, the aforementioned cushioning variables, as well as the variable stress. If action is taken on the above variables, then the probabilities of suffering high levels of stress may be reduced. Such action may improve the quality of life of people at work and in the family.
Directory of Open Access Journals (Sweden)
Paul B. Slater
2015-01-01
Full Text Available Previously, a formula, incorporating a 5F4 hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments ρPTnρk/ρk of 4×4 density-matrices (ρ and their partial transposes (|ρPT|, was applied with k=0 to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities (k=1,2,… are found—via a high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (α=1/2, (standard two-qubit (α=1, and two-quater[nionic]bit (α=2 cases. We deduce rather simple companion (rebit, qubit, quaterbit, … formulas that successfully reproduce the rational values assumed for general k. These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula.
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.
Cannon, Alex J.
2018-01-01
Most bias correction algorithms used in climatology, for example quantile mapping, are applied to univariate time series. They neglect the dependence between different variables. Those that are multivariate often correct only limited measures of joint dependence, such as Pearson or Spearman rank correlation. Here, an image processing technique designed to transfer colour information from one image to another—the N-dimensional probability density function transform—is adapted for use as a multivariate bias correction algorithm (MBCn) for climate model projections/predictions of multiple climate variables. MBCn is a multivariate generalization of quantile mapping that transfers all aspects of an observed continuous multivariate distribution to the corresponding multivariate distribution of variables from a climate model. When applied to climate model projections, changes in quantiles of each variable between the historical and projection period are also preserved. The MBCn algorithm is demonstrated on three case studies. First, the method is applied to an image processing example with characteristics that mimic a climate projection problem. Second, MBCn is used to correct a suite of 3-hourly surface meteorological variables from the Canadian Centre for Climate Modelling and Analysis Regional Climate Model (CanRCM4) across a North American domain. Components of the Canadian Forest Fire Weather Index (FWI) System, a complicated set of multivariate indices that characterizes the risk of wildfire, are then calculated and verified against observed values. Third, MBCn is used to correct biases in the spatial dependence structure of CanRCM4 precipitation fields. Results are compared against a univariate quantile mapping algorithm, which neglects the dependence between variables, and two multivariate bias correction algorithms, each of which corrects a different form of inter-variable correlation structure. MBCn outperforms these alternatives, often by a large margin
On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables
Al-Naffouri, Tareq Y.
2015-10-30
© 2015 IEEE. In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-meansquare (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables.We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.
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
Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables
Directory of Open Access Journals (Sweden)
S. K. Barik
2012-01-01
Full Text Available Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure.
Keyser, Alisa; Westerling, Anthony LeRoy
2017-05-01
A long history of fire suppression in the western United States has significantly changed forest structure and ecological function, leading to increasingly uncharacteristic fires in terms of size and severity. Prior analyses of fire severity in California forests showed that time since last fire and fire weather conditions predicted fire severity very well, while a larger regional analysis showed that topography and climate were important predictors of high severity fire. There has not yet been a large-scale study that incorporates topography, vegetation and fire-year climate to determine regional scale high severity fire occurrence. We developed models to predict the probability of high severity fire occurrence for the western US. We predict high severity fire occurrence with some accuracy, and identify the relative importance of predictor classes in determining the probability of high severity fire. The inclusion of both vegetation and fire-year climate predictors was critical for model skill in identifying fires with high fractional fire severity. The inclusion of fire-year climate variables allows this model to forecast inter-annual variability in areas at future risk of high severity fire, beyond what slower-changing fuel conditions alone can accomplish. This allows for more targeted land management, including resource allocation for fuels reduction treatments to decrease the risk of high severity fire.
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.
On Generating Optimal Signal Probabilities for Random Tests: A Genetic Approach
Directory of Open Access Journals (Sweden)
M. Srinivas
1996-01-01
Full Text Available Genetic Algorithms are robust search and optimization techniques. A Genetic Algorithm based approach for determining the optimal input distributions for generating random test vectors is proposed in the paper. A cost function based on the COP testability measure for determining the efficacy of the input distributions is discussed. A brief overview of Genetic Algorithms (GAs and the specific details of our implementation are described. Experimental results based on ISCAS-85 benchmark circuits are presented. The performance of our GAbased approach is compared with previous results. While the GA generates more efficient input distributions than the previous methods which are based on gradient descent search, the overheads of the GA in computing the input distributions are larger.
Directory of Open Access Journals (Sweden)
Wahner-Roedler Dietlind
2008-10-01
Full Text Available Abstract Background Breast cancer risk education enables women make informed decisions regarding their options for screening and risk reduction. We aimed to determine whether patient education regarding breast cancer risk using a bar graph, with or without a frequency format diagram, improved the accuracy of risk perception. Methods We conducted a prospective, randomized trial among women at increased risk for breast cancer. The main outcome measurement was patients' estimation of their breast cancer risk before and after education with a bar graph (BG group or bar graph plus a frequency format diagram (BG+FF group, which was assessed by previsit and postvisit questionnaires. Results Of 150 women in the study, 74 were assigned to the BG group and 76 to the BG+FF group. Overall, 72% of women overestimated their risk of breast cancer. The improvement in accuracy of risk perception from the previsit to the postvisit questionnaire (BG group, 19% to 61%; BG+FF group, 13% to 67% was not significantly different between the 2 groups (P = .10. Among women who inaccurately perceived very high risk (≥ 50% risk, inaccurate risk perception decreased significantly in the BG+FF group (22% to 3% compared with the BG group (28% to 19% (P = .004. Conclusion Breast cancer risk communication using a bar graph plus a frequency format diagram can improve the short-term accuracy of risk perception among women perceiving inaccurately high risk.
The Random Walk of Cars and Their Collision Probabilities with Planets
Directory of Open Access Journals (Sweden)
Hanno Rein
2018-05-01
Full Text Available On 6 February 2018, SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster’s orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant.
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.
Some limit theorems for negatively associated random variables
Indian Academy of Sciences (India)
random sampling without replacement, and (i) joint distribution of ranks. ... wide applications in multivariate statistical analysis and system reliability, the ... strong law of large numbers for negatively associated sequences under the case where.
Rossi, R.; Hendrix, E.M.T.
2014-01-01
We discuss the problem of computing optimal linearisation parameters for the first order loss function of a family of arbitrarily distributed random variable. We demonstrate that, in contrast to the problem in which parameters must be determined for the loss function of a single random variable,
Strong Laws of Large Numbers for Arrays of Rowwise NA and LNQD Random Variables
Directory of Open Access Journals (Sweden)
Jiangfeng Wang
2011-01-01
Full Text Available Some strong laws of large numbers and strong convergence properties for arrays of rowwise negatively associated and linearly negative quadrant dependent random variables are obtained. The results obtained not only generalize the result of Hu and Taylor to negatively associated and linearly negative quadrant dependent random variables, but also improve it.
ESEARCH OF THE LAW OF DISTRIBUTION OF THE RANDOM VARIABLE OF THE COMPRESSION
Directory of Open Access Journals (Sweden)
I. Sarayeva
2011-01-01
Full Text Available At research of diagnosing the process of modern automobile engines by means of methods of mathematical statistics the experimental data of the random variable of compression are analysed and it is proved that the random variable of compression has the form of the normal law of distribution.
Directory of Open Access Journals (Sweden)
Bogdan Gheorghe Munteanu
2013-01-01
Full Text Available Using the stochastic approximations, in this paper it was studiedthe convergence in distribution of the fractional parts of the sum of random variables to the truncated exponential distribution with parameter lambda. This fact is feasible by means of the Fourier-Stieltjes sequence (FSS of the random variable.
Raw and Central Moments of Binomial Random Variables via Stirling Numbers
Griffiths, Martin
2013-01-01
We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…
Directory of Open Access Journals (Sweden)
Yang Yang
2013-01-01
Full Text Available We investigate the tailed asymptotic behavior of the randomly weighted sums with increments with convolution-equivalent distributions. Our obtained result can be directly applied to a discrete-time insurance risk model with insurance and financial risks and derive the asymptotics for the finite-time probability of the above risk model.
International Nuclear Information System (INIS)
Millwater, Harry; Singh, Gulshan; Cortina, Miguel
2012-01-01
There are many methods to identify the important variable out of a set of random variables, i.e., “inter-variable” importance; however, to date there are no comparable methods to identify the “region” of importance within a random variable, i.e., “intra-variable” importance. Knowledge of the critical region of an input random variable (tail, near-tail, and central region) can provide valuable information towards characterizing, understanding, and improving a model through additional modeling or testing. As a result, an intra-variable probabilistic sensitivity method was developed and demonstrated for independent random variables that computes the partial derivative of a probabilistic response with respect to a localized perturbation in the CDF values of each random variable. These sensitivities are then normalized in absolute value with respect to the largest sensitivity within a distribution to indicate the region of importance. The methodology is implemented using the Score Function kernel-based method such that existing samples can be used to compute sensitivities for negligible cost. Numerical examples demonstrate the accuracy of the method through comparisons with finite difference and numerical integration quadrature estimates. - Highlights: ► Probabilistic sensitivity methodology. ► Determines the “region” of importance within random variables such as left tail, near tail, center, right tail, etc. ► Uses the Score Function approach to reuse the samples, hence, negligible cost. ► No restrictions on the random variable types or limit states.
Stochastic Optimal Estimation with Fuzzy Random Variables and Fuzzy Kalman Filtering
Institute of Scientific and Technical Information of China (English)
FENG Yu-hu
2005-01-01
By constructing a mean-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts: a real-valued non-random recurrence equation and the standard Kalman filtering.
Bias in random forest variable importance measures: Illustrations, sources and a solution
Directory of Open Access Journals (Sweden)
Hothorn Torsten
2007-01-01
Full Text Available Abstract Background Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories. Results Simulation studies are presented illustrating that, when random forest variable importance measures are used with data of varying types, the results are misleading because suboptimal predictor variables may be artificially preferred in variable selection. The two mechanisms underlying this deficiency are biased variable selection in the individual classification trees used to build the random forest on one hand, and effects induced by bootstrap sampling with replacement on the other hand. Conclusion We propose to employ an alternative implementation of random forests, that provides unbiased variable selection in the individual classification trees. When this method is applied using subsampling without replacement, the resulting variable importance measures can be used reliably for variable selection even in situations where the potential predictor variables vary in their scale of measurement or their number of categories. The usage of both random forest algorithms and their variable importance measures in the R system for statistical computing is illustrated and
Concentrated Hitting Times of Randomized Search Heuristics with Variable Drift
DEFF Research Database (Denmark)
Lehre, Per Kristian; Witt, Carsten
2014-01-01
Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target...
Indian Academy of Sciences (India)
An axiomatic development of such a model is given below. It is also shown ... teacher needs to decide which students deserve to be promoted to the next class - it is not ... whether an unborn child would be a boy or a girl, the total number of births in a ..... that the outcome of the previous trials has no influence on the next trial.
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.
Fast analytical method for the addition of random variables
International Nuclear Information System (INIS)
Senna, V.; Milidiu, R.L.; Fleming, P.V.; Salles, M.R.; Oliveria, L.F.S.
1983-01-01
Using the minimal cut sets representation of a fault tree, a new approach to the method of moments is proposed in order to estimate confidence bounds to the top event probability. The method utilizes two or three moments either to fit a distribution (the normal and lognormal families) or to evaluate bounds from standard inequalities (e.g. Markov, Tchebycheff, etc.) Examples indicate that the results obtained by the log-normal family are in good agreement with those obtained by Monte Carlo simulation
On mean square displacement behaviors of anomalous diffusions with variable and random orders
International Nuclear Information System (INIS)
Sun Hongguang; Chen Wen; Sheng Hu; Chen Yangquan
2010-01-01
Mean square displacement (MSD) is used to characterize anomalous diffusion. Recently, models of anomalous diffusion with variable-order and random-order were proposed, but no MSD analysis has been given so far. The purpose of this Letter is to offer a concise derivation of MSD functions for the variable-order model and the random-order model. Numerical results are presented to illustrate the analytical results. In addition, we show how to establish a variable-random-order model for a given MSD function which has clear application potentials.
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.
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.
Hung, Tran Loc; Giang, Le Truong
2016-01-01
Using the Stein-Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.
Random forest (RF) modeling has emerged as an important statistical learning method in ecology due to its exceptional predictive performance. However, for large and complex ecological datasets there is limited guidance on variable selection methods for RF modeling. Typically, e...
Zero Distribution of System with Unknown Random Variables Case Study: Avoiding Collision Path
Directory of Open Access Journals (Sweden)
Parman Setyamartana
2014-07-01
Full Text Available This paper presents the stochastic analysis of finding the feasible trajectories of robotics arm motion at obstacle surrounding. Unknown variables are coefficients of polynomials joint angle so that the collision-free motion is achieved. ãk is matrix consisting of these unknown feasible polynomial coefficients. The pattern of feasible polynomial in the obstacle environment shows as random. This paper proposes to model the pattern of this randomness values using random polynomial with unknown variables as coefficients. The behavior of the system will be obtained from zero distribution as the characteristic of such random polynomial. Results show that the pattern of random polynomial of avoiding collision can be constructed from zero distribution. Zero distribution is like building block of the system with obstacles as uncertainty factor. By scale factor k, which has range, the random coefficient pattern can be predicted.
The quotient of normal random variables and application to asset price fat tails
Caginalp, Carey; Caginalp, Gunduz
2018-06-01
The quotient of random variables with normal distributions is examined and proven to have power law decay, with density f(x) ≃f0x-2, with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability densities for each of the four quadrants given by the signs of the numerator and denominator for arbitrary correlation ρ ∈ [ - 1 , 1) . For ρ = - 1 we obtain a particularly simple closed form solution for all x ∈ R. The results are applied to a basic issue in economics and finance, namely the density of relative price changes. Classical finance stipulates a normal distribution of relative price changes, though empirical studies suggest a power law at the tail end. By considering the supply and demand in a basic price change model, we prove that the relative price change has density that decays with an x-2 power law. Various parameter limits are established.
An introduction to probability and stochastic processes
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.
Output variability caused by random seeds in a multi-agent transport simulation model
DEFF Research Database (Denmark)
Paulsen, Mads; Rasmussen, Thomas Kjær; Nielsen, Otto Anker
2018-01-01
Dynamic transport simulators are intended to support decision makers in transport-related issues, and as such it is valuable that the random variability of their outputs is as small as possible. In this study we analyse the output variability caused by random seeds of a multi-agent transport...... simulator (MATSim) when applied to a case study of Santiago de Chile. Results based on 100 different random seeds shows that the relative accuracies of estimated link loads tend to increase with link load, but that relative errors of up to 10 % do occur even for links with large volumes. Although...
A Variable Impacts Measurement in Random Forest for Mobile Cloud Computing
Directory of Open Access Journals (Sweden)
Jae-Hee Hur
2017-01-01
Full Text Available Recently, the importance of mobile cloud computing has increased. Mobile devices can collect personal data from various sensors within a shorter period of time and sensor-based data consists of valuable information from users. Advanced computation power and data analysis technology based on cloud computing provide an opportunity to classify massive sensor data into given labels. Random forest algorithm is known as black box model which is hardly able to interpret the hidden process inside. In this paper, we propose a method that analyzes the variable impact in random forest algorithm to clarify which variable affects classification accuracy the most. We apply Shapley Value with random forest to analyze the variable impact. Under the assumption that every variable cooperates as players in the cooperative game situation, Shapley Value fairly distributes the payoff of variables. Our proposed method calculates the relative contributions of the variables within its classification process. In this paper, we analyze the influence of variables and list the priority of variables that affect classification accuracy result. Our proposed method proves its suitability for data interpretation in black box model like a random forest so that the algorithm is applicable in mobile cloud computing environment.
Partial summations of stationary sequences of non-Gaussian random variables
DEFF Research Database (Denmark)
Mohr, Gunnar; Ditlevsen, Ove Dalager
1996-01-01
The distribution of the sum of a finite number of identically distributed random variables is in many cases easily determined given that the variables are independent. The moments of any order of the sum can always be expressed by the moments of the single term without computational problems...... of convergence of the distribution of a sum (or an integral) of mutually dependent random variables to the Gaussian distribution. The paper is closely related to the work in Ditlevsen el al. [Ditlevsen, O., Mohr, G. & Hoffmeyer, P. Integration of non-Gaussian fields. Prob. Engng Mech 11 (1996) 15-23](2)....... lognormal variables or polynomials of standard Gaussian variables. The dependency structure is induced by specifying the autocorrelation structure of the sequence of standard Gaussian variables. Particularly useful polynomials are the Winterstein approximations that distributionally fit with non...
A large-scale study of the random variability of a coding sequence: a study on the CFTR gene.
Modiano, Guido; Bombieri, Cristina; Ciminelli, Bianca Maria; Belpinati, Francesca; Giorgi, Silvia; Georges, Marie des; Scotet, Virginie; Pompei, Fiorenza; Ciccacci, Cinzia; Guittard, Caroline; Audrézet, Marie Pierre; Begnini, Angela; Toepfer, Michael; Macek, Milan; Ferec, Claude; Claustres, Mireille; Pignatti, Pier Franco
2005-02-01
Coding single nucleotide substitutions (cSNSs) have been studied on hundreds of genes using small samples (n(g) approximately 100-150 genes). In the present investigation, a large random European population sample (average n(g) approximately 1500) was studied for a single gene, the CFTR (Cystic Fibrosis Transmembrane conductance Regulator). The nonsynonymous (NS) substitutions exhibited, in accordance with previous reports, a mean probability of being polymorphic (q > 0.005), much lower than that of the synonymous (S) substitutions, but they showed a similar rate of subpolymorphic (q < 0.005) variability. This indicates that, in autosomal genes that may have harmful recessive alleles (nonduplicated genes with important functions), genetic drift overwhelms selection in the subpolymorphic range of variability, making disadvantageous alleles behave as neutral. These results imply that the majority of the subpolymorphic nonsynonymous alleles of these genes are selectively negative or even pathogenic.
International Nuclear Information System (INIS)
Tierney, M.S.
1990-12-01
A five-step procedure was used in the 1990 performance simulations to construct probability distributions of the uncertain variables appearing in the mathematical models used to simulate the Waste Isolation Pilot Plant's (WIPP's) performance. This procedure provides a consistent approach to the construction of probability distributions in cases where empirical data concerning a variable are sparse or absent and minimizes the amount of spurious information that is often introduced into a distribution by assumptions of nonspecialists. The procedure gives first priority to the professional judgment of subject-matter experts and emphasizes the use of site-specific empirical data for the construction of the probability distributions when such data are available. In the absence of sufficient empirical data, the procedure employs the Maximum Entropy Formalism and the subject-matter experts' subjective estimates of the parameters of the distribution to construct a distribution that can be used in a performance simulation. (author)
Energy Technology Data Exchange (ETDEWEB)
Tierney, M S
1990-12-15
A five-step procedure was used in the 1990 performance simulations to construct probability distributions of the uncertain variables appearing in the mathematical models used to simulate the Waste Isolation Pilot Plant's (WIPP's) performance. This procedure provides a consistent approach to the construction of probability distributions in cases where empirical data concerning a variable are sparse or absent and minimizes the amount of spurious information that is often introduced into a distribution by assumptions of nonspecialists. The procedure gives first priority to the professional judgment of subject-matter experts and emphasizes the use of site-specific empirical data for the construction of the probability distributions when such data are available. In the absence of sufficient empirical data, the procedure employs the Maximum Entropy Formalism and the subject-matter experts' subjective estimates of the parameters of the distribution to construct a distribution that can be used in a performance simulation. (author)
DEFF Research Database (Denmark)
Yura, Harold; Hanson, Steen Grüner
2012-01-01
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...
A Particle Swarm Optimization Algorithm with Variable Random Functions and Mutation
Institute of Scientific and Technical Information of China (English)
ZHOU Xiao-Jun; YANG Chun-Hua; GUI Wei-Hua; DONG Tian-Xue
2014-01-01
The convergence analysis of the standard particle swarm optimization (PSO) has shown that the changing of random functions, personal best and group best has the potential to improve the performance of the PSO. In this paper, a novel strategy with variable random functions and polynomial mutation is introduced into the PSO, which is called particle swarm optimization algorithm with variable random functions and mutation (PSO-RM). Random functions are adjusted with the density of the population so as to manipulate the weight of cognition part and social part. Mutation is executed on both personal best particle and group best particle to explore new areas. Experiment results have demonstrated the effectiveness of the strategy.
Flouri, Marilena; Zhai, Shuyan; Mathew, Thomas; Bebu, Ionut
2017-05-01
This paper addresses the problem of deriving one-sided tolerance limits and two-sided tolerance intervals for a ratio of two random variables that follow a bivariate normal distribution, or a lognormal/normal distribution. The methodology that is developed uses nonparametric tolerance limits based on a parametric bootstrap sample, coupled with a bootstrap calibration in order to improve accuracy. The methodology is also adopted for computing confidence limits for the median of the ratio random variable. Numerical results are reported to demonstrate the accuracy of the proposed approach. The methodology is illustrated using examples where ratio random variables are of interest: an example on the radioactivity count in reverse transcriptase assays and an example from the area of cost-effectiveness analysis in health economics. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
DEFF Research Database (Denmark)
Kessler, Timo Christian; Nilsson, Bertel; Klint, Knud Erik
2010-01-01
(TPROGS) of alternating geological facies. The second method, multiple-point statistics, uses training images to estimate the conditional probability of sand-lenses at a certain location. Both methods respect field observations such as local stratigraphy, however, only the multiple-point statistics can...... of sand-lenses in clay till. Sand-lenses mainly account for horizontal transport and are prioritised in this study. Based on field observations, the distribution has been modeled using two different geostatistical approaches. One method uses a Markov chain model calculating the transition probabilities...
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.
Higher order moments of a sum of random variables: remarks and applications.
Directory of Open Access Journals (Sweden)
Luisa Tibiletti
1996-02-01
Full Text Available The moments of a sum of random variables depend on both the pure moments of each random addendum and on the addendum mixed moments. In this note we introduce a simple measure to evaluate the relative impedance to attach to the latter. Once the pure moments are fixed, the functional relation between the random addenda leading to the extreme values is also provided. Applications to Finance, Decision Theory and Actuarial Sciences are also suggested.
Stable Graphical Model Estimation with Random Forests for Discrete, Continuous, and Mixed Variables
Fellinghauer, Bernd; Bühlmann, Peter; Ryffel, Martin; von Rhein, Michael; Reinhardt, Jan D.
2011-01-01
A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among mixed-type, i.e. continuous and discrete, variables. The number of edges is a tuning parameter in any graphical model estimator and there is no obvious number that constitutes a good choice. Stability Selection helps choosing this parameter with respect to...
Directory of Open Access Journals (Sweden)
Correchel Vladia
2005-01-01
Full Text Available The precision of the 137Cs fallout redistribution technique for the evaluation of soil erosion rates is strongly dependent on the quality of an average inventory taken at a representative reference site. The knowledge of the sources and of the degree of variation of the 137Cs fallout spatial distribution plays an important role on its use. Four reference sites were selected in the South-Central region of Brazil which were characterized in terms of soil chemical, physical and mineralogical aspects as well as the spatial variability of 137Cs inventories. Some important differences in the patterns of 137Cs depth distribution in the soil profiles of the different sites were found. They are probably associated to chemical, physical, mineralogical and biological differences of the soils but many questions still remain open for future investigation, mainly those regarding the adsorption and dynamics of the 137Cs ions in soil profiles under tropical conditions. The random spatial variability (inside each reference site was higher than the systematic spatial variability (between reference sites but their causes were not clearly identified as possible consequences of chemical, physical, mineralogical variability, and/or precipitation.
International Nuclear Information System (INIS)
Lehua Pan; G.S. Bodvarsson
2001-01-01
Multiscale features of transport processes in fractured porous media make numerical modeling a difficult task, both in conceptualization and computation. Modeling the mass transfer through the fracture-matrix interface is one of the critical issues in the simulation of transport in a fractured porous medium. Because conventional dual-continuum-based numerical methods are unable to capture the transient features of the diffusion depth into the matrix (unless they assume a passive matrix medium), such methods will overestimate the transport of tracers through the fractures, especially for the cases with large fracture spacing, resulting in artificial early breakthroughs. We have developed a new method for calculating the particle-transfer probability that can capture the transient features of diffusion depth into the matrix within the framework of the dual-continuum random-walk particle method (RWPM) by introducing a new concept of activity range of a particle within the matrix. Unlike the multiple-continuum approach, the new dual-continuum RWPM does not require using additional grid blocks to represent the matrix. It does not assume a passive matrix medium and can be applied to the cases where global water flow exists in both continua. The new method has been verified against analytical solutions for transport in the fracture-matrix systems with various fracture spacing. The calculations of the breakthrough curves of radionuclides from a potential repository to the water table in Yucca Mountain demonstrate the effectiveness of the new method for simulating 3-D, mountain-scale transport in a heterogeneous, fractured porous medium under variably saturated conditions
Nam, Sungsik
2010-11-01
Order statistics find applications in various areas of communications and signal processing. In this paper, we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables (RVs). With the proposed approach, we can systematically derive the joint statistics of any partial sums of ordered statistics, in terms of the moment generating function (MGF) and the probability density function (PDF). Our MGF-based approach applies not only when all the K ordered RVs are involved but also when only the Ks(Ks < K) best RVs are considered. In addition, we present the closed-form expressions for the exponential RV special case. These results apply to the performance analysis of various wireless communication systems over fading channels. © 2006 IEEE.
Statistical Analysis for Multisite Trials Using Instrumental Variables with Random Coefficients
Raudenbush, Stephen W.; Reardon, Sean F.; Nomi, Takako
2012-01-01
Multisite trials can clarify the average impact of a new program and the heterogeneity of impacts across sites. Unfortunately, in many applications, compliance with treatment assignment is imperfect. For these applications, we propose an instrumental variable (IV) model with person-specific and site-specific random coefficients. Site-specific IV…
van der Zwan, J.E.; de Vente, W.; Huizink, A.C.; Bögels, S.M.; de Bruin, E.I.
2015-01-01
In contemporary western societies stress is highly prevalent, therefore the need for stress-reducing methods is great. This randomized controlled trial compared the efficacy of self-help physical activity (PA), mindfulness meditation (MM), and heart rate variability biofeedback (HRV-BF) in reducing
Sums and Products of Jointly Distributed Random Variables: A Simplified Approach
Stein, Sheldon H.
2005-01-01
Three basic theorems concerning expected values and variances of sums and products of random variables play an important role in mathematical statistics and its applications in education, business, the social sciences, and the natural sciences. A solid understanding of these theorems requires that students be familiar with the proofs of these…
Central limit theorem for the Banach-valued weakly dependent random variables
International Nuclear Information System (INIS)
Dmitrovskij, V.A.; Ermakov, S.V.; Ostrovskij, E.I.
1983-01-01
The central limit theorem (CLT) for the Banach-valued weakly dependent random variables is proved. In proving CLT convergence of finite-measured (i.e. cylindrical) distributions is established. A weak compactness of the family of measures generated by a certain sequence is confirmed. The continuity of the limiting field is checked
Non-uniform approximations for sums of discrete m-dependent random variables
Vellaisamy, P.; Cekanavicius, V.
2013-01-01
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow easily from our results. The results are then exemplified by the approximation of Poisson binomial distribution, 2-runs and $m$-dependent $(k_1,k_2)$-events.
J.L. Geluk (Jaap); L. Peng (Liang); C.G. de Vries (Casper)
1999-01-01
textabstractThe paper characterizes first and second order tail behavior of convolutions of i.i.d. heavy tailed random variables with support on the real line. The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model.
Directory of Open Access Journals (Sweden)
Thandi Kapwata
2016-11-01
Full Text Available Malaria is an environmentally driven disease. In order to quantify the spatial variability of malaria transmission, it is imperative to understand the interactions between environmental variables and malaria epidemiology at a micro-geographic level using a novel statistical approach. The random forest (RF statistical learning method, a relatively new variable-importance ranking method, measures the variable importance of potentially influential parameters through the percent increase of the mean squared error. As this value increases, so does the relative importance of the associated variable. The principal aim of this study was to create predictive malaria maps generated using the selected variables based on the RF algorithm in the Ehlanzeni District of Mpumalanga Province, South Africa. From the seven environmental variables used [temperature, lag temperature, rainfall, lag rainfall, humidity, altitude, and the normalized difference vegetation index (NDVI], altitude was identified as the most influential predictor variable due its high selection frequency. It was selected as the top predictor for 4 out of 12 months of the year, followed by NDVI, temperature and lag rainfall, which were each selected twice. The combination of climatic variables that produced the highest prediction accuracy was altitude, NDVI, and temperature. This suggests that these three variables have high predictive capabilities in relation to malaria transmission. Furthermore, it is anticipated that the predictive maps generated from predictions made by the RF algorithm could be used to monitor the progression of malaria and assist in intervention and prevention efforts with respect to malaria.
DEFF Research Database (Denmark)
Krøigård, Thomas; Gaist, David; Otto, Marit
2014-01-01
SUMMARY: The reproducibility of variables commonly included in studies of peripheral nerve conduction in healthy individuals has not previously been analyzed using a random effects regression model. We examined the temporal changes and variability of standard nerve conduction measures in the leg...... reexamined after 2 and 26 weeks. There was no change in the variables except for a minor decrease in sural nerve sensory action potential amplitude and a minor increase in tibial nerve minimal F-wave latency. Reproducibility was best for peroneal nerve distal motor latency and motor conduction velocity......, sural nerve sensory conduction velocity, and tibial nerve minimal F-wave latency. Between-subject variability was greater than within-subject variability. Sample sizes ranging from 21 to 128 would be required to show changes twice the magnitude of the spontaneous changes observed in this study. Nerve...
1981-05-01
Education, 10 (2), A45-A49 (1976). 48. Rain&, R. K., and C. L. Kaul (Koul), "Some inequalities involving the Fox’s H- function," Proceedings of the Indian...1973). 51. Srivastava , A., and K. C. Gupta, "On certain recurrence rela- tions," Mathematische Nachrichten, 46, 13- 23 (1970), 49, 187- 197 (1971). 52...34 Vilnana Parishad Anusandhan Patrika, 10, 205- 217 (1967). 69. Gupta, K. C., and A. Srivastava , "On finite expansions for the H- function," Indian Journal
SOERP, Statistics and 2. Order Error Propagation for Function of Random Variables
International Nuclear Information System (INIS)
Cox, N. D.; Miller, C. F.
1985-01-01
1 - Description of problem or function: SOERP computes second-order error propagation equations for the first four moments of a function of independently distributed random variables. SOERP was written for a rigorous second-order error propagation of any function which may be expanded in a multivariable Taylor series, the input variables being independently distributed. The required input consists of numbers directly related to the partial derivatives of the function, evaluated at the nominal values of the input variables and the central moments of the input variables from the second through the eighth. 2 - Method of solution: The development of equations for computing the propagation of errors begins by expressing the function of random variables in a multivariable Taylor series expansion. The Taylor series expansion is then truncated, and statistical operations are applied to the series in order to obtain equations for the moments (about the origin) of the distribution of the computed value. If the Taylor series is truncated after powers of two, the procedure produces second-order error propagation equations. 3 - Restrictions on the complexity of the problem: The maximum number of component variables allowed is 30. The IBM version will only process one set of input data per run
Introduction to probability and statistics for science, engineering, and finance
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
Oracle Efficient Variable Selection in Random and Fixed Effects Panel Data Models
DEFF Research Database (Denmark)
Kock, Anders Bredahl
This paper generalizes the results for the Bridge estimator of Huang et al. (2008) to linear random and fixed effects panel data models which are allowed to grow in both dimensions. In particular we show that the Bridge estimator is oracle efficient. It can correctly distinguish between relevant...... and irrelevant variables and the asymptotic distribution of the estimators of the coefficients of the relevant variables is the same as if only these had been included in the model, i.e. as if an oracle had revealed the true model prior to estimation. In the case of more explanatory variables than observations......, we prove that the Marginal Bridge estimator can asymptotically correctly distinguish between relevant and irrelevant explanatory variables. We do this without restricting the dependence between covariates and without assuming sub Gaussianity of the error terms thereby generalizing the results...
Wang, Kezhi
2015-06-01
Exact results for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of ratios of products (SRP) and the sum of products (SP) of independent α-μ random variables (RVs) are derived. They are in the form of 1-D integral based on the existing works on the products and ratios of α-μ RVs. In the derivation, generalized Gamma (GG) ratio approximation (GGRA) is proposed to approximate SRP. Gamma ratio approximation (GRA) is proposed to approximate SRP and the ratio of sums of products (RSP). GG approximation (GGA) and Gamma approximation (GA) are used to approximate SP. The proposed results of the SRP can be used to calculate the outage probability (OP) for wireless multihop relaying systems or multiple scattering channels with interference. The proposed results of the SP can be used to calculate the OP for these systems without interference. In addition, the proposed approximate result of the RSP can be used to calculate the OP of the signal-To-interference ratio (SIR) in a multiple scattering system with interference. © 1967-2012 IEEE.
Wang, Kezhi; Wang, Tian; Chen, Yunfei; Alouini, Mohamed-Slim
2015-01-01
Exact results for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of ratios of products (SRP) and the sum of products (SP) of independent α-μ random variables (RVs) are derived. They are in the form of 1-D integral based on the existing works on the products and ratios of α-μ RVs. In the derivation, generalized Gamma (GG) ratio approximation (GGRA) is proposed to approximate SRP. Gamma ratio approximation (GRA) is proposed to approximate SRP and the ratio of sums of products (RSP). GG approximation (GGA) and Gamma approximation (GA) are used to approximate SP. The proposed results of the SRP can be used to calculate the outage probability (OP) for wireless multihop relaying systems or multiple scattering channels with interference. The proposed results of the SP can be used to calculate the OP for these systems without interference. In addition, the proposed approximate result of the RSP can be used to calculate the OP of the signal-To-interference ratio (SIR) in a multiple scattering system with interference. © 1967-2012 IEEE.
Using Random Forests to Select Optimal Input Variables for Short-Term Wind Speed Forecasting Models
Directory of Open Access Journals (Sweden)
Hui Wang
2017-10-01
Full Text Available Achieving relatively high-accuracy short-term wind speed forecasting estimates is a precondition for the construction and grid-connected operation of wind power forecasting systems for wind farms. Currently, most research is focused on the structure of forecasting models and does not consider the selection of input variables, which can have significant impacts on forecasting performance. This paper presents an input variable selection method for wind speed forecasting models. The candidate input variables for various leading periods are selected and random forests (RF is employed to evaluate the importance of all variable as features. The feature subset with the best evaluation performance is selected as the optimal feature set. Then, kernel-based extreme learning machine is constructed to evaluate the performance of input variables selection based on RF. The results of the case study show that by removing the uncorrelated and redundant features, RF effectively extracts the most strongly correlated set of features from the candidate input variables. By finding the optimal feature combination to represent the original information, RF simplifies the structure of the wind speed forecasting model, shortens the training time required, and substantially improves the model’s accuracy and generalization ability, demonstrating that the input variables selected by RF are effective.
Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family
Directory of Open Access Journals (Sweden)
M. M. Mohie EL-Din
2015-01-01
Full Text Available For a system, which is observed at time t, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.
Directory of Open Access Journals (Sweden)
Qunying Wu
2017-05-01
Full Text Available Abstract In this paper, we study the equivalent conditions of complete moment convergence for sequences of identically distributed extended negatively dependent random variables. As a result, we extend and generalize some results of complete moment convergence obtained by Chow (Bull. Inst. Math. Acad. Sin. 16:177-201, 1988 and Li and Spătaru (J. Theor. Probab. 18:933-947, 2005 from the i.i.d. case to extended negatively dependent sequences.
An edgeworth expansion for a sum of M-Dependent random variables
Directory of Open Access Journals (Sweden)
Wan Soo Rhee
1985-01-01
Full Text Available Given a sequence X1,X2,…,Xn of m-dependent random variables with moments of order 3+α (0<α≦1, we give an Edgeworth expansion of the distribution of Sσ−1(S=X1+X2+…+Xn, σ2=ES2 under the assumption that E[exp(it Sσ1] is small away from the origin. The result is of the best possible order.
Geluk, Jaap; Peng, Liang; de Vries, Casper G.
1999-01-01
Suppose X1,X2 are independent random variables satisfying a second-order regular variation condition on the tail-sum and a balance condition on the tails. In this paper we give a description of the asymptotic behaviour as t → ∞ for P(X1 + X2 > t). The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model.
AUTOCLASSIFICATION OF THE VARIABLE 3XMM SOURCES USING THE RANDOM FOREST MACHINE LEARNING ALGORITHM
International Nuclear Information System (INIS)
Farrell, Sean A.; Murphy, Tara; Lo, Kitty K.
2015-01-01
In the current era of large surveys and massive data sets, autoclassification of astrophysical sources using intelligent algorithms is becoming increasingly important. In this paper we present the catalog of variable sources in the Third XMM-Newton Serendipitous Source catalog (3XMM) autoclassified using the Random Forest machine learning algorithm. We used a sample of manually classified variable sources from the second data release of the XMM-Newton catalogs (2XMMi-DR2) to train the classifier, obtaining an accuracy of ∼92%. We also evaluated the effectiveness of identifying spurious detections using a sample of spurious sources, achieving an accuracy of ∼95%. Manual investigation of a random sample of classified sources confirmed these accuracy levels and showed that the Random Forest machine learning algorithm is highly effective at automatically classifying 3XMM sources. Here we present the catalog of classified 3XMM variable sources. We also present three previously unidentified unusual sources that were flagged as outlier sources by the algorithm: a new candidate supergiant fast X-ray transient, a 400 s X-ray pulsar, and an eclipsing 5 hr binary system coincident with a known Cepheid.
Energy Technology Data Exchange (ETDEWEB)
Al-Muslim, Husain Mohammed; Arif, Abul Fazal M. [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia)
2010-07-01
Mechanical damage in transportation pipelines is an issue of extreme importance to pipeline operators and many others. Appropriate procedures for severity assessment are necessary. This paper mainly studies the effect of geometry, material and pressure variability on strain and stress fields in dented pipelines subjected to static and cyclic pressure. Finite element analysis (FEA) has often been used to overcome the limitations of a full-scale test, but it is still impossible to run FEA for all possible combinations of parameters. Probabilistic analysis offers an excellent alternative method to determine the sensitivity of the strain and stress fields to each of those input parameters. A hundred cases were randomly generated with Monte Carlo simulations and analyzed, a general formula was proposed to relate the output variables in terms of practically measured variables, and regression analysis was performed to confirm the appropriateness of the general formula.
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.
Martínez, Carlos Alberto; Khare, Kshitij; Banerjee, Arunava; Elzo, Mauricio A
2017-03-21
It is important to consider heterogeneity of marker effects and allelic frequencies in across population genome-wide prediction studies. Moreover, all regression models used in genome-wide prediction overlook randomness of genotypes. In this study, a family of hierarchical Bayesian models to perform across population genome-wide prediction modeling genotypes as random variables and allowing population-specific effects for each marker was developed. Models shared a common structure and differed in the priors used and the assumption about residual variances (homogeneous or heterogeneous). Randomness of genotypes was accounted for by deriving the joint probability mass function of marker genotypes conditional on allelic frequencies and pedigree information. As a consequence, these models incorporated kinship and genotypic information that not only permitted to account for heterogeneity of allelic frequencies, but also to include individuals with missing genotypes at some or all loci without the need for previous imputation. This was possible because the non-observed fraction of the design matrix was treated as an unknown model parameter. For each model, a simpler version ignoring population structure, but still accounting for randomness of genotypes was proposed. Implementation of these models and computation of some criteria for model comparison were illustrated using two simulated datasets. Theoretical and computational issues along with possible applications, extensions and refinements were discussed. Some features of the models developed in this study make them promising for genome-wide prediction, the use of information contained in the probability distribution of genotypes is perhaps the most appealing. Further studies to assess the performance of the models proposed here and also to compare them with conventional models used in genome-wide prediction are needed. Copyright © 2017 Elsevier Ltd. All rights reserved.
Using randomized variable practice in the treatment of childhood apraxia of speech.
Skelton, Steven L; Hagopian, Aubrie Lynn
2014-11-01
The purpose of this study was to determine if randomized variable practice, a central component of concurrent treatment, would be effective and efficient in treating childhood apraxia of speech (CAS). Concurrent treatment is a treatment program that takes the speech task hierarchy and randomizes it so that all tasks are worked on in one session. Previous studies have shown the treatment program to be effective and efficient in treating phonological and articulation disorders. The program was adapted to be used with children with CAS. A research design of multiple baselines across participants was used. Probes of generalization to untaught words were administered every fifth session. Three children, ranging in age from 4 to 6 years old, were the participants. Data were collected as percent correct productions during baseline, treatment, and probes of generalization of target sounds to untaught words and three-word phrases. All participants showed an increase in correct productions during treatment and during probes. Effect sizes (standard mean difference) for treatment were 3.61-5.00, and for generalization probes, they were 3.15-8.51. The results obtained from this study suggest that randomized variable practice as used in concurrent treatment can be adapted for use in treating children with CAS. Replication of this study with other children presenting CAS will be needed to establish generality of the findings.
THE COVARIATION FUNCTION FOR SYMMETRIC &ALPHA;-STABLE RANDOM VARIABLES WITH FINITE FIRST MOMENTS
Directory of Open Access Journals (Sweden)
Dedi Rosadi
2012-05-01
Full Text Available In this paper, we discuss a generalized dependence measure which is designed to measure dependence of two symmetric α-stable random variables with finite mean(1<α<=2 and contains the covariance function as the special case (when α=2. Weshortly discuss some basic properties of the function and consider several methods to estimate the function and further investigate the numerical properties of the estimatorusing the simulated data. We show how to apply this function to measure dependence of some stock returns on the composite index LQ45 in Indonesia Stock Exchange.
A Method of Approximating Expectations of Functions of Sums of Independent Random Variables
Klass, Michael J.
1981-01-01
Let $X_1, X_2, \\cdots$ be a sequence of independent random variables with $S_n = \\sum^n_{i = 1} X_i$. Fix $\\alpha > 0$. Let $\\Phi(\\cdot)$ be a continuous, strictly increasing function on $\\lbrack 0, \\infty)$ such that $\\Phi(0) = 0$ and $\\Phi(cx) \\leq c^\\alpha\\Phi(x)$ for all $x > 0$ and all $c \\geq 2$. Suppose $a$ is a real number and $J$ is a finite nonempty subset of the positive integers. In this paper we are interested in approximating $E \\max_{j \\in J} \\Phi(|a + S_j|)$. We construct a nu...
Dai, James Y.; Chan, Kwun Chuen Gary; Hsu, Li
2014-01-01
Instrumental variable regression is one way to overcome unmeasured confounding and estimate causal effect in observational studies. Built on structural mean models, there has been considerale work recently developed for consistent estimation of causal relative risk and causal odds ratio. Such models can sometimes suffer from identification issues for weak instruments. This hampered the applicability of Mendelian randomization analysis in genetic epidemiology. When there are multiple genetic variants available as instrumental variables, and causal effect is defined in a generalized linear model in the presence of unmeasured confounders, we propose to test concordance between instrumental variable effects on the intermediate exposure and instrumental variable effects on the disease outcome, as a means to test the causal effect. We show that a class of generalized least squares estimators provide valid and consistent tests of causality. For causal effect of a continuous exposure on a dichotomous outcome in logistic models, the proposed estimators are shown to be asymptotically conservative. When the disease outcome is rare, such estimators are consistent due to the log-linear approximation of the logistic function. Optimality of such estimators relative to the well-known two-stage least squares estimator and the double-logistic structural mean model is further discussed. PMID:24863158
Nam, Sungsik; Alouini, Mohamed-Slim; Yang, Hongchuan
2010-01-01
Order statistics find applications in various areas of communications and signal processing. In this paper, we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables (RVs
Nam, Sungsik
2014-08-01
The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed (i.i.d.) random variables was recently presented. However, the identical distribution assumption may not be valid in several real-world applications. With this motivation in mind, we consider in this paper the more general case in which the random variables are independent but not necessarily identically distributed (i.n.d.). More specifically, we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE receivers operating over frequency-selective fading channels with a non-uniform power delay profile. © 1991-2012 IEEE.
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....
Gómez-Gómez, Enrique; Carrasco-Valiente, Julia; Blanca-Pedregosa, Ana; Barco-Sánchez, Beatriz; Fernandez-Rueda, Jose Luis; Molina-Abril, Helena; Valero-Rosa, Jose; Font-Ugalde, Pilar; Requena-Tapia, Maria José
2017-04-01
To externally validate the European Randomized Study of Screening for Prostate Cancer (ERSPC) risk calculator (RC) and to evaluate its variability between 2 consecutive prostate-specific antigen (PSA) values. We prospectively catalogued 1021 consecutive patients before prostate biopsy for suspicion of prostate cancer (PCa). The risk of PCa and significant PCa (Gleason score ≥7) from 749 patients was calculated according to ERSPC-RC (digital rectal examination-based version 3 of 4) for 2 consecutive PSA tests per patient. The calculators' predictions were analyzed using calibration plots and the area under the receiver operating characteristic curve (area under the curve). Cohen kappa coefficient was used to compare the ability and variability. Of 749 patients, PCa was detected in 251 (33.5%) and significant PCa was detected in 133 (17.8%). Calibration plots showed an acceptable parallelism and similar discrimination ability for both PSA levels with an area under the curve of 0.69 for PCa and 0.74 for significant PCa. The ERSPC showed 226 (30.2%) unnecessary biopsies with the loss of 10 significant PCa. The variability of the RC was 16% for PCa and 20% for significant PCa, and a higher variability was associated with a reduced risk of significant PCa. We can conclude that the performance of the ERSPC-RC in the present cohort shows a high similitude between the 2 PSA levels; however, the RC variability value is associated with a decreased risk of significant PCa. The use of the ERSPC in our cohort detects a high number of unnecessary biopsies. Thus, the incorporation of ERSPC-RC could help the clinical decision to carry out a prostate biopsy. Copyright © 2016 Elsevier Inc. All rights reserved.
Yagui, Ana Cristina Zanon; Vale, Luciana Assis Pires Andrade; Haddad, Luciana Branco; Prado, Cristiane; Rossi, Felipe Souza; Deutsch, Alice D Agostini; Rebello, Celso Moura
2011-01-01
To evaluate the efficacy and safety of nasal continuous positive airway pressure (NCPAP) using devices with variable flow or bubble continuous positive airway pressure (CPAP) regarding CPAP failure, presence of air leaks, total CPAP and oxygen time, and length of intensive care unit and hospital stay in neonates with moderate respiratory distress (RD) and birth weight (BW) ≥ 1,500 g. Forty newborns requiring NCPAP were randomized into two study groups: variable flow group (VF) and continuous flow group (CF). The study was conducted between October 2008 and April 2010. Demographic data, CPAP failure, presence of air leaks, and total CPAP and oxygen time were recorded. Categorical outcomes were tested using the chi-square test or the Fisher's exact test. Continuous variables were analyzed using the Mann-Whitney test. The level of significance was set at p CPAP failure (21.1 and 20.0% for VF and CF, respectively; p = 1.000), air leak syndrome (10.5 and 5.0%, respectively; p = 0.605), total CPAP time (median: 22.0 h, interquartile range [IQR]: 8.00-31.00 h and median: 22.0 h, IQR: 6.00-32.00 h, respectively; p = 0.822), and total oxygen time (median: 24.00 h, IQR: 7.00-85.00 h and median: 21.00 h, IQR: 9.50-66.75 h, respectively; p = 0.779). In newborns with BW ≥ 1,500 g and moderate RD, the use of continuous flow NCPAP showed the same benefits as the use of variable flow NCPAP.
Directory of Open Access Journals (Sweden)
Lindsay S. Nagamatsu
2013-01-01
Full Text Available We report secondary findings from a randomized controlled trial on the effects of exercise on memory in older adults with probable MCI. We randomized 86 women aged 70–80 years with subjective memory complaints into one of three groups: resistance training, aerobic training, or balance and tone (control. All participants exercised twice per week for six months. We measured verbal memory and learning using the Rey Auditory Verbal Learning Test (RAVLT and spatial memory using a computerized test, before and after trial completion. We found that the aerobic training group remembered significantly more items in the loss after interference condition of the RAVLT compared with the control group after six months of training. In addition, both experimental groups showed improved spatial memory performance in the most difficult condition where they were required to memorize the spatial location of three items, compared with the control group. Lastly, we found a significant correlation between spatial memory performance and overall physical capacity after intervention in the aerobic training group. Taken together, our results provide support for the prevailing notion that exercise can positively impact cognitive functioning and may represent an effective strategy to improve memory in those who have begun to experience cognitive decline.
On the strong law of large numbers for $\\varphi$-subgaussian random variables
Zajkowski, Krzysztof
2016-01-01
For $p\\ge 1$ let $\\varphi_p(x)=x^2/2$ if $|x|\\le 1$ and $\\varphi_p(x)=1/p|x|^p-1/p+1/2$ if $|x|>1$. For a random variable $\\xi$ let $\\tau_{\\varphi_p}(\\xi)$ denote $\\inf\\{a\\ge 0:\\;\\forall_{\\lambda\\in\\mathbb{R}}\\; \\ln\\mathbb{E}\\exp(\\lambda\\xi)\\le\\varphi_p(a\\lambda)\\}$; $\\tau_{\\varphi_p}$ is a norm in a space $Sub_{\\varphi_p}=\\{\\xi:\\;\\tau_{\\varphi_p}(\\xi)1$) there exist positive constants $c$ and $\\alpha$ such that for every natural number $n$ the following inequality $\\tau_{\\varphi_p}(\\sum_{i=1...
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
MODELING THE TIME VARIABILITY OF SDSS STRIPE 82 QUASARS AS A DAMPED RANDOM WALK
International Nuclear Information System (INIS)
MacLeod, C. L.; Ivezic, Z.; Bullock, E.; Kimball, A.; Sesar, B.; Westman, D.; Brooks, K.; Gibson, R.; Becker, A. C.; Kochanek, C. S.; Kozlowski, S.; Kelly, B.; De Vries, W. H.
2010-01-01
We model the time variability of ∼9000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk (DRW). Using 2.7 million photometric measurements collected over 10 yr, we confirm the results of Kelly et al. and Kozlowski et al. that this model can explain quasar light curves at an impressive fidelity level (0.01-0.02 mag). The DRW model provides a simple, fast (O(N) for N data points), and powerful statistical description of quasar light curves by a characteristic timescale (τ) and an asymptotic rms variability on long timescales (SF ∞ ). We searched for correlations between these two variability parameters and physical parameters such as luminosity and black hole mass, and rest-frame wavelength. Our analysis shows SF ∞ to increase with decreasing luminosity and rest-frame wavelength as observed previously, and without a correlation with redshift. We find a correlation between SF ∞ and black hole mass with a power-law index of 0.18 ± 0.03, independent of the anti-correlation with luminosity. We find that τ increases with increasing wavelength with a power-law index of 0.17, remains nearly constant with redshift and luminosity, and increases with increasing black hole mass with a power-law index of 0.21 ± 0.07. The amplitude of variability is anti-correlated with the Eddington ratio, which suggests a scenario where optical fluctuations are tied to variations in the accretion rate. However, we find an additional dependence on luminosity and/or black hole mass that cannot be explained by the trend with Eddington ratio. The radio-loudest quasars have systematically larger variability amplitudes by about 30%, when corrected for the other observed trends, while the distribution of their characteristic timescale is indistinguishable from that of the full sample. We do not detect any statistically robust differences in the characteristic timescale and variability amplitude between the full sample and the small subsample of quasars detected
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...
International Nuclear Information System (INIS)
Levegruen, Sabine; Jackson, Andrew; Zelefsky, Michael J.; Venkatraman, Ennapadam S.; Skwarchuk, Mark W.; Schlegel, Wolfgang; Fuks, Zvi; Leibel, Steven A.; Ling, C. Clifton
2000-01-01
Purpose: To investigate tumor control following three-dimensional conformal radiation therapy (3D-CRT) of prostate cancer and to identify dose-distribution variables that correlate with local control assessed through posttreatment prostate biopsies. Methods and Material: Data from 132 patients, treated at Memorial Sloan-Kettering Cancer Center (MSKCC), who had a prostate biopsy 2.5 years or more after 3D-CRT for T1c-T3 prostate cancer with prescription doses of 64.8-81 Gy were analyzed. Variables derived from the dose distribution in the PTV included: minimum dose (Dmin), maximum dose (Dmax), mean dose (Dmean), dose to n% of the PTV (Dn), where n = 1%, ..., 99%. The concept of the equivalent uniform dose (EUD) was evaluated for different values of the surviving fraction at 2 Gy (SF 2 ). Four tumor control probability (TCP) models (one phenomenologic model using a logistic function and three Poisson cell kill models) were investigated using two sets of input parameters, one for low and one for high T-stage tumors. Application of both sets to all patients was also investigated. In addition, several tumor-related prognostic variables were examined (including T-stage, Gleason score). Univariate and multivariate logistic regression analyses were performed. The ability of the logistic regression models (univariate and multivariate) to predict the biopsy result correctly was tested by performing cross-validation analyses and evaluating the results in terms of receiver operating characteristic (ROC) curves. Results: In univariate analysis, prescription dose (Dprescr), Dmax, Dmean, dose to n% of the PTV with n of 70% or less correlate with outcome (p 2 : EUD correlates significantly with outcome for SF 2 of 0.4 or more, but not for lower SF 2 values. Using either of the two input parameters sets, all TCP models correlate with outcome (p 2 , is limited because the low dose region may not coincide with the tumor location. Instead, for MSKCC prostate cancer patients with their
What variables are important in predicting bovine viral diarrhea virus? A random forest approach.
Machado, Gustavo; Mendoza, Mariana Recamonde; Corbellini, Luis Gustavo
2015-07-24
Bovine viral diarrhea virus (BVDV) causes one of the most economically important diseases in cattle, and the virus is found worldwide. A better understanding of the disease associated factors is a crucial step towards the definition of strategies for control and eradication. In this study we trained a random forest (RF) prediction model and performed variable importance analysis to identify factors associated with BVDV occurrence. In addition, we assessed the influence of features selection on RF performance and evaluated its predictive power relative to other popular classifiers and to logistic regression. We found that RF classification model resulted in an average error rate of 32.03% for the negative class (negative for BVDV) and 36.78% for the positive class (positive for BVDV).The RF model presented area under the ROC curve equal to 0.702. Variable importance analysis revealed that important predictors of BVDV occurrence were: a) who inseminates the animals, b) number of neighboring farms that have cattle and c) rectal palpation performed routinely. Our results suggest that the use of machine learning algorithms, especially RF, is a promising methodology for the analysis of cross-sectional studies, presenting a satisfactory predictive power and the ability to identify predictors that represent potential risk factors for BVDV investigation. We examined classical predictors and found some new and hard to control practices that may lead to the spread of this disease within and among farms, mainly regarding poor or neglected reproduction management, which should be considered for disease control and eradication.
High throughput nonparametric probability density estimation.
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.
DEFF Research Database (Denmark)
Asmussen, Søren; Albrecher, Hansjörg
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities......, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially...... updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber–Shiu functions and dependence....
Probability theory a comprehensive course
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...
Introduction to probability with statistical applications
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
Generalized Probability-Probability Plots
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 AUC-based permutation variable importance measure for random forests.
Janitza, Silke; Strobl, Carolin; Boulesteix, Anne-Laure
2013-04-05
The random forest (RF) method is a commonly used tool for classification with high dimensional data as well as for ranking candidate predictors based on the so-called random forest variable importance measures (VIMs). However the classification performance of RF is known to be suboptimal in case of strongly unbalanced data, i.e. data where response class sizes differ considerably. Suggestions were made to obtain better classification performance based either on sampling procedures or on cost sensitivity analyses. However to our knowledge the performance of the VIMs has not yet been examined in the case of unbalanced response classes. In this paper we explore the performance of the permutation VIM for unbalanced data settings and introduce an alternative permutation VIM based on the area under the curve (AUC) that is expected to be more robust towards class imbalance. We investigated the performance of the standard permutation VIM and of our novel AUC-based permutation VIM for different class imbalance levels using simulated data and real data. The results suggest that the new AUC-based permutation VIM outperforms the standard permutation VIM for unbalanced data settings while both permutation VIMs have equal performance for balanced data settings. The standard permutation VIM loses its ability to discriminate between associated predictors and predictors not associated with the response for increasing class imbalance. It is outperformed by our new AUC-based permutation VIM for unbalanced data settings, while the performance of both VIMs is very similar in the case of balanced classes. The new AUC-based VIM is implemented in the R package party for the unbiased RF variant based on conditional inference trees. The codes implementing our study are available from the companion website: http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/070_drittmittel/janitza/index.html.
Earth Data Analysis Center, University of New Mexico — USFS, State Forestry, BLM, and DOI fire occurrence point locations from 1987 to 2008 were combined and converted into a fire occurrence probability or density grid...
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.
Directory of Open Access Journals (Sweden)
Coletta Filho Helvécio Della
2000-01-01
Full Text Available RAPD analysis of 19 Ponkan mandarin accessions was performed using 25 random primers. Of 112 amplification products selected, only 32 were polymorphic across five accessions. The absence of genetic variability among the other 14 accessions suggested that they were either clonal propagations with different local names, or that they had undetectable genetic variability, such as point mutations which cannot be detected by RAPD.
How Far Is Quasar UV/Optical Variability from a Damped Random Walk at Low Frequency?
Energy Technology Data Exchange (ETDEWEB)
Guo Hengxiao; Wang Junxian; Cai Zhenyi; Sun Mouyuan, E-mail: hengxiaoguo@gmail.com, E-mail: jxw@ustc.edu.cn [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei 230026 (China)
2017-10-01
Studies have shown that UV/optical light curves of quasars can be described using the prevalent damped random walk (DRW) model, also known as the Ornstein–Uhlenbeck process. A white noise power spectral density (PSD) is expected at low frequency in this model; however, a direct observational constraint to the low-frequency PSD slope is difficult due to the limited lengths of the light curves available. Meanwhile, quasars show scatter in their DRW parameters that is too large to be attributed to uncertainties in the measurements and dependence on the variation of known physical factors. In this work we present simulations showing that, if the low-frequency PSD deviates from the DRW, the red noise leakage can naturally produce large scatter in the variation parameters measured from simulated light curves. The steeper the low-frequency PSD slope, the larger scatter we expect. Based on observations of SDSS Stripe 82 quasars, we find that the low-frequency PSD slope should be no steeper than −1.3. The actual slope could be flatter, which consequently requires that the quasar variabilities should be influenced by other unknown factors. We speculate that the magnetic field and/or metallicity could be such additional factors.
Nicodemus, Kristin K; Malley, James D; Strobl, Carolin; Ziegler, Andreas
2010-02-27
Random forests (RF) have been increasingly used in applications such as genome-wide association and microarray studies where predictor correlation is frequently observed. Recent works on permutation-based variable importance measures (VIMs) used in RF have come to apparently contradictory conclusions. We present an extended simulation study to synthesize results. In the case when both predictor correlation was present and predictors were associated with the outcome (HA), the unconditional RF VIM attributed a higher share of importance to correlated predictors, while under the null hypothesis that no predictors are associated with the outcome (H0) the unconditional RF VIM was unbiased. Conditional VIMs showed a decrease in VIM values for correlated predictors versus the unconditional VIMs under HA and was unbiased under H0. Scaled VIMs were clearly biased under HA and H0. Unconditional unscaled VIMs are a computationally tractable choice for large datasets and are unbiased under the null hypothesis. Whether the observed increased VIMs for correlated predictors may be considered a "bias" - because they do not directly reflect the coefficients in the generating model - or if it is a beneficial attribute of these VIMs is dependent on the application. For example, in genetic association studies, where correlation between markers may help to localize the functionally relevant variant, the increased importance of correlated predictors may be an advantage. On the other hand, we show examples where this increased importance may result in spurious signals.
Quantum Probabilities as Behavioral Probabilities
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
DIYAH MARTANTI
2008-10-01
Full Text Available Amorphophallus muelleri Blume (Araceae is valued for its glucomanan content for use in food industry (healthy diet food, paper industry, pharmacy and cosmetics. The species is triploid (2n=3x=39 and the seed is developed apomictically. The present research is aimed to identify genetic variability of six population of A. muelleri from Java (consisted of 50 accessions using random amplified polymorphic DNA (RAPD. The six populations of the species are: East Java: (1 Silo-Jember, (2 Saradan-Madiun, (3 IPB (cultivated, from Saradan-Madiun, (4 Panti-Jember, (5 Probolinggo; and Central Java: (6 Cilacap. The results showed that five RAPD primers generated 42 scorable bands of which 29 (69.05% were polymorphic. Size of the bands varied from 300bp to 1.5kbp. The 50 accessions of A. muelleri were divided into two main clusters, some of them were grouped based on their populations, and some others were not. The range of individual genetic dissimilarity was from 0.02 to 0.36. The results showed that among six populations investigated, Saradan population showed the highest levels of genetic variation with mean values of na = 1.500+ 0.5061, ne = 1.3174 + 0.3841, PLP = 50% and He = 0, 0.1832+0.2054, whereas Silo-Jember population showed the lowest levels of genetic variation with mean values na = 1.2619+ 0.4450, ne = 1.1890 + 0.3507, PLP = 26.19% and He = 0.1048+0.1887. Efforts to conserve, domesticate, cultivate and improve genetically should be based on the genetic properties of each population and individual within population, especially Saradan population which has the highest levels of genetic variation, need more attention for its conservation.
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
Grinstead, Charles M; Snell, J Laurie
2011-01-01
This book explores four real-world topics through the lens of probability theory. It can be used to supplement a standard text in probability or statistics. Most elementary textbooks present the basic theory and then illustrate the ideas with some neatly packaged examples. Here the authors assume that the reader has seen, or is learning, the basic theory from another book and concentrate in some depth on the following topics: streaks, the stock market, lotteries, and fingerprints. This extended format allows the authors to present multiple approaches to problems and to pursue promising side discussions in ways that would not be possible in a book constrained to cover a fixed set of topics. To keep the main narrative accessible, the authors have placed the more technical mathematical details in appendices. The appendices can be understood by someone who has taken one or two semesters of calculus.
Dorogovtsev, A Ya; Skorokhod, A V; Silvestrov, D S; Skorokhod, A V
1997-01-01
This book of problems is intended for students in pure and applied mathematics. There are problems in traditional areas of probability theory and problems in the theory of stochastic processes, which has wide applications in the theory of automatic control, queuing and reliability theories, and in many other modern science and engineering fields. Answers to most of the problems are given, and the book provides hints and solutions for more complicated problems.
Information-theoretic methods for estimating of complicated probability distributions
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
Spieth, Peter M; Güldner, Andreas; Uhlig, Christopher; Bluth, Thomas; Kiss, Thomas; Schultz, Marcus J; Pelosi, Paolo; Koch, Thea; Gama de Abreu, Marcelo
2014-05-02
General anesthesia usually requires mechanical ventilation, which is traditionally accomplished with constant tidal volumes in volume- or pressure-controlled modes. Experimental studies suggest that the use of variable tidal volumes (variable ventilation) recruits lung tissue, improves pulmonary function and reduces systemic inflammatory response. However, it is currently not known whether patients undergoing open abdominal surgery might benefit from intraoperative variable ventilation. The PROtective VARiable ventilation trial ('PROVAR') is a single center, randomized controlled trial enrolling 50 patients who are planning for open abdominal surgery expected to last longer than 3 hours. PROVAR compares conventional (non-variable) lung protective ventilation (CV) with variable lung protective ventilation (VV) regarding pulmonary function and inflammatory response. The primary endpoint of the study is the forced vital capacity on the first postoperative day. Secondary endpoints include further lung function tests, plasma cytokine levels, spatial distribution of ventilation assessed by means of electrical impedance tomography and postoperative pulmonary complications. We hypothesize that VV improves lung function and reduces systemic inflammatory response compared to CV in patients receiving mechanical ventilation during general anesthesia for open abdominal surgery longer than 3 hours. PROVAR is the first randomized controlled trial aiming at intra- and postoperative effects of VV on lung function. This study may help to define the role of VV during general anesthesia requiring mechanical ventilation. Clinicaltrials.gov NCT01683578 (registered on September 3 3012).
A Non-Simulation Based Method for Inducing Pearson’s Correlation Between Input Random Variables
2008-04-23
Systems 500 Auxillary Systems 600 Outfit & Furnishings 700 Weapons 800 Integration & Engineering 900 Ship Assembly & Support Total SWBS Description...Upside Probable Downside 000 Administration 100 Hull 200 Propulsion 300 Electric Plant 400 Electonics Systems 500 Auxillary Systems 600 Outfit
Relative efficiency and sample size for cluster randomized trials with variable cluster sizes.
You, Zhiying; Williams, O Dale; Aban, Inmaculada; Kabagambe, Edmond Kato; Tiwari, Hemant K; Cutter, Gary
2011-02-01
The statistical power of cluster randomized trials depends on two sample size components, the number of clusters per group and the numbers of individuals within clusters (cluster size). Variable cluster sizes are common and this variation alone may have significant impact on study power. Previous approaches have taken this into account by either adjusting total sample size using a designated design effect or adjusting the number of clusters according to an assessment of the relative efficiency of unequal versus equal cluster sizes. This article defines a relative efficiency of unequal versus equal cluster sizes using noncentrality parameters, investigates properties of this measure, and proposes an approach for adjusting the required sample size accordingly. We focus on comparing two groups with normally distributed outcomes using t-test, and use the noncentrality parameter to define the relative efficiency of unequal versus equal cluster sizes and show that statistical power depends only on this parameter for a given number of clusters. We calculate the sample size required for an unequal cluster sizes trial to have the same power as one with equal cluster sizes. Relative efficiency based on the noncentrality parameter is straightforward to calculate and easy to interpret. It connects the required mean cluster size directly to the required sample size with equal cluster sizes. Consequently, our approach first determines the sample size requirements with equal cluster sizes for a pre-specified study power and then calculates the required mean cluster size while keeping the number of clusters unchanged. Our approach allows adjustment in mean cluster size alone or simultaneous adjustment in mean cluster size and number of clusters, and is a flexible alternative to and a useful complement to existing methods. Comparison indicated that we have defined a relative efficiency that is greater than the relative efficiency in the literature under some conditions. Our measure
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.
Rosenblum, Michael; van der Laan, Mark J.
2010-01-01
Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we prove the maximum likelihood estimate of the coefficient corresponding to the treatment variable is an asymptotically unbiased estimator of the marginal log rate ratio, even when the working model is arbitrarily misspecified. This is the log-linear analog of ANCOVA for linear models. Our results demonstrate one application of targeted maximum likelihood estimation. PMID:20628636
Rosenblum, Michael; van der Laan, Mark J
2010-04-01
Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we prove the maximum likelihood estimate of the coefficient corresponding to the treatment variable is an asymptotically unbiased estimator of the marginal log rate ratio, even when the working model is arbitrarily misspecified. This is the log-linear analog of ANCOVA for linear models. Our results demonstrate one application of targeted maximum likelihood estimation.
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
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
Genetic variability of cultivated cowpea in Benin assessed by random amplified polymorphic DNA
Zannou, A.; Kossou, D.K.; Ahanchédé, A.; Zoundjihékpon, J.; Agbicodo, E.; Struik, P.C.; Sanni, A.
2008-01-01
Characterization of genetic diversity among cultivated cowpea [Vigna unguiculata (L.) Walp.] varieties is important to optimize the use of available genetic resources by farmers, local communities, researchers and breeders. Random amplified polymorphic DNA (RAPD) markers were used to evaluate the
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.
Probability theory and statistical applications a profound treatise for self-study
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.
Deal, J. H.
1975-01-01
One approach to the problem of simplifying complex nonlinear filtering algorithms is through using stratified probability approximations where the continuous probability density functions of certain random variables are represented by discrete mass approximations. This technique is developed in this paper and used to simplify the filtering algorithms developed for the optimum receiver for signals corrupted by both additive and multiplicative noise.
DEFF Research Database (Denmark)
Hallas, Jesper; Pottegård, Anton; Støvring, Henrik
2017-01-01
generated adjusted ORs in the upper range (4.37-4.75) while at the same time having the most narrow confidence intervals (ratio between upper and lower confidence limit, 1.46-1.50). Some ORs generated by conventional measures were higher than the probabilistic ORs, but only when the assumed period of intake......BACKGROUND: In register-based pharmacoepidemiological studies, each day of follow-up is usually categorized either as exposed or unexposed. However, there is an underlying continuous probability of exposure, and by insisting on a dichotomy, researchers unwillingly force a nondifferential...... misclassification into their analyses. We have recently developed a model whereby probability of exposure can be modeled, and we tested this on an empirical case of nonsteroidal anti-inflammatory drug (NSAID)-induced upper gastrointestinal bleeding (UGIB). METHODS: We used a case-controls data set, consisting...
Ambrogioni, Luca; Güçlü, Umut; van Gerven, Marcel A. J.; Maris, Eric
2017-01-01
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of kernel functions centered at a subset of training points. The weights are determined by the outer layer of a deep neural network, trained by minimizing the negative log likelihood. This generalizes the popular quantized softmax approach, which can be seen ...
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
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....
DEFF Research Database (Denmark)
Nielsen, Erland Hejn
2003-01-01
of the estimation of the probability of critically delayed delivery beyond a specified threshold value given a certain production batch size and try to establish a relation to certain parameters that can be linked to the degree of regularity of the arrival stream of parts to the job/flow-shop. This last aspect...... relates remotely to the Lean Thinking philosophy that praises the smooth and uninterrupted production flow to be beneficial to the overall operation of productive plants in general, and we will link our findings to this discussion as well....
DEFF Research Database (Denmark)
Nielsen, Erland Hejn
2003-01-01
In this paper we will discuss aspects of the computation of tail-probabilities by simulation in the context of a generic job/flow-shop model consisting of structural elements such as bottle-necks, re-entrance as well as a mixture of these two fundamental types of production complexity and all thi...... relates remotely to the Lean Thinking philosophy that praises the smooth and uninterrupted production flow to be beneficial to the overall operation of productive plants in general, and we will link our findings to this discussion as well....
Boezen, H M; Schouten, J. P.; Postma, D S; Rijcken, B
1994-01-01
Peak expiratory flow (PEF) variability can be considered as an index of bronchial lability. Population studies on PEF variability are few. The purpose of the current paper is to describe the distribution of PEF variability in a random population sample of adults with a wide age range (20-70 yrs),
Plass-Johnson, Jeremiah G; Taylor, Marc H; Husain, Aidah A A; Teichberg, Mirta C; Ferse, Sebastian C A
2016-01-01
Changes in the coral reef complex can affect predator-prey relationships, resource availability and niche utilisation in the associated fish community, which may be reflected in decreased stability of the functional traits present in a community. This is because particular traits may be favoured by a changing environment, or by habitat degradation. Furthermore, other traits can be selected against because degradation can relax the association between fishes and benthic habitat. We characterised six important ecological traits for fish species occurring at seven sites across a disturbed coral reef archipelago in Indonesia, where reefs have been exposed to eutrophication and destructive fishing practices for decades. Functional diversity was assessed using two complementary indices (FRic and RaoQ) and correlated to important environmental factors (live coral cover and rugosity, representing local reef health, and distance from shore, representing a cross-shelf environmental gradient). Indices were examined for both a change in their mean, as well as temporal (short-term; hours) and spatial (cross-shelf) variability, to assess whether fish-habitat association became relaxed along with habitat degradation. Furthermore, variability in individual traits was examined to identify the traits that are most affected by habitat change. Increases in the general reef health indicators, live coral cover and rugosity (correlated with distance from the mainland), were associated with decreases in the variability of functional diversity and with community-level changes in the abundance of several traits (notably home range size, maximum length, microalgae, detritus and small invertebrate feeding and reproductive turnover). A decrease in coral cover increased variability of RaoQ while rugosity and distance both inversely affected variability of FRic; however, averages for these indices did not reveal patterns associated with the environment. These results suggest that increased
Indian Academy of Sciences (India)
IAS Admin
statistics at all levels. .... P(Ai) for k < ∞ and A1,A2, ··· ,Ak ∈ F and Ai ∩ Aj = ∅ for i = j. Next, it is reasonable to require that F be closed .... roll of dice, card games such as Bridge. ..... ing data (i.e., generating random variables) according to ...
Randomness and variability of the neuronal activity described by the Ornstein-Uhlenbeck model
Czech Academy of Sciences Publication Activity Database
Košťál, Lubomír; Lánský, Petr; Zucca, Ch.
2007-01-01
Roč. 18, č. 1 (2007), s. 63-75 ISSN 0954-898X R&D Projects: GA MŠk(CZ) LC554; GA AV ČR(CZ) 1ET400110401; GA AV ČR(CZ) KJB100110701 Grant - others:MIUR(IT) PRIN-Cofin 2005 Institutional research plan: CEZ:AV0Z50110509 Keywords : Ornstein-Uhlenbeck * entropy * randomness Subject RIV: FH - Neurology Impact factor: 1.385, year: 2007
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...
International Nuclear Information System (INIS)
Maestrini, A.P.
1979-04-01
Several problems related to the application of the theory of random by means of state variables are studied. The well-known equations that define the propagation of the mean and the variance for linear and non-linear systems are first presented. The Monte Carlo method is next resorted to in order to determine the applicability of the hypothesis of a normally distributed output in case of linear systems subjected to non-Gaussian excitations. Finally, attention is focused on the properties of linear filters and modulation functions proposed to simulate seismic excitations as non stationary random processes. Acceleration spectra obtained by multiplying rms spectra by a constant factor are compared with design spectra suggested by several authors for various soil conditions. In every case, filter properties are given. (Author) [pt
Czech Academy of Sciences Publication Activity Database
Rusticucci, M.; Kyselý, Jan; Almeira, G.; Lhotka, Ondřej
2016-01-01
Roč. 124, č. 3 (2016), s. 679-689 ISSN 0177-798X R&D Projects: GA MŠk 7AMB15AR001 Institutional support: RVO:68378289 Keywords : heat waves * long-term variability * climate extremes Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 2.640, year: 2016 http://link.springer.com/article/10.1007%2Fs00704-015-1445-7
International Nuclear Information System (INIS)
Stotland, Alexander; Peer, Tal; Cohen, Doron; Budoyo, Rangga; Kottos, Tsampikos
2008-01-01
The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming 'mesoscopic' circumstances the analysis of the electro-driven transitions shows similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to capture the essential ingredients of the problem, and leads to a generalized variable range hopping picture. (fast track communication)
APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS
Directory of Open Access Journals (Sweden)
T. I. Aliev
2013-03-01
Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.
International Nuclear Information System (INIS)
Wilson, Brandon M; Smith, Barton L
2013-01-01
Uncertainties are typically assumed to be constant or a linear function of the measured value; however, this is generally not true. Particle image velocimetry (PIV) is one example of a measurement technique that has highly nonlinear, time varying local uncertainties. Traditional uncertainty methods are not adequate for the estimation of the uncertainty of measurement statistics (mean and variance) in the presence of nonlinear, time varying errors. Propagation of instantaneous uncertainty estimates into measured statistics is performed allowing accurate uncertainty quantification of time-mean and statistics of measurements such as PIV. It is shown that random errors will always elevate the measured variance, and thus turbulent statistics such as u'u'-bar. Within this paper, nonlinear, time varying errors are propagated from instantaneous measurements into the measured mean and variance using the Taylor-series method. With these results and knowledge of the systematic and random uncertainty of each measurement, the uncertainty of the time-mean, the variance and covariance can be found. Applicability of the Taylor-series uncertainty equations to time varying systematic and random errors and asymmetric error distributions are demonstrated with Monte-Carlo simulations. The Taylor-series uncertainty estimates are always accurate for uncertainties on the mean quantity. The Taylor-series variance uncertainty is similar to the Monte-Carlo results for cases in which asymmetric random errors exist or the magnitude of the instantaneous variations in the random and systematic errors is near the ‘true’ variance. However, the Taylor-series method overpredicts the uncertainty in the variance as the instantaneous variations of systematic errors are large or are on the same order of magnitude as the ‘true’ variance. (paper)
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.
r2VIM: A new variable selection method for random forests in genome-wide association studies.
Szymczak, Silke; Holzinger, Emily; Dasgupta, Abhijit; Malley, James D; Molloy, Anne M; Mills, James L; Brody, Lawrence C; Stambolian, Dwight; Bailey-Wilson, Joan E
2016-01-01
Machine learning methods and in particular random forests (RFs) are a promising alternative to standard single SNP analyses in genome-wide association studies (GWAS). RFs provide variable importance measures (VIMs) to rank SNPs according to their predictive power. However, in contrast to the established genome-wide significance threshold, no clear criteria exist to determine how many SNPs should be selected for downstream analyses. We propose a new variable selection approach, recurrent relative variable importance measure (r2VIM). Importance values are calculated relative to an observed minimal importance score for several runs of RF and only SNPs with large relative VIMs in all of the runs are selected as important. Evaluations on simulated GWAS data show that the new method controls the number of false-positives under the null hypothesis. Under a simple alternative hypothesis with several independent main effects it is only slightly less powerful than logistic regression. In an experimental GWAS data set, the same strong signal is identified while the approach selects none of the SNPs in an underpowered GWAS. The novel variable selection method r2VIM is a promising extension to standard RF for objectively selecting relevant SNPs in GWAS while controlling the number of false-positive results.
Energy Technology Data Exchange (ETDEWEB)
Oldenburg, Curtis M. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Budnitz, Robert J. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2016-08-31
If Carbon dioxide Capture and Storage (CCS) is to be effective in mitigating climate change, it will need to be carried out on a very large scale. This will involve many thousands of miles of dedicated high-pressure pipelines in order to transport many millions of tonnes of CO_{2} annually, with the CO_{2} delivered to many thousands of wells that will inject the CO_{2} underground. The new CCS infrastructure could rival in size the current U.S. upstream natural gas pipeline and well infrastructure. This new infrastructure entails hazards for life, health, animals, the environment, and natural resources. Pipelines are known to rupture due to corrosion, from external forces such as impacts by vehicles or digging equipment, by defects in construction, or from the failure of valves and seals. Similarly, wells are vulnerable to catastrophic failure due to corrosion, cement degradation, or operational mistakes. While most accidents involving pipelines and wells will be minor, there is the inevitable possibility of accidents with very high consequences, especially to public health. The most important consequence of concern is CO_{2} release to the environment in concentrations sufficient to cause death by asphyxiation to nearby populations. Such accidents are thought to be very unlikely, but of course they cannot be excluded, even if major engineering effort is devoted (as it will be) to keeping their probability low and their consequences minimized. This project has developed a methodology for analyzing the risks of these rare but high-consequence accidents, using a step-by-step probabilistic methodology. A key difference between risks for pipelines and wells is that the former are spatially distributed along the pipe whereas the latter are confined to the vicinity of the well. Otherwise, the methodology we develop for risk assessment of pipeline and well failures is similar and provides an analysis both of the annual probabilities of
Random variables in forest policy: A systematic sensitivity analysis using CGE models
International Nuclear Information System (INIS)
Alavalapati, J.R.R.
1999-01-01
Computable general equilibrium (CGE) models are extensively used to simulate economic impacts of forest policies. Parameter values used in these models often play a central role in their outcome. Since econometric studies and best guesses are the main sources of these parameters, some randomness exists about the 'true' values of these parameters. Failure to incorporate this randomness into these models may limit the degree of confidence in the validity of the results. In this study, we conduct a systematic sensitivity analysis (SSA) to assess the economic impacts of: 1) a 1 % increase in tax on Canadian lumber and wood products exports to the United States (US), and 2) a 1% decrease in technical change in the lumber and wood products and pulp and paper sectors of the US and Canada. We achieve this task by using an aggregated version of global trade model developed by Hertel (1997) and the automated SSA procedure developed by Arndt and Pearson (1996). The estimated means and standard deviations suggest that certain impacts are more likely than others. For example, an increase in export tax is likely to cause a decrease in Canadian income, while an increase in US income is unlikely. On the other hand, a decrease in US welfare is likely, while an increase in Canadian welfare is unlikely, in response to an increase in tax. It is likely that income and welfare both fall in Canada and the US in response to a decrease in the technical change in lumber and wood products and pulp and paper sectors 21 refs, 1 fig, 5 tabs
International Nuclear Information System (INIS)
Bunzl, K.
2002-01-01
In the field, the distribution coefficient, K d , for the sorption of a radionuclide by the soil cannot be expected to be constant. Even in a well defined soil horizon, K d will vary stochastically in horizontal as well as in vertical direction around a mean value. The horizontal random variability of K d produce a pronounced tailing effect in the concentration depth profile of a fallout radionuclide, much less is known on the corresponding effect of the vertical random variability. To analyze this effect theoretically, the classical convection-dispersion model in combination with the random-walk particle method was applied. The concentration depth profile of a radionuclide was calculated one year after deposition assuming constant values of the pore water velocity, the diffusion/dispersion coefficient, and the distribution coefficient (K d = 100 cm 3 x g -1 ) and exhibiting a vertical variability for K d according to a log-normal distribution with a geometric mean of 100 cm 3 x g -1 and a coefficient of variation of CV 0.53. The results show that these two concentration depth profiles are only slightly different, the location of the peak is shifted somewhat upwards, and the dispersion of the concentration depth profile is slightly larger. A substantial tailing effect of the concentration depth profile is not perceivable. Especially with respect to the location of the peak, a very good approximation of the concentration depth profile is obtained if the arithmetic mean of the K d -values (K d = 113 cm 3 x g -1 ) and a slightly increased dispersion coefficient are used in the analytical solution of the classical convection-dispersion equation with constant K d . The evaluation of the observed concentration depth profile with the analytical solution of the classical convection-dispersion equation with constant parameters will, within the usual experimental limits, hardly reveal the presence of a log-normal random distribution of K d in the vertical direction in
Directory of Open Access Journals (Sweden)
David Shilane
2013-01-01
Full Text Available The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data's expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's inequality. We now propose growth estimators of the negative binomial mean. Under high dispersion, zero values are likely to be overrepresented in the data. A growth estimator constructs a normal-style confidence interval by effectively removing a small, predetermined number of zeros from the data. We propose growth estimators based upon multiplicative adjustments of the sample mean and direct removal of zeros from the sample. These methods do not require estimating the nuisance dispersion parameter. We will demonstrate that the growth estimators' confidence intervals provide improved coverage over a wide range of parameter values and asymptotically converge to the sample mean. Interestingly, the proposed methods succeed despite adding both bias and variance to the normal approximation.
Probability Machines: Consistent Probability Estimation Using Nonparametric Learning Machines
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
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
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.
A brief introduction to probability.
Di Paola, Gioacchino; Bertani, Alessandro; De Monte, Lavinia; Tuzzolino, Fabio
2018-02-01
The theory of probability has been debated for centuries: back in 1600, French mathematics used the rules of probability to place and win bets. Subsequently, the knowledge of probability has significantly evolved and is now an essential tool for statistics. In this paper, the basic theoretical principles of probability will be reviewed, with the aim of facilitating the comprehension of statistical inference. After a brief general introduction on probability, we will review the concept of the "probability distribution" that is a function providing the probabilities of occurrence of different possible outcomes of a categorical or continuous variable. Specific attention will be focused on normal distribution that is the most relevant distribution applied to statistical analysis.
Park, Hame; Lueckmann, Jan-Matthis; von Kriegstein, Katharina; Bitzer, Sebastian; Kiebel, Stefan J.
2016-01-01
Decisions in everyday life are prone to error. Standard models typically assume that errors during perceptual decisions are due to noise. However, it is unclear how noise in the sensory input affects the decision. Here we show that there are experimental tasks for which one can analyse the exact spatio-temporal details of a dynamic sensory noise and better understand variability in human perceptual decisions. Using a new experimental visual tracking task and a novel Bayesian decision making model, we found that the spatio-temporal noise fluctuations in the input of single trials explain a significant part of the observed responses. Our results show that modelling the precise internal representations of human participants helps predict when perceptual decisions go wrong. Furthermore, by modelling precisely the stimuli at the single-trial level, we were able to identify the underlying mechanism of perceptual decision making in more detail than standard models. PMID:26752272
Scruggs, Stacie; Mama, Scherezade K; Carmack, Cindy L; Douglas, Tommy; Diamond, Pamela; Basen-Engquist, Karen
2018-01-01
This study examined whether a physical activity intervention affects transtheoretical model (TTM) variables that facilitate exercise adoption in breast cancer survivors. Sixty sedentary breast cancer survivors were randomized to a 6-month lifestyle physical activity intervention or standard care. TTM variables that have been shown to facilitate exercise adoption and progress through the stages of change, including self-efficacy, decisional balance, and processes of change, were measured at baseline, 3 months, and 6 months. Differences in TTM variables between groups were tested using repeated measures analysis of variance. The intervention group had significantly higher self-efficacy ( F = 9.55, p = .003) and perceived significantly fewer cons of exercise ( F = 5.416, p = .025) at 3 and 6 months compared with the standard care group. Self-liberation, counterconditioning, and reinforcement management processes of change increased significantly from baseline to 6 months in the intervention group, and self-efficacy and reinforcement management were significantly associated with improvement in stage of change. The stage-based physical activity intervention increased use of select processes of change, improved self-efficacy, decreased perceptions of the cons of exercise, and helped participants advance in stage of change. These results point to the importance of using a theory-based approach in interventions to increase physical activity in cancer survivors.
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.)
Applied probability and stochastic processes
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...
Ben Issaid, Chaouki; Rached, Nadhir B.; Kammoun, Abla; Alouini, Mohamed-Slim; Tempone, Raul
2017-01-01
the outage probability achieved by some diversity techniques over this kind of channels is of major practical importance. In many circumstances, this is related to the difficult question of analyzing the statistics of a sum of Gamma- Gamma random variables
Probability Aggregates in Probability Answer Set Programming
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...
Bryan, Stephanie; Pinto Zipp, Genevieve; Parasher, Raju
2012-01-01
Physical inactivity is a serious issue for the American public. Because of conditions that result from inactivity, individuals incur close to $1 trillion USD in health-care costs, and approximately 250 000 premature deaths occur per year. Researchers have linked engaging in yoga to improved overall fitness, including improved muscular strength, muscular endurance, flexibility, and balance. Researchers have not yet investigated the impact of yoga on exercise adherence. The research team assessed the effects of 10 weeks of yoga classes held twice a week on exercise adherence in previously sedentary adults. The research team designed a randomized controlled pilot trial. The team collected data from the intervention (yoga) and control groups at baseline, midpoint, and posttest (posttest 1) and also collected data pertaining to exercise adherence for the yoga group at 5 weeks posttest (posttest 2). The pilot took place in a yoga studio in central New Jersey in the United States. The pretesting occurred at the yoga studio for all participants. Midpoint testing and posttesting occurred at the studio for the yoga group and by mail for the control group. Participants were 27 adults (mean age 51 y) who had been physically inactive for a period of at least 6 months prior to the study. Interventions The intervention group (yoga group) received hour-long hatha yoga classes that met twice a week for 10 weeks. The control group did not participate in classes during the research study; however, they were offered complimentary post research classes. Outcome Measures The study's primary outcome measure was exercise adherence as measured by the 7-day Physical Activity Recall. The secondary measures included (1) exercise self-efficacy as measured by the Multidimensional Self-Efficacy for Exercise Scale, (2) general well-being as measured by the General Well-Being Schedule, (3) exercise-group cohesion as measured by the Group Environment Questionnaire (GEQ), (4) acute feeling response
Takahashi, Fumihiro; Morita, Satoshi
2018-02-08
Phase II clinical trials are conducted to determine the optimal dose of the study drug for use in Phase III clinical trials while also balancing efficacy and safety. In conducting these trials, it may be important to consider subpopulations of patients grouped by background factors such as drug metabolism and kidney and liver function. Determining the optimal dose, as well as maximizing the eﬀectiveness of the study drug by analyzing patient subpopulations, requires a complex decision-making process. In extreme cases, drug development has to be terminated due to inadequate efficacy or severe toxicity. Such a decision may be based on a particular subpopulation. We propose a Bayesian utility approach (BUART) to randomized Phase II clinical trials which uses a first-order bivariate normal dynamic linear model for efficacy and safety in order to determine the optimal dose and study population in a subsequent Phase III clinical trial. We carried out a simulation study under a wide range of clinical scenarios to evaluate the performance of the proposed method in comparison with a conventional method separately analyzing efficacy and safety in each patient population. The proposed method showed more favorable operating characteristics in determining the optimal population and dose.
Models for probability and statistical inference theory and applications
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...
Probability with applications and R
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
Scaling Qualitative Probability
Burgin, Mark
2017-01-01
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability structures and is more coherent than existing approaches. This setting makes it possible proving that any comparative probability is induced by some probability structure (Theorem 2.1), that classical probability is a probability structure (Theorem 2.2) and that i...
Confidence intervals for the lognormal probability distribution
International Nuclear Information System (INIS)
Smith, D.L.; Naberejnev, D.G.
2004-01-01
The present communication addresses the topic of symmetric confidence intervals for the lognormal probability distribution. This distribution is frequently utilized to characterize inherently positive, continuous random variables that are selected to represent many physical quantities in applied nuclear science and technology. The basic formalism is outlined herein and a conjured numerical example is provided for illustration. It is demonstrated that when the uncertainty reflected in a lognormal probability distribution is large, the use of a confidence interval provides much more useful information about the variable used to represent a particular physical quantity than can be had by adhering to the notion that the mean value and standard deviation of the distribution ought to be interpreted as best value and corresponding error, respectively. Furthermore, it is shown that if the uncertainty is very large a disturbing anomaly can arise when one insists on interpreting the mean value and standard deviation as the best value and corresponding error, respectively. Reliance on using the mode and median as alternative parameters to represent the best available knowledge of a variable with large uncertainties is also shown to entail limitations. Finally, a realistic physical example involving the decay of radioactivity over a time period that spans many half-lives is presented and analyzed to further illustrate the concepts discussed in this communication
2014-01-01
Background Cluster randomized trials (CRTs) present unique ethical challenges. In the absence of a uniform standard for their ethical design and conduct, problems such as variability in procedures and requirements by different research ethics committees will persist. We aimed to assess the need for ethics guidelines for CRTs among research ethics chairs internationally, investigate variability in procedures for research ethics review of CRTs within and among countries, and elicit research ethics chairs’ perspectives on specific ethical issues in CRTs, including the identification of research subjects. The proper identification of research subjects is a necessary requirement in the research ethics review process, to help ensure, on the one hand, that subjects are protected from harm and exploitation, and on the other, that reviews of CRTs are completed efficiently. Methods A web-based survey with closed- and open-ended questions was administered to research ethics chairs in Canada, the United States, and the United Kingdom. The survey presented three scenarios of CRTs involving cluster-level, professional-level, and individual-level interventions. For each scenario, a series of questions was posed with respect to the type of review required (full, expedited, or no review) and the identification of research subjects at cluster and individual levels. Results A total of 189 (35%) of 542 chairs responded. Overall, 144 (84%, 95% CI 79 to 90%) agreed or strongly agreed that there is a need for ethics guidelines for CRTs and 158 (92%, 95% CI 88 to 96%) agreed or strongly agreed that research ethics committees could be better informed about distinct ethical issues surrounding CRTs. There was considerable variability among research ethics chairs with respect to the type of review required, as well as the identification of research subjects. The cluster-cluster and professional-cluster scenarios produced the most disagreement. Conclusions Research ethics committees
Randomized Item Response Theory Models
Fox, Gerardus J.A.
2005-01-01
The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by
Briggs, William M.
2012-01-01
The probability leakage of model M with respect to evidence E is defined. Probability leakage is a kind of model error. It occurs when M implies that events $y$, which are impossible given E, have positive probability. Leakage does not imply model falsification. Models with probability leakage cannot be calibrated empirically. Regression models, which are ubiquitous in statistical practice, often evince probability leakage.
Directory of Open Access Journals (Sweden)
Ahmet Kuzu
2014-01-01
Full Text Available This paper proposes two novel master-slave configurations that provide improvements in both control and communication aspects of teleoperation systems to achieve an overall improved performance in position control. The proposed novel master-slave configurations integrate modular control and communication approaches, consisting of a delay regulator to address problems related to variable network delay common to such systems, and a model tracking control that runs on the slave side for the compensation of uncertainties and model mismatch on the slave side. One of the configurations uses a sliding mode observer and the other one uses a modified Smith predictor scheme on the master side to ensure position transparency between the master and slave, while reference tracking of the slave is ensured by a proportional-differentiator type controller in both configurations. Experiments conducted for the networked position control of a single-link arm under system uncertainties and randomly varying network delays demonstrate significant performance improvements with both configurations over the past literature.
Staley, James R.
2017-01-01
ABSTRACT Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure‐outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure‐outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs metaregression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure‐outcome relationship well, particularly when the relationship was a fractional polynomial (for the fractional polynomial method) or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure. PMID:28317167
Directory of Open Access Journals (Sweden)
Sornkitja Boonprong
2018-05-01
Full Text Available Burnt forest recovery is normally monitored with a time-series analysis of satellite data because of its proficiency for large observation areas. Traditional methods, such as linear correlation plotting, have been proven to be effective, as forest recovery naturally increases with time. However, these methods are complicated and time consuming when increasing the number of observed parameters. In this work, we present a random forest variable importance (RF-VIMP scheme called multilevel RF-VIMP to compare and assess the relationship between 36 spectral indices (parameters of burnt boreal forest recovery in the Great Xing’an Mountain, China. Six Landsat images were acquired in the same month 0, 1, 4, 14, 16, and 20 years after a fire, and 39,380 fixed-location samples were then extracted to calculate the effectiveness of the 36 parameters. Consequently, the proposed method was applied to find correlations between the forest recovery indices. The experiment showed that the proposed method is suitable for explaining the efficacy of those spectral indices in terms of discrimination and trend analysis, and for showing the satellite data and forest succession dynamics when applied in a time series. The results suggest that the tasseled cap transformation wetness, brightness, and the shortwave infrared bands (both 1 and 2 perform better than other indices for both classification and monitoring.
Contributions to quantum probability
International Nuclear Information System (INIS)
Fritz, Tobias
2010-01-01
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a finite set can occur as the outcome
Contributions to quantum probability
Energy Technology Data Exchange (ETDEWEB)
Fritz, Tobias
2010-06-25
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a
Koo, Reginald; Jones, Martin L.
2011-01-01
Quite a number of interesting problems in probability feature an event with probability equal to 1/e. This article discusses three such problems and attempts to explain why this probability occurs with such frequency.
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.
Directory of Open Access Journals (Sweden)
Qingwu Gao
2012-01-01
Full Text Available We discuss the uniformly asymptotic estimate of the finite-time ruin probability for all times in a generalized compound renewal risk model, where the interarrival times of successive accidents and all the claim sizes caused by an accident are two sequences of random variables following a wide dependence structure. This wide dependence structure allows random variables to be either negatively dependent or positively dependent.
Probability, random processes, and ergodic properties
Gray, Robert M
2014-01-01
In this new edition of this classic text, much of the material has been rearranged and revised for pedagogical reasons. Many classic inequalities and proofs are now incorporated into the text, and many citations have been added.
Austin, Peter C; Schuster, Tibor; Platt, Robert W
2015-10-15
Estimating statistical power is an important component of the design of both randomized controlled trials (RCTs) and observational studies. Methods for estimating statistical power in RCTs have been well described and can be implemented simply. In observational studies, statistical methods must be used to remove the effects of confounding that can occur due to non-random treatment assignment. Inverse probability of treatment weighting (IPTW) using the propensity score is an attractive method for estimating the effects of treatment using observational data. However, sample size and power calculations have not been adequately described for these methods. We used an extensive series of Monte Carlo simulations to compare the statistical power of an IPTW analysis of an observational study with time-to-event outcomes with that of an analysis of a similarly-structured RCT. We examined the impact of four factors on the statistical power function: number of observed events, prevalence of treatment, the marginal hazard ratio, and the strength of the treatment-selection process. We found that, on average, an IPTW analysis had lower statistical power compared to an analysis of a similarly-structured RCT. The difference in statistical power increased as the magnitude of the treatment-selection model increased. The statistical power of an IPTW analysis tended to be lower than the statistical power of a similarly-structured RCT.
Aggregate and Individual Replication Probability within an Explicit Model of the Research Process
Miller, Jeff; Schwarz, Wolf
2011-01-01
We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by…
WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS
Directory of Open Access Journals (Sweden)
Mr. Vladimir A. Smagin
2016-12-01
Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.
Directory of Open Access Journals (Sweden)
Qinghui Du
2014-01-01
Full Text Available We consider semi-implicit Euler methods for stochastic age-dependent capital system with variable delays and random jump magnitudes, and investigate the convergence of the numerical approximation. It is proved that the numerical approximate solutions converge to the analytical solutions in the mean-square sense under given conditions.
Quantum probability measures and tomographic probability densities
Amosov, GG; Man'ko, [No Value
2004-01-01
Using a simple relation of the Dirac delta-function to generalized the theta-function, the relationship between the tomographic probability approach and the quantum probability measure approach with the description of quantum states is discussed. The quantum state tomogram expressed in terms of the
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.
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.
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.
Excluding joint probabilities from quantum theory
Allahverdyan, Armen E.; Danageozian, Arshag
2018-03-01
Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.
Lin, Shu-Ling; Huang, Ching-Ya; Shiu, Shau-Ping; Yeh, Shu-Hui
2015-08-01
Mental health professionals experiencing work-related stress may experience burn out, leading to a negative impact on their organization and patients. The aim of this study was to examine the effects of yoga classes on work-related stress, stress adaptation, and autonomic nerve activity among mental health professionals. A randomized controlled trial was used, which compared the outcomes between the experimental (e.g., yoga program) and the control groups (e.g., no yoga exercise) for 12 weeks. Work-related stress and stress adaptation were assessed before and after the program. Heart rate variability (HRV) was measured at baseline, midpoint through the weekly yoga classes (6 weeks), and postintervention (after 12 weeks of yoga classes). The results showed that the mental health professionals in the yoga group experienced a significant reduction in work-related stress (t = -6.225, p control group revealed no significant changes. Comparing the mean differences in pre- and posttest scores between yoga and control groups, we found the yoga group significantly decreased work-related stress (t = -3.216, p = .002), but there was no significant change in stress adaptation (p = .084). While controlling for the pretest scores of work-related stress, participants in yoga, but not the control group, revealed a significant increase in autonomic nerve activity at midpoint (6 weeks) test (t = -2.799, p = .007), and at posttest (12 weeks; t = -2.099, p = .040). Because mental health professionals experienced a reduction in work-related stress and an increase in autonomic nerve activity in a weekly yoga program for 12 weeks, clinicians, administrators, and educators should offer yoga classes as a strategy to help health professionals reduce their work-related stress and balance autonomic nerve activities. © 2015 The Authors. Worldviews on Evidence-Based Nursing published by Wiley Periodicals, Inc. on behalf of Society for Worldviews on Evidence-Based Nursing.
Probability theory a foundational course
Pakshirajan, R P
2013-01-01
This book shares the dictum of J. L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics analysed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdos-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject.
Schein, Aso; Correa, Aps; Casali, Karina Rabello; Schaan, Beatriz D
2016-01-20
Physical exercise reduces glucose levels and glucose variability in patients with type 2 diabetes. Acute inspiratory muscle exercise has been shown to reduce these parameters in a small group of patients with type 2 diabetes, but these results have yet to be confirmed in a well-designed study. The aim of this study is to investigate the effect of acute inspiratory muscle exercise on glucose levels, glucose variability, and cardiovascular autonomic function in patients with type 2 diabetes. This study will use a randomized clinical trial crossover design. A total of 14 subjects will be recruited and randomly allocated to two groups to perform acute inspiratory muscle loading at 2 % of maximal inspiratory pressure (PImax, placebo load) or 60 % of PImax (experimental load). Inspiratory muscle training could be a novel exercise modality to be used to decrease glucose levels and glucose variability. ClinicalTrials.gov NCT02292810 .
Failure probability under parameter uncertainty.
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.
Toward a generalized probability theory: conditional probabilities
International Nuclear Information System (INIS)
Cassinelli, G.
1979-01-01
The main mathematical object of interest in the quantum logic approach to the foundations of quantum mechanics is the orthomodular lattice and a set of probability measures, or states, defined by the lattice. This mathematical structure is studied per se, independently from the intuitive or physical motivation of its definition, as a generalized probability theory. It is thought that the building-up of such a probability theory could eventually throw light on the mathematical structure of Hilbert-space quantum mechanics as a particular concrete model of the generalized theory. (Auth.)
Spieth, Peter M.; Güldner, Andreas; Uhlig, Christopher; Bluth, Thomas; Kiss, Thomas; Schultz, Marcus J.; Pelosi, Paolo; Koch, Thea; Gama de Abreu, Marcelo
2014-01-01
General anesthesia usually requires mechanical ventilation, which is traditionally accomplished with constant tidal volumes in volume- or pressure-controlled modes. Experimental studies suggest that the use of variable tidal volumes (variable ventilation) recruits lung tissue, improves pulmonary
Probably not future prediction using probability and statistical inference
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 ...
Palomba, S; Falbo, A; Giallauria, F; Russo, T; Rocca, M; Tolino, A; Zullo, F; Orio, F
2010-11-01
Clomiphene citrate (CC) is the first-line therapy for the induction of ovulation in infertile women with polycystic ovary syndrome (PCOS), but ∼20% of patients are unresponsive. The aim of the current study was to test the hypothesis that a 6-week intervention that consisted of structured exercise training (SET) and hypocaloric diet increases the probability of ovulation after CC in overweight and obese CC-resistant PCOS patients. A cohort of 96 overweight and obese CC-resistant PCOS patients was enrolled consecutively in a three-arm randomized, parallel, controlled, assessor-blinded clinical trial. The three interventions were: SET plus hypocaloric diet for 6 weeks (Group A); 2 weeks of observation followed by one cycle of CC therapy (Group B); and SET plus hypocaloric diet for 6 weeks, with one cycle of CC after the first 2 weeks (Group C). The primary end-point was the ovulation rate. Other reproductive data, as well as anthropometric, hormonal and metabolic data, were also collected and considered as secondary end points. After 6 weeks of SET plus hypocaloric diet, the ovulation rate was significantly (P =0.008) higher in Group C [12/32 (37.5%)] than in Groups A [4/32 (12.5%)] and B [3/32 (9.4%)] with relative risks of 3.9 [95% confidence interval (CI) 1.1-8.3; P = 0.035] and 4.0 (95% CI 1.2-12.8; P = 0.020) compared with Groups A and B, respectively. Compared with baseline, in Groups A and C, a significant improvement in clinical and biochemical androgen and insulin sensitivity indexes was observed. In the same two groups, the insulin sensitivity index was significantly (P hypocaloric diet was effective in increasing the probability of ovulation under CC treatment. The study was registered at Clinicaltrials.gov:NCT0100468.
Allen, Alexander R; Gullixson, Leah R; Wolhart, Sarah C; Kost, Susan L; Schroeder, Darrell R; Eisenach, John H
2014-02-01
Dietary sodium influences intermediate physiological traits in healthy adults independent of changes in blood pressure. The purpose of this study was to test the hypothesis that dietary sodium affects cardiac autonomic modulation during mental stress. In a prospective, randomized cross-over design separated by 1 month between diets, 70 normotensive healthy young adults (F/M: 44/26, aged 18-38 years) consumed a 5-day low (10 mmol/day), normal (150 mmol), and high (400 mmol) sodium diet followed by heart rate variability (HRV) recordings at rest and during 5-min computerized mental arithmetic. Women were studied in the low hormone phase of the menstrual cycle following each diet. Diet did not affect resting blood pressure, but heart rate (HR) (mean ± SE) was 66 ± 1, 64 ± 1, and 63 ± 1 bpm in low, normal, and high sodium conditions, respectively (analysis of variance P = 0.02). For HRV, there was a main effect of sodium on resting SD of normalized RR intervals (SDNN), square root of the mean squared difference of successive normalized RR intervals (RMSSD), high frequency, low-frequency normalized units (LFnu), and high-frequency normalized units (HFnu) (P sodium was most marked and consistent with sympathetic activation and reduced vagal activity, with increased LFnu and decreased SDNN, RMSSD, and HFnu compared to both normal and high sodium conditions (P ≤0.05 for all). Dietary sodium-by-mental stress interactions were significant for mean NN, RMSSD, high-frequency power, LFnu, and low frequency/high frequency ratio (P sodium restriction evoked an increase in resting sympathetic activity and reduced vagal activity to the extent that mental stress caused modest additional disruptions in autonomic balance. Conversely, normal and high sodium evoked a reduction in resting sympathetic activity and incremental increase in resting vagal activity, which were disrupted to a greater extent during mental stress compared to low sodium. We conclude that autonomic control of
2013-01-01
Background Chronic work-related stress is an independent risk factor for cardiometabolic diseases and associated mortality, particularly when compounded by a sedentary work environment. The purpose of this study was to determine if an office worksite-based hatha yoga program could improve physiological stress, evaluated via heart rate variability (HRV), and associated health-related outcomes in a cohort of office workers. Methods Thirty-seven adults employed in university-based office positions were randomized upon the completion of baseline testing to an experimental or control group. The experimental group completed a 10-week yoga program prescribed three sessions per week during lunch hour (50 min per session). An experienced instructor led the sessions, which emphasized asanas (postures) and vinyasa (exercises). The primary outcome was the high frequency (HF) power component of HRV. Secondary outcomes included additional HRV parameters, musculoskeletal fitness (i.e. push-up, side-bridge, and sit & reach tests) and psychological indices (i.e. state and trait anxiety, quality of life and job satisfaction). Results All measures of HRV failed to change in the experimental group versus the control group, except that the experimental group significantly increased LF:HF (p = 0.04) and reduced pNN50 (p = 0.04) versus control, contrary to our hypotheses. Flexibility, evaluated via sit & reach test increased in the experimental group versus the control group (p yoga sessions (n = 11) to control (n = 19) yielded the same findings, except that the high adherers also reduced state anxiety (p = 0.02) and RMSSD (p = 0.05), and tended to improve the push-up test (p = 0.07) versus control. Conclusions A 10-week hatha yoga intervention delivered at the office worksite during lunch hour did not improve HF power or other HRV parameters. However, improvements in flexibility, state anxiety and musculoskeletal fitness were noted with high adherence
Directory of Open Access Journals (Sweden)
Chang Dennis
2011-07-01
Full Text Available Abstract Background Chronic work-related stress is a significant and independent risk factor for cardiovascular and metabolic diseases and associated mortality, particularly when compounded by a sedentary work environment. Heart rate variability (HRV provides an estimate of parasympathetic and sympathetic autonomic control, and can serve as a marker of physiological stress. Hatha yoga is a physically demanding practice that can help to reduce stress; however, time constraints incurred by work and family life may limit participation. The purpose of the present study is to determine if a 10-week, worksite-based yoga program delivered during lunch hour can improve resting HRV and related physical and psychological parameters in sedentary office workers. Methods and design This is a parallel-arm RCT that will compare the outcomes of participants assigned to the experimental treatment group (yoga to those assigned to a no-treatment control group. Participants randomized to the experimental condition will engage in a 10-week yoga program delivered at their place of work. The yoga sessions will be group-based, prescribed three times per week during lunch hour, and will be led by an experienced yoga instructor. The program will involve teaching beginner students safely and progressively over 10 weeks a yoga sequence that incorporates asanas (poses and postures, vinyasa (exercises, pranayama (breathing control and meditation. The primary outcome of this study is the high frequency (HF spectral power component of HRV (measured in absolute units; i.e. ms2, a measure of parasympathetic autonomic control. Secondary outcomes include additional frequency and time domains of HRV, and measures of physical functioning and psychological health status. Measures will be collected prior to and following the intervention period, and at 6 months follow-up to determine the effect of intervention withdrawal. Discussion This study will determine the effect of worksite
Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks
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.
Philosophical theories of probability
Gillies, Donald
2000-01-01
The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.
International Nuclear Information System (INIS)
Choi, Seon Soon
2012-01-01
The primary aim of this paper was to evaluate several probabilistic fatigue crack propagation models using the residual of a random variable, and to present the model fit for probabilistic fatigue behavior in Mg Al Zn alloys. The proposed probabilistic models are the probabilistic Paris Erdogan model, probabilistic Walker model, probabilistic Forman model, and probabilistic modified Forman models. These models were prepared by applying a random variable to the empirical fatigue crack propagation models with these names. The best models for describing fatigue crack propagation models with these names. The best models for describing fatigue crack propagation models with these names. The best models for describing fatigue crack propagation models with these names. The best models vor describing fatigue crack propagation behavior in Mg Al Zn alloys were generally the probabilistic Paris Erdogan and probabilistic Walker models. The probabilistic Forman model was a good model only for a specimen with a thickness of 9.45mm
47 CFR 1.1623 - Probability calculation.
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...
Simulations of Probabilities for Quantum Computing
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.
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
Interpretations of probability
Khrennikov, Andrei
2009-01-01
This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.
DEFF Research Database (Denmark)
Andersen, Andreas; Rieckmann, Andreas
2016-01-01
In this article, we illustrate how to use mi impute chained with intreg to fit an analysis of covariance analysis of censored and nondetectable immunological concentrations measured in a randomized pretest–posttest design.......In this article, we illustrate how to use mi impute chained with intreg to fit an analysis of covariance analysis of censored and nondetectable immunological concentrations measured in a randomized pretest–posttest design....
Probability theory a concise course
Rozanov, Y A
1977-01-01
This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, a detailed treatment of Markov chains, continuous Markov processes, and more. Includes 150 problems, many with answers. Indispensable to mathematicians and natural scientists alike.
International Nuclear Information System (INIS)
Pfeifle, T.W.; Mellegard, K.D.; Munson, D.E.
1992-10-01
The modified Munson-Dawson (M-D) constitutive model that describes the creep behavior of salt will be used in performance assessment calculations to assess compliance of the Waste Isolation Pilot Plant (WIPP) facility with requirements governing the disposal of nuclear waste. One of these standards requires that the uncertainty of future states of the system, material model parameters, and data be addressed in the performance assessment models. This paper presents a method in which measurement uncertainty and the inherent variability of the material are characterized by treating the M-D model parameters as random variables. The random variables can be described by appropriate probability distribution functions which then can be used in Monte Carlo or structural reliability analyses. Estimates of three random variables in the M-D model were obtained by fitting a scalar form of the model to triaxial compression creep data generated from tests of WIPP salt. Candidate probability distribution functions for each of the variables were then fitted to the estimates and their relative goodness-of-fit tested using the Kolmogorov-Smirnov statistic. A sophisticated statistical software package obtained from BMDP Statistical Software, Inc. was used in the M-D model fitting. A separate software package, STATGRAPHICS, was used in fitting the candidate probability distribution functions to estimates of the variables. Skewed distributions, i.e., lognormal and Weibull, were found to be appropriate for the random variables analyzed
Normal probability plots with confidence.
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.
De Ruiter, Naomi M. P.; Den Hartigh, Ruud J. R.; Cox, Ralf F. A.; Van Geert, Paul L. C.; Kunnen, E. Saskia
2015-01-01
Research regarding the variability of state self-esteem (SSE) commonly focuses on the magnitude of variability. In this article we provide the first empirical test of the temporalstructure of SSE as a real-time process during parent-adolescent interactions. We adopt a qualitative phenomenological
DEFF Research Database (Denmark)
Schjær-Jacobsen, Hans
2012-01-01
uncertainty can be calculated. The possibility approach is particular well suited for representation of uncertainty of a non-statistical nature due to lack of knowledge and requires less information than the probability approach. Based on the kind of uncertainty and knowledge present, these aspects...... to the understanding of similarities and differences of the two approaches as well as practical applications. The probability approach offers a good framework for representation of randomness and variability. Once the probability distributions of uncertain parameters and their correlations are known the resulting...... are thoroughly discussed in the case of rectangular representation of uncertainty by the uniform probability distribution and the interval, respectively. Also triangular representations are dealt with and compared. Calculation of monotonic as well as non-monotonic functions of variables represented...
Allegrucci, M; Newman, B A; Young-Cooper, G O; Alexander, C B; Meier, D; Kelus, A S; Mage, R G
1990-07-01
Rabbits of the Alicia strain have a mutation (ali) that segregates with the immunoglobulin heavy-chain (lgh) locus and has a cis effect upon the expression of heavy-chain variable-region (VH) genes encoding the a2 allotype. In heterozygous a1/ali or a3/ali rabbits, serum immunoglobulins are almost entirely the products of the normal a1 or a3 allele and only traces of a2 immunoglobulin are detectable. Adult homozygous ali/ali rabbits likewise have normal immunoglobulin levels resulting from increased production of a-negative immunoglobulins and some residual ability to produce the a2 allotype. By contrast, the majority of the immunoglobulins of wild-type a2 rabbits are a2-positive and only a small percentage are a-negative. Genomic DNAs from homozygous mutant and wild-type animals were indistinguishable by Southern analyses using a variety of restriction enzyme digests and lgh probes. However, when digests with infrequently cutting enzymes were analyzed by transverse alternating-field electrophoresis, the ali DNA fragments were 10-15 kilobases smaller than the wild type. These fragments hybridized to probes both for VH and for a region of DNA a few kilobases downstream of the VH genes nearest the joining region. We suggest that this relatively small deletion affects a segment containing 3' VH genes with important regulatory functions, the loss of which leads to the ali phenotype. These results, and the fact that the 3' VH genes rearrange early in B-cell development, indicate that the 3' end of the VH locus probably plays a key role in regulation of VH gene expression.
Directory of Open Access Journals (Sweden)
Shuiqing Yu
2013-01-01
Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.
International Nuclear Information System (INIS)
Fraassen, B.C. van
1979-01-01
The interpretation of probabilities in physical theories are considered, whether quantum or classical. The following points are discussed 1) the functions P(μ, Q) in terms of which states and propositions can be represented, are classical (Kolmogoroff) probabilities, formally speaking, 2) these probabilities are generally interpreted as themselves conditional, and the conditions are mutually incompatible where the observables are maximal and 3) testing of the theory typically takes the form of confronting the expectation values of observable Q calculated with probability measures P(μ, Q) for states μ; hence, of comparing the probabilities P(μ, Q)(E) with the frequencies of occurrence of the corresponding events. It seems that even the interpretation of quantum mechanics, in so far as it concerns what the theory says about the empirical (i.e. actual, observable) phenomena, deals with the confrontation of classical probability measures with observable frequencies. This confrontation is studied. (Auth./C.F.)
Probability of satellite collision
Mccarter, J. W.
1972-01-01
A method is presented for computing the probability of a collision between a particular artificial earth satellite and any one of the total population of earth satellites. The collision hazard incurred by the proposed modular Space Station is assessed using the technique presented. The results of a parametric study to determine what type of satellite orbits produce the greatest contribution to the total collision probability are presented. Collision probability for the Space Station is given as a function of Space Station altitude and inclination. Collision probability was also parameterized over miss distance and mission duration.
Florescu, Ionut
2013-01-01
THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability. The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introductio
Ash, Robert B; Lukacs, E
1972-01-01
Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory.Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of var
Risk estimation using probability machines
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
Freund, John E
1993-01-01
Thorough, lucid coverage of permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, binomial distribution, geometric distribution, standard deviation, law of large numbers, and much more. Exercises with some solutions. Summary. Bibliography. Includes 42 black-and-white illustrations. 1973 edition.
Probability, Nondeterminism and Concurrency
DEFF Research Database (Denmark)
Varacca, Daniele
Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particula...
Rocchi, Paolo
2014-01-01
The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability. Beyond the radical followers of the two schools, a circle of pluralist thinkers tends to reconcile the opposing concepts. The author uses two theorems in order to prove that the various interpretations of probability do not come into opposition and can be used in different contexts. The goal here is to clarify the multifold nature of probability by means of a purely mathematical approach and to show how philosophical arguments can only serve to deepen actual intellectual contrasts. The book can be considered as one of the most important contributions in the analysis of probability interpretation in the last 10-15 years.
Siegelaar, S. E.; Kulik, W.; van Lenthe, H.; Mukherjee, R.; Hoekstra, J. B. L.; DeVries, J. H.
2009-01-01
To assess the effect of three times daily mealtime inhaled insulin therapy compared with once daily basal insulin glargine therapy on 72-h glucose profiles, glucose variability and oxidative stress in type 2 diabetes patients. In an inpatient crossover study, 40 subjects with type 2 diabetes were
Billingsley, Patrick
2012-01-01
Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this
International Nuclear Information System (INIS)
Bitsakis, E.I.; Nicolaides, C.A.
1989-01-01
The concept of probability is now, and always has been, central to the debate on the interpretation of quantum mechanics. Furthermore, probability permeates all of science, as well as our every day life. The papers included in this volume, written by leading proponents of the ideas expressed, embrace a broad spectrum of thought and results: mathematical, physical epistemological, and experimental, both specific and general. The contributions are arranged in parts under the following headings: Following Schroedinger's thoughts; Probability and quantum mechanics; Aspects of the arguments on nonlocality; Bell's theorem and EPR correlations; Real or Gedanken experiments and their interpretation; Questions about irreversibility and stochasticity; and Epistemology, interpretation and culture. (author). refs.; figs.; tabs
Shorack, Galen R
2017-01-01
This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians—a textbook for courses in probability for students in mathematical statistics. It is recommended to anyone interested in the probability underlying modern statistics, providing a solid grounding in the probabilistic tools and techniques necessary to do theoretical research in statistics. For the teaching of probability theory to post graduate statistics students, this is one of the most attractive books available. Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. Martingale coverage includes coverage of censored data martingales. The text includes measure theoretic...
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
Probability and Statistical Inference
Prosper, Harrison B.
2006-01-01
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
Hartmann, Stephan
2011-01-01
Many results of modern physics--those of quantum mechanics, for instance--come in a probabilistic guise. But what do probabilistic statements in physics mean? Are probabilities matters of objective fact and part of the furniture of the world, as objectivists think? Or do they only express ignorance or belief, as Bayesians suggest? And how are probabilistic hypotheses justified and supported by empirical evidence? Finally, what does the probabilistic nature of physics imply for our understanding of the world? This volume is the first to provide a philosophical appraisal of probabilities in all of physics. Its main aim is to make sense of probabilistic statements as they occur in the various physical theories and models and to provide a plausible epistemology and metaphysics of probabilities. The essays collected here consider statistical physics, probabilistic modelling, and quantum mechanics, and critically assess the merits and disadvantages of objectivist and subjectivist views of probabilities in these fie...
Hemmo, Meir
2012-01-01
What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.
Probability in quantum mechanics
Directory of Open Access Journals (Sweden)
J. G. Gilson
1982-01-01
Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
Quantum computing and probability.
Ferry, David K
2009-11-25
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.
Quantum computing and probability
International Nuclear Information System (INIS)
Ferry, David K
2009-01-01
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction. (viewpoint)
International Nuclear Information System (INIS)
Cabout, T.; Buckley, J.; Cagli, C.; Jousseaume, V.; Nodin, J.-F.; Salvo, B. de; Bocquet, M.; Muller, Ch.
2013-01-01
This paper deals with the role of platinum or titanium–titanium nitride electrodes on variability of resistive switching characteristics and electrical performances of HfO 2 -based memory elements. Capacitor-like Pt/HfO 2 (10 nm)/Pt and Ti/HfO 2 (10 nm)/TiN structures were fabricated on top of a tungsten pillar bottom electrode and integrated in-between two interconnect metal lines. First, quasi-static measurements were performed to apprehend the role of electrodes on electroforming, set and reset operations and their corresponding switching parameters. Memory elements with Pt as top and bottom electrodes exhibited a non-polar behavior with sharp decrease of current during reset operation while Ti/HfO 2 /TiN capacitors showed a bipolar switching behavior, with a gradual reset. In a second step, statistical distributions of switching parameters (voltage and resistance) were extracted from data obtained on few hundreds of capacitors. Even if the resistance in low resistive state and reset voltage was found to be comparable for both types of electrodes, the progressive reset operation observed on samples with Ti/TiN electrodes led to a lower variability of resistance in high resistive state and concomitantly of set voltage. In addition Ti–TiN electrodes enabled gaining: (i) lower forming and set voltages with significantly narrower capacitor-to-capacitor distributions; (ii) a better data retention capability (10 years at 65 °C instead of 10 years at 50 °C for Pt electrodes); (iii) satisfactory dynamic performances with lower set and reset voltages for ramp speed ranging from 10 −2 to 10 7 V/s. The significant improvement of switching behavior with Ti–TiN electrodes is mainly attributed to the formation of a native interface layer between HfO 2 oxide and Ti top electrode. - Highlights: ► HfO2 based capacitor-like structures were fabricated with Pt and Ti based electrodes. ► Influence of electrode materials on switching parameter variability is assessed.
Directory of Open Access Journals (Sweden)
Helmut Prodinger
2007-01-01
Full Text Available In words, generated by independent geometrically distributed random variables, we study the l th descent, which is, roughly speaking, the l th occurrence of a neighbouring pair ab with a>b. The value a is called the initial height, and b the end height. We study these two random variables (and some similar ones by combinatorial and probabilistic tools. We find in all instances a generating function Ψ(v,u, where the coefficient of v j u i refers to the j th descent (ascent, and i to the initial (end height. From this, various conclusions can be drawn, in particular expected values. In the probabilistic part, a Markov chain model is used, which allows to get explicit expressions for the heights of the second descent. In principle, one could go further, but the complexity of the results forbids it. This is extended to permutations of a large number of elements. Methods from q-analysis are used to simplify the expressions. This is the reason that we confine ourselves to the geometric distribution only. For general discrete distributions, no such tools are available.
Algebraic polynomials with random coefficients
Directory of Open Access Journals (Sweden)
K. Farahmand
2002-01-01
Full Text Available This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω+a1(ω(n11/2x+a2(ω(n21/2x2+…an(ω(nn1/2xn when n is large. The coefficients {aj(w}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr. A special case of dependent coefficients is also studied.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
The perception of probability.
Gallistel, C R; Krishan, Monika; Liu, Ye; Miller, Reilly; Latham, Peter E
2014-01-01
We present a computational model to explain the results from experiments in which subjects estimate the hidden probability parameter of a stepwise nonstationary Bernoulli process outcome by outcome. The model captures the following results qualitatively and quantitatively, with only 2 free parameters: (a) Subjects do not update their estimate after each outcome; they step from one estimate to another at irregular intervals. (b) The joint distribution of step widths and heights cannot be explained on the assumption that a threshold amount of change must be exceeded in order for them to indicate a change in their perception. (c) The mapping of observed probability to the median perceived probability is the identity function over the full range of probabilities. (d) Precision (how close estimates are to the best possible estimate) is good and constant over the full range. (e) Subjects quickly detect substantial changes in the hidden probability parameter. (f) The perceived probability sometimes changes dramatically from one observation to the next. (g) Subjects sometimes have second thoughts about a previous change perception, after observing further outcomes. (h) The frequency with which they perceive changes moves in the direction of the true frequency over sessions. (Explaining this finding requires 2 additional parametric assumptions.) The model treats the perception of the current probability as a by-product of the construction of a compact encoding of the experienced sequence in terms of its change points. It illustrates the why and the how of intermittent Bayesian belief updating and retrospective revision in simple perception. It suggests a reinterpretation of findings in the recent literature on the neurobiology of decision making. (PsycINFO Database Record (c) 2014 APA, all rights reserved).
Sharma, Vivek Kumar; Subramanian, Senthil Kumar; Radhakrishnan, Krishnakumar; Rajendran, Rajathi; Ravindran, Balasubramanian Sulur; Arunachalam, Vinayathan
2017-05-01
Physical inactivity contributes to many health issues. The WHO-recommended physical activity for adolescents encompasses aerobic, resistance, and bone strengthening exercises aimed at achieving health-related physical fitness. Heart rate variability (HRV) and maximal aerobic capacity (VO2max) are considered as noninvasive measures of cardiovascular health. The objective of this study is to compare the effect of structured and unstructured physical training on maximal aerobic capacity and HRV among adolescents. We designed a single blinded, parallel, randomized active-controlled trial (Registration No. CTRI/2013/08/003897) to compare the physiological effects of 6 months of globally recommended structured physical activity (SPA), with that of unstructured physical activity (USPA) in healthy school-going adolescents. We recruited 439 healthy student volunteers (boys: 250, girls: 189) in the age group of 12-17 years. Randomization across the groups was done using age and gender stratified randomization method, and the participants were divided into two groups: SPA (n=219, boys: 117, girls: 102) and USPA (n=220, boys: 119, girls: 101). Depending on their training status and gender the participants in both SPA and USPA groups were further subdivided into the following four sub-groups: SPA athlete boys (n=22) and girls (n=17), SPA nonathlete boys (n=95) and girls (n=85), USPA athlete boys (n=23) and girls (n=17), and USPA nonathlete boys (n=96) and girls (n=84). We recorded HRV, body fat%, and VO2 max using Rockport Walk Fitness test before and after the intervention. Maximum aerobic capacity and heart rate variability increased significantly while heart rate, systolic blood pressure, diastolic blood pressure, and body fat percentage decreased significantly after both SPA and USPA intervention. However, the improvement was more in SPA as compared to USPA. SPA is more beneficial for improving cardiorespiratory fitness, HRV, and reducing body fat percentage in terms of
Papakostas, George I; Martinson, Max A; Fava, Maurizio; Iovieno, Nadia
2016-05-01
The aim of this work is to compare the efficacy of pharmacologic agents for the treatment of major depressive disorder (MDD) and bipolar depression. MEDLINE/PubMed databases were searched for studies published in English between January 1980 and September 2014 by cross-referencing the search term placebo with each of the antidepressant agents identified and with bipolar. The search was supplemented by manual bibliography review. We selected double-blind, randomized, placebo-controlled trials of antidepressant monotherapies for the treatment of MDD and of oral drug monotherapies for the treatment of bipolar depression. 196 trials in MDD and 19 trials in bipolar depression were found eligible for inclusion in our analysis. Data were extracted by one of the authors and checked for accuracy by a second one. Data extracted included year of publication, number of patients randomized, probability of receiving placebo, duration of the trial, baseline symptom severity, dosing schedule, study completion rates, and clinical response rates. Response rates for drug versus placebo in trials of MDD and bipolar depression were 52.7% versus 37.5% and 54.7% versus 40.5%, respectively. The random-effects meta-analysis indicated that drug therapy was more effective than placebo in both MDD (risk ratio for response = 1.373; P depression (risk ratio = 1.257; P depression trials in favor of MDD (P = .008). Although a statistically significantly greater treatment effect size was noted in MDD relative to bipolar depression studies, the absolute magnitude of the difference was numerically small. Therefore, the present study suggests no clinically significant differences in the overall short-term efficacy of pharmacologic monotherapies for MDD and bipolar depression. © Copyright 2016 Physicians Postgraduate Press, Inc.
Data envelopment analysis of randomized ranks
Directory of Open Access Journals (Sweden)
Sant'Anna Annibal P.
2002-01-01
Full Text Available Probabilities and odds, derived from vectors of ranks, are here compared as measures of efficiency of decision-making units (DMUs. These measures are computed with the goal of providing preliminary information before starting a Data Envelopment Analysis (DEA or the application of any other evaluation or composition of preferences methodology. Preferences, quality and productivity evaluations are usually measured with errors or subject to influence of other random disturbances. Reducing evaluations to ranks and treating the ranks as estimates of location parameters of random variables, we are able to compute the probability of each DMU being classified as the best according to the consumption of each input and the production of each output. Employing the probabilities of being the best as efficiency measures, we stretch distances between the most efficient units. We combine these partial probabilities in a global efficiency score determined in terms of proximity to the efficiency frontier.
Forni, Valentina; Bianchi, Giorgia; Ogna, Adam; Salvadé, Igor; Vuistiner, Philippe; Burnier, Michel; Gabutti, Luca
2013-07-22
In a simulation based on a pharmacokinetic model we demonstrated that increasing the erythropoiesis stimulating agents (ESAs) half-life or shortening their administration interval decreases hemoglobin variability. The benefit of reducing the administration interval was however lessened by the variability induced by more frequent dosage adjustments. The purpose of this study was to analyze the reticulocyte and hemoglobin kinetics and variability under different ESAs and administration intervals in a collective of chronic hemodialysis patients. The study was designed as an open-label, randomized, four-period cross-over investigation, including 30 patients under chronic hemodialysis at the regional hospital of Locarno (Switzerland) in February 2010 and lasting 2 years. Four subcutaneous treatment strategies (C.E.R.A. every 4 weeks Q4W and every 2 weeks Q2W, Darbepoetin alfa Q4W and Q2W) were compared with each other. The mean square successive difference of hemoglobin, reticulocyte count and ESAs dose was used to quantify variability. We distinguished a short- and a long-term variability based respectively on the weekly and monthly successive difference. No difference was found in the mean values of biological parameters (hemoglobin, reticulocytes, and ferritin) between the 4 strategies. ESAs type did not affect hemoglobin and reticulocyte variability, but C.E.R.A induced a more sustained reticulocytes response over time and increased the risk of hemoglobin overshooting (OR 2.7, p = 0.01). Shortening the administration interval lessened the amplitude of reticulocyte count fluctuations but resulted in more frequent ESAs dose adjustments and in amplified reticulocyte and hemoglobin variability. Q2W administration interval was however more favorable in terms of ESAs dose, allowing a 38% C.E.R.A. dose reduction, and no increase of Darbepoetin alfa. The reticulocyte dynamic was a more sensitive marker of time instability of the hemoglobin response under ESAs therapy
On the probability distribution of the stochastic saturation scale in QCD
International Nuclear Information System (INIS)
Marquet, C.; Soyez, G.; Xiao Bowen
2006-01-01
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations
International Nuclear Information System (INIS)
Birchall, A.; Muirhead, C.R.; James, A.C.
1988-01-01
An analytical expression has been derived for the k-sum distribution, formed by summing k random variables from a lognormal population. Poisson statistics are used with this distribution to derive distribution of intake when breathing an atmosphere with a constant particle number concentration. Bayesian inference is then used to calculate the posterior probability distribution of concentrations from a given measurement. This is combined with the above intake distribution to give the probability distribution of intake resulting from a single measurement of activity made by an ideal sampler. It is shown that the probability distribution of intake is very dependent on the prior distribution used in Bayes' theorem. The usual prior assumption, that all number concentrations are equally probable, leads to an imbalance in the posterior intake distribution. This can be resolved if a new prior proportional to w -2/3 is used, where w is the expected number of particles collected. (author)
Vila-Castelar, Clara; Ly, Jenny J; Kaplan, Lillian; Van Dyk, Kathleen; Berger, Jeffrey T; Macina, Lucy O; Stewart, Jennifer L; Foldi, Nancy S
2018-04-09
Donepezil is widely used to treat Alzheimer's disease (AD), but detecting early response remains challenging for clinicians. Acetylcholine is known to directly modulate attention, particularly under high cognitive conditions, but no studies to date test whether measures of attention under high load can detect early effects of donepezil. We hypothesized that load-dependent attention tasks are sensitive to short-term treatment effects of donepezil, while global and other domain-specific cognitive measures are not. This longitudinal, randomized, double-blind, placebo-controlled pilot trial (ClinicalTrials.gov Identifier: NCT03073876) evaluated 23 participants newly diagnosed with AD initiating de novo donepezil treatment (5 mg). After baseline assessment, participants were randomized into Drug (n = 12) or Placebo (n = 11) groups, and retested after approximately 6 weeks. Cognitive assessment included: (a) attention tasks (Foreperiod Effect, Attentional Blink, and Covert Orienting tasks) measuring processing speed, top-down accuracy, orienting, intra-individual variability, and fatigue; (b) global measures (Alzheimer's Disease Assessment Scale-Cognitive Subscale, Mini-Mental Status Examination, Dementia Rating Scale); and (c) domain-specific measures (memory, language, visuospatial, and executive function). The Drug but not the Placebo group showed benefits of treatment at high-load measures by preserving top-down accuracy, improving intra-individual variability, and averting fatigue. In contrast, other global or cognitive domain-specific measures could not detect treatment effects over the same treatment interval. The pilot-study suggests that attention measures targeting accuracy, variability, and fatigue under high-load conditions could be sensitive to short-term cholinergic treatment. Given the central role of acetylcholine in attentional function, load-dependent attentional measures may be valuable cognitive markers of early treatment response.
Irreversibility and conditional probability
International Nuclear Information System (INIS)
Stuart, C.I.J.M.
1989-01-01
The mathematical entropy - unlike physical entropy - is simply a measure of uniformity for probability distributions in general. So understood, conditional entropies have the same logical structure as conditional probabilities. If, as is sometimes supposed, conditional probabilities are time-reversible, then so are conditional entropies and, paradoxically, both then share this symmetry with physical equations of motion. The paradox is, of course that probabilities yield a direction to time both in statistical mechanics and quantum mechanics, while the equations of motion do not. The supposed time-reversibility of both conditionals seems also to involve a form of retrocausality that is related to, but possibly not the same as, that described by Costa de Beaurgard. The retrocausality is paradoxically at odds with the generally presumed irreversibility of the quantum mechanical measurement process. Further paradox emerges if the supposed time-reversibility of the conditionals is linked with the idea that the thermodynamic entropy is the same thing as 'missing information' since this confounds the thermodynamic and mathematical entropies. However, it is shown that irreversibility is a formal consequence of conditional entropies and, hence, of conditional probabilities also. 8 refs. (Author)
Experimental Probability in Elementary School
Andrew, Lane
2009-01-01
Concepts in probability can be more readily understood if students are first exposed to probability via experiment. Performing probability experiments encourages students to develop understandings of probability grounded in real events, as opposed to merely computing answers based on formulae.
Improving Ranking Using Quantum Probability
Melucci, Massimo
2011-01-01
The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of ...
Collision Probability Analysis
DEFF Research Database (Denmark)
Hansen, Peter Friis; Pedersen, Preben Terndrup
1998-01-01
It is the purpose of this report to apply a rational model for prediction of ship-ship collision probabilities as function of the ship and the crew characteristics and the navigational environment for MS Dextra sailing on a route between Cadiz and the Canary Islands.The most important ship and crew...... characteristics are: ship speed, ship manoeuvrability, the layout of the navigational bridge, the radar system, the number and the training of navigators, the presence of a look out etc. The main parameters affecting the navigational environment are ship traffic density, probability distributions of wind speeds...... probability, i.e. a study of the navigator's role in resolving critical situations, a causation factor is derived as a second step.The report documents the first step in a probabilistic collision damage analysis. Future work will inlcude calculation of energy released for crushing of structures giving...
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.
Estimating Subjective Probabilities
DEFF Research Database (Denmark)
Andersen, Steffen; Fountain, John; Harrison, Glenn W.
2014-01-01
either construct elicitation mechanisms that control for risk aversion, or construct elicitation mechanisms which undertake 'calibrating adjustments' to elicited reports. We illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration adjustments...... that theory calls for. We illustrate this approach using data from a controlled experiment with real monetary consequences to the subjects. This allows the observer to make inferences about the latent subjective probability, under virtually any well-specified model of choice under subjective risk, while still...
Introduction to imprecise probabilities
Augustin, Thomas; de Cooman, Gert; Troffaes, Matthias C M
2014-01-01
In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, includin
Classic Problems of Probability
Gorroochurn, Prakash
2012-01-01
"A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin
Integration, measure and probability
Pitt, H R
2012-01-01
Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.
DEFF Research Database (Denmark)
Moeller, Niels C; Korsholm, Lars; Kristensen, Peter L
2008-01-01
BACKGROUND: Potentially, unit-specific in-vitro calibration of accelerometers could increase field data quality and study power. However, reduced inter-unit variability would only be important if random instrument variability contributes considerably to the total variation in field data. Therefor...
Random walks on reductive groups
Benoist, Yves
2016-01-01
The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Counterexamples in probability
Stoyanov, Jordan M
2013-01-01
While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix.
Plotnitsky, Arkady
2010-01-01
Offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schrodinger; in quantum mechanics; and in modern physics. This book considers the implications of these relationships and of quantum theory for our understanding of the nature of thinking and knowledge in general
Transition probabilities for atoms
International Nuclear Information System (INIS)
Kim, Y.K.
1980-01-01
Current status of advanced theoretical methods for transition probabilities for atoms and ions is discussed. An experiment on the f values of the resonance transitions of the Kr and Xe isoelectronic sequences is suggested as a test for the theoretical methods
Eliciting conditional and unconditional rank correlations from conditional probabilities
International Nuclear Information System (INIS)
Morales, O.; Kurowicka, D.; Roelen, A.
2008-01-01
Causes of uncertainties may be interrelated and may introduce dependencies. Ignoring these dependencies may lead to large errors. A number of graphical models in probability theory such as dependence trees, vines and (continuous) Bayesian belief nets [Cooke RM. Markov and entropy properties of tree and vine-dependent variables. In: Proceedings of the ASA section on Bayesian statistical science, 1997; Kurowicka D, Cooke RM. Distribution-free continuous Bayesian belief nets. In: Proceedings of mathematical methods in reliability conference, 2004; Bedford TJ, Cooke RM. Vines-a new graphical model for dependent random variables. Ann Stat 2002; 30(4):1031-68; Kurowicka D, Cooke RM. Uncertainty analysis with high dimensional dependence modelling. New York: Wiley; 2006; Hanea AM, et al. Hybrid methods for quantifying and analyzing Bayesian belief nets. In: Proceedings of the 2005 ENBIS5 conference, 2005; Shachter RD, Kenley CR. Gaussian influence diagrams. Manage Sci 1998; 35(5) .] have been developed to capture dependencies between random variables. The input for these models are various marginal distributions and dependence information, usually in the form of conditional rank correlations. Often expert elicitation is required. This paper focuses on dependence representation, and dependence elicitation. The techniques presented are illustrated with an application from aviation safety
Exclusion probabilities and likelihood ratios with applications to mixtures.
Slooten, Klaas-Jan; Egeland, Thore
2016-01-01
The statistical evidence obtained from mixed DNA profiles can be summarised in several ways in forensic casework including the likelihood ratio (LR) and the Random Man Not Excluded (RMNE) probability. The literature has seen a discussion of the advantages and disadvantages of likelihood ratios and exclusion probabilities, and part of our aim is to bring some clarification to this debate. In a previous paper, we proved that there is a general mathematical relationship between these statistics: RMNE can be expressed as a certain average of the LR, implying that the expected value of the LR, when applied to an actual contributor to the mixture, is at least equal to the inverse of the RMNE. While the mentioned paper presented applications for kinship problems, the current paper demonstrates the relevance for mixture cases, and for this purpose, we prove some new general properties. We also demonstrate how to use the distribution of the likelihood ratio for donors of a mixture, to obtain estimates for exceedance probabilities of the LR for non-donors, of which the RMNE is a special case corresponding to L R>0. In order to derive these results, we need to view the likelihood ratio as a random variable. In this paper, we describe how such a randomization can be achieved. The RMNE is usually invoked only for mixtures without dropout. In mixtures, artefacts like dropout and drop-in are commonly encountered and we address this situation too, illustrating our results with a basic but widely implemented model, a so-called binary model. The precise definitions, modelling and interpretation of the required concepts of dropout and drop-in are not entirely obvious, and we attempt to clarify them here in a general likelihood framework for a binary model.
Negative probability in the framework of combined probability
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...
Directory of Open Access Journals (Sweden)
Fabrizio Maturo
2016-06-01
Full Text Available In practical applications relating to business and management sciences, there are many variables that, for their own nature, are better described by a pair of ordered values (i.e. financial data. By summarizing this measurement with a single value, there is a loss of information; thus, in these situations, data are better described by interval values rather than by single values. Interval arithmetic studies and analyzes this type of imprecision; however, if the intervals has no sharp boundaries, fuzzy set theory is the most suitable instrument. Moreover, fuzzy regression models are able to overcome some typical limitation of classical regression because they do not need the same strong assumptions. In this paper, we present a review of the main methods introduced in the literature on this topic and introduce some recent developments regarding the concept of randomness in fuzzy regression.
Chelminiak, P.; Dixon, J. M.; Tuszyński, J. A.; Marsh, R. E.
2006-05-01
This paper discusses an application of a random network with a variable number of links and traps to the elimination of drug molecules from the body by the liver. The nodes and links represent the transport vessels, and the traps represent liver cells with metabolic enzymes that eliminate drug molecules. By varying the number and configuration of links and nodes, different disease states of the liver related to vascular damage have been simulated, and the effects on the rate of elimination of a drug have been investigated. Results of numerical simulations show the prevalence of exponential decay curves with rates that depend on the concentration of links. In the case of fractal lattices at the percolation threshold, we find that the decay of the concentration is described by exponential functions for high trap concentrations but transitions to stretched exponential behavior at low trap concentrations.
Directory of Open Access Journals (Sweden)
Nuria eRuffini
2015-08-01
Full Text Available Context: Heart Rate Variability (HRV indicates how heart rate changes in response to inner and external stimuli. HRV is linked to health status and it is an indirect marker of the autonomic nervous system (ANS function. Objective: To investigate the influence of osteopathic manipulative treatment (OMT on ANS activity through changes of High Frequency, a heart rate variability index indicating the parasympathetic activity, in healthy subjects, compared with sham therapy and control group.Methods: Sixty-six healthy subjects, both male and female, were included in the present 3-armed randomized placebo controlled within subject cross-over single blinded study. Participants were asymptomatic adults, both smokers and non-smokers and not on medications. At enrollment subjects were randomized in 3 groups: A, B, C. Standardized structural evaluation followed by a patient need-based osteopathic treatment was performed in the first session of group A and in the second session of group B. Standardized evaluation followed by a protocoled sham treatment was provided in the second session of group A and in the first session of group B. No intervention was performed in the two sessions of group C, acting as a time-control. The trial was registered on clinicaltrials.gov identifier: NCT01908920.Main Outcomes Measures: HRV was calculated from electrocardiography before, during and after the intervention, for a total amount time of 25 minutes.Results: OMT engendered a statistically significant increase of parasympathetic activity, as shown by High Frequency rate (p<0.001, and decrease of sympathetic activity, as revealed by Low Frequency rate (p<0.01; results also showed a reduction of Low Frequency/High Frequency ratio (p<0.001 and Detrended fluctuation scaling exponent (p<0.05. Conclusions: Findings suggested that OMT can influence ANS activity increasing parasympathetic function and decreasing sympathetic activity, compared to sham therapy and control group.
Menezes, Regina; Rodriguez-Mateos, Ana; Kaltsatou, Antonia; González-Sarrías, Antonio; Greyling, Arno; Giannaki, Christoforos; Andres-Lacueva, Cristina; Milenkovic, Dragan; Gibney, Eileen R.; Dumont, Julie; Schär, Manuel; Garcia-Aloy, Mar; Palma-Duran, Susana Alejandra; Ruskovska, Tatjana; Maksimova, Viktorija; Combet, Emilie; Pinto, Paula
2017-01-01
Several epidemiological studies have linked flavonols with decreased risk of cardiovascular disease (CVD). However, some heterogeneity in the individual physiological responses to the consumption of these compounds has been identified. This meta-analysis aimed to study the effect of flavonol supplementation on biomarkers of CVD risk such as, blood lipids, blood pressure and plasma glucose, as well as factors affecting their inter-individual variability. Data from 18 human randomized controlled trials were pooled and the effect was estimated using fixed or random effects meta-analysis model and reported as difference in means (DM). Variability in the response of blood lipids to supplementation with flavonols was assessed by stratifying various population subgroups: age, sex, country, and health status. Results showed significant reductions in total cholesterol (DM = −0.10 mmol/L; 95% CI: −0.20, −0.01), LDL cholesterol (DM = −0.14 mmol/L; 95% CI: −0.21, 0.07), and triacylglycerol (DM = −0.10 mmol/L; 95% CI: −0.18, 0.03), and a significant increase in HDL cholesterol (DM = 0.05 mmol/L; 95% CI: 0.02, 0.07). A significant reduction was also observed in fasting plasma glucose (DM = −0.18 mmol/L; 95% CI: −0.29, −0.08), and in blood pressure (SBP: DM = −4.84 mmHg; 95% CI: −5.64, −4.04; DBP: DM = −3.32 mmHg; 95% CI: −4.09, −2.55). Subgroup analysis showed a more pronounced effect of flavonol intake in participants from Asian countries and in participants with diagnosed disease or dyslipidemia, compared to healthy and normal baseline values. In conclusion, flavonol consumption improved biomarkers of CVD risk, however, country of origin and health status may influence the effect of flavonol intake on blood lipid levels. PMID:28208791
Bhatti, A; Khan, J; Murki, S; Sundaram, V; Saini, S S; Kumar, P
2015-11-01
To compare the failure rates between Jet continuous positive airway pressure device (J-CPAP-variable flow) and Bubble continuous positive airway device (B-CPAP) in preterm infants with respiratory distress. Preterm newborns CPAP (a variable flow device) or B-CPAP (continuous flow device). A standardized protocol was followed for titration, weaning and removal of CPAP. Pressure was monitored close to the nares in both the devices every 6 hours and settings were adjusted to provide desired CPAP. The primary outcome was CPAP failure rate within 72 h of life. Secondary outcomes were CPAP failure within 7 days of life, need for surfactant post-randomization, time to CPAP failure, duration of CPAP and complications of prematurity. An intention to treat analysis was done. One-hundred seventy neonates were randomized, 80 to J-CPAP and 90 to B-CPAP. CPAP failure rates within 72 h were similar in infants who received J-CPAP and in those who received B-CPAP (29 versus 21%; relative risks 1.4 (0.8 to 2.3), P=0.25). Mean (95% confidence intervals) time to CPAP failure was 59 h (54 to 64) in the Jet CPAP group in comparison with 65 h (62 to 68) in the Bubble CPAP group (log rank P=0.19). All other secondary outcomes were similar between the two groups. In preterm infants with respiratory distress starting within 6 h of life, CPAP failure rates were similar with Jet CPAP and Bubble CPAP.
A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses
Vasdekis, Vassilis G. S.; Cagnone, Silvia; Moustaki, Irini
2012-01-01
The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate…
Sampling, Probability Models and Statistical Reasoning -RE ...
Indian Academy of Sciences (India)
random sampling allows data to be modelled with the help of probability ... g based on different trials to get an estimate of the experimental error. ... research interests lie in the .... if e is indeed the true value of the proportion of defectives in the.
Concurrency meets probability: theory and practice (abstract)
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
Comparing linear probability model coefficients across groups
DEFF Research Database (Denmark)
Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt
2015-01-01
of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate......This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more...... these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons....
Waste Package Misload Probability
International Nuclear Information System (INIS)
Knudsen, J.K.
2001-01-01
The objective of this calculation is to calculate the probability of occurrence for fuel assembly (FA) misloads (i.e., Fa placed in the wrong location) and FA damage during FA movements. The scope of this calculation is provided by the information obtained from the Framatome ANP 2001a report. The first step in this calculation is to categorize each fuel-handling events that occurred at nuclear power plants. The different categories are based on FAs being damaged or misloaded. The next step is to determine the total number of FAs involved in the event. Using the information, a probability of occurrence will be calculated for FA misload and FA damage events. This calculation is an expansion of preliminary work performed by Framatome ANP 2001a
Probability theory and applications
Hsu, Elton P
1999-01-01
This volume, with contributions by leading experts in the field, is a collection of lecture notes of the six minicourses given at the IAS/Park City Summer Mathematics Institute. It introduces advanced graduates and researchers in probability theory to several of the currently active research areas in the field. Each course is self-contained with references and contains basic materials and recent results. Topics include interacting particle systems, percolation theory, analysis on path and loop spaces, and mathematical finance. The volume gives a balanced overview of the current status of probability theory. An extensive bibliography for further study and research is included. This unique collection presents several important areas of current research and a valuable survey reflecting the diversity of the field.
Paradoxes in probability theory
Eckhardt, William
2013-01-01
Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.
Measurement uncertainty and probability
Willink, Robin
2013-01-01
A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.
Retrocausality and conditional probability
International Nuclear Information System (INIS)
Stuart, C.I.J.M.
1989-01-01
Costa de Beauregard has proposed that physical causality be identified with conditional probability. The proposal is shown to be vulnerable on two accounts. The first, though mathematically trivial, seems to be decisive so far as the current formulation of the proposal is concerned. The second lies in a physical inconsistency which seems to have its source in a Copenhagenlike disavowal of realism in quantum mechanics. 6 refs. (Author)
Whittle, Peter
1992-01-01
This book is a complete revision of the earlier work Probability which ap peared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, de manding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept, and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 (reproduced below, together with that to the Russian edition of 1982) I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text...
Sandberg, Jonna C; Björck, Inger M E; Nilsson, Anne C
2016-01-01
Whole grain has shown potential to prevent obesity, cardiovascular disease and type 2 diabetes. Possible mechanism could be related to colonic fermentation of specific indigestible carbohydrates, i.e. dietary fiber (DF). The aim of this study was to investigate effects on cardiometabolic risk factors and appetite regulation the next day when ingesting rye kernel bread rich in DF as an evening meal. Whole grain rye kernel test bread (RKB) or a white wheat flour based bread (reference product, WWB) was provided as late evening meals to healthy young adults in a randomized cross-over design. The test products RKB and WWB were provided in two priming settings: as a single evening meal or as three consecutive evening meals prior to the experimental days. Test variables were measured in the morning, 10.5-13.5 hours after ingestion of RKB or WWB. The postprandial phase was analyzed for measures of glucose metabolism, inflammatory markers, appetite regulating hormones and short chain fatty acids (SCFA) in blood, hydrogen excretion in breath and subjective appetite ratings. With the exception of serum CRP, no significant differences in test variables were observed depending on length of priming (P>0.05). The RKB evening meal increased plasma concentrations of PYY (0-120 min, Pappetite ratings during the whole experimental period (Pappetite sensation could be beneficial in preventing obesity. These effects could possibly be mediated through colonic fermentation. ClinicalTrials.gov NCT02093481.
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
Bayesian optimization for computationally extensive probability distributions.
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.
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)
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).
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 of causation approach
International Nuclear Information System (INIS)
Jose, D.E.
1988-01-01
Probability of causation (PC) is sometimes viewed as a great improvement by those persons who are not happy with the present rulings of courts in radiation cases. The author does not share that hope and expects that PC will not play a significant role in these issues for at least the next decade. If it is ever adopted in a legislative compensation scheme, it will be used in a way that is unlikely to please most scientists. Consequently, PC is a false hope for radiation scientists, and its best contribution may well lie in some of the spin-off effects, such as an influence on medical practice
Generalized Probability Functions
Directory of Open Access Journals (Sweden)
Alexandre Souto Martinez
2009-01-01
Full Text Available From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs. A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.
2014-06-30
precisely the content of the following result. The price we pay is that the assumption that A is a packing in (F, k ·k1) is too weak to make this happen...Regularité des trajectoires des fonctions aléatoires gaussiennes. In: École d’Été de Probabilités de Saint- Flour , IV-1974, pp. 1–96. Lecture Notes in...Lectures on probability theory and statistics (Saint- Flour , 1994), Lecture Notes in Math., vol. 1648, pp. 165–294. Springer, Berlin (1996) 50. Ledoux
Assessing the clinical probability of pulmonary embolism
International Nuclear Information System (INIS)
Miniati, M.; Pistolesi, M.
2001-01-01
Clinical assessment is a cornerstone of the recently validated diagnostic strategies for pulmonary embolism (PE). Although the diagnostic yield of individual symptoms, signs, and common laboratory tests is limited, the combination of these variables, either by empirical assessment or by a prediction rule, can be used to express a clinical probability of PE. The latter may serve as pretest probability to predict the probability of PE after further objective testing (posterior or post-test probability). Over the last few years, attempts have been made to develop structured prediction models for PE. In a Canadian multicenter prospective study, the clinical probability of PE was rated as low, intermediate, or high according to a model which included assessment of presenting symptoms and signs, risk factors, and presence or absence of an alternative diagnosis at least as likely as PE. Recently, a simple clinical score was developed to stratify outpatients with suspected PE into groups with low, intermediate, or high clinical probability. Logistic regression was used to predict parameters associated with PE. A score ≤ 4 identified patients with low probability of whom 10% had PE. The prevalence of PE in patients with intermediate (score 5-8) and high probability (score ≥ 9) was 38 and 81%, respectively. As opposed to the Canadian model, this clinical score is standardized. The predictor variables identified in the model, however, were derived from a database of emergency ward patients. This model may, therefore, not be valid in assessing the clinical probability of PE in inpatients. In the PISA-PED study, a clinical diagnostic algorithm was developed which rests on the identification of three relevant clinical symptoms and on their association with electrocardiographic and/or radiographic abnormalities specific for PE. Among patients who, according to the model, had been rated as having a high clinical probability, the prevalence of proven PE was 97%, while it was 3
Energy Technology Data Exchange (ETDEWEB)
Dong, Jing [ORNL; Mahmassani, Hani S. [Northwestern University, Evanston
2011-01-01
This paper proposes a methodology to produce random flow breakdown endogenously in a mesoscopic operational model, by capturing breakdown probability and duration. Based on previous research findings that probability of flow breakdown can be represented as a function of flow rate and the duration can be characterized by a hazard model. By generating random flow breakdown at various levels and capturing the traffic characteristics at the onset of the breakdown, the stochastic network simulation model provides a tool for evaluating travel time variability. The proposed model can be used for (1) providing reliability related traveler information; (2) designing ITS (intelligent transportation systems) strategies to improve reliability; and (3) evaluating reliability-related performance measures of the system.
Operant Variability: Some Random Thoughts
Marr, M. Jackson
2012-01-01
Barba's (2012) paper is a serious and thoughtful analysis of a vexing problem in behavior analysis: Just what should count as an operant class and how do people know? The slippery issue of a "generalized operant" or functional response class illustrates one aspect of this problem, and "variation" or "novelty" as an operant appears to fall into…
Comparing coefficients of nested nonlinear probability models
DEFF Research Database (Denmark)
Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders
2011-01-01
In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...
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...
Probable maximum flood control
International Nuclear Information System (INIS)
DeGabriele, C.E.; Wu, C.L.
1991-11-01
This study proposes preliminary design concepts to protect the waste-handling facilities and all shaft and ramp entries to the underground from the probable maximum flood (PMF) in the current design configuration for the proposed Nevada Nuclear Waste Storage Investigation (NNWSI) repository protection provisions were furnished by the United States Bureau of Reclamation (USSR) or developed from USSR data. Proposed flood protection provisions include site grading, drainage channels, and diversion dikes. Figures are provided to show these proposed flood protection provisions at each area investigated. These areas are the central surface facilities (including the waste-handling building and waste treatment building), tuff ramp portal, waste ramp portal, men-and-materials shaft, emplacement exhaust shaft, and exploratory shafts facility
Probability Theory Plus Noise: Descriptive Estimation and Inferential Judgment.
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.
Trending in Probability of Collision Measurements via a Bayesian Zero-Inflated Beta Mixed Model
Vallejo, Jonathon; Hejduk, Matt; Stamey, James
2015-01-01
We investigate the performance of a generalized linear mixed model in predicting the Probabilities of Collision (Pc) for conjunction events. Specifically, we apply this model to the log(sub 10) transformation of these probabilities and argue that this transformation yields values that can be considered bounded in practice. Additionally, this bounded random variable, after scaling, is zero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, and utilize the Bayesian paradigm and the mixed model framework to borrow information from past and current events. This provides a natural way to model the data and provides a basis for answering questions of interest, such as what is the likelihood of observing a probability of collision equal to the effective value of zero on a subsequent observation.
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.
Directory of Open Access Journals (Sweden)
Aras Dicle
2016-03-01
Full Text Available ABSTRACT: Regular physical activity can cause some long term effects on human body. The purpose of this research was to examine the effect of sport rock climbing (SRC training at 70 % HRmax level on echocardiography (ECHO and heart rate variability (HRV for one hour a day and three days a week in an eight-week period. A total of 19 adults participated in this study voluntarily. The subjects were randomly divided into two groups as experimental (EG and control (CG. While the EG went and did climbing training by using the top-rope method for 60 minutes a day, three days a week for 8 weeks and didn’t join any other physical activity programs, CG didn’t train and take part in any physical activity during the course of the study. Same measurements were repeated at the end of eight weeks. According to the findings, no significant change was observed in any of the ECHO and HRV parameters. However, an improvement was seen in some HRV parameters [average heart rate (HRave, standard deviation of all NN intervals (SDNN, standard deviation of the averages of NN intervals in all five-minute segments of the entire recording (SDANN, percent of difference between adjacent NN intervals that are greater than 50 ms (PNN50, square root of the mean of the sum of the squares of differences between adjacent NN interval (RMSSD] in EG. An exercise program based on SRC should be made more than eight weeks in order to have statistically significant changes with the purpose of observing an improvement in heart structure and functions. Keywords: Echocardiography, heart rate variability, sport rock climbing
Fifty challenging problems in probability with solutions
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
VISA-2, Reactor Vessel Failure Probability Under Thermal Shock
International Nuclear Information System (INIS)
Simonen, F.; Johnson, K.
1992-01-01
1 - Description of program or function: VISA2 (Vessel Integrity Simulation Analysis) was developed to estimate the failure probability of nuclear reactor pressure vessels under pressurized thermal shock conditions. The deterministic portion of the code performs heat transfer, stress, and fracture mechanics calculations for a vessel subjected to a user-specified temperature and pressure transient. The probabilistic analysis performs a Monte Carlo simulation to estimate the probability of vessel failure. Parameters such as initial crack size and position, copper and nickel content, fluence, and the fracture toughness values for crack initiation and arrest are treated as random variables. Linear elastic fracture mechanics methods are used to model crack initiation and growth. This includes cladding effects in the heat transfer, stress, and fracture mechanics calculations. The simulation procedure treats an entire vessel and recognizes that more than one flaw can exist in a given vessel. The flaw model allows random positioning of the flaw within the vessel wall thickness, and the user can specify either flaw length or length-to-depth aspect ratio for crack initiation and arrest predictions. The flaw size distribution can be adjust on the basis of different inservice inspection techniques and inspection conditions. The toughness simulation model includes a menu of alternative equations for predicting the shift in the reference temperature of the nil-ductility transition. 2 - Method of solution: The solution method uses closed form equations for temperatures, stresses, and stress intensity factors. A polynomial fitting procedure approximates the specified pressure and temperature transient. Failure probabilities are calculated by a Monte Carlo simulation. 3 - Restrictions on the complexity of the problem: Maxima of 30 welds. VISA2 models only the belt-line (cylindrical) region of a reactor vessel. The stresses are a function of the radial (through-wall) coordinate only
Misclassification probability as obese or lean in hypercaloric and normocaloric diet
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ANDRÉ F NASCIMENTO
2008-01-01
Full Text Available The aim of the present study was to determine the classification error probabilities, as lean or obese, in hypercaloric diet-induced obesity, which depends on the variable used to characterize animal obesity. In addition, the misclassification probabilities in animáis submitted to normocaloric diet were also evaluated. Male Wistar rats were randomly distributed into two groups: normal diet (ND; n=31; 3,5 Kcal/g and hypercaloric diet (HD; n=31; 4,6 Kcal/g. The ND group received commercial Labina rat feed and HD animáis a cycle of five hypercaloric diets for a 14-week period. The variables analysed were body weight, body composition, body weight to length ratio, Lee Índex, body mass Índex and misclassification probability. A 5% significance level was used. The hypercaloric pellet-diet cycle promoted increase of body weight, carcass fat, body weight to length ratio and Lee Índex. The total misclassification probabilities ranged from 19.21% to 40.91%. In conclusión, the results of this experiment show that misclassification probabilities occur when dietary manipulation is used to promote obesity in animáis. This misjudgement ranges from 19.49% to 40.52% in hypercaloric diet and 18.94% to 41.30% in normocaloric diet.
Nam, Sung Sik
2017-06-19
Complex wireless transmission systems require multi-dimensional joint statistical techniques for performance evaluation. Here, we first present the exact closed-form results on order statistics of any arbitrary partial sums of Gamma random variables with the closedform results of core functions specialized for independent and identically distributed Nakagami-m fading channels based on a moment generating function-based unified analytical framework. These both exact closed-form results have never been published in the literature. In addition, as a feasible application example in which our new offered derived closed-form results can be applied is presented. In particular, we analyze the outage performance of the finger replacement schemes over Nakagami fading channels as an application of our method. Note that these analysis results are directly applicable to several applications, such as millimeter-wave communication systems in which an antenna diversity scheme operates using an finger replacement schemes-like combining scheme, and other fading scenarios. Note also that the statistical results can provide potential solutions for ordered statistics in any other research topics based on Gamma distributions or other advanced wireless communications research topics in the presence of Nakagami fading.
Brugnera, Agostino; Zarbo, Cristina; Tarvainen, Mika P; Marchettini, Paolo; Adorni, Roberta; Compare, Angelo
2018-05-01
Acute psychosocial stress is typically investigated in laboratory settings using protocols with distinctive characteristics. For example, some tasks involve the action of speaking, which seems to alter Heart Rate Variability (HRV) through acute changes in respiration patterns. However, it is still unknown which task induces the strongest subjective and autonomic stress response. The present cross-over randomized trial sought to investigate the differences in perceived stress and in linear and non-linear analyses of HRV between three different verbal (Speech and Stroop) and non-verbal (Montreal Imaging Stress Task; MIST) stress tasks, in a sample of 60 healthy adults (51.7% females; mean age = 25.6 ± 3.83 years). Analyses were run controlling for respiration rates. Participants reported similar levels of perceived stress across the three tasks. However, MIST induced a stronger cardiovascular response than Speech and Stroop tasks, even after controlling for respiration rates. Finally, women reported higher levels of perceived stress and lower HRV both at rest and in response to acute psychosocial stressors, compared to men. Taken together, our results suggest the presence of gender-related differences during psychophysiological experiments on stress. They also suggest that verbal activity masked the vagal withdrawal through altered respiration patterns imposed by speaking. Therefore, our findings support the use of highly-standardized math task, such as MIST, as a valid and reliable alternative to verbal protocols during laboratory studies on stress. Copyright © 2018 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Yingxue Cui
2013-01-01
Full Text Available Objective. To determine the effects of the moxa smoke on human heart rate (HR and heart rate variability (HRV. Methods. Fifty-five healthy young adults were randomly divided into experimental (n=28 and control (n=27 groups. Experimental subjects were exposed to moxa smoke (2.5 ± 0.5 mg/m3 twice for 25 minutes in one week. ECG monitoring was performed before, during, and after exposure. Control subjects were exposed to normal indoor air in a similar environment and similarly monitored. Followup was performed the following week. Short-term (5 min HRV parameters were analyzed with HRV analysis software. SPSS software was used for statistical analysis. Results. During and after the first exposure, comparison of percentage changes or changes in all parameters between groups showed no significant differences. During the second exposure, percentage decrease in HR, percentage increases in lnTP, lnHF, lnLF, and RMSSD, and increase in PNN50 were significantly greater in the experimental group than in control. Conclusion. No significant adverse HRV effects were associated with this clinically routine 25-minute exposure to moxa smoke, and the data suggests that short-term exposure to moxa smoke might have positive regulating effects on human autonomic function. Further studies are warranted to confirm these findings.
Parr, Evelyn B; Coffey, Vernon G; Cato, Louise E; Phillips, Stuart M; Burke, Louise M; Hawley, John A
2016-05-01
This study determined the effects of 16-week high-dairy-protein, variable-carbohydrate (CHO) diets and exercise training (EXT) on body composition in men and women with overweight/obesity. One hundred and eleven participants (age 47 ± 6 years, body mass 90.9 ± 11.7 kg, BMI 33 ± 4 kg/m(2) , values mean ± SD) were randomly stratified to diets with either: high dairy protein, moderate CHO (40% CHO: 30% protein: 30% fat; ∼4 dairy servings); high dairy protein, high CHO (55%: 30%: 15%; ∼4 dairy servings); or control (55%: 15%: 30%; ∼1 dairy serving). Energy restriction (500 kcal/day) was achieved through diet (∼250 kcal/day) and EXT (∼250 kcal/day). Body composition was measured using dual-energy X-ray absorptiometry before, midway, and upon completion of the intervention. Eighty-nine (25 M/64 F) of 115 participants completed the 16-week intervention, losing 7.7 ± 3.2 kg fat mass (P exercise stimulus. © 2016 The Obesity Society.
Al-Qahtani, Fawaz S.
2011-09-01
In this paper, we investigate the outage performance of a dual-hop relaying systems with partial relay selection and feedback delay. The analysis considers the case of Rayleigh fading channels when the relaying station as well as the destination undergo mutually independent interfering signals. Particularly, we derive the cumulative distribution function (c.d.f.) of a new type of random variable involving sum of multiple independent exponential random variables, based on which, we present closed-form expressions for the exact outage probability of a fixed amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Numerical results are provided to illustrate the joint effect of the delayed feedback and co-channel interference on the outage probability. © 2011 IEEE.
Probability and rational choice
Directory of Open Access Journals (Sweden)
David Botting
2014-05-01
Full Text Available http://dx.doi.org/10.5007/1808-1711.2014v18n1p1 In this paper I will discuss the rationality of reasoning about the future. There are two things that we might like to know about the future: which hypotheses are true and what will happen next. To put it in philosophical language, I aim to show that there are methods by which inferring to a generalization (selecting a hypothesis and inferring to the next instance (singular predictive inference can be shown to be normative and the method itself shown to be rational, where this is due in part to being based on evidence (although not in the same way and in part on a prior rational choice. I will also argue that these two inferences have been confused, being distinct not only conceptually (as nobody disputes but also in their results (the value given to the probability of the hypothesis being not in general that given to the next instance and that methods that are adequate for one are not by themselves adequate for the other. A number of debates over method founder on this confusion and do not show what the debaters think they show.
Vanmarcke, Erik
1983-03-01
Random variation over space and time is one of the few attributes that might safely be predicted as characterizing almost any given complex system. Random fields or "distributed disorder systems" confront astronomers, physicists, geologists, meteorologists, biologists, and other natural scientists. They appear in the artifacts developed by electrical, mechanical, civil, and other engineers. They even underlie the processes of social and economic change. The purpose of this book is to bring together existing and new methodologies of random field theory and indicate how they can be applied to these diverse areas where a "deterministic treatment is inefficient and conventional statistics insufficient." Many new results and methods are included. After outlining the extent and characteristics of the random field approach, the book reviews the classical theory of multidimensional random processes and introduces basic probability concepts and methods in the random field context. It next gives a concise amount of the second-order analysis of homogeneous random fields, in both the space-time domain and the wave number-frequency domain. This is followed by a chapter on spectral moments and related measures of disorder and on level excursions and extremes of Gaussian and related random fields. After developing a new framework of analysis based on local averages of one-, two-, and n-dimensional processes, the book concludes with a chapter discussing ramifications in the important areas of estimation, prediction, and control. The mathematical prerequisite has been held to basic college-level calculus.
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Bogdan Ozga-Zielinski
2016-06-01
New hydrological insights for the region: The results indicated that the 2D normal probability distribution model gives a better probabilistic description of snowmelt floods characterized by the 2-dimensional random variable (Qmax,f, Vf compared to the elliptical Gaussian copula and Archimedean 1-parameter Gumbel–Hougaard copula models, in particular from the view point of probability of exceedance as well as complexity and time of computation. Nevertheless, the copula approach offers a new perspective in estimating the 2D probability distribution for multidimensional random variables. Results showed that the 2D model for snowmelt floods built using the Gumbel–Hougaard copula is much better than the model built using the Gaussian copula.
International Nuclear Information System (INIS)
Eisawy, E.A.
2011-01-01
The aim of this paper is to develop a practical method to evaluate the actual step and touch potential distributions in order to determine the risk of failure of the grounding system. The failure probability, indicating the safety level of the grounding system, is related to both applied (stress) and withstand (strength) step or touch potentials. The probability distributions of the applied step and touch potentials as well as the corresponding withstand step and touch potentials which represent the capability of the human body to resist stress potentials are presented. These two distributions are used to evaluate the failure probability of the grounding system which denotes the probability that the applied potential exceeds the withstand potential. The method is accomplished in considering the resistance of the human body, the foot contact resistance and the fault clearing time as an independent random variables, rather than fixed values as treated in the previous analysis in determining the safety requirements for a given grounding system
Ahern, Jennifer; Galea, Sandro; Resnick, Heidi; Vlahov, David
2004-03-01
Television viewing has been associated with posttraumatic stress disorder (PTSD) symptoms after disasters and traumas; we examined characteristics that may explain this association among New Yorkers after September 11, 2001. Among 2001 respondents to a random-digit dial telephone survey conducted 4 months after September 11, people who viewed more television images in the 7 days after September 11 had more probable PTSD. People in the highest third of viewing had a 2.32 times greater odds of probable PTSD after September 11 compared with people in the lowest third of viewing; after adjustment for explanatory variables, the relative odds of probable PTSD were 1.66. Adjustment for perievent panic accounted for 44% of the reduction in association between television and probable PTSD, suggesting that perievent emotional reactions may play an important role in the television and psychopathology association. Television may merit consideration as a potential exposure to a traumatic event.
Calculating the Probability of Returning a Loan with Binary Probability Models
Directory of Open Access Journals (Sweden)
Julian Vasilev
2014-12-01
Full Text Available The purpose of this article is to give a new approach in calculating the probability of returning a loan. A lot of factors affect the value of the probability. In this article by using statistical and econometric models some influencing factors are proved. The main approach is concerned with applying probit and logit models in loan management institutions. A new aspect of the credit risk analysis is given. Calculating the probability of returning a loan is a difficult task. We assume that specific data fields concerning the contract (month of signing, year of signing, given sum and data fields concerning the borrower of the loan (month of birth, year of birth (age, gender, region, where he/she lives may be independent variables in a binary logistics model with a dependent variable “the probability of returning a loan”. It is proved that the month of signing a contract, the year of signing a contract, the gender and the age of the loan owner do not affect the probability of returning a loan. It is proved that the probability of returning a loan depends on the sum of contract, the remoteness of the loan owner and the month of birth. The probability of returning a loan increases with the increase of the given sum, decreases with the proximity of the customer, increases for people born in the beginning of the year and decreases for people born at the end of the year.
Falk, Ruma; Kendig, Keith
2013-01-01
Two contestants debate the notorious probability problem of the sex of the second child. The conclusions boil down to explication of the underlying scenarios and assumptions. Basic principles of probability theory are highlighted.
Visualizing and Understanding Probability and Statistics: Graphical Simulations Using Excel
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…
Redwine, Laura S; Henry, Brook L; Pung, Meredith A; Wilson, Kathleen; Chinh, Kelly; Knight, Brian; Jain, Shamini; Rutledge, Thomas; Greenberg, Barry; Maisel, Alan; Mills, Paul J
2016-01-01
Stage B, asymptomatic heart failure (HF) presents a therapeutic window for attenuating disease progression and development of HF symptoms, and improving quality of life. Gratitude, the practice of appreciating positive life features, is highly related to quality of life, leading to development of promising clinical interventions. However, few gratitude studies have investigated objective measures of physical health; most relied on self-report measures. We conducted a pilot study in Stage B HF patients to examine whether gratitude journaling improved biomarkers related to HF prognosis. Patients (n = 70; mean [standard deviation] age = 66.2 [7.6] years) were randomized to an 8-week gratitude journaling intervention or treatment as usual. Baseline (T1) assessments included the six-item Gratitude Questionnaire, resting heart rate variability (HRV), and an inflammatory biomarker index. At T2 (midintervention), the six-item Gratitude Questionnaire was measured. At T3 (postintervention), T1 measures were repeated but also included a gratitude journaling task. The gratitude intervention was associated with improved trait gratitude scores (F = 6.0, p = .017, η = 0.10), reduced inflammatory biomarker index score over time (F = 9.7, p = .004, η = 0.21), and increased parasympathetic HRV responses during the gratitude journaling task (F = 4.2, p = .036, η = 0.15), compared with treatment as usual. However, there were no resting preintervention to postintervention group differences in HRV (p values > .10). Gratitude journaling may improve biomarkers related to HF morbidity, such as reduced inflammation; large-scale studies with active control conditions are needed to confirm these findings. Clinicaltrials.govidentifier:NCT01615094.
Surprisingly rational: probability theory plus noise explains biases in judgment.
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.
Uniqueness conditions for finitely dependent random fields
International Nuclear Information System (INIS)
Dobrushin, R.L.; Pecherski, E.A.
1981-01-01
The authors consider a random field for which uniqueness and some additional conditions guaranteeing that the correlations between the variables of the field decrease rapidly enough with the distance between the values of the parameter occur. The main result of the paper states that in such a case uniqueness is true for any other field with transition probabilities sufficiently close to those of the original field. Then they apply this result to some ''degenerate'' classes of random fields for which one can check this condition of correlation to decay, and thus obtain some new conditions of uniqueness. (Auth.)
Internal Medicine residents use heuristics to estimate disease probability
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...
p-adic probability interpretation of Bell's inequality
International Nuclear Information System (INIS)
Khrennikov, A.
1995-01-01
We study the violation of Bell's inequality using a p-adic generalization of the theory of probability. p-adic probability is introduced as a limit of relative frequencies but this limit exists with respect to a p-adic metric. In particular, negative probability distributions are well defined on the basis of the frequency definition. This new type of stochastics can be used to describe hidden-variables distributions of some quantum models. If the hidden variables have a p-adic probability distribution, Bell's inequality is not valid and it is not necessary to discuss the experimental violations of this inequality. ((orig.))
Ross, Sheldon
2014-01-01
A First Course in Probability, Ninth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.
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.
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....
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
Randomized central limit theorems: A unified theory.
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.
Fracture fragility of HFIR vessel caused by random crack size or random toughness
International Nuclear Information System (INIS)
Chang, Shih-Jung; Proctor, L.D.
1993-01-01
This report discuses the probability of fracture (fracture fragility) versus a range of applied hoop stresses along the HFIR vessel which is obtained as an estimate of its fracture capacity. Both the crack size and the fracture toughness are assumed to be random variables that follow given distribution functions. Possible hoop stress is based on the numerical solution of the vessel response by applying a point pressure-pulse it the center of the fluid volume within the vessel. Both the fluid-structure interaction and radiation embrittlement are taken into consideration. Elastic fracture mechanics is used throughout the analysis. The probability of vessel fracture for a single crack caused by either a variable crack depth or a variable toughness is first derived. Then the probability of fracture with multiple number of cracks is obtained. The probability of fracture is further extended to include different levels of confidence and variability. It, therefore, enables one to estimate the high confidence and low probability capacity accident load
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)
National Research Council Canada - National Science Library
Nuttall, Albert
2001-01-01
... other. Although this assumption greatly simplifies the analysis, it can lead to very misleading probability measures, especially on the tails of the distributions, where the exact details of the particular...
Probability and Statistics The Science of Uncertainty (Revised Edition)
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
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
Kruppa, Jochen; Liu, Yufeng; Biau, Gérard; Kohler, Michael; König, Inke R; Malley, James D; Ziegler, Andreas
2014-07-01
Probability estimation for binary and multicategory outcome using logistic and multinomial logistic regression has a long-standing tradition in biostatistics. However, biases may occur if the model is misspecified. In contrast, outcome probabilities for individuals can be estimated consistently with machine learning approaches, including k-nearest neighbors (k-NN), bagged nearest neighbors (b-NN), random forests (RF), and support vector machines (SVM). Because machine learning methods are rarely used by applied biostatisticians, the primary goal of this paper is to explain the concept of probability estimation with these methods and to summarize recent theoretical findings. Probability estimation in k-NN, b-NN, and RF can be embedded into the class of nonparametric regression learning machines; therefore, we start with the construction of nonparametric regression estimates and review results on consistency and rates of convergence. In SVMs, outcome probabilities for individuals are estimated consistently by repeatedly solving classification problems. For SVMs we review classification problem and then dichotomous probability estimation. Next we extend the algorithms for estimating probabilities using k-NN, b-NN, and RF to multicategory outcomes and discuss approaches for the multicategory probability estimation problem using SVM. In simulation studies for dichotomous and multicategory dependent variables we demonstrate the general validity of the machine learning methods and compare it with logistic regression. However, each method fails in at least one simulation scenario. We conclude with a discussion of the failures and give recommendations for selecting and tuning the methods. Applications to real data and example code are provided in a companion article (doi:10.1002/bimj.201300077). © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Predicting the probability of slip in gait: methodology and distribution study.
Gragg, Jared; Yang, James
2016-01-01
The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.
DEFF Research Database (Denmark)
Asmussen, J.C.; Ibrahim, S.R.; Brincker, Rune
Abstraet Thispaper demansirates how to use the Random Decrement (RD) technique for identification o flinear structures subjected to ambient excitation. The theory behind the technique will be presented and guidelines how to choose the different variables will be given. This is done by introducing...
DEFF Research Database (Denmark)
Asmussen, J. C.; Ibrahim, S. R.; Brincker, Rune
This paper demonstrates how to use the Random Decrement (RD) technique for identification of linear structures subjected to ambient excitation. The theory behind the technique will be presented and guidelines how to choose the different variables will be given. This is done by introducing a new...
DEFF Research Database (Denmark)
Asmussen, J. C.; Ibrahim, R.; Brincker, Rune
1998-01-01
This paper demonstrates how to use the Random Decrement (RD) technique for identification of linear structures subjected to ambient excitation. The theory behind the technique will be presented and guidelines how to choose the different variables will be given. This is done by introducing a new...
Propensity, Probability, and Quantum Theory
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Causal inference, probability theory, and graphical insights.
Baker, Stuart G
2013-11-10
Causal inference from observational studies is a fundamental topic in biostatistics. The causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies. In contrast, the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons. First, probability theory is generally more flexible than causal graphs: Besides explaining such causal graph topics as M-bias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical controls, which does not fit into a causal graph framework. Second, probability theory is the basis for insightful graphical displays including the BK-Plot for understanding Simpson's paradox with a binary confounder, the BK2-Plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder, and the PAD-Plot for understanding the principal stratification component of the paired availability design. Published 2013. This article is a US Government work and is in the public domain in the USA.
Directory of Open Access Journals (Sweden)
Evropi Theodoratou
Full Text Available Vitamin D deficiency has been associated with several common diseases, including cancer and is being investigated as a possible risk factor for these conditions. We reported the striking prevalence of vitamin D deficiency in Scotland. Previous epidemiological studies have reported an association between low dietary vitamin D and colorectal cancer (CRC. Using a case-control study design, we tested the association between plasma 25-hydroxy-vitamin D (25-OHD and CRC (2,001 cases, 2,237 controls. To determine whether plasma 25-OHD levels are causally linked to CRC risk, we applied the control function instrumental variable (IV method of the mendelian randomization (MR approach using four single nucleotide polymorphisms (rs2282679, rs12785878, rs10741657, rs6013897 previously shown to be associated with plasma 25-OHD. Low plasma 25-OHD levels were associated with CRC risk in the crude model (odds ratio (OR: 0.76, 95% Confidence Interval (CI: 0.71, 0.81, p: 1.4×10(-14 and after adjusting for age, sex and other confounding factors. Using an allele score that combined all four SNPs as the IV, the estimated causal effect was OR 1.16 (95% CI 0.60, 2.23, whilst it was 0.94 (95% CI 0.46, 1.91 and 0.93 (0.53, 1.63 when using an upstream (rs12785878, rs10741657 and a downstream allele score (rs2282679, rs6013897, respectively. 25-OHD levels were inversely associated with CRC risk, in agreement with recent meta-analyses. The fact that this finding was not replicated when the MR approach was employed might be due to weak instruments, giving low power to demonstrate an effect (<0.35. The prevalence and degree of vitamin D deficiency amongst individuals living in northerly latitudes is of considerable importance because of its relationship to disease. To elucidate the effect of vitamin D on CRC cancer risk, additional large studies of vitamin D and CRC risk are required and/or the application of alternative methods that are less sensitive to weak instrument
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.
Probability theory for 3-layer remote sensing radiative transfer model: univariate case.
Ben-David, Avishai; Davidson, Charles E
2012-04-23
A probability model for a 3-layer radiative transfer model (foreground layer, cloud layer, background layer, and an external source at the end of line of sight) has been developed. The 3-layer model is fundamentally important as the primary physical model in passive infrared remote sensing. The probability model is described by the Johnson family of distributions that are used as a fit for theoretically computed moments of the radiative transfer model. From the Johnson family we use the SU distribution that can address a wide range of skewness and kurtosis values (in addition to addressing the first two moments, mean and variance). In the limit, SU can also describe lognormal and normal distributions. With the probability model one can evaluate the potential for detecting a target (vapor cloud layer), the probability of observing thermal contrast, and evaluate performance (receiver operating characteristics curves) in clutter-noise limited scenarios. This is (to our knowledge) the first probability model for the 3-layer remote sensing geometry that treats all parameters as random variables and includes higher-order statistics. © 2012 Optical Society of America
Poisson Processes in Free Probability
An, Guimei; Gao, Mingchu
2015-01-01
We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisso...
PROBABILITY SURVEYS , CONDITIONAL PROBABILITIES AND ECOLOGICAL RISK ASSESSMENT
We show that probability-based environmental resource monitoring programs, such as the U.S. Environmental Protection Agency's (U.S. EPA) Environmental Monitoring and Assessment Program, and conditional probability analysis can serve as a basis for estimating ecological risk over ...
Modelling soft error probability in firmware: A case study
African Journals Online (AJOL)
The purpose is to estimate the probability that external disruptive events (such as ..... also changed the 16-bit magic variable to its unique 'magic' value. .... is mutually independent, not only over registers but over spikes, such that the above.
Optimal design of unit hydrographs using probability distribution and ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
optimization formulation is solved using binary-coded genetic algorithms. The number of variables to ... Unit hydrograph; rainfall-runoff; hydrology; genetic algorithms; optimization; probability ..... Application of the model. Data derived from the ...
Probability of crack-initiation and application to NDE
Energy Technology Data Exchange (ETDEWEB)
Prantl, G [Nuclear Safety Inspectorate HSK, (Switzerland)
1988-12-31
Fracture toughness is a property with a certain variability. When a statistical distribution is assumed, the probability of crack initiation may be calculated for a given problem defined by its geometry and the applied stress. Experiments have shown, that cracks which experience a certain small amount of ductile growth can reliably be detected by acoustic emission measurements. The probability of crack detection by AE-techniques may be estimated using this experimental finding and the calculated probability of crack initiation. (author).
THE BLACK HOLE FORMATION PROBABILITY
Energy Technology Data Exchange (ETDEWEB)
Clausen, Drew; Piro, Anthony L.; Ott, Christian D., E-mail: dclausen@tapir.caltech.edu [TAPIR, Walter Burke Institute for Theoretical Physics, California Institute of Technology, Mailcode 350-17, Pasadena, CA 91125 (United States)
2015-02-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P {sub BH}(M {sub ZAMS}). Although we find that it is difficult to derive a unique P {sub BH}(M {sub ZAMS}) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P {sub BH}(M {sub ZAMS}) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P {sub BH}(M {sub ZAMS}) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment.
THE BLACK HOLE FORMATION PROBABILITY
International Nuclear Information System (INIS)
Clausen, Drew; Piro, Anthony L.; Ott, Christian D.
2015-01-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P BH (M ZAMS ). Although we find that it is difficult to derive a unique P BH (M ZAMS ) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P BH (M ZAMS ) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P BH (M ZAMS ) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment
The Black Hole Formation Probability
Clausen, Drew; Piro, Anthony L.; Ott, Christian D.
2015-02-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P BH(M ZAMS). Although we find that it is difficult to derive a unique P BH(M ZAMS) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P BH(M ZAMS) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P BH(M ZAMS) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment.
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.
What Are Probability Surveys used by the National Aquatic Resource Surveys?
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.
Randomness and locality in quantum mechanics
International Nuclear Information System (INIS)
Bub, J.
1976-01-01
This paper considers the problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space. The Kochen and Specker theorem proves the impossibility of embedding the possibility structure of a quantum mechanical system into a Boolean algebra. It is shown that a hidden variable theory involves a Boolean representation which is not an embedding, and that such a representation cannot recover the quantum statistics for sequential probabilities without introducing a randomization process for the hidden variables which is assumed to apply only on measurement. It is suggested that the relation of incompatability is to be understood as a type of stochastic independence, and that the indeterminism of a quantum mechanical system is engendered by the existence of independent families of properties. Thus, the statistical relations reflect the possibility structure of the system: the probabilities are logical. The hidden variable thesis is influenced by the Copenhagen interpretation of quantum mechanics, i.e. by some version of the disturbance theory of measurement. Hence, the significance of the representation problem is missed, and the completeness of quantum mechanics is seen to turn on the possibility of recovering the quantum statistics by a hidden variable scheme which satisfies certain physically motivated conditions, such as locality. Bell's proof that no local hidden variable theory can reproduce the statistical relations of quantum mechanics is considered. (Auth.)
Probability and statistics for particle physics
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...
Probability shapes perceptual precision: A study in orientation estimation.
Jabar, Syaheed B; Anderson, Britt
2015-12-01
Probability is known to affect perceptual estimations, but an understanding of mechanisms is lacking. Moving beyond binary classification tasks, we had naive participants report the orientation of briefly viewed gratings where we systematically manipulated contingent probability. Participants rapidly developed faster and more precise estimations for high-probability tilts. The shapes of their error distributions, as indexed by a kurtosis measure, also showed a distortion from Gaussian. This kurtosis metric was robust, capturing probability effects that were graded, contextual, and varying as a function of stimulus orientation. Our data can be understood as a probability-induced reduction in the variability or "shape" of estimation errors, as would be expected if probability affects the perceptual representations. As probability manipulations are an implicit component of many endogenous cuing paradigms, changes at the perceptual level could account for changes in performance that might have traditionally been ascribed to "attention." (c) 2015 APA, all rights reserved).
Probability inequalities for decomposition integrals
Czech Academy of Sciences Publication Activity Database
Agahi, H.; Mesiar, Radko
2017-01-01
Roč. 315, č. 1 (2017), s. 240-248 ISSN 0377-0427 Institutional support: RVO:67985556 Keywords : Decomposition integral * Superdecomposition integral * Probability inequalities Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/E/mesiar-0470959.pdf
Expected utility with lower probabilities
DEFF Research Database (Denmark)
Hendon, Ebbe; Jacobsen, Hans Jørgen; Sloth, Birgitte
1994-01-01
An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory...
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...
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
Babuška, Ivo; Nobile, Fabio; Tempone, Raul
2010-01-01
This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It treats easily a wide range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction of the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. Finally, we include a section with developments posterior to the original publication of this work. There we review sparse grid stochastic collocation methods, which are effective collocation strategies for problems that depend on a moderately large number of random variables.
Invariant probabilities of transition functions
Zaharopol, Radu
2014-01-01
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of t...
Nam, Sungsik; Yang, Hongchuan; Alouini, Mohamed-Slim; Kim, Dongin
2014-01-01
framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE
International Nuclear Information System (INIS)
Conover, W.J.; Cox, D.D.; Martz, H.F.
1997-12-01
When using parametric empirical Bayes estimation methods for estimating the binomial or Poisson parameter, the validity of the assumed beta or gamma conjugate prior distribution is an important diagnostic consideration. Chi-square goodness-of-fit tests of the beta or gamma prior hypothesis are developed for use when the binomial sample sizes or Poisson exposure times vary. Nine examples illustrate the application of the methods, using real data from such diverse applications as the loss of feedwater flow rates in nuclear power plants, the probability of failure to run on demand and the failure rates of the high pressure coolant injection systems at US commercial boiling water reactors, the probability of failure to run on demand of emergency diesel generators in US commercial nuclear power plants, the rate of failure of aircraft air conditioners, baseball batting averages, the probability of testing positive for toxoplasmosis, and the probability of tumors in rats. The tests are easily applied in practice by means of corresponding Mathematica reg-sign computer programs which are provided
Linear positivity and virtual probability
International Nuclear Information System (INIS)
Hartle, James B.
2004-01-01
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. The objective of any quantum theory of a closed system, most generally the universe, is the prediction of probabilities for the individual members of sets of alternative coarse-grained histories of the system. Quantum interference between members of a set of alternative histories is an obstacle to assigning probabilities that are consistent with the rules of probability theory. A quantum theory of closed systems therefore requires two elements: (1) a condition specifying which sets of histories may be assigned probabilities and (2) a rule for those probabilities. The linear positivity condition of Goldstein and Page is the weakest of the general conditions proposed so far. Its general properties relating to exact probability sum rules, time neutrality, and conservation laws are explored. Its inconsistency with the usual notion of independent subsystems in quantum mechanics is reviewed. Its relation to the stronger condition of medium decoherence necessary for classicality is discussed. The linear positivity of histories in a number of simple model systems is investigated with the aim of exhibiting linearly positive sets of histories that are not decoherent. The utility of extending the notion of probability to include values outside the range of 0-1 is described. Alternatives with such virtual probabilities cannot be measured or recorded, but can be used in the intermediate steps of calculations of real probabilities. Extended probabilities give a simple and general way of formulating quantum theory. The various decoherence conditions are compared in terms of their utility for characterizing classicality and the role they might play in further generalizations of quantum mechanics
THREE-MOMENT BASED APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING SYSTEMS
Directory of Open Access Journals (Sweden)
T. I. Aliev
2014-03-01
Full Text Available The paper deals with the problem of approximation of probability distributions of random variables defined in positive area of real numbers with coefficient of variation different from unity. While using queueing systems as models for computer networks, calculation of characteristics is usually performed at the level of expectation and variance. At the same time, one of the main characteristics of multimedia data transmission quality in computer networks is delay jitter. For jitter calculation the function of packets time delay distribution should be known. It is shown that changing the third moment of distribution of packets delay leads to jitter calculation difference in tens or hundreds of percent, with the same values of the first two moments – expectation value and delay variation coefficient. This means that delay distribution approximation for the calculation of jitter should be performed in accordance with the third moment of delay distribution. For random variables with coefficients of variation greater than unity, iterative approximation algorithm with hyper-exponential two-phase distribution based on three moments of approximated distribution is offered. It is shown that for random variables with coefficients of variation less than unity, the impact of the third moment of distribution becomes negligible, and for approximation of such distributions Erlang distribution with two first moments should be used. This approach gives the possibility to obtain upper bounds for relevant characteristics, particularly, the upper bound of delay jitter.
STRIP: stream learning of influence probabilities
DEFF Research Database (Denmark)
Kutzkov, Konstantin
2013-01-01
cascades, and developing applications such as viral marketing. Motivated by modern microblogging platforms, such as twitter, in this paper we study the problem of learning influence probabilities in a data-stream scenario, in which the network topology is relatively stable and the challenge of a learning...... algorithm is to keep up with a continuous stream of tweets using a small amount of time and memory. Our contribution is a number of randomized approximation algorithms, categorized according to the available space (superlinear, linear, and sublinear in the number of nodes n) and according to dierent models...
Probable Inference and Quantum Mechanics
International Nuclear Information System (INIS)
Grandy, W. T. Jr.
2009-01-01
In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.
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...
A philosophical essay on probabilities
Laplace, Marquis de
1996-01-01
A classic of science, this famous essay by ""the Newton of France"" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences.Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles and general results of his theory ""to the most important questions of life, which are, in effect, for the most part, problems in probability."" Thus, without the use of higher mathematics, he demonstrates the application
Approaches to Evaluating Probability of Collision Uncertainty
Hejduk, Matthew D.; Johnson, Lauren C.
2016-01-01
While the two-dimensional probability of collision (Pc) calculation has served as the main input to conjunction analysis risk assessment for over a decade, it has done this mostly as a point estimate, with relatively little effort made to produce confidence intervals on the Pc value based on the uncertainties in the inputs. The present effort seeks to try to carry these uncertainties through the calculation in order to generate a probability density of Pc results rather than a single average value. Methods for assessing uncertainty in the primary and secondary objects' physical sizes and state estimate covariances, as well as a resampling approach to reveal the natural variability in the calculation, are presented; and an initial proposal for operationally-useful display and interpretation of these data for a particular conjunction is given.