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.
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)
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...
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...
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.
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
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
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…
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.
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.
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.
Analytic results for asymmetric random walk with exponential transition probabilities
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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
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.
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.
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
Identifying probable suicide clusters in wales using national mortality data.
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Phillip Jones
Full Text Available Up to 2% of suicides in young people may occur in clusters i.e., close together in time and space. In early 2008 unprecedented attention was given by national and international news media to a suspected suicide cluster among young people living in Bridgend, Wales. This paper investigates the strength of statistical evidence for this apparent cluster, its size, and temporal and geographical limits.The analysis is based on official mortality statistics for Wales for 2000-2009 provided by the UK's Office for National Statistics (ONS. Temporo-spatial analysis was performed using Space Time Permutation Scan Statistics with SaTScan v9.1 for suicide deaths aged 15 and over, with a sub-group analysis focussing on cases aged 15-34 years. These analyses were conducted for deaths coded by ONS as: (i suicide or of undetermined intent (probable suicides and (ii for a combination of suicide, undetermined, and accidental poisoning and hanging (possible suicides. The temporo-spatial analysis did not identify any clusters of suicide or undetermined intent deaths (probable suicides. However, analysis of all deaths by suicide, undetermined intent, accidental poisoning and accidental hanging (possible suicides identified a temporo-spatial cluster (p = 0.029 involving 10 deaths amongst 15-34 year olds centred on the County Borough of Bridgend for the period 27(th December 2007 to 19(th February 2008. Less than 1% of possible suicides in younger people in Wales in the ten year period were identified as being cluster-related.There was a possible suicide cluster in young people in Bridgend between December 2007 and February 2008. This cluster was smaller, shorter in duration, and predominantly later than the phenomenon that was reported in national and international print media. Further investigation of factors leading to the onset and termination of this series of deaths, in particular the role of the media, is required.
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
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…
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.
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.
Probability for human intake of an atom randomly released into ground, rivers, oceans and air
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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...
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
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)
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.
Fortran code for generating random probability vectors, unitaries, and quantum states
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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.
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)
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.
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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.
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.
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).
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
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.
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).
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
Directory of Open Access Journals (Sweden)
Khvedelidze Arsen
2018-01-01
Full Text Available The generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. In particular, we consider the generation of random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.
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
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.
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…
A random spatial sampling method in a rural developing nation
Michelle C. Kondo; Kent D.W. Bream; Frances K. Barg; Charles C. Branas
2014-01-01
Nonrandom sampling of populations in developing nations has limitations and can inaccurately estimate health phenomena, especially among hard-to-reach populations such as rural residents. However, random sampling of rural populations in developing nations can be challenged by incomplete enumeration of the base population. We describe a stratified random sampling method...
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.
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.
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.
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
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.
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
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...
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.
Singh, Betsy; Liu, Xiao-Dong; Der-Martirosian, Claudia; Hardy, Mary; Singh, Vijay; Shepard, Neil; Gandhi, Sonal; Khorsan, Raheleh
2005-09-01
This survey intended to clarify physicians' understanding of the issues surrounding women, menopause, alternative medicine, and drug therapy for the treatment of menopause. This study was designed as a national probability sample survey of primary care physicians and gynecologists nationwide. Its focus was to identify major concerns and issues identified by patients about menopause and perceived communication with effectiveness how to communicate with their patients. Physicians were also asked to rate their comfort level in recommending the use of herbal remedies and which herbal remedy they felt comfortable recommending to interested patients. Data indicated that a patient's complaint about menopausal symptoms was the most common factor leading to discussion of menopausal issues with physicians (91%) and that the primary concern to the patient was management of menopausal symptoms. Other factors were controversies about hormone replacement therapy, long-term health implications of menopause, and hormone replacement therapy. Eighty percent of the physician found confusing messages with regard to menopause to be the most challenging aspect in patient communication. The second most challenging issue is "inconclusive data about hormone replacement therapy" (56%). Seventy-six percent of the physicians found "showing sympathy" to be the most important factor for the physicians to communicate effectively with patients, whereas "being honest and open" was the most important patient attitude cited for the same purpose. When it comes to herbal therapy for menopause symptom control, only 4% of the physicians indicated that none of their patients take any remedies. Only 18% were not very comfortable in discussing or recommending herbal therapies, whereas the rest ranged from fairly comfortable to completely comfortable. This study has provided data with regard to physician understanding of menopause treatment options and their primary interaction with patients on this issue
Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables
Directory of Open Access Journals (Sweden)
Andrew Rosalsky
2004-12-01
Full Text Available Let {X,Xn;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±.
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.
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.
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.
Prevalence of masturbation and associated factors in a British national probability survey
Gerressu, Makeda; Mercer, Catherine H.; Graham, Cynthia A.; Wellings, Kaye; Johnson, Anne M.
2008-01-01
This is the post-print version of the article. The official published version can be found at the link below. A stratified probability sample survey of the British general population, aged 16 to 44 years, was conducted from 1999 to 2001 (N = 11,161) using face-to-face interviewing and computer-assisted self-interviewing. We used these data to estimate the population prevalence of masturbation, and to identify sociodemographic, sexual behavioral, and attitudinal factors associated with repo...
Energy Technology Data Exchange (ETDEWEB)
Habte, Aron M [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Roberts, Billy J [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Kutchenreiter, Mark C [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Sengupta, Manajit [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Wilcox, Steve [Solar Resource Solutions, LLC, Lakewood, CO (United States); Stoffel, Tom [Solar Resource Solutions, LLC, Lakewood, CO (United States)
2017-07-21
The National Renewable Energy Laboratory (NREL) and collaborators have created a clear-sky probability analysis to help guide viewers of the August 21, 2017, total solar eclipse, the first continent-spanning eclipse in nearly 100 years in the United States. Using cloud and solar data from NREL's National Solar Radiation Database (NSRDB), the analysis provides cloudless sky probabilities specific to the date and time of the eclipse. Although this paper is not intended to be an eclipse weather forecast, the detailed maps can help guide eclipse enthusiasts to likely optimal viewing locations. Additionally, high-resolution data are presented for the centerline of the path of totality, representing the likelihood for cloudless skies and atmospheric clarity. The NSRDB provides industry, academia, and other stakeholders with high-resolution solar irradiance data to support feasibility analyses for photovoltaic and concentrating solar power generation projects.
National Oceanic and Atmospheric Administration, Department of Commerce — Zooplankton communities have been well studied in the northeast Atlantic (Sherman et al., 1983) and on Georges Bank within the Gulf of Maine (Bigelow, 1927; Davis,...
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.
Prevalence of masturbation and associated factors in a British national probability survey.
Gerressu, Makeda; Mercer, Catherine H; Graham, Cynthia A; Wellings, Kaye; Johnson, Anne M
2008-04-01
A stratified probability sample survey of the British general population, aged 16 to 44 years, was conducted from 1999 to 2001 (N = 11,161) using face-to-face interviewing and computer-assisted self-interviewing. We used these data to estimate the population prevalence of masturbation, and to identify sociodemographic, sexual behavioral, and attitudinal factors associated with reporting this behavior. Seventy-three percent of men and 36.8% of women reported masturbating in the 4 weeks prior to interview (95% confidence interval 71.5%-74.4% and 35.4%-38.2%, respectively). A number of sociodemographic and behavioral factors were associated with reporting masturbation. Among both men and women, reporting masturbation increased with higher levels of education and social class and was more common among those reporting sexual function problems. For women, masturbation was more likely among those who reported more frequent vaginal sex in the last four weeks, a greater repertoire of sexual activity (such as reporting oral and anal sex), and more sexual partners in the last year. In contrast, the prevalence of masturbation was lower among men reporting more frequent vaginal sex. Both men and women reporting same-sex partner(s) were significantly more likely to report masturbation. Masturbation is a common sexual practice with significant variations in reporting between men and women.
Directory of Open Access Journals (Sweden)
Virginia Homfray
Full Text Available It is well-established that male circumcision reduces acquisition of HIV, herpes simplex virus 2, chancroid, and syphilis. However, the effect on the acquisition of non-ulcerative sexually transmitted infections (STIs remains unclear. We examined the relationship between circumcision and biological measures of three STIs: human papillomavirus (HPV, Chlamydia trachomatis and Mycoplasma genitalium.A probability sample survey of 15,162 men and women aged 16-74 years (including 4,060 men aged 16-44 years was carried out in Britain between 2010 and 2012. Participants completed a computer-assisted personal interview, including a computer-assisted self-interview, which asked about experience of STI diagnoses, and circumcision. Additionally, 1,850 urine samples from sexually-experienced men aged 16-44 years were collected and tested for STIs. Multivariable logistic regression was used to calculate adjusted odds ratios (AOR to quantify associations between circumcision and i self-reporting any STI diagnosis and ii presence of STIs in urine, in men aged 16-44 years, adjusting for key socio-demographic and sexual behavioural factors.The prevalence of circumcision in sexually-experienced men aged 16-44 years was 17.4% (95%CI 16.0-19.0. There was no association between circumcision and reporting any previous STI diagnoses, and specifically previous chlamydia or genital warts. However, circumcised men were less likely to have any HPV type (AOR 0.26, 95% confidence interval (CI 0.13-0.50 including high-risk HPV types (HPV-16, 18, 31, 33, 35, 39, 45, 51, 52, 56, 58, 59 and/or 68 (AOR 0.14, 95% CI 0.05-0.40 detected in urine.Circumcised men had reduced odds of HPV detection in urine. These findings have implications for improving the precision of models of STI transmission in populations with different circumcision prevalence and in designing interventions to reduce STI acquisition.
Using the Internet for Health-Related Activities: Findings From a National Probability Sample
Saperstein, Sandra L; Pleis, John
2009-01-01
Background eHealth tools on the Internet have the potential to help people manage their health and health care. However, little is known about the distribution and use of different kinds of eHealth tools across the population or within population subgroups. Objective The purpose of this study was to examine the prevalence and predictors of participation in specific online health-related activities. Methods A secondary data analysis of the National Cancer Institute’s Health Information National Trends Survey (HINTS) 2005 was conducted to study three online behaviors among Internet users (n = 3244): searching for health information for oneself, participating in a support group for those with similar health or medical conditions, and purchasing medicine or vitamins. Results A total of 58% of Internet users reported searching for health information for themselves, 3.8% used online support groups, and 12.8% bought medicine or vitamins online in the past year. Multivariate analysis found that those seeking health information were more likely to be women (OR = 2.23, 95% CI = 1.60, 3.09), have cable or satellite Internet connections (OR = 1.73, 95% CI = 1.22, 2.45) or DSL connections (OR = 1.94, 95% CI = 1.36, 2.76), have Internet access from work (OR = 2.43, 95% CI = 1.27, 4.67) or from home and work (OR = 1.73, 95% CI = 1.31, 2.30), and report more hours of weekday Internet use (OR = 4.12, 95% CI = 2.41, 7.07). Those with a high school education or less (OR = 0.44, 95% CI = 0.31, 0.63) and those with some college (OR = 0.66, 95% CI = 0.49, 0.89) were less likely to search for health information. Online support groups were more likely to be used by those with “fair” health (OR = 3.28, 95% CI = 1.21, 8.92) and “poor” health (OR = 5.98, 95% CI = 1.49, 24.07) and those with lower incomes (OR = 2.64, 95% CI = 1.09, 6.41) and less likely to be used by those with Internet access both at home and work (OR = 0.56, 95% CI = 0.35, 0.90). Those who were age 35-49 (OR = 2
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.
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...
Herbenick, Debby; Reece, Michael; Schick, Vanessa; Sanders, Stephanie A; Dodge, Brian; Fortenberry, J Dennis
2010-10-01
Past surveys of sexual behavior have demonstrated that female sexual behavior is influenced by medical and sociocultural changes. To be most attentive to women and their sexual lives, it is important to have an understanding of the continually evolving sexual behaviors of contemporary women in the United States. The purpose of this study, the National Survey of Sexual Health and Behavior (NSSHB), was to, in a national probability survey of women ages 18-92, assess the proportion of women in various age cohorts who had engaged in solo and partnered sexual activities in the past 90 days and to explore associations with participants' sexual behavior and their relationship and perceived health status. Past year frequencies of masturbation, vaginal intercourse, and anal intercourse were also assessed. A national probability sample of 2,523 women ages 18 to 92 completed a cross-sectional internet based survey about their sexual behavior. Relationship status; perceived health status; experience of solo masturbation, partnered masturbation, giving oral sex, receiving oral sex, vaginal intercourse, anal intercourse, in the past 90 days; frequency of solo masturbation, vaginal intercourse, and anal intercourse in the past year. Recent solo masturbation, oral sex, and vaginal intercourse were prevalent among women, decreased with age, and varied in their associations with relationship and perceived health status. Recent anal sex and same-sex oral sex were uncommonly reported. Solo masturbation was most frequent among women ages 18 to 39, vaginal intercourse was most frequent among women ages 18 to 29 and anal sex was infrequently reported. Contemporary women in the United States engage in a diverse range of solo and partnered sexual activities, though sexual behavior is less common and more infrequent among older age cohorts. © 2010 International Society for Sexual Medicine.
Directory of Open Access Journals (Sweden)
Debby Herbenick
Full Text Available In 2015, we conducted a cross-sectional, Internet-based, U.S. nationally representative probability survey of 2,021 adults (975 men, 1,046 women focused on a broad range of sexual behaviors. Individuals invited to participate were from the GfK KnowledgePanel®. The survey was titled the 2015 Sexual Exploration in America Study and survey completion took about 12 to 15 minutes. The survey was confidential and the researchers never had access to respondents' identifiers. Respondents reported on demographic items, lifetime and recent sexual behaviors, and the appeal of 50+ sexual behaviors. Most (>80% reported lifetime masturbation, vaginal sex, and oral sex. Lifetime anal sex was reported by 43% of men (insertive and 37% of women (receptive. Common lifetime sexual behaviors included wearing sexy lingerie/underwear (75% women, 26% men, sending/receiving digital nude/semi-nude photos (54% women, 65% men, reading erotic stories (57% of participants, public sex (≥43%, role-playing (≥22%, tying/being tied up (≥20%, spanking (≥30%, and watching sexually explicit videos/DVDs (60% women, 82% men. Having engaged in threesomes (10% women, 18% men and playful whipping (≥13% were less common. Lifetime group sex, sex parties, taking a sexuality class/workshop, and going to BDSM parties were uncommon (each <8%. More Americans identified behaviors as "appealing" than had engaged in them. Romantic/affectionate behaviors were among those most commonly identified as appealing for both men and women. The appeal of particular behaviors was associated with greater odds that the individual had ever engaged in the behavior. This study contributes to our understanding of more diverse adult sexual behaviors than has previously been captured in U.S. nationally representative probability surveys. Implications for sexuality educators, clinicians, and individuals in the general population are discussed.
Reece, Michael; Herbenick, Debby; Schick, Vanessa; Sanders, Stephanie A; Dodge, Brian; Fortenberry, J Dennis
2010-10-01
To provide a foundation for those who provide sexual health services and programs to men in the United States, the need for population-based data that describes men's sexual behaviors and their correlates remains. The purpose of this study was to, in a national probability survey of men ages 18-94 years, assess the occurrence and frequency of sexual behaviors and their associations with relationship status and health status. A national probability sample of 2,522 men aged 18 to 94 completed a cross-sectional survey about their sexual behaviors, relationship status, and health. Relationship status; health status; experience of solo masturbation, partnered masturbation, giving oral sex, receiving oral sex, vaginal intercourse and anal intercourse, in the past 90 days; frequency of solo masturbation, vaginal intercourse and anal intercourse in the past year. Masturbation, oral intercourse, and vaginal intercourse are prevalent among men throughout most of their adult life, with both occurrence and frequency varying with age and as functions of relationship type and physical health status. Masturbation is prevalent and frequent across various stages of life and for both those with and without a relational partner, with fewer men with fair to poor health reporting recent masturbation. Patterns of giving oral sex to a female partner were similar to those for receiving oral sex. Vaginal intercourse in the past 90 days was more prevalent among men in their late 20s and 30s than in the other age groups, although being reported by approximately 50% of men in the sixth and seventh decades of life. Anal intercourse and sexual interactions with other men were less common than all other sexual behaviors. Contemporary men in the United States engage in diverse solo and partnered sexual activities; however, sexual behavior is less common and more infrequent among older age cohorts. © 2010 International Society for Sexual Medicine.
Herbenick, Debby; Bowling, Jessamyn; Fu, Tsung-Chieh (Jane); Guerra-Reyes, Lucia; Sanders, Stephanie
2017-01-01
In 2015, we conducted a cross-sectional, Internet-based, U.S. nationally representative probability survey of 2,021 adults (975 men, 1,046 women) focused on a broad range of sexual behaviors. Individuals invited to participate were from the GfK KnowledgePanel®. The survey was titled the 2015 Sexual Exploration in America Study and survey completion took about 12 to 15 minutes. The survey was confidential and the researchers never had access to respondents’ identifiers. Respondents reported on demographic items, lifetime and recent sexual behaviors, and the appeal of 50+ sexual behaviors. Most (>80%) reported lifetime masturbation, vaginal sex, and oral sex. Lifetime anal sex was reported by 43% of men (insertive) and 37% of women (receptive). Common lifetime sexual behaviors included wearing sexy lingerie/underwear (75% women, 26% men), sending/receiving digital nude/semi-nude photos (54% women, 65% men), reading erotic stories (57% of participants), public sex (≥43%), role-playing (≥22%), tying/being tied up (≥20%), spanking (≥30%), and watching sexually explicit videos/DVDs (60% women, 82% men). Having engaged in threesomes (10% women, 18% men) and playful whipping (≥13%) were less common. Lifetime group sex, sex parties, taking a sexuality class/workshop, and going to BDSM parties were uncommon (each <8%). More Americans identified behaviors as “appealing” than had engaged in them. Romantic/affectionate behaviors were among those most commonly identified as appealing for both men and women. The appeal of particular behaviors was associated with greater odds that the individual had ever engaged in the behavior. This study contributes to our understanding of more diverse adult sexual behaviors than has previously been captured in U.S. nationally representative probability surveys. Implications for sexuality educators, clinicians, and individuals in the general population are discussed. PMID:28727762
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.
Herbenick, Debby; Friedman, M. Reuel; Schick, Vanessa; Fu, Tsung-Chieh (Jane); Bostwick, Wendy; Bartelt, Elizabeth; Muñoz-Laboy, Miguel; Pletta, David; Reece, Michael; Sandfort, Theo G. M.
2016-01-01
As bisexual individuals in the United States (U.S.) face significant health disparities, researchers have posited that these differences may be fueled, at least in part, by negative attitudes, prejudice, stigma, and discrimination toward bisexual individuals from heterosexual and gay/lesbian individuals. Previous studies of individual and social attitudes toward bisexual men and women have been conducted almost exclusively with convenience samples, with limited generalizability to the broader U.S. population. Our study provides an assessment of attitudes toward bisexual men and women among a nationally representative probability sample of heterosexual, gay, lesbian, and other-identified adults in the U.S. Data were collected from the 2015 National Survey of Sexual Health and Behavior (NSSHB), via an online questionnaire with a probability sample of adults (18 years and over) from throughout the U.S. We included two modified 5-item versions of the Bisexualities: Indiana Attitudes Scale (BIAS), validated sub-scales that were developed to measure attitudes toward bisexual men and women. Data were analyzed using descriptive statistics, gamma regression, and paired t-tests. Gender, sexual identity, age, race/ethnicity, income, and educational attainment were all significantly associated with participants' attitudes toward bisexual individuals. In terms of responses to individual scale items, participants were most likely to “neither agree nor disagree” with all attitudinal statements. Across sexual identities, self-identified other participants reported the most positive attitudes, while heterosexual male participants reported the least positive attitudes. As in previous research on convenience samples, we found a wide range of demographic characteristics were related with attitudes toward bisexual individuals in our nationally-representative study of heterosexual, gay/lesbian, and other-identified adults in the U.S. In particular, gender emerged as a significant
Dodge, Brian; Herbenick, Debby; Friedman, M Reuel; Schick, Vanessa; Fu, Tsung-Chieh Jane; Bostwick, Wendy; Bartelt, Elizabeth; Muñoz-Laboy, Miguel; Pletta, David; Reece, Michael; Sandfort, Theo G M
2016-01-01
As bisexual individuals in the United States (U.S.) face significant health disparities, researchers have posited that these differences may be fueled, at least in part, by negative attitudes, prejudice, stigma, and discrimination toward bisexual individuals from heterosexual and gay/lesbian individuals. Previous studies of individual and social attitudes toward bisexual men and women have been conducted almost exclusively with convenience samples, with limited generalizability to the broader U.S. Our study provides an assessment of attitudes toward bisexual men and women among a nationally representative probability sample of heterosexual, gay, lesbian, and other-identified adults in the U.S. Data were collected from the 2015 National Survey of Sexual Health and Behavior (NSSHB), via an online questionnaire with a probability sample of adults (18 years and over) from throughout the U.S. We included two modified 5-item versions of the Bisexualities: Indiana Attitudes Scale (BIAS), validated sub-scales that were developed to measure attitudes toward bisexual men and women. Data were analyzed using descriptive statistics, gamma regression, and paired t-tests. Gender, sexual identity, age, race/ethnicity, income, and educational attainment were all significantly associated with participants' attitudes toward bisexual individuals. In terms of responses to individual scale items, participants were most likely to "neither agree nor disagree" with all attitudinal statements. Across sexual identities, self-identified other participants reported the most positive attitudes, while heterosexual male participants reported the least positive attitudes. As in previous research on convenience samples, we found a wide range of demographic characteristics were related with attitudes toward bisexual individuals in our nationally-representative study of heterosexual, gay/lesbian, and other-identified adults in the U.S. In particular, gender emerged as a significant characteristic
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
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...
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.
Herbenick, Debby; Reece, Michael; Schick, Vanessa; Sanders, Stephanie A; Dodge, Brian; Fortenberry, J Dennis
2010-10-01
Despite a demonstrated relationship between sexual behaviors and health, including clinical risks, little is known about contemporary sexual behavior. To assess the rates of sexual behavior among adolescents and adults in the United States. We report the recent (past month, past year) and lifetime prevalence of sexual behaviors in a nationally representative probability sample of 5,865 men and women ages 14 to 94 in the United States (2,936 men, 2,929 women). Behaviors assessed included solo masturbation, partnered masturbation, giving and receiving oral sex, vaginal intercourse, and anal intercourse. Masturbation was common throughout the lifespan and more common than partnered sexual activities during adolescence and older age (70+). Although uncommon among 14- to 15-year olds, in the past year 18.3% of 16- to 17-year-old males and 22.4% of 16- to 17-year-old females performed oral sex with an other-sex partner. Also in the past year, more than half of women and men ages 18 to 49 engaged in oral sex. The proportion of adults who reported vaginal sex in the past year was highest among men ages 25-39 and for women ages 20-29, then progressively declined among older age groups. More than 20% of men ages 25-49 and women ages 20-39 reported anal sex in the past year. Same-sex sexual behaviors occurring in the past year were uncommonly reported. Men and women engage in a diverse range of solo and partnered sexual behaviors throughout the life course. The rates of contemporary sexual behavior provided in this report will be valuable to those who develop, implement, and evaluate programs that seek to improve societal knowledge related to the prevalence of sexual behaviors and to sexual health clinicians whose work to improve sexual health among the population often requires such rates of behavior. © 2010 International Society for Sexual Medicine.
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
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
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...
The quantum probability calculus
International Nuclear Information System (INIS)
Jauch, J.M.
1976-01-01
The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)
Choice Probability Generating Functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel 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....
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
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.
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...
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...
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....
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
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...
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
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.
Mercer, Catherine H; Copas, Andrew J; Sonnenberg, Pam; Johnson, Anne M; McManus, Sally; Erens, Bob; Cassell, Jackie A
2009-02-01
Sexually transmitted infection (STI) risk is determined both by partner numbers and partnership characteristics. Studies describing only recent partnership(s) overestimate long-term partnerships and underestimate the contribution of casual partnerships to STI transmission in populations. We describe all heterosexual partnerships in the past year in terms of partnership type, age and geographical mixing and how these characteristics relate to condom use. Probability sample survey of 11 161 men and women aged 16-44 resident in Britain, 1999-2001. Computer-assisted self-interviews asked respondents about partner numbers and detailed questions about their three most recent partnerships. We weight these data to represent partnerships for which detailed questions were not asked to present estimates for the population of partnerships. Of 15 488 heterosexuals partnerships, 39.1% (95% CI 36.6-41.7%) of men's partnerships were 'not (yet) regular' vs 20.0% (95% CI 18.2-21.9%) of women's partnerships. While condoms were used at last sex in 37.1% (95% CI 35.0-39.3%) of men's and 28.8% (95% CI 27.1-30.6%) of women's partnerships, and for 55.3% (95% CI 52.6-58.0%) of first sex with new partners, these proportions declined with age. When partnerships involved an age difference of 5+ years [26.2% (95% CI 23.0-29.6%) of men's and 36.5% (95% CI 33.0-40.1%) of women's partnerships], condoms were less commonly used at first sex than when partners were closer in age [44.1% (95% CI 39.1-48.4%) vs 60.8% (95% CI 57.3-64.2%)]. Sex occurred within 24 h in 23.4% (95% CI 19.7-27.5%) of men's and 10.7% (95% CI 8.3-13.6%) of women's partnerships. A substantial minority of partnerships in the population is casual. The proportion of partnerships not protected by condoms is high, especially for partnerships involving larger age differences and people in their 30s and 40s. Condom use with new partners needs to be promoted among all age-groups.
Flórez-Salamanca, Ludwing; Secades-Villa, Roberto; Budney, Alan J; García-Rodríguez, Olaya; Wang, Shuai; Blanco, Carlos
2013-09-01
This study aims to estimate the odds and predictors of Cannabis Use Disorders (CUD) relapse among individuals in remission. Analyses were done on the subsample of individuals with lifetime history of a CUD (abuse or dependence) who were in full remission at baseline (Wave 1) of the National Epidemiological Survey of Alcohol and Related Conditions (NESARC) (n=2350). Univariate logistic regression models and hierarchical logistic regression model were implemented to estimate odds of relapse and identify predictors of relapse at 3 years follow up (Wave 2). The relapse rate of CUD was 6.63% over an average of 3.6 year follow-up period. In the multivariable model, the odds of relapse were inversely related to time in remission, whereas having a history of conduct disorder or a major depressive disorder after Wave 1 increased the risk of relapse. Our findings suggest that maintenance of remission is the most common outcome for individuals in remission from a CUD. Treatment approaches may improve rates of sustained remission of individuals with CUD and conduct disorder or major depressive disorder. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
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
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.
[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.
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.
Tiwari, Aseem K; Bhati-Kushwaha, Himakshi; Kukreja, Pooja; Mishra, Vikash C; Tyagi, Neetu; Sharma, Ashish; Raina, Vimarsh
2015-06-01
With an increase in the number of transplants happening globally, hematopoietic stem cells (HSC) transplantation from matched unrelated donor (MUD) has begun. The increasing trend of MUD transplants across countries has been largely facilitated with the conspicuous growth of volunteer HSC donor noted in the last decade i.e. 8 million HSC donors in 2002 to more than 22 million in 2013 registered in 71 member registries of the Bone Marrow Donor Worldwide (BMDW). Some populations of the world are still very poorly represented in these registries. Since, the chances of successful engraftment and disease free survival are directly proportional to the HLA compatibility between the recipient and the prospective donor, the diversity of the HLA system at the antigenic and allelic level and the heterogeneity of HLA data of the registered donors has a bearing on the probability of finding a volunteer unrelated HSC donor for patients from such populations. In the present study 126 patients were identified suffering from hematological diseases requiring MUD transplant. Their HLA typing was performed and search was done using BMDW database. The search results for these Indian patients in the multinational registry as well as in the Indian Registries were analyzed using mean, range, standard deviation and finally evaluated in terms of probability for finding matched donor (MUD). Total Asian population is only 11 % in the BMDW making it difficult to find a MUD for an Asian patient. The current study supports this, experimentally; revealing that the probability of finding an allele match for an Indian patient in the multinational Human Leukocyte Antigen (HLA) registries is 16 % and a dismal 0.008 % in the Indian registries (donors in Indian registries is just 33,678 as compared to 22.5 million in BMDW). This greatly, emphasizes on enhancing the number of Indian donors in Indian and multi-national registries.
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...
Herbenick, Debby; Schick, Vanessa; Reece, Michael; Sanders, Stephanie A; Fortenberry, J Dennis
2013-06-01
Numerous factors may affect men's sexual experiences, including their health status, past trauma or abuse, medication use, relationships, mood, anxiety, and body image. Little research has assessed the influence of men's genital self-image on their sexual function or behaviors and none has done so in a nationally representative sample. The purpose of this study was to, in a nationally representative probability sample of men ages 18 to 60, assess the reliability and validity of the Male Genital Self-Image Scale (MGSIS), and to examine the relationship between scores on the MGSIS and men's scores on the International Index of Erectile Function (IIEF). The MGSIS was developed in two stages. Phase One involved a review of the literature and an analysis of cross-sectional survey data. Phase Two involved an administration of the scale items to a nationally representative sample of men in the United States ages 18 to 60. Measures include demographic items, the IIEF, and the MGSIS. Overall, most men felt positively about their genitals. However, 24.6% of men expressed some discomfort letting a healthcare provider examine their genitals and about 20% reported dissatisfaction with their genital size. The MGSIS was found to be reliable and valid, with the MGSIS-5 (consisting of five items) being the best fit to the data. The MGSIS was found to be a reliable and valid measure. In addition, men's scores on the MGSIS-5 were found to be positively related to men's scores on the IIEF. © 2013 International Society for Sexual Medicine.
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here are benthic habitat imagery that result from benthic photo-quadrat surveys conducted along transects at stratified random sites across...
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
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....
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)
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)
Haggard, Megan C; Kang, Linda L; Rowatt, Wade C; Shen, Megan Johnson
2015-01-01
The connection between religiousness and volunteering for the community can be explained through two distinct features of religion. First, religious organizations are social groups that encourage members to help others through planned opportunities. Second, helping others is regarded as an important value for members in religious organizations to uphold. We examined the relationship between religiousness and self-reported community volunteering in two independent national random surveys of American adults (i.e., the 2005 and 2007 waves of the Baylor Religion Survey). In both waves, frequency of religious service attendance was associated with an increase in likelihood that individuals would volunteer, whether through their religious organization or not, whereas frequency of reading sacred texts outside of religious services was associated with an increase in likelihood of volunteering only for or through their religious organization. The role of religion in community volunteering is discussed in light of these findings.
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
McCauley, Jenna L; Kilpatrick, Dean G; Walsh, Kate; Resnick, Heidi S
2013-04-01
To examine post-rape substance use, associated post rape medical and social concern variables, and past year substance abuse among women reporting having received medical care following a most recent or only lifetime incident of rape. Using a subsample of women who received post-rape medical care following a most recent or only rape incident (n=104) drawn from a national household probability sample of U.S. women, the current study described the extent of peritraumatic substance use, past year substance misuse behaviors, post-rape HIV and pregnancy concerns, and lifetime mental health service utilization as a function of substance use at time of incident. One-third (33%) of women seeking post-rape medical attention reported consuming alcohol or drugs at the time of their rape incident. Nearly one in four (24.7%) and one in seven (15%) women seeking medical attention following their most recent rape incident endorsed drug (marijuana, illicit, non-medical use of prescription drugs, or club drug) use or met substance abuse criteria, respectively, in the past year. One in twelve (8.4%) women reported at least monthly binge drinking in the past year. Approximately two-thirds of women reported seeking services for mental health needs in their lifetime. Post-rape concerns among women reporting peritraumatic substance use were not significantly different from those of women not reporting such use. Substance use was reported by approximately one-third of women and past year substance abuse was common among those seeking post-rape medical care. Implications for service delivery, intervention implementation, and future research are discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.
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.
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...
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.
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...
International Nuclear Information System (INIS)
Harvey, L D Danny
2007-01-01
Article 2 of the United Nations Framework Convention on Climate Change (UNFCCC) calls for stabilization of greenhouse gas (GHG) concentrations at levels that prevent dangerous anthropogenic interference (DAI) in the climate system. Until recently, the consensus viewpoint was that the climate sensitivity (the global mean equilibrium warming for a doubling of atmospheric CO 2 concentration) was 'likely' to fall between 1.5 and 4.5 K. However, a number of recent studies have generated probability distribution functions (pdfs) for climate sensitivity with the 95th percentile of the expected climate sensitivity as large as 10 K, while some studies suggest that the climate sensitivity is likely to fall in the lower half of the long-standing 1.5-4.5 K range. This paper examines the allowable CO 2 concentration as a function of the 95th percentile of the climate sensitivity pdf (ranging from 2 to 8 K) and for the following additional assumptions: (i) the 50th percentile for the pdf of the minimum sustained global mean warming that causes unacceptable harm equal to 1.5 or 2.5 K; and (ii) 1%, 5% or 10% allowable risks of unacceptable harm. For a 1% risk tolerance and the more stringent harm-threshold pdf, the allowable CO 2 concentration ranges from 323 to 268 ppmv as the 95th percentile of the climate sensitivity pdf increases from 2 to 8 K, while for a 10% risk tolerance and the less stringent harm-threshold pdf, the allowable CO 2 concentration ranges from 531 to 305 ppmv. In both cases it is assumed that non-CO 2 GHG radiative forcing can be reduced to half of its present value, otherwise; the allowable CO 2 concentration is even smaller. Accounting for the fact that the CO 2 concentration will gradually fall if emissions are reduced to zero, and that peak realized warming will then be less than the peak equilibrium warming (related to peak radiative forcing) allows the CO 2 concentration to peak at 10-40 ppmv higher than the limiting values given above for a climate
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.
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.
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
de Moraes, Vinícius Ynoe; Moreira, Cesar Domingues; Tamaoki, Marcel Jun Sugawara; Faloppa, Flávio; Belloti, Joao Carlos
2015-01-01
Objective: To assess whether there has been any improvement in the quality and quantity of randomized controlled trials (RCTs) in nationally published journals through the application of standardized and validated scores. Methods: We electronically selected all RCTs published in the two indexed Brazilian journals that focus on orthopedics, over the period 2000-2009: Acta Ortopédica Brasileira (AOB) and Revista Brasileira de Ortopedia (RBO). These RCTs were identified and scored by two independent researchers in accordance with the Jadad scale and the Cochrane Bone, Joint and Muscle Trauma Group score. The studies selected were grouped as follows: 1) publication period (2000-2004 or 2004-2009); 2) journal of publication (AOB or RBO). Results: Twenty-two papers were selected: 10 from AOB and 12 from RBO. No statistically significant differences were found between the proportions (nRCT/nTotal of published papers) of RCTs published in the two journals (p = 0.458), or in the Jadad score (p = 0.722) and Cochrane score (p = 0.630). Conclusion: The relative quality and quantity of RCTs in the journals analyzed were similar. There was a trend towards improvement of quality, but there was no increase in the number of RCTs between the two periods analyzed. PMID:27026971
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...
Gómez Toledo, Verónica; Gutiérrez Farfán, Ileana; Verduzco-Mendoza, Antonio; Arch-Tirado, Emilio
Tinnitus is defined as the conscious perception of a sensation of sound that occurs in the absence of an external stimulus. This audiological symptom affects 7% to 19% of the adult population. The aim of this study is to describe the associated comorbidities present in patients with tinnitus usingjoint and conditional probability analysis. Patients of both genders, diagnosed with unilateral or bilateral tinnitus, aged between 20 and 45 years, and had a full computerised medical record, were selected. Study groups were formed on the basis of the following clinical aspects: 1) audiological findings; 2) vestibular findings; 3) comorbidities such as, temporomandibular dysfunction, tubal dysfunction, otosclerosis and, 4) triggering factors of tinnitus noise exposure, respiratory tract infection, use of ototoxic and/or drugs. Of the patients with tinnitus, 27 (65%) reported hearing loss, 11 (26.19%) temporomandibular dysfunction, and 11 (26.19%) with vestibular disorders. When performing the joint probability analysis, it was found that the probability that a patient with tinnitus having hearing loss was 2742 0.65, and 2042 0.47 for bilateral type. The result for P (A ∩ B)=30%. Bayes' theorem P (AiB) = P(Ai∩B)P(B) was used, and various probabilities were calculated. Therefore, in patients with temporomandibulardysfunction and vestibular disorders, a posterior probability of P (Aі/B)=31.44% was calculated. Consideration should be given to the joint and conditional probability approach as tools for the study of different pathologies. Copyright © 2016 Academia Mexicana de Cirugía A.C. Publicado por Masson Doyma México S.A. All rights reserved.
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.
National Cluster-Randomized Trial of Duty-Hour Flexibility in Surgical Training.
Bilimoria, Karl Y; Chung, Jeanette W; Hedges, Larry V; Dahlke, Allison R; Love, Remi; Cohen, Mark E; Hoyt, David B; Yang, Anthony D; Tarpley, John L; Mellinger, John D; Mahvi, David M; Kelz, Rachel R; Ko, Clifford Y; Odell, David D; Stulberg, Jonah J; Lewis, Frank R
2016-02-25
Concerns persist regarding the effect of current surgical resident duty-hour policies on patient outcomes, resident education, and resident well-being. We conducted a national, cluster-randomized, pragmatic, noninferiority trial involving 117 general surgery residency programs in the United States (2014-2015 academic year). Programs were randomly assigned to current Accreditation Council for Graduate Medical Education (ACGME) duty-hour policies (standard-policy group) or more flexible policies that waived rules on maximum shift lengths and time off between shifts (flexible-policy group). Outcomes included the 30-day rate of postoperative death or serious complications (primary outcome), other postoperative complications, and resident perceptions and satisfaction regarding their well-being, education, and patient care. In an analysis of data from 138,691 patients, flexible, less-restrictive duty-hour policies were not associated with an increased rate of death or serious complications (9.1% in the flexible-policy group and 9.0% in the standard-policy group, P=0.92; unadjusted odds ratio for the flexible-policy group, 0.96; 92% confidence interval, 0.87 to 1.06; P=0.44; noninferiority criteria satisfied) or of any secondary postoperative outcomes studied. Among 4330 residents, those in programs assigned to flexible policies did not report significantly greater dissatisfaction with overall education quality (11.0% in the flexible-policy group and 10.7% in the standard-policy group, P=0.86) or well-being (14.9% and 12.0%, respectively; P=0.10). Residents under flexible policies were less likely than those under standard policies to perceive negative effects of duty-hour policies on multiple aspects of patient safety, continuity of care, professionalism, and resident education but were more likely to perceive negative effects on personal activities. There were no significant differences between study groups in resident-reported perception of the effect of fatigue on
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.
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.
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.
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.
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
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.)
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.
International Nuclear Information System (INIS)
Fullwood, R.R.
1989-04-01
The Advanced Neutron Source (ANS) (Difilippo, 1986; Gamble, 1986; West, 1986; Selby, 1987) will be the world's best facility for low energy neutron research. This performance requires the highest flux density of all non-pulsed reactors with concomitant low thermal inertial and fast response to upset conditions. One of the primary concerns is that a flow cessation of the order of a second may result in fuel damage. Such a flow stoppage could be the result of break in the primary piping. This report is a review of methods for assessing pipe break probabilities based on historical operating experience in power reactors, scaling methods, fracture mechanics and fracture growth models. The goal of this work is to develop parametric guidance for the ANS design to make the event highly unlikely. It is also to review and select methods that may be used in an interactive IBM-PC model providing fast and reasonably accurate models to aid the ANS designers in achieving the safety requirements. 80 refs., 7 figs
Borstlap, Waa; Deijen, C. L.; den Dulk, M.; Bonjer, H. J.; van de Velde, C. J.; Bemelman, W. A.; Tanis, P. J.; Aalbers, A.; Acherman, Y.; Algie, G. D.; Alting von Geusau, B.; Amelung, F.; Aukema, T. S.; Bakker, I. S.; Basha, S.; Bastiaansen, A. J. N. M.; Belgers, E.; Bleeker, W.; Blok, J.; Bosker, R. J. I.; Bosmans, J. W.; Boute, M. C.; Bouvy, N. D.; Bouwman, H.; Brandt-Kerkhof, A.; Brinkman, D. J.; Bruin, S.; Bruns, E. R. J.; Burbach, J. P. M.; Burger, J. W. A.; Buskens, C. J.; Clermonts, S.; Coenen, P. P. L. O.; Compaan, C.; Consten, E. C. J.; Darbyshire, T.; de Mik, S. M. L.; de Graaf, E. J. R.; de Groot, I.; de Vos Tot Nederveen Cappel, R. J. L.; de Wilt, J. H. W.; van der Wolde, J.; den Boer, F. C.; Dekker, J. W. T.; Demirkiran, A.; van Duijvendijk, P.; Musters, G. D.; van Rossem, C. C.; Schreuder, A. M.; Swank, H. A.
2017-01-01
Aim A Snapshot study design eliminates changes in treatment and outcome over time. This population based Snapshot study aimed to determine current practice and outcome of rectal cancer treatment with published landmark randomized controlled trials as a benchmark. Method In this collaborative
Borstlap, W. A. A.; Deijen, C. L.; den Dulk, M.; Bonjer, H. J.; van de Velde, C. J.; Bemelman, W. A.; Tanis, P. J.; Aalbers, A.; Acherman, Y.; Algie, G. D.; von Geu-sau, B. Alting; Amelung, F.; Aukema, T. S.; Bakker, I. S.; Bartels, S. A.; Basha, S.; Bastiaansen, A. J. N. M.; Belgers, E.; Bleeker, W.; Blok, J.; Bosker, R. J. I.; Bosmans, J. W.; Boute, M. C.; Bouvy, N. D.; Bouwman, H.; Brandt-Kerkhof, A.; Brinkman, D. J.; Bruin, S.; Bruns, E. R. J.; Burbach, J. P. M.; Burger, J. W. A.; Buskens, C. J.; Clermonts, S.; Coene, P. P. L. O.; Compaan, C.; Consten, E. C. J.; Darbyshire, T.; de Mik, S. M. L.; de Graaf, E. J. R.; de Groot, I.; Cappel, R. J. L. de Vos Tot Nederveen; de Wilt, J. H. W.; van der Wolde, J.; den Boer, F. C.; Furnee, E. J. B.; Havenga, K.; Klaase, J.; Holzik, M. F. Lutke; Meerdink, M.; Wevers, K.
Aim A Snapshot study design eliminates changes in treatment and outcome over time. This population based Snapshot study aimed to determine current practice and outcome of rectal cancer treatment with published landmark randomized controlled trials as a benchmark. Method In this collaborative
Directory of Open Access Journals (Sweden)
Christina Salmivalli
2012-12-01
Full Text Available The effects of a Finnish national school-based antibullying program (KiVa were evaluated in a randomized controlled trial (2007–2009 and during nationwide implementation (since 2009. The KiVa program is been found to reduce bullying and victimization and increase empathy towards victimized peers and self-efficacy to support and defend them. KiVa increases school liking and motivation and contributes to significant reductions in anxiety, depression, and negative peer perceptions. Somewhat larger reductions in bullying and victimization were found in the randomized controlled trial than in the broad rollout, and the largest effects were obtained in primary school (grades 1–6. The uptake of the KiVa program is remarkable, with 90 percent of Finnish comprehensive schools currently registered as program users.
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.
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.
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.
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.
Knowledge typology for imprecise probabilities.
Energy Technology Data Exchange (ETDEWEB)
Wilson, G. D. (Gregory D.); Zucker, L. J. (Lauren J.)
2002-01-01
When characterizing the reliability of a complex system there are often gaps in the data available for specific subsystems or other factors influencing total system reliability. At Los Alamos National Laboratory we employ ethnographic methods to elicit expert knowledge when traditional data is scarce. Typically, we elicit expert knowledge in probabilistic terms. This paper will explore how we might approach elicitation if methods other than probability (i.e., Dempster-Shafer, or fuzzy sets) prove more useful for quantifying certain types of expert knowledge. Specifically, we will consider if experts have different types of knowledge that may be better characterized in ways other than standard probability theory.
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic photo-quadrat surveys conducted along transects at stratified random sites across American Samoa in 2015 as a part of...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here are benthic habitat imagery that result from benthic photo-quadrat surveys conducted along transects at stratified random sites across...
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.
A national study of the psychological impact of bank robbery with a randomized control group
DEFF Research Database (Denmark)
Hansen, Maj; Armour, Cherie; Shevlin, Mark
of bank employees exposed to robbery (response rate: 73.6 %). Several related factors were also investigated including prior traumatic exposure, anxiety, and general traumatic symptoms. The results were compared to a randomized control group of bank employees never exposed to robbery (N= 303...... but surprisingly significantly higher than the follow-up robbery group. The results are discussed in relation to existing research and the effect of other factors such as prior traumatic exposure. In conclusion bank robberies are a traumatizing event for the employees, especially when disregarding avoidance...
Blaya, J A; Shin, S S; Yale, G; Suarez, C; Asencios, L; Contreras, C; Rodriguez, P; Kim, J; Cegielski, P; Fraser, H S F
2010-08-01
To evaluate the impact of the e-Chasqui laboratory information system in reducing reporting errors compared to the current paper system. Cluster randomized controlled trial in 76 health centers (HCs) between 2004 and 2008. Baseline data were collected every 4 months for 12 months. HCs were then randomly assigned to intervention (e-Chasqui) or control (paper). Further data were collected for the same months the following year. Comparisons were made between intervention and control HCs, and before and after the intervention. Intervention HCs had respectively 82% and 87% fewer errors in reporting results for drug susceptibility tests (2.1% vs. 11.9%, P = 0.001, OR 0.17, 95%CI 0.09-0.31) and cultures (2.0% vs. 15.1%, P Chasqui users sent on average three electronic error reports per week to the laboratories. e-Chasqui reduced the number of missing laboratory results at point-of-care health centers. Clinical users confirmed viewing electronic results not available on paper. Reporting errors to the laboratory using e-Chasqui promoted continuous quality improvement. The e-Chasqui laboratory information system is an important part of laboratory infrastructure improvements to support multidrug-resistant tuberculosis care in Peru.
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.)
Sefa, Eunice; Adimazoya, Edward Akolgo; Yartey, Emmanuel; Lenzi, Rachel; Tarpo, Cindy; Heward-Mills, Nii Lante; Lew, Katherine; Ampeh, Yvonne
2018-01-01
Introduction Generating a nationally representative sample in low and middle income countries typically requires resource-intensive household level sampling with door-to-door data collection. High mobile phone penetration rates in developing countries provide new opportunities for alternative sampling and data collection methods, but there is limited information about response rates and sample biases in coverage and nonresponse using these methods. We utilized data from an interactive voice response, random-digit dial, national mobile phone survey in Ghana to calculate standardized response rates and assess representativeness of the obtained sample. Materials and methods The survey methodology was piloted in two rounds of data collection. The final survey included 18 demographic, media exposure, and health behavior questions. Call outcomes and response rates were calculated according to the American Association of Public Opinion Research guidelines. Sample characteristics, productivity, and costs per interview were calculated. Representativeness was assessed by comparing data to the Ghana Demographic and Health Survey and the National Population and Housing Census. Results The survey was fielded during a 27-day period in February-March 2017. There were 9,469 completed interviews and 3,547 partial interviews. Response, cooperation, refusal, and contact rates were 31%, 81%, 7%, and 39% respectively. Twenty-three calls were dialed to produce an eligible contact: nonresponse was substantial due to the automated calling system and dialing of many unassigned or non-working numbers. Younger, urban, better educated, and male respondents were overrepresented in the sample. Conclusions The innovative mobile phone data collection methodology yielded a large sample in a relatively short period. Response rates were comparable to other surveys, although substantial coverage bias resulted from fewer women, rural, and older residents completing the mobile phone survey in
L'Engle, Kelly; Sefa, Eunice; Adimazoya, Edward Akolgo; Yartey, Emmanuel; Lenzi, Rachel; Tarpo, Cindy; Heward-Mills, Nii Lante; Lew, Katherine; Ampeh, Yvonne
2018-01-01
Generating a nationally representative sample in low and middle income countries typically requires resource-intensive household level sampling with door-to-door data collection. High mobile phone penetration rates in developing countries provide new opportunities for alternative sampling and data collection methods, but there is limited information about response rates and sample biases in coverage and nonresponse using these methods. We utilized data from an interactive voice response, random-digit dial, national mobile phone survey in Ghana to calculate standardized response rates and assess representativeness of the obtained sample. The survey methodology was piloted in two rounds of data collection. The final survey included 18 demographic, media exposure, and health behavior questions. Call outcomes and response rates were calculated according to the American Association of Public Opinion Research guidelines. Sample characteristics, productivity, and costs per interview were calculated. Representativeness was assessed by comparing data to the Ghana Demographic and Health Survey and the National Population and Housing Census. The survey was fielded during a 27-day period in February-March 2017. There were 9,469 completed interviews and 3,547 partial interviews. Response, cooperation, refusal, and contact rates were 31%, 81%, 7%, and 39% respectively. Twenty-three calls were dialed to produce an eligible contact: nonresponse was substantial due to the automated calling system and dialing of many unassigned or non-working numbers. Younger, urban, better educated, and male respondents were overrepresented in the sample. The innovative mobile phone data collection methodology yielded a large sample in a relatively short period. Response rates were comparable to other surveys, although substantial coverage bias resulted from fewer women, rural, and older residents completing the mobile phone survey in comparison to household surveys. Random digit dialing of mobile
Directory of Open Access Journals (Sweden)
Kelly L'Engle
Full Text Available Generating a nationally representative sample in low and middle income countries typically requires resource-intensive household level sampling with door-to-door data collection. High mobile phone penetration rates in developing countries provide new opportunities for alternative sampling and data collection methods, but there is limited information about response rates and sample biases in coverage and nonresponse using these methods. We utilized data from an interactive voice response, random-digit dial, national mobile phone survey in Ghana to calculate standardized response rates and assess representativeness of the obtained sample.The survey methodology was piloted in two rounds of data collection. The final survey included 18 demographic, media exposure, and health behavior questions. Call outcomes and response rates were calculated according to the American Association of Public Opinion Research guidelines. Sample characteristics, productivity, and costs per interview were calculated. Representativeness was assessed by comparing data to the Ghana Demographic and Health Survey and the National Population and Housing Census.The survey was fielded during a 27-day period in February-March 2017. There were 9,469 completed interviews and 3,547 partial interviews. Response, cooperation, refusal, and contact rates were 31%, 81%, 7%, and 39% respectively. Twenty-three calls were dialed to produce an eligible contact: nonresponse was substantial due to the automated calling system and dialing of many unassigned or non-working numbers. Younger, urban, better educated, and male respondents were overrepresented in the sample.The innovative mobile phone data collection methodology yielded a large sample in a relatively short period. Response rates were comparable to other surveys, although substantial coverage bias resulted from fewer women, rural, and older residents completing the mobile phone survey in comparison to household surveys. Random digit
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
National randomized controlled trial of virtual house calls for Parkinson disease.
Beck, Christopher A; Beran, Denise B; Biglan, Kevin M; Boyd, Cynthia M; Dorsey, E Ray; Schmidt, Peter N; Simone, Richard; Willis, Allison W; Galifianakis, Nicholas B; Katz, Maya; Tanner, Caroline M; Dodenhoff, Kristen; Aldred, Jason; Carter, Julie; Fraser, Andrew; Jimenez-Shahed, Joohi; Hunter, Christine; Spindler, Meredith; Reichwein, Suzanne; Mari, Zoltan; Dunlop, Becky; Morgan, John C; McLane, Dedi; Hickey, Patrick; Gauger, Lisa; Richard, Irene Hegeman; Mejia, Nicte I; Bwala, Grace; Nance, Martha; Shih, Ludy C; Singer, Carlos; Vargas-Parra, Silvia; Zadikoff, Cindy; Okon, Natalia; Feigin, Andrew; Ayan, Jean; Vaughan, Christina; Pahwa, Rajesh; Dhall, Rohit; Hassan, Anhar; DeMello, Steven; Riggare, Sara S; Wicks, Paul; Achey, Meredith A; Elson, Molly J; Goldenthal, Steven; Keenan, H Tait; Korn, Ryan; Schwarz, Heidi; Sharma, Saloni; Stevenson, E Anna; Zhu, William
2017-09-12
To determine whether providing remote neurologic care into the homes of people with Parkinson disease (PD) is feasible, beneficial, and valuable. In a 1-year randomized controlled trial, we compared usual care to usual care supplemented by 4 virtual visits via video conferencing from a remote specialist into patients' homes. Primary outcome measures were feasibility, as measured by the proportion who completed at least one virtual visit and the proportion of virtual visits completed on time; and efficacy, as measured by the change in the Parkinson's Disease Questionnaire-39, a quality of life scale. Secondary outcomes included quality of care, caregiver burden, and time and travel savings. A total of 927 individuals indicated interest, 210 were enrolled, and 195 were randomized. Participants had recently seen a specialist (73%) and were largely college-educated (73%) and white (96%). Ninety-five (98% of the intervention group) completed at least one virtual visit, and 91% of 388 virtual visits were completed. Quality of life did not improve in those receiving virtual house calls (0.3 points worse on a 100-point scale; 95% confidence interval [CI] -2.0 to 2.7 points; p = 0.78) nor did quality of care or caregiver burden. Each virtual house call saved patients a median of 88 minutes (95% CI 70-120; p < 0.0001) and 38 miles per visit (95% CI 36-56; p < 0.0001). Providing remote neurologic care directly into the homes of people with PD was feasible and was neither more nor less efficacious than usual in-person care. Virtual house calls generated great interest and provided substantial convenience. NCT02038959. This study provides Class III evidence that for patients with PD, virtual house calls from a neurologist are feasible and do not significantly change quality of life compared to in-person visits. The study is rated Class III because it was not possible to mask patients to visit type. © 2017 American Academy of Neurology.
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.
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...
Avram, Robert; Marquis-Gravel, Guillaume; Simard, François; Pacheco, Christine; Couture, Étienne; Tremblay-Gravel, Maxime; Desplantie, Olivier; Malhamé, Isabelle; Bibas, Lior; Mansour, Samer; Parent, Marie-Claude; Farand, Paul; Harvey, Luc; Lessard, Marie-Gabrielle; Ly, Hung; Liu, Geoffrey; Hay, Annette E; Marc Jolicoeur, E
2018-07-01
Use of health administrative databases is proposed for screening and monitoring of participants in randomized registry trials. However, access to these databases raises privacy concerns. We assessed patient's preferences regarding use of personal information to link their research records with national health databases, as part of a hypothetical randomized registry trial. Cardiology patients were invited to complete an anonymous self-reported survey that ascertained preferences related to the concept of accessing government health databases for research, the type of personal identifiers to be shared and the type of follow-up preferred as participants in a hypothetical trial. A total of 590 responders completed the survey (90% response rate), the majority of which were Caucasians (90.4%), male (70.0%) with a median age of 65years (interquartile range, 8). The majority responders (80.3%) would grant researchers access to health administrative databases for screening and follow-up. To this end, responders endorsed the recording of their personal identifiers by researchers for future record linkage, including their name (90%), and health insurance number (83.9%), but fewer responders agreed with the recording of their social security number (61.4%, pgranting researchers access to the administrative databases (OR: 1.69, 95% confidence interval: 1.03-2.90; p=0.04). The majority of Cardiology patients surveyed were supportive of use of their personal identifiers to access administrative health databases and conduct long-term monitoring in the context of a randomized registry trial. Copyright © 2018 Elsevier Ireland Ltd. All rights reserved.
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
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
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 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)
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).
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.
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.
Ondari, Joshua Nyaribari; Masika, Moses Muia; Ombachi, Richard Bwana; Ating'a, John Ernest
2016-10-01
To determine the difference in infection rate between 24h versus five days of prophylactic antibiotic use in management of Gustilo II open tibia fractures. Unblinded randomized control trial. Accident and Emergency, orthopedic wards and outpatient clinics at Kenyatta National Hospital (KNH). The study involved patients aged 18-80 years admitted through accident and emergency department with Gustilo II traumatic open tibia fractures. Patients were randomized into either 24hour or five day group and antibiotics started for 24hours or five days after surgical debridement. The wounds were exposed and scored using ASEPSIS wound scoring system for infection after 48h, 5days and at 14days. The main outcomes of interest were presence of infection at days 2, 5 and 14 and effect of duration to antibiotic administration on infection rate. There was no significant difference in infection rates between 24-hour and 5-day groups with infection rates of 23% (9/40) vs. 19% (7/37) respectively (p=0.699). The infection rate was significantly associated with time lapsed before administration of antibiotics (p=0.004). In the use of prophylactic antibiotics for the management of Gustilo II traumatic open tibia fractures, there is no difference in infection rate between 24hours and five days regimen but time to antibiotic administration correlates with infection rate. Antibiotic use for 24hours only has proven adequate prophylaxis against infection. This is underlined in our study which we hope shall inform practice in our setting. A larger, more appropriately controlled study would be useful. Copyright © 2016 Elsevier Ltd. All rights reserved.
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.
Susukida, Ryoko; Crum, Rosa M; Stuart, Elizabeth A; Ebnesajjad, Cyrus; Mojtabai, Ramin
2016-07-01
To compare the characteristics of individuals participating in randomized controlled trials (RCTs) of treatments of substance use disorder (SUD) with individuals receiving treatment in usual care settings, and to provide a summary quantitative measure of differences between characteristics of these two groups of individuals using propensity score methods. Design Analyses using data from RCT samples from the National Institute of Drug Abuse Clinical Trials Network (CTN) and target populations of patients drawn from the Treatment Episodes Data Set-Admissions (TEDS-A). Settings Multiple clinical trial sites and nation-wide usual SUD treatment settings in the United States. A total of 3592 individuals from 10 CTN samples and 1 602 226 individuals selected from TEDS-A between 2001 and 2009. Measurements The propensity scores for enrolling in the RCTs were computed based on the following nine observable characteristics: sex, race/ethnicity, age, education, employment status, marital status, admission to treatment through criminal justice, intravenous drug use and the number of prior treatments. Findings The proportion of those with ≥ 12 years of education and the proportion of those who had full-time jobs were significantly higher among RCT samples than among target populations (in seven and nine trials, respectively, at P difference in the mean propensity scores between the RCTs and the target population was 1.54 standard deviations and was statistically significant at P different from individuals receiving treatment in usual care settings. Notably, RCT participants tend to have more years of education and a greater likelihood of full-time work compared with people receiving care in usual care settings. © 2016 Society for the Study of Addiction.
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
Directory of Open Access Journals (Sweden)
Swapnil Vishnu Lale
2013-01-01
Full Text Available Background: One of the important components of revised national tuberculosis control programme is Good quality diagnosis, primarily by sputum smear microscopy. All efforts are made to ensure that the designated microscopy centers function at optimal level. The process of Random Blinded Re-Checking (RBRCof Acid Fast Bacillus slides is built in the programme. Objectives: To study the relationship of different types of errors detected in RBRC with respect to time, place and cost. To study the stability and capability of the process of RBRC. Methods: Analysis of secondary data of external quality assessment of Solapur district since January 2006 is supplemented by direct implementation of the programme since April 2011 till date. Data analysis is done using statistical software Minitab version 16.Results: Since January 2006 to May 2012;42191 slides were re-checked in 77 RBRC sessions at District Tuberculosis Center, Solapur.Different types of 69 errors were detected. Onsite evaluation and panel testing did not show any discordance. Barshi and Mangalwedha Tuberculosis Units (TU showed significantly higher number of errors as compared to Karmala TU. (P<0.002 Weighted Pareto Chart revealed that the costliest form of errors is high false negatives and low false negatives. Conclusion:Detection of errors in RBRC sessions follows Poisson distribution. The process of RBRC is found to be in control and capable of achieving the desired target of detection of errors.
Abroms, Lorien C; Chiang, Shawn; Macherelli, Laura; Leavitt, Leah; Montgomery, Margaret
2017-10-03
Automated text messages on mobile phones have been found to be effective for smoking cessation in adult smokers. This study aims to test the acceptability and feasibility of SmokefreeMOM, a national smoking cessation text-messaging program for pregnant smokers. Participants were recruited from prenatal care and randomized to receive SmokefreeMOM (n=55), an automated smoking cessation text-messaging program, or a control text message quitline referral (n=44). Participants were surveyed by phone at baseline and at 1 month and 3 months after enrollment. Results indicate that the SmokefreeMOM program was highly rated overall and rated more favorably than the control condition in its helpfulness at 3-month follow-up (Pmessaging at both 1-month and 3-month follow-ups (Pmessages, and few participants unsubscribed from the program. There were no significant differences between groups on the use of extra treatment resources or on smoking-related outcomes. However, at the 3-month follow-up, some outcomes favored the intervention group. SmokefreeMOM is acceptable for pregnant smokers. It is recommended that SmokefreeMOM be further refined and evaluated. Clinicaltrials.gov NCT02412956; https://clinicaltrials.gov/ct2/show/NCT02412956 (Archived by WebCite at http://www.webcitation.org/6tcmeRnbC). ©Lorien C Abroms, Shawn Chiang, Laura Macherelli, Leah Leavitt, Margaret Montgomery. Originally published in the Journal of Medical Internet Research (http://www.jmir.org), 03.10.2017.
National Aeronautics and Space Administration — PROBABILITY CALIBRATION BY THE MINIMUM AND MAXIMUM PROBABILITY SCORES IN ONE-CLASS BAYES LEARNING FOR ANOMALY DETECTION GUICHONG LI, NATHALIE JAPKOWICZ, IAN HOFFMAN,...
Cohn, Amy M; Zinzow, Heidi M; Resnick, Heidi S; Kilpatrick, Dean G
2013-02-01
Rape tactics, rape incident characteristics, and mental health problems (lifetime depression, PTSD, and substance abuse) were investigated as correlates of eight different reasons for not reporting a rape to police among women who had experienced but did not report a rape to police (n = 441) within a national telephone household probability sample. Rape tactics (nonmutually exclusive) included drug or alcohol-facilitated or incapacitated rape (DAFR/IR; n = 119) and forcible rape (FR; n = 376). Principal Components Analysis (PCA) was conducted to extract a dominant set of patterns among the eight reasons for not reporting, and to reduce the set of dependent variables. PCA results indicated three unique factors: Not Wanting Others to Know, Nonacknowledgment of Rape, and Criminal Justice Concerns. Hierarchical regression analyses showed DAFR/IR and FR were both positively and significantly associated with Criminal Justice Concerns, whereas DAFR/IR, but not FR, was associated with Nonacknowledgment as a reason for not reporting to police. Neither DAFR/IR nor FR emerged as significant predictors of Others Knowing after controlling for fear of death or injury at the time of the incident. Correlations among variables showed that the Criminal Justice Concerns factor was positively related to lifetime depression and PTSD and the Nonacknowledgement factor was negatively related to lifetime PTSD. Findings suggest prevention programs should educate women about the definition of rape, which may include incapacitation due to alcohol or drugs, to increase acknowledgement and decrease barriers to police reporting.
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...
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
DEFF Research Database (Denmark)
Østergaard, Uffe
2014-01-01
Nation er et gammelt begreb, som kommer af det latinske ord for fødsel, natio. Nationalisme bygger på forestillingen om, at mennesker har én og kun én national identitet og har ret til deres egen nationalstat. Ordet og forestillingen er kun godt 200 år gammel, og i 1900-tallet har ideologien bredt...
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
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
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...
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 ...
Gorin, Amy A; Lenz, Erin M; Cornelius, Talea; Huedo-Medina, Tania; Wojtanowski, Alexis C; Foster, Gary D
2018-03-01
For married couples, when one spouse participates in weight loss treatment, the untreated spouse can also experience weight loss. This study examined this ripple effect in a nationally available weight management program. One hundred thirty dyads were randomized to Weight Watchers (WW; n = 65) or to a self-guided control group (SG; n = 65) and assessed at 0, 3, and 6 months. Inclusion criteria were age ≥ 25 years, BMI 27 to 40 kg/m 2 (≥ 25 kg/m 2 for untreated spouses), and no weight loss contraindications. WW participants received 6 months of free access to in-person meetings and online tools. SG participants received a weight loss handout. Spouses did not receive treatment. Untreated spouses lost weight at 3 months (WW = -1.5 ± 2.9 kg; SG = -1.1 ± 3.3 kg) and 6 months (WW = -2.2 ± 4.2 kg; SG = -1.9 ± 3.6 kg), but weight losses did not differ by condition. Overall, 32.0% of untreated spouses lost ≥ 3% of initial body weight by 6 months. Baseline weight was significantly correlated within couples (r = 0.26; P ripple effect was found in untreated spouses in both formal and self-guided weight management approaches. These data suggest that weight loss can spread within couples, and that widely available lifestyle programs have weight loss effects beyond the treated individual. © 2018 The Authors. Obesity published by Wiley Periodicals, Inc. on behalf of The Obesity Society (TOS).
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
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.
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.
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
Beskow, Laura M.; Lin, Li; Dombeck, Carrie B.; Gao, Emily; Weinfurt, Kevin P.
2016-01-01
Purpose: To determine the individual and combined effects of a simplified form and a review/retest intervention on biobanking consent comprehension. Methods: We conducted a national online survey in which participants were randomized within four educational strata to review a simplified or traditional consent form. Participants then completed a comprehension quiz; for each item answered incorrectly, they reviewed the corresponding consent form section and answered another quiz item on that to...
Determining probabilities of geologic events and processes
International Nuclear Information System (INIS)
Hunter, R.L.; Mann, C.J.; Cranwell, R.M.
1985-01-01
The Environmental Protection Agency has recently published a probabilistic standard for releases of high-level radioactive waste from a mined geologic repository. The standard sets limits for contaminant releases with more than one chance in 100 of occurring within 10,000 years, and less strict limits for releases of lower probability. The standard offers no methods for determining probabilities of geologic events and processes, and no consensus exists in the waste-management community on how to do this. Sandia National Laboratories is developing a general method for determining probabilities of a given set of geologic events and processes. In addition, we will develop a repeatable method for dealing with events and processes whose probability cannot be determined. 22 refs., 4 figs
Investigating Probability with the NBA Draft Lottery.
Quinn, Robert J.
1997-01-01
Investigates an interesting application of probability in the world of sports. Considers the role of permutations in the lottery system used by the National Basketball Association (NBA) in the United States to determine the order in which nonplayoff teams select players from the college ranks. Presents a lesson on this topic in which students work…
Neutrosophic Probability, Set, And Logic (first version)
Smarandache, Florentin
2000-01-01
This project is a part of a National Science Foundation interdisciplinary project proposal. Starting from a new viewpoint in philosophy, the neutrosophy, one extends the classical "probability theory", "fuzzy set" and "fuzzy logic" to , and respectively. They are useful in artificial intelligence, neural networks, evolutionary programming, neutrosophic dynamic systems, and quantum mechanics.
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.
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…
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.
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...
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
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
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
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.
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)
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
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic photo-quadrat surveys conducted along transects at stratified random sites across the Mariana archipelago in 2014 as a...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic photo-quadrat surveys conducted along transects at stratified random sites across American Samoa in 2015 as a part of...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here are benthic habitat imagery that result from benthic photo-quadrat surveys conducted along transects at stratified random sites across the...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here are benthic habitat imagery that result from benthic photo-quadrat surveys conducted along transects at stratified random sites across Wake...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here are benthic habitat imagery that result from benthic photo-quadrat surveys conducted along transects at stratified random sites across the...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic photo-quadrat surveys conducted along transects at stratified random sites across the Hawaiian archipelago in 2016 as a...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic photo-quadrat surveys conducted along transects at stratified random sites across the Hawaiian archipelago in 2013 as a...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic photo-quadrat surveys conducted along transects at stratified random sites across the Pacific Remote Island Areas since...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here are benthic habitat imagery that result from benthic photo-quadrat surveys conducted along transects at stratified random sites across the...
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.
Probable Unusual Transmission of Zika Virus
Centers for Disease Control (CDC) Podcasts
2011-05-23
This podcast discusses a study about the probable unusual transmission of Zika Virus Infection from a scientist to his wife, published in the May 2011 issue of Emerging Infectious Diseases. Dr. Brian Foy, Associate Professor at Colorado State University, shares details of this event. Created: 5/23/2011 by National Center for Emerging Zoonotic and Infectious Diseases (NCEZID). Date Released: 5/25/2011.
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 ...
Sulaiman, Nabil; Albadawi, Salah; Abusnana, Salah; Fikri, Mahmoud; Madani, Abdulrazzag; Mairghani, Maisoon; Alawadi, Fatheya; Zimmet, Paul; Shaw, Jonathan
2015-09-01
The prevalence of diabetes has risen rapidly in the Middle East, particularly in the Gulf Region. However, some prevalence estimates have not fully accounted for large migrant worker populations and have focused on minority indigenous populations. The objectives of the UAE National Diabetes and Lifestyle Study are to: (i) define the prevalence of, and risk factors for, T2DM; (ii) describe the distribution and determinants of T2DM risk factors; (iii) study health knowledge, attitudes, and (iv) identify gene-environment interactions; and (v) develop baseline data for evaluation of future intervention programs. Given the high burden of diabetes in the region and the absence of accurate data on non-UAE nationals in the UAE, a representative sample of the non-UAE nationals was essential. We used an innovative methodology in which non-UAE nationals were sampled when attending the mandatory biannual health check that is required for visa renewal. Such an approach could also be used in other countries in the region. Complete data were available for 2719 eligible non-UAE nationals (25.9% Arabs, 70.7% Asian non-Arabs, 1.1% African non-Arabs, and 2.3% Westerners). Most were men < 65 years of age. The response rate was 68%, and the non-response was greater among women than men; 26.9% earned less than UAE Dirham (AED) 24 000 (US$6500) and the most common areas of employment were as managers or professionals, in service and sales, and unskilled occupations. Most (37.4%) had completed high school and 4.1% had a postgraduate degree. This novel methodology could provide insights for epidemiological studies in the UAE and other Gulf States, particularly for expatriates. © 2015 Ruijin Hospital, Shanghai Jiaotong University School of Medicine and Wiley Publishing Asia Pty Ltd.
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 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...
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...
International Nuclear Information System (INIS)
Roswit, B.; Higgins, G.A.; Keehn, R.J.
1975-01-01
In 1964 the Veterans Administration Surgical Adjuvant Group (VASAG) initiated a large-scale, controlled, randomized protocol to study the role of low-dose preoperative irradiation (2000 to 2500 rads/10 fractions/12 days) in patients with operable adenocarcinoma of the sigmoid colon and rectum. This report analyzes the data in 700 patients, all at 5-year risk. There appears to be a definite benefit to irradiated patients who undergo abdominoperineal resections, when compared with the controls. This advantage is reflected in improvement of 5-year survival, and reductions in lymph node invasion, local recurrence, and distant metastases. A second protocol has been initiated in 30 VA hospitals employing a higher dose (3150 rads) to extended portals (to L2) to male patients who require abdominoperineal resections. (U.S.)
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
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...
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.
Global Grid of Probabilities of Urban Expansion to 2030
National Aeronautics and Space Administration — The Global Grid of Probabilities of Urban Expansion to 2030 presents spatially explicit probabilistic forecasts of global urban land cover change from 2000 to 2030...
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
Logic, probability, and human reasoning.
Johnson-Laird, P N; Khemlani, Sangeet S; Goodwin, Geoffrey P
2015-04-01
This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn - not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction. Copyright © 2015 Elsevier Ltd. All rights reserved.
Introduction to probability and measure
Parthasarathy, K R
2005-01-01
According to a remark attributed to Mark Kac 'Probability Theory is a measure theory with a soul'. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both these aesthetic and practical aspects into account.
Default probabilities and default correlations
Erlenmaier, Ulrich; Gersbach, Hans
2001-01-01
Starting from the Merton framework for firm defaults, we provide the analytics and robustness of the relationship between default correlations. We show that loans with higher default probabilities will not only have higher variances but also higher correlations between loans. As a consequence, portfolio standard deviation can increase substantially when loan default probabilities rise. This result has two important implications. First, relative prices of loans with different default probabili...
The Probabilities of Unique Events
2012-08-30
Washington, DC USA Max Lotstein and Phil Johnson-Laird Department of Psychology Princeton University Princeton, NJ USA August 30th 2012...social justice and also participated in antinuclear demonstrations. The participants ranked the probability that Linda is a feminist bank teller as...retorted that such a flagrant violation of the probability calculus was a result of a psychological experiment that obscured the rationality of the
Probability Matching, Fast and Slow
Koehler, Derek J.; James, Greta
2014-01-01
A prominent point of contention among researchers regarding the interpretation of probability-matching behavior is whether it represents a cognitively sophisticated, adaptive response to the inherent uncertainty of the tasks or settings in which it is observed, or whether instead it represents a fundamental shortcoming in the heuristics that support and guide human decision making. Put crudely, researchers disagree on whether probability matching is "smart" or "dumb." Here, we consider eviden...
International Nuclear Information System (INIS)
Otsuka, Naoto
2013-01-01
Highlights: • A theoretical foundation is presented for more efficient Integrated Safeguards (IS). • Probability of undetected nuclear proliferation activities should be maintained low. • For nations under IS, the probability to start proliferation activities is very low. • The fact can decrease the detection probability of IS by dozens of percentage points. • The cost of IS per nation can be cut down by reducing inspection frequencies etc. - Abstract: A theoretical foundation is presented for implementing more efficiently the present International Atomic Energy Agency (IAEA) integrated safeguards (ISs) on the basis of fuzzy evaluation of the probability that the evaluated nation will continue peaceful activities. It is shown that by determining the presence probability of undetected nuclear proliferating activities, nations under IS can be maintained at acceptably low proliferation risk levels even if the detection probability of current IS is decreased by dozens of percentage from the present value. This makes it possible to reduce inspection frequency and the number of collected samples, allowing the IAEA to cut costs per nation. This will contribute to further promotion and application of IS to more nations by the IAEA, and more efficient utilization of IAEA resources from the viewpoint of whole IS framework
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
Probabilities the little numbers that rule our lives
Olofsson, Peter
2014-01-01
Praise for the First Edition"If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real-world situations."- Keith Devlin, Stanford University, National Public Radio's "Math Guy" and author of The Math Gene and The Unfinished GameFrom probable improbabilities to regular irregularities, Probabilities: The Little Numbers That Rule Our Lives, Second Edition investigates the often surprising effects of risk and chance in our lives. Featur
Directory of Open Access Journals (Sweden)
Karunamuni Nandini
2008-12-01
Full Text Available Abstract Background Aerobic physical activity (PA and resistance training are paramount in the treatment and management of type 2 diabetes (T2D, but few studies have examined the determinants of both types of exercise in the same sample. Objective The primary purpose was to investigate the utility of the Theory of Planned Behavior (TPB in explaining aerobic PA and resistance training in a population sample of T2D adults. Methods A total of 244 individuals were recruited through a random national sample which was created by generating a random list of household phone numbers. The list was proportionate to the actual number of household telephone numbers for each Canadian province (with the exception of Quebec. These individuals completed self-report TPB constructs of attitude, subjective norm, perceived behavioral control and intention, and a 3-month follow-up that assessed aerobic PA and resistance training. Results TPB explained 10% and 8% of the variance respectively for aerobic PA and resistance training; and accounted for 39% and 45% of the variance respectively for aerobic PA and resistance training intentions. Conclusion These results may guide the development of appropriate PA interventions for aerobic PA and resistance training based on the TPB.
Theory of overdispersion in counting statistics caused by fluctuating probabilities
International Nuclear Information System (INIS)
Semkow, Thomas M.
1999-01-01
It is shown that the random Lexis fluctuations of probabilities such as probability of decay or detection cause the counting statistics to be overdispersed with respect to the classical binomial, Poisson, or Gaussian distributions. The generating and the distribution functions for the overdispersed counting statistics are derived. Applications to radioactive decay with detection and more complex experiments are given, as well as distinguishing between the source and background, in the presence of overdispersion. Monte-Carlo verifications are provided
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
Event Discrimination Using Seismoacoustic Catalog Probabilities
Albert, S.; Arrowsmith, S.; Bowman, D.; Downey, N.; Koch, C.
2017-12-01
Presented here are three seismoacoustic catalogs from various years and locations throughout Utah and New Mexico. To create these catalogs, we combine seismic and acoustic events detected and located using different algorithms. Seismoacoustic events are formed based on similarity of origin time and location. Following seismoacoustic fusion, the data is compared against ground truth events. Each catalog contains events originating from both natural and anthropogenic sources. By creating these seismoacoustic catalogs, we show that the fusion of seismic and acoustic data leads to a better understanding of the nature of individual events. The probability of an event being a surface blast given its presence in each seismoacoustic catalog is quantified. We use these probabilities to discriminate between events from natural and anthropogenic sources. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.
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.
Biagini, Francesca
2016-01-01
This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics.
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.
Betting on Illusory Patterns: Probability Matching in Habitual Gamblers.
Gaissmaier, Wolfgang; Wilke, Andreas; Scheibehenne, Benjamin; McCanney, Paige; Barrett, H Clark
2016-03-01
Why do people gamble? A large body of research suggests that cognitive distortions play an important role in pathological gambling. Many of these distortions are specific cases of a more general misperception of randomness, specifically of an illusory perception of patterns in random sequences. In this article, we provide further evidence for the assumption that gamblers are particularly prone to perceiving illusory patterns. In particular, we compared habitual gamblers to a matched sample of community members with regard to how much they exhibit the choice anomaly 'probability matching'. Probability matching describes the tendency to match response proportions to outcome probabilities when predicting binary outcomes. It leads to a lower expected accuracy than the maximizing strategy of predicting the most likely event on each trial. Previous research has shown that an illusory perception of patterns in random sequences fuels probability matching. So does impulsivity, which is also reported to be higher in gamblers. We therefore hypothesized that gamblers will exhibit more probability matching than non-gamblers, which was confirmed in a controlled laboratory experiment. Additionally, gamblers scored much lower than community members on the cognitive reflection task, which indicates higher impulsivity. This difference could account for the difference in probability matching between the samples. These results suggest that gamblers are more willing to bet impulsively on perceived illusory patterns.
Introduction to probability and stochastic processes with applications
Castañ, Blanco; Arunachalam, Viswanathan; Dharmaraja, Selvamuthu
2012-01-01
An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic t
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.
VIBRATION ISOLATION SYSTEM PROBABILITY ANALYSIS
Directory of Open Access Journals (Sweden)
Smirnov Vladimir Alexandrovich
2012-10-01
Full Text Available The article deals with the probability analysis for a vibration isolation system of high-precision equipment, which is extremely sensitive to low-frequency oscillations even of submicron amplitude. The external sources of low-frequency vibrations may include the natural city background or internal low-frequency sources inside buildings (pedestrian activity, HVAC. Taking Gauss distribution into account, the author estimates the probability of the relative displacement of the isolated mass being still lower than the vibration criteria. This problem is being solved in the three dimensional space, evolved by the system parameters, including damping and natural frequency. According to this probability distribution, the chance of exceeding the vibration criteria for a vibration isolation system is evaluated. Optimal system parameters - damping and natural frequency - are being developed, thus the possibility of exceeding vibration criteria VC-E and VC-D is assumed to be less than 0.04.
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
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.
Random broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Model uncertainty: Probabilities for models?
International Nuclear Information System (INIS)
Winkler, R.L.
1994-01-01
Like any other type of uncertainty, model uncertainty should be treated in terms of probabilities. The question is how to do this. The most commonly-used approach has a drawback related to the interpretation of the probabilities assigned to the models. If we step back and look at the big picture, asking what the appropriate focus of the model uncertainty question should be in the context of risk and decision analysis, we see that a different probabilistic approach makes more sense, although it raise some implementation questions. Current work that is underway to address these questions looks very promising
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
Statistical probability tables CALENDF program
International Nuclear Information System (INIS)
Ribon, P.
1989-01-01
The purpose of the probability tables is: - to obtain dense data representation - to calculate integrals by quadratures. They are mainly used in the USA for calculations by Monte Carlo and in the USSR and Europe for self-shielding calculations by the sub-group method. The moment probability tables, in addition to providing a more substantial mathematical basis and calculation methods, are adapted for condensation and mixture calculations, which are the crucial operations for reactor physics specialists. However, their extension is limited by the statistical hypothesis they imply. Efforts are being made to remove this obstacle, at the cost, it must be said, of greater complexity
Probability, statistics, and queueing theory
Allen, Arnold O
1990-01-01
This is a textbook on applied probability and statistics with computer science applications for students at the upper undergraduate level. It may also be used as a self study book for the practicing computer science professional. The successful first edition of this book proved extremely useful to students who need to use probability, statistics and queueing theory to solve problems in other fields, such as engineering, physics, operations research, and management science. The book has also been successfully used for courses in queueing theory for operations research students. This second edit
Probability and Statistics: 5 Questions
DEFF Research Database (Denmark)
Probability and Statistics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in probability and statistics. We hear their views on the fields, aims, scopes, the future direction of research and how their work fits...... in these respects. Interviews with Nick Bingham, Luc Bovens, Terrence L. Fine, Haim Gaifman, Donald Gillies, James Hawthorne, Carl Hoefer, James M. Joyce, Joseph B. Kadane Isaac Levi, D.H. Mellor, Patrick Suppes, Jan von Plato, Carl Wagner, Sandy Zabell...
Dynamic SEP event probability forecasts
Kahler, S. W.; Ling, A.
2015-10-01
The forecasting of solar energetic particle (SEP) event probabilities at Earth has been based primarily on the estimates of magnetic free energy in active regions and on the observations of peak fluxes and fluences of large (≥ M2) solar X-ray flares. These forecasts are typically issued for the next 24 h or with no definite expiration time, which can be deficient for time-critical operations when no SEP event appears following a large X-ray flare. It is therefore important to decrease the event probability forecast with time as a SEP event fails to appear. We use the NOAA listing of major (≥10 pfu) SEP events from 1976 to 2014 to plot the delay times from X-ray peaks to SEP threshold onsets as a function of solar source longitude. An algorithm is derived to decrease the SEP event probabilities with time when no event is observed to reach the 10 pfu threshold. In addition, we use known SEP event size distributions to modify probability forecasts when SEP intensity increases occur below the 10 pfu event threshold. An algorithm to provide a dynamic SEP event forecast, Pd, for both situations of SEP intensities following a large flare is derived.
Conditional Independence in Applied Probability.
Pfeiffer, Paul E.
This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…
Stretching Probability Explorations with Geoboards
Wheeler, Ann; Champion, Joe
2016-01-01
Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Swedish earthquakes and acceleration probabilities
International Nuclear Information System (INIS)
Slunga, R.
1979-03-01
A method to assign probabilities to ground accelerations for Swedish sites is described. As hardly any nearfield instrumental data is available we are left with the problem of interpreting macroseismic data in terms of acceleration. By theoretical wave propagation computations the relation between seismic strength of the earthquake, focal depth, distance and ground accelerations are calculated. We found that most Swedish earthquake of the area, the 1904 earthquake 100 km south of Oslo, is an exception and probably had a focal depth exceeding 25 km. For the nuclear power plant sites an annual probability of 10 -5 has been proposed as interesting. This probability gives ground accelerations in the range 5-20 % for the sites. This acceleration is for a free bedrock site. For consistency all acceleration results in this study are given for bedrock sites. When applicating our model to the 1904 earthquake and assuming the focal zone to be in the lower crust we get the epicentral acceleration of this earthquake to be 5-15 % g. The results above are based on an analyses of macrosismic data as relevant instrumental data is lacking. However, the macroseismic acceleration model deduced in this study gives epicentral ground acceleration of small Swedish earthquakes in agreement with existent distant instrumental data. (author)
DECOFF Probabilities of Failed Operations
DEFF Research Database (Denmark)
Gintautas, Tomas
2015-01-01
A statistical procedure of estimation of Probabilities of Failed Operations is described and exemplified using ECMWF weather forecasts and SIMO output from Rotor Lift test case models. Also safety factor influence is investigated. DECOFF statistical method is benchmarked against standard Alpha-factor...
Probability and statistics: A reminder
International Nuclear Information System (INIS)
Clement, B.
2013-01-01
The main purpose of these lectures is to provide the reader with the tools needed to data analysis in the framework of physics experiments. Basic concepts are introduced together with examples of application in experimental physics. The lecture is divided into two parts: probability and statistics. It is build on the introduction from 'data analysis in experimental sciences' given in [1]. (authors)
Nash equilibrium with lower probabilities
DEFF Research Database (Denmark)
Groes, Ebbe; Jacobsen, Hans Jørgen; Sloth, Birgitte
1998-01-01
We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible...
On probability-possibility transformations
Klir, George J.; Parviz, Behzad
1992-01-01
Several probability-possibility transformations are compared in terms of the closeness of preserving second-order properties. The comparison is based on experimental results obtained by computer simulation. Two second-order properties are involved in this study: noninteraction of two distributions and projections of a joint distribution.
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.
Determination of bounds on failure probability in the presence of ...
Indian Academy of Sciences (India)
In particular, fuzzy set theory provides a more rational framework for ..... indicating that the random variations inT andO2 do not affect failure probability significantly. ... The upper-bound for PF shown in figure 6 can be used in decision-making.
Flipping Out: Calculating Probability with a Coin Game
Degner, Kate
2015-01-01
In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…
The probability that a pair of group elements is autoconjugate
Indian Academy of Sciences (India)
Let and ℎ be arbitrary elements of a given finite group . Then and ℎ are said to be autoconjugate if there exists some automorphism of such that ℎ = . In this article, we construct some sharp bounds for the probability that two random elements of are autoconjugate, denoted by P a ( G ) . It is also shown that P ...
Estimating the joint survival probabilities of married individuals
Sanders, Lisanne; Melenberg, Bertrand
We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squared
Two-slit experiment: quantum and classical probabilities
International Nuclear Information System (INIS)
Khrennikov, Andrei
2015-01-01
Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum–classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane). (paper)
Large deviations and idempotent probability
Puhalskii, Anatolii
2001-01-01
In the view of many probabilists, author Anatolii Puhalskii''s research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak convergence results.Large Deviations and Idempotent Probability expounds upon the recent methodology of building large deviation theory along the lines of weak convergence theory. The author develops an idempotent (or maxitive) probability theory, introduces idempotent analogues of martingales (maxingales), Wiener and Poisson processes, and Ito differential equations, and studies their properties. The large deviation principle for stochastic processes is formulated as a certain type of convergence of stochastic processes to idempotent processes. The author calls this large deviation convergence.The approach to establishing large deviation convergence uses novel com...
Probability biases as Bayesian inference
Directory of Open Access Journals (Sweden)
Andre; C. R. Martins
2006-11-01
Full Text Available In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions. %XX In that sense, it should be no surprise that humans reason with % probability as it has been observed.
Probability matching and strategy availability.
Koehler, Derek J; James, Greta
2010-09-01
Findings from two experiments indicate that probability matching in sequential choice arises from an asymmetry in strategy availability: The matching strategy comes readily to mind, whereas a superior alternative strategy, maximizing, does not. First, compared with the minority who spontaneously engage in maximizing, the majority of participants endorse maximizing as superior to matching in a direct comparison when both strategies are described. Second, when the maximizing strategy is brought to their attention, more participants subsequently engage in maximizing. Third, matchers are more likely than maximizers to base decisions in other tasks on their initial intuitions, suggesting that they are more inclined to use a choice strategy that comes to mind quickly. These results indicate that a substantial subset of probability matchers are victims of "underthinking" rather than "overthinking": They fail to engage in sufficient deliberation to generate a superior alternative to the matching strategy that comes so readily to mind.
Probability as a Physical Motive
Directory of Open Access Journals (Sweden)
Peter Martin
2007-04-01
Full Text Available Recent theoretical progress in nonequilibrium thermodynamics, linking thephysical principle of Maximum Entropy Production (Ã¢Â€ÂœMEPÃ¢Â€Â to the information-theoreticalÃ¢Â€ÂœMaxEntÃ¢Â€Â principle of scientific inference, together with conjectures from theoreticalphysics that there may be no fundamental causal laws but only probabilities for physicalprocesses, and from evolutionary theory that biological systems expand Ã¢Â€Âœthe adjacentpossibleÃ¢Â€Â as rapidly as possible, all lend credence to the proposition that probability shouldbe recognized as a fundamental physical motive. It is further proposed that spatial order andtemporal order are two aspects of the same thing, and that this is the essence of the secondlaw of thermodynamics.
Logic, Probability, and Human Reasoning
2015-01-01
accordingly suggest a way to integrate probability and deduction. The nature of deductive reasoning To be rational is to be able to make deductions...3–6] and they underlie mathematics, science, and tech- nology [7–10]. Plato claimed that emotions upset reason- ing. However, individuals in the grip...fundamental to human rationality . So, if counterexamples to its principal predictions occur, the theory will at least explain its own refutation
Probability Measures on Groups IX
1989-01-01
The latest in this series of Oberwolfach conferences focussed on the interplay between structural probability theory and various other areas of pure and applied mathematics such as Tauberian theory, infinite-dimensional rotation groups, central limit theorems, harmonizable processes, and spherical data. Thus it was attended by mathematicians whose research interests range from number theory to quantum physics in conjunction with structural properties of probabilistic phenomena. This volume contains 5 survey articles submitted on special invitation and 25 original research papers.
Probability matching and strategy availability
J. Koehler, Derek; Koehler, Derek J.; James, Greta
2010-01-01
Findings from two experiments indicate that probability matching in sequential choice arises from an asymmetry in strategy availability: The matching strategy comes readily to mind, whereas a superior alternative strategy, maximizing, does not. First, compared with the minority who spontaneously engage in maximizing, the majority of participants endorse maximizing as superior to matching in a direct comparison when both strategies are described. Second, when the maximizing strategy is brought...
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
Zero field reversal probability in thermally assisted magnetization reversal
Prasetya, E. B.; Utari; Purnama, B.
2017-11-01
This paper discussed about zero field reversal probability in thermally assisted magnetization reversal (TAMR). Appearance of reversal probability in zero field investigated through micromagnetic simulation by solving stochastic Landau-Lifshitz-Gibert (LLG). The perpendicularly anisotropy magnetic dot of 50×50×20 nm3 is considered as single cell magnetic storage of magnetic random acces memory (MRAM). Thermally assisted magnetization reversal was performed by cooling writing process from near/almost Curie point to room temperature on 20 times runs for different randomly magnetized state. The results show that the probability reversal under zero magnetic field decreased with the increase of the energy barrier. The zero-field probability switching of 55% attained for energy barrier of 60 k B T and the reversal probability become zero noted at energy barrier of 2348 k B T. The higest zero-field switching probability of 55% attained for energy barrier of 60 k B T which corespond to magnetif field of 150 Oe for switching.
Beskow, Laura M.; Lin, Li; Dombeck, Carrie B.; Gao, Emily; Weinfurt, Kevin P.
2017-01-01
Purpose: To determine the individual and combined effects of a simplified form and a review/retest intervention on biobanking consent comprehension. Methods: We conducted a national online survey in which participants were randomized within four educational strata to review a simplified or traditional consent form. Participants then completed a comprehension quiz; for each item answered incorrectly, they reviewed the corresponding consent form section and answered another quiz item on that topic. Results: Consistent with our first hypothesis, comprehension among those who received the simplified form was not inferior to that among those who received the traditional form. Contrary to expectations, receipt of the simplified form did not result in significantly better comprehension compared with the traditional form among those in the lowest educational group. The review/retest procedure significantly improved quiz scores in every combination of consent form and education level. Although improved, comprehension remained a challenge in the lowest-education group. Higher quiz scores were significantly associated with willingness to participate. Conclusion: Ensuring consent comprehension remains a challenge, but simplified forms have virtues independent of their impact on understanding. A review/retest intervention may have a significant effect, but assessing comprehension raises complex questions about setting thresholds for understanding and consequences of not meeting them. Genet Med advance online publication 13 October 2016 PMID:27735922
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.
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 for Weather and Climate
Smith, L. A.
2013-12-01
Over the last 60 years, the availability of large-scale electronic computers has stimulated rapid and significant advances both in meteorology and in our understanding of the Earth System as a whole. The speed of these advances was due, in large part, to the sudden ability to explore nonlinear systems of equations. The computer allows the meteorologist to carry a physical argument to its conclusion; the time scales of weather phenomena then allow the refinement of physical theory, numerical approximation or both in light of new observations. Prior to this extension, as Charney noted, the practicing meteorologist could ignore the results of theory with good conscience. Today, neither the practicing meteorologist nor the practicing climatologist can do so, but to what extent, and in what contexts, should they place the insights of theory above quantitative simulation? And in what circumstances can one confidently estimate the probability of events in the world from model-based simulations? Despite solid advances of theory and insight made possible by the computer, the fidelity of our models of climate differs in kind from the fidelity of models of weather. While all prediction is extrapolation in time, weather resembles interpolation in state space, while climate change is fundamentally an extrapolation. The trichotomy of simulation, observation and theory which has proven essential in meteorology will remain incomplete in climate science. Operationally, the roles of probability, indeed the kinds of probability one has access too, are different in operational weather forecasting and climate services. Significant barriers to forming probability forecasts (which can be used rationally as probabilities) are identified. Monte Carlo ensembles can explore sensitivity, diversity, and (sometimes) the likely impact of measurement uncertainty and structural model error. The aims of different ensemble strategies, and fundamental differences in ensemble design to support of
Energy Technology Data Exchange (ETDEWEB)
Lu, S; Streit, R D; Chou, C K
1980-01-01
This report summarizes work performed for the U.S. Nuclear Regulatory Commission (NRC) by the Load Combination Program at the Lawrence Livermore National Laboratory to establish a technical basis for the NRC to use in reassessing its requirement that earthquake and large loss-of-coolant accident (LOCA) loads be combined in the design of nuclear power plants. A systematic probabilistic approach is used to treat the random nature of earthquake and transient loading to estimate the probability of large LOCAs that are directly and indirectly induced by earthquakes. A large LOCA is defined in this report as a double-ended guillotine break of the primary reactor coolant loop piping (the hot leg, cold leg, and crossover) of a pressurized water reactor (PWR). Unit 1 of the Zion Nuclear Power Plant, a four-loop PWR-1, is used for this study. To estimate the probability of a large LOCA directly induced by earthquakes, only fatigue crack growth resulting from the combined effects of thermal, pressure, seismic, and other cyclic loads is considered. Fatigue crack growth is simulated with a deterministic fracture mechanics model that incorporates stochastic inputs of initial crack size distribution, material properties, stress histories, and leak detection probability. Results of the simulation indicate that the probability of a double-ended guillotine break, either with or without an earthquake, is very small (on the order of 10{sup -12}). The probability of a leak was found to be several orders of magnitude greater than that of a complete pipe rupture. A limited investigation involving engineering judgment of a double-ended guillotine break indirectly induced by an earthquake is also reported. (author)
International Nuclear Information System (INIS)
Lu, S.; Streit, R.D.; Chou, C.K.
1980-01-01
This report summarizes work performed for the U.S. Nuclear Regulatory Commission (NRC) by the Load Combination Program at the Lawrence Livermore National Laboratory to establish a technical basis for the NRC to use in reassessing its requirement that earthquake and large loss-of-coolant accident (LOCA) loads be combined in the design of nuclear power plants. A systematic probabilistic approach is used to treat the random nature of earthquake and transient loading to estimate the probability of large LOCAs that are directly and indirectly induced by earthquakes. A large LOCA is defined in this report as a double-ended guillotine break of the primary reactor coolant loop piping (the hot leg, cold leg, and crossover) of a pressurized water reactor (PWR). Unit 1 of the Zion Nuclear Power Plant, a four-loop PWR-1, is used for this study. To estimate the probability of a large LOCA directly induced by earthquakes, only fatigue crack growth resulting from the combined effects of thermal, pressure, seismic, and other cyclic loads is considered. Fatigue crack growth is simulated with a deterministic fracture mechanics model that incorporates stochastic inputs of initial crack size distribution, material properties, stress histories, and leak detection probability. Results of the simulation indicate that the probability of a double-ended guillotine break, either with or without an earthquake, is very small (on the order of 10 -12 ). The probability of a leak was found to be several orders of magnitude greater than that of a complete pipe rupture. A limited investigation involving engineering judgment of a double-ended guillotine break indirectly induced by an earthquake is also reported. (author)
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2012-01-01
This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and
Probability, statistics, and computational science.
Beerenwinkel, Niko; Siebourg, Juliane
2012-01-01
In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.
Sensitivity analysis using probability bounding
International Nuclear Information System (INIS)
Ferson, Scott; Troy Tucker, W.
2006-01-01
Probability bounds analysis (PBA) provides analysts a convenient means to characterize the neighborhood of possible results that would be obtained from plausible alternative inputs in probabilistic calculations. We show the relationship between PBA and the methods of interval analysis and probabilistic uncertainty analysis from which it is jointly derived, and indicate how the method can be used to assess the quality of probabilistic models such as those developed in Monte Carlo simulations for risk analyses. We also illustrate how a sensitivity analysis can be conducted within a PBA by pinching inputs to precise distributions or real values
International Nuclear Information System (INIS)
Tercariol, Cesar Augusto Sangaletti; Kiipper, Felipe de Moura; Martinez, Alexandre Souto
2007-01-01
Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability P (d,N) m,n that an arbitrary point is the mth nearest neighbour to its own nth nearest neighbour (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we propose a simpler derivation of Cox probabilities, where we stress the role played by the system dimensionality d. In the limit d → ∞, the distances between pair of points become independent (random link model) and closed analytical forms for the neighbourhood probabilities are obtained both for the thermodynamic limit and finite-size system. Breaking the distance symmetry constraint drives us to the random map model, for which the Cox probabilities are obtained for two cases: whether a point is its own nearest neighbour or not
Molchanov, Ilya
2017-01-01
This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integ...
Lectures on probability and statistics
International Nuclear Information System (INIS)
Yost, G.P.
1984-09-01
These notes are based on a set of statistics lectures delivered at Imperial College to the first-year postgraduate students in High Energy Physics. They are designed for the professional experimental scientist. We begin with the fundamentals of probability theory, in which one makes statements about the set of possible outcomes of an experiment, based upon a complete a priori understanding of the experiment. For example, in a roll of a set of (fair) dice, one understands a priori that any given side of each die is equally likely to turn up. From that, we can calculate the probability of any specified outcome. We finish with the inverse problem, statistics. Here, one begins with a set of actual data (e.g., the outcomes of a number of rolls of the dice), and attempts to make inferences about the state of nature which gave those data (e.g., the likelihood of seeing any given side of any given die turn up). This is a much more difficult problem, of course, and one's solutions often turn out to be unsatisfactory in one respect or another
Willekens, F.J.C.
2013-01-01
Throughout history, humans engaged in games in which randomness plays a role. In the 17th century, scientists started to approach chance scientifically and to develop a theory of probability. Courgeau describes how the relationship between probability theory and social sciences emerged and evolved
Generation of pseudo-random numbers
Howell, L. W.; Rheinfurth, M. H.
1982-01-01
Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.
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
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
Eliazar, Iddo; Klafter, Joseph
2010-01-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.
Digital dice computational solutions to practical probability problems
Nahin, Paul J
2013-01-01
Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the
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.
Focus in High School Mathematics: Statistics and Probability
National Council of Teachers of Mathematics, 2009
2009-01-01
Reasoning about and making sense of statistics and probability are essential to students' future success. This volume belongs to a series that supports National Council of Teachers of Mathematics' (NCTM's) "Focus in High School Mathematics: Reasoning and Sense Making" by providing additional guidance for making reasoning and sense making part of…
Investigation of Probability Distributions Using Dice Rolling Simulation
Lukac, Stanislav; Engel, Radovan
2010-01-01
Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…
Blocked Randomization with Randomly Selected Block Sizes
Directory of Open Access Journals (Sweden)
Jimmy Efird
2010-12-01
Full Text Available When planning a randomized clinical trial, careful consideration must be given to how participants are selected for various arms of a study. Selection and accidental bias may occur when participants are not assigned to study groups with equal probability. A simple random allocation scheme is a process by which each participant has equal likelihood of being assigned to treatment versus referent groups. However, by chance an unequal number of individuals may be assigned to each arm of the study and thus decrease the power to detect statistically significant differences between groups. Block randomization is a commonly used technique in clinical trial design to reduce bias and achieve balance in the allocation of participants to treatment arms, especially when the sample size is small. This method increases the probability that each arm will contain an equal number of individuals by sequencing participant assignments by block. Yet still, the allocation process may be predictable, for example, when the investigator is not blind and the block size is fixed. This paper provides an overview of blocked randomization and illustrates how to avoid selection bias by using random block sizes.
International Nuclear Information System (INIS)
Coveyou, R.R.
1974-01-01
The subject of random number generation is currently controversial. Differing opinions on this subject seem to stem from implicit or explicit differences in philosophy; in particular, from differing ideas concerning the role of probability in the real world of physical processes, electronic computers, and Monte Carlo calculations. An attempt is made here to reconcile these views. The role of stochastic ideas in mathematical models is discussed. In illustration of these ideas, a mathematical model of the use of random number generators in Monte Carlo calculations is constructed. This model is used to set up criteria for the comparison and evaluation of random number generators. (U.S.)
On randomly interrupted diffusion
International Nuclear Information System (INIS)
Luczka, J.
1993-01-01
Processes driven by randomly interrupted Gaussian white noise are considered. An evolution equation for single-event probability distributions in presented. Stationary states are considered as a solution of a second-order ordinary differential equation with two imposed conditions. A linear model is analyzed and its stationary distributions are explicitly given. (author). 10 refs
Hitting probabilities for nonlinear systems of stochastic waves
Dalang, Robert C
2015-01-01
The authors consider a d-dimensional random field u = \\{u(t,x)\\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \\in \\{1,2,3\\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \\beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \\mathbb{R}^d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap
K-forbidden transition probabilities
International Nuclear Information System (INIS)
Saitoh, T.R.; Sletten, G.; Bark, R.A.; Hagemann, G.B.; Herskind, B.; Saitoh-Hashimoto, N.; Tsukuba Univ., Ibaraki
2000-01-01
Reduced hindrance factors of K-forbidden transitions are compiled for nuclei with A∝180 where γ-vibrational states are observed. Correlations between these reduced hindrance factors and Coriolis forces, statistical level mixing and γ-softness have been studied. It is demonstrated that the K-forbidden transition probabilities are related to γ-softness. The decay of the high-K bandheads has been studied by means of the two-state mixing, which would be induced by the γ-softness, with the use of a number of K-forbidden transitions compiled in the present work, where high-K bandheads are depopulated by both E2 and ΔI=1 transitions. The validity of the two-state mixing scheme has been examined by using the proposed identity of the B(M1)/B(E2) ratios of transitions depopulating high-K bandheads and levels of low-K bands. A break down of the identity might indicate that other levels would mediate transitions between high- and low-K states. (orig.)
Direct probability mapping of contaminants
International Nuclear Information System (INIS)
Rautman, C.A.
1993-01-01
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. Geostatistical simulation provides powerful tools for investigating contaminant levels, and in particular, for identifying and using the spatial interrelationships among a set of isolated sample values. This additional information can be used to assess the likelihood of encountering contamination at unsampled locations and to evaluate the risk associated with decisions to remediate or not to remediate specific regions within a site. Past operation of the DOE Feed Materials Production Center has contaminated a site near Fernald, Ohio, with natural uranium. Soil geochemical data have been collected as part of the Uranium-in-Soils Integrated Demonstration Project. These data have been used to construct a number of stochastic images of potential contamination for parcels approximately the size of a selective remediation unit. Each such image 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. Evaluation of the geostatistical simulations can yield maps representing the expected magnitude of the contamination for various regions and other information that may be important in determining a suitable remediation process or in sizing equipment to accomplish the restoration
Psychophysics of the probability weighting function
Takahashi, Taiki
2011-03-01
A probability weighting function w(p) for an objective probability p in decision under risk plays a pivotal role in Kahneman-Tversky prospect theory. Although recent studies in econophysics and neuroeconomics widely utilized probability weighting functions, psychophysical foundations of the probability weighting functions have been unknown. Notably, a behavioral economist Prelec (1998) [4] axiomatically derived the probability weighting function w(p)=exp(-() (01e)=1e,w(1)=1), which has extensively been studied in behavioral neuroeconomics. The present study utilizes psychophysical theory to derive Prelec's probability weighting function from psychophysical laws of perceived waiting time in probabilistic choices. Also, the relations between the parameters in the probability weighting function and the probability discounting function in behavioral psychology are derived. Future directions in the application of the psychophysical theory of the probability weighting function in econophysics and neuroeconomics are discussed.
Aude, Y Wady; Agatston, Arthur S; Lopez-Jimenez, Francisco; Lieberman, Eric H; Marie Almon; Hansen, Melinda; Rojas, Gerardo; Lamas, Gervasio A; Hennekens, Charles H
2004-10-25
In the United States, obesity is a major clinical and public health problem causing diabetes, dyslipidemia, and hypertension, as well as increasing cardiovascular and total mortality. Dietary restrictions of calories and saturated fat are beneficial. However, it remains unclear whether replacement of saturated fat with carbohydrates (as in the US National Cholesterol Education Program [NCEP] diet) or protein and monounsaturated fat (as in our isocaloric modified low-carbohydrate [MLC] diet, which is lower in total carbohydrates but higher in protein, monounsaturated fat, and complex carbohydrates) is optimal. We randomized 60 participants (29 women and 31 men) to the NCEP or the MLC diet and evaluated them every 2 weeks for 12 weeks. They were aged 28 to 71 years (mean age, 44 years in the NCEP and 46 years in the MLC group). A total of 36% of participants from the NCEP group and 35% from the MLC group had a body mass index (calculated as weight in kilograms divided by the square of height in meters) greater than 27. The primary end point was weight loss, and secondary end points were blood lipid levels and waist-to-hip ratio. Weight loss was significantly greater in the MLC (13.6 lb) than in the NCEP group (7.5 lb), a difference of 6.1 lb (P = .02). There were no significant differences between the groups for total, low density, and high-density lipoprotein cholesterol, triglycerides, or the proportion of small, dense low-density lipoprotein particles. There were significantly favorable changes in all lipid levels within the MLC but not within the NCEP group. Waist-to-hip ratio was not significantly reduced between the groups (P = .27), but it significantly decreased within the MLC group (P = .009). Compared with the NCEP diet, the MLC diet, which is lower in total carbohydrates but higher in complex carbohydrates, protein, and monounsaturated fat, caused significantly greater weight loss over 12 weeks. There were no significant differences between the groups in
Christensen, John L; Miller, Lynn Carol; Appleby, Paul Robert; Corsbie-Massay, Charisse; Godoy, Carlos Gustavo; Marsella, Stacy C; Read, Stephen J
2013-11-13
Men who have sex with men (MSM) often face socially sanctioned disapproval of sexual deviance from the heterosexual "normal." Such sexual stigma can be internalized producing a painful affective state (i.e., shame). Although shame (e.g., addiction) can predict risk-taking (e.g., alcohol abuse), sexual shame's link to sexual risk-taking is unclear. Socially Optimized Learning in Virtual Environments (SOLVE) was designed to reduce MSM's sexual shame, but whether it does so, and if that reduction predicts HIV risk reduction, is unclear. To test if at baseline, MSM's reported past unprotected anal intercourse (UAI) is related to shame; MSM's exposure to SOLVE compared to a wait-list control (WLC) condition reduces MSM's shame; and shame-reduction mediates the link between WLC condition and UAI risk reduction. HIV-negative, self-identified African American, Latino or White MSM, aged 18-24 years, who had had UAI with a non-primary/casual partner in the past three months were recruited for a national online study. Eligible MSM were computer randomized to either WLC or a web-delivered SOLVE. Retained MSM completed baseline measures (e.g., UAI in the past three months; current level of shame) and, in the SOLVE group, viewed at least one level of the game. At the end of the first session, shame was measured again. MSM completed follow-up UAI measures three months later. All data from 921 retained MSM (WLC condition, 484; SOLVE condition, 437) were analyzed, with missing data multiply imputed. At baseline, MSM reporting more risky sexual behaviour reported more shame (r s=0.21; peffect was significant (point estimate -0.10, 95% bias-corrected CI [-0.01 to -0.23] such that participants in the SOLVE treatment condition reported greater reductions in shame, which in turn predicted reductions in risky sexual behaviour at follow-up. The direct effect, however, was not significant. SOLVE is the first intervention to: (1) significantly reduce shame for MSM; and (2) demonstrate that
XI Symposium on Probability and Stochastic Processes
Pardo, Juan; Rivero, Víctor; Bravo, Gerónimo
2015-01-01
This volume features lecture notes and a collection of contributed articles from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes. The book starts with notes from the mini-course given by Louigi Addario-Berry with an accessible description of some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. It includes a number of exercises and a section on unanswered questions. Further contributions provide the reader with a broad perspective on the state-of-the art of active areas of research. Contributions by: Louigi Addario-Berry Octavio Arizmendi Fabrice Baudoin Jochen Blath Loïc Chaumont J. Armando Domínguez-Molina Bjarki Eldon Shui Feng Tulio Gaxiola Adrián González Casanova Evgueni Gordienko Daniel...
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.
Random vibrations theory and practice
Wirsching, Paul H; Ortiz, Keith
1995-01-01
Random Vibrations: Theory and Practice covers the theory and analysis of mechanical and structural systems undergoing random oscillations due to any number of phenomena— from engine noise, turbulent flow, and acoustic noise to wind, ocean waves, earthquakes, and rough pavement. For systems operating in such environments, a random vibration analysis is essential to the safety and reliability of the system. By far the most comprehensive text available on random vibrations, Random Vibrations: Theory and Practice is designed for readers who are new to the subject as well as those who are familiar with the fundamentals and wish to study a particular topic or use the text as an authoritative reference. It is divided into three major sections: fundamental background, random vibration development and applications to design, and random signal analysis. Introductory chapters cover topics in probability, statistics, and random processes that prepare the reader for the development of the theory of random vibrations a...
Edgington, Eugene
2007-01-01
Statistical Tests That Do Not Require Random Sampling Randomization Tests Numerical Examples Randomization Tests and Nonrandom Samples The Prevalence of Nonrandom Samples in Experiments The Irrelevance of Random Samples for the Typical Experiment Generalizing from Nonrandom Samples Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References Randomized Experiments Unique Benefits of Experiments Experimentation without Mani
Fixation probability in a two-locus intersexual selection model.
Durand, Guillermo; Lessard, Sabin
2016-06-01
We study a two-locus model of intersexual selection in a finite haploid population reproducing according to a discrete-time Moran model with a trait locus expressed in males and a preference locus expressed in females. We show that the probability of ultimate fixation of a single mutant allele for a male ornament introduced at random at the trait locus given any initial frequency state at the preference locus is increased by weak intersexual selection and recombination, weak or strong. Moreover, this probability exceeds the initial frequency of the mutant allele even in the case of a costly male ornament if intersexual selection is not too weak. On the other hand, the probability of ultimate fixation of a single mutant allele for a female preference towards a male ornament introduced at random at the preference locus is increased by weak intersexual selection and weak recombination if the female preference is not costly, and is strong enough in the case of a costly male ornament. The analysis relies on an extension of the ancestral recombination-selection graph for samples of haplotypes to take into account events of intersexual selection, while the symbolic calculation of the fixation probabilities is made possible in a reasonable time by an optimizing algorithm. Copyright © 2016 Elsevier Inc. All rights reserved.
Data-driven probability concentration and sampling on manifold
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2016-09-15
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation method for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.
Foundations of the theory of probability
Kolmogorov, AN
2018-01-01
This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.
The Probability Distribution for a Biased Spinner
Foster, Colin
2012-01-01
This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)
Conditional Probability Modulates Visual Search Efficiency
Directory of Open Access Journals (Sweden)
Bryan eCort
2013-10-01
Full Text Available We investigated the effects of probability on visual search. Previous work has shown that people can utilize spatial and sequential probability information to improve target detection. We hypothesized that performance improvements from probability information would extend to the efficiency of visual search. Our task was a simple visual search in which the target was always present among a field of distractors, and could take one of two colors. The absolute probability of the target being either color was 0.5; however, the conditional probability – the likelihood of a particular color given a particular combination of two cues – varied from 0.1 to 0.9. We found that participants searched more efficiently for high conditional probability targets and less efficiently for low conditional probability targets, but only when they were explicitly informed of the probability relationship between cues and target color.
Analytic Neutrino Oscillation Probabilities in Matter: Revisited
Energy Technology Data Exchange (ETDEWEB)
Parke, Stephen J. [Fermilab; Denton, Peter B. [Copenhagen U.; Minakata, Hisakazu [Madrid, IFT
2018-01-02
We summarize our recent paper on neutrino oscillation probabilities in matter, explaining the importance, relevance and need for simple, highly accurate approximations to the neutrino oscillation probabilities in matter.
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Liu, W. F.
2013-01-01
Estimation of extreme response and failure probability of structures subjected to ultimate design loads is essential for structural design of wind turbines according to the new standard IEC61400-1. This task is focused on in the present paper in virtue of probability density evolution method (PDEM......), which underlies the schemes of random vibration analysis and structural reliability assessment. The short-term rare failure probability of 5-mega-watt wind turbines, for illustrative purposes, in case of given mean wind speeds and turbulence levels is investigated through the scheme of extreme value...... distribution instead of any other approximate schemes of fitted distribution currently used in statistical extrapolation techniques. Besides, the comparative studies against the classical fitted distributions and the standard Monte Carlo techniques are carried out. Numerical results indicate that PDEM exhibits...
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.
Void probability scaling in hadron nucleus interactions
International Nuclear Information System (INIS)
Ghosh, Dipak; Deb, Argha; Bhattacharyya, Swarnapratim; Ghosh, Jayita; Bandyopadhyay, Prabhat; Das, Rupa; Mukherjee, Sima
2002-01-01
Heygi while investigating with the rapidity gap probability (that measures the chance of finding no particle in the pseudo-rapidity interval Δη) found that a scaling behavior in the rapidity gap probability has a close correspondence with the scaling of a void probability in galaxy correlation study. The main aim in this paper is to study the scaling behavior of the rapidity gap probability
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.
Interpretation of the results of statistical measurements. [search for basic probability model
Olshevskiy, V. V.
1973-01-01
For random processes, the calculated probability characteristic, and the measured statistical estimate are used in a quality functional, which defines the difference between the two functions. Based on the assumption that the statistical measurement procedure is organized so that the parameters for a selected model are optimized, it is shown that the interpretation of experimental research is a search for a basic probability model.
Ruin probability with claims modeled by a stationary ergodic stable process
Mikosch, T.; Samorodnitsky, G.
2000-01-01
For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin
Probability Judgements in Multi-Stage Problems : Experimental Evidence of Systematic Biases
Gneezy, U.
1996-01-01
We report empirical evidence that in problems of random walk with positive drift, bounded rationality leads individuals to under-estimate the probability of success in the long run.In particular, individuals who were given the stage by stage probability distribution failed to aggregate this
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.
On the Determinants of the Conjunction Fallacy: Probability versus Inductive Confirmation
Tentori, Katya; Crupi, Vincenzo; Russo, Selena
2013-01-01
Major recent interpretations of the conjunction fallacy postulate that people assess the probability of a conjunction according to (non-normative) averaging rules as applied to the constituents' probabilities or represent the conjunction fallacy as an effect of random error in the judgment process. In the present contribution, we contrast such…
Pre-Service Teachers' Conceptions of Probability
Odafe, Victor U.
2011-01-01
Probability knowledge and skills are needed in science and in making daily decisions that are sometimes made under uncertain conditions. Hence, there is the need to ensure that the pre-service teachers of our children are well prepared to teach probability. Pre-service teachers' conceptions of probability are identified, and ways of helping them…
Using Playing Cards to Differentiate Probability Interpretations
López Puga, Jorge
2014-01-01
The aprioristic (classical, naïve and symmetric) and frequentist interpretations of probability are commonly known. Bayesian or subjective interpretation of probability is receiving increasing attention. This paper describes an activity to help students differentiate between the three types of probability interpretations.
134Cs emission probabilities determination by gamma spectrometry
de Almeida, M. C. M.; Poledna, R.; Delgado, J. U.; Silva, R. L.; Araujo, M. T. F.; da Silva, C. J.
2018-03-01
The National Laboratory for Ionizing Radiation Metrology (LNMRI/IRD/CNEN) of Rio de Janeiro performed primary and secondary standardization of different radionuclides reaching satisfactory uncertainties. A solution of 134Cs radionuclide was purchased from commercial supplier to emission probabilities determination of some of its energies. 134Cs is a beta gamma emitter with 754 days of half-life. This radionuclide is used as standard in environmental, water and food control. It is also important to germanium detector calibration. The gamma emission probabilities (Pγ) were determined mainly for some energies of the 134Cs by efficiency curve method and the Pγ absolute uncertainties obtained were below 1% (k=1).
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
Dependent Human Error Probability Assessment
International Nuclear Information System (INIS)
Simic, Z.; Mikulicic, V.; Vukovic, I.
2006-01-01
This paper presents an assessment of the dependence between dynamic operator actions modeled in a Nuclear Power Plant (NPP) PRA and estimate the associated impact on Core damage frequency (CDF). This assessment was done improve HEP dependencies implementation inside existing PRA. All of the dynamic operator actions modeled in the NPP PRA are included in this assessment. Determining the level of HEP dependence and the associated influence on CDF are the major steps of this assessment. A decision on how to apply the results, i.e., should permanent HEP model changes be made, is based on the resulting relative CDF increase. Some CDF increase was selected as a threshold based on the NPP base CDF value and acceptance guidelines from the Regulatory Guide 1.174. HEP dependence resulting in a CDF increase of > 5E-07 would be considered potential candidates for specific incorporation into the baseline model. The approach used to judge the level of dependence between operator actions is based on dependency level categories and conditional probabilities developed in the Handbook of Human Reliability Analysis with Emphasis on Nuclear Power Plant Applications NUREG/CR-1278. To simplify the process, NUREG/CR-1278 identifies five levels of dependence: ZD (zero dependence), LD (low dependence), MD (moderate dependence), HD (high dependence), and CD (complete dependence). NUREG/CR-1278 also identifies several qualitative factors that could be involved in determining the level of dependence. Based on the NUREG/CR-1278 information, Time, Function, and Spatial attributes were judged to be the most important considerations when determining the level of dependence between operator actions within an accident sequence. These attributes were used to develop qualitative criteria (rules) that were used to judge the level of dependence (CD, HD, MD, LD, ZD) between the operator actions. After the level of dependence between the various HEPs is judged, quantitative values associated with the
Probability sampling design in ethnobotanical surveys of medicinal plants
Directory of Open Access Journals (Sweden)
Mariano Martinez Espinosa
2012-07-01
Full Text Available Non-probability sampling design can be used in ethnobotanical surveys of medicinal plants. However, this method does not allow statistical inferences to be made from the data generated. The aim of this paper is to present a probability sampling design that is applicable in ethnobotanical studies of medicinal plants. The sampling design employed in the research titled "Ethnobotanical knowledge of medicinal plants used by traditional communities of Nossa Senhora Aparecida do Chumbo district (NSACD, Poconé, Mato Grosso, Brazil" was used as a case study. Probability sampling methods (simple random and stratified sampling were used in this study. In order to determine the sample size, the following data were considered: population size (N of 1179 families; confidence coefficient, 95%; sample error (d, 0.05; and a proportion (p, 0.5. The application of this sampling method resulted in a sample size (n of at least 290 families in the district. The present study concludes that probability sampling methods necessarily have to be employed in ethnobotanical studies of medicinal plants, particularly where statistical inferences have to be made using data obtained. This can be achieved by applying different existing probability sampling methods, or better still, a combination of such methods.
An Objective Theory of Probability (Routledge Revivals)
Gillies, Donald
2012-01-01
This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises' views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises' definition of probability in terms of limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axioma
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
Probability judgments under ambiguity and conflict.
Smithson, Michael
2015-01-01
Whether conflict and ambiguity are distinct kinds of uncertainty remains an open question, as does their joint impact on judgments of overall uncertainty. This paper reviews recent advances in our understanding of human judgment and decision making when both ambiguity and conflict are present, and presents two types of testable models of judgments under conflict and ambiguity. The first type concerns estimate-pooling to arrive at "best" probability estimates. The second type is models of subjective assessments of conflict and ambiguity. These models are developed for dealing with both described and experienced information. A framework for testing these models in the described-information setting is presented, including a reanalysis of a multi-nation data-set to test best-estimate models, and a study of participants' assessments of conflict, ambiguity, and overall uncertainty reported by Smithson (2013). A framework for research in the experienced-information setting is then developed, that differs substantially from extant paradigms in the literature. This framework yields new models of "best" estimates and perceived conflict. The paper concludes with specific suggestions for future research on judgment and decision making under conflict and ambiguity.
Component fragility data base for reliability and probability studies
International Nuclear Information System (INIS)
Bandyopadhyay, K.; Hofmayer, C.; Kassier, M.; Pepper, S.
1989-01-01
Safety-related equipment in a nuclear plant plays a vital role in its proper operation and control, and failure of such equipment due to an earthquake may pose a risk to the safe operation of the plant. Therefore, in order to assess the overall reliability of a plant, the reliability of performance of the equipment should be studied first. The success of a reliability or a probability study depends to a great extent on the data base. To meet this demand, Brookhaven National Laboratory (BNL) has formed a test data base relating the seismic capacity of equipment specimens to the earthquake levels. Subsequently, the test data have been analyzed for use in reliability and probability studies. This paper describes the data base and discusses the analysis methods. The final results that can be directly used in plant reliability and probability studies are also presented in this paper
Loadman, William; Sprague, Kim; Hamilton, Jennifer; Coffey, Deb; Faddis, Bonnie
2010-01-01
In 2005, the U.S. Department of Education awarded eight Striving Readers grants to projects around the country. The goal of Striving Readers is to improve literacy skills and achievement for struggling readers in middle and high school and to increase the research base using randomized clinical research to address improvement in adolescent…
Directory of Open Access Journals (Sweden)
Romain Guignard
Full Text Available OBJECTIVES: It is crucial for policy makers to monitor the evolution of tobacco smoking prevalence. In France, this monitoring is based on a series of cross-sectional general population surveys, the Health Barometers, conducted every five years and based on random samples. A methodological study has been carried out to assess the reliability of a monitoring system based on regular quota sampling surveys for smoking prevalence. DESIGN / OUTCOME MEASURES: In 2010, current and daily tobacco smoking prevalences obtained in a quota survey on 8,018 people were compared with those of the 2010 Health Barometer carried out on 27,653 people. Prevalences were assessed separately according to the telephone equipment of the interviewee (landline phone owner vs "mobile-only", and logistic regressions were conducted in the pooled database to assess the impact of the telephone equipment and of the survey mode on the prevalences found. Finally, logistic regressions adjusted for sociodemographic characteristics were conducted in the random sample in order to determine the impact of the needed number of calls to interwiew "hard-to-reach" people on the prevalence found. RESULTS: Current and daily prevalences were higher in the random sample (respectively 33.9% and 27.5% in 15-75 years-old than in the quota sample (respectively 30.2% and 25.3%. In both surveys, current and daily prevalences were lower among landline phone owners (respectively 31.8% and 25.5% in the random sample and 28.9% and 24.0% in the quota survey. The required number of calls was slightly related to the smoking status after adjustment for sociodemographic characteristics. CONCLUSION: Random sampling appears to be more effective than quota sampling, mainly by making it possible to interview hard-to-reach populations.
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic coral demographic surveys for two life stages (juveniles, adults) across the Hawaiian archipelago since 2013. Juvenile...
National Oceanic and Atmospheric Administration, Department of Commerce — Data provided in this data set were collected as part of the NOAA Pacific Islands Fisheries Science Center (PIFSC), Coral Reef Ecosystem Program (CREP) led NCRMP...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic coral demographic surveys for two life stages (juveniles, adults) across American Samoa in 2015. Juvenile colony surveys...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic coral demographic surveys for two life stages (juveniles, adults) across the Pacific Remote Island Areas since 2014....
National Oceanic and Atmospheric Administration, Department of Commerce — The stationary point count (SPC) method is used to conduct reef fish surveys in the Hawaiian and Mariana Archipelagos, American Samoa, and the Pacific Remote Island...
National Oceanic and Atmospheric Administration, Department of Commerce — The data described here result from benthic coral demographic surveys for two life stages (juveniles, adults) across the Mariana archipelago since 2014. Juvenile...
National Oceanic and Atmospheric Administration, Department of Commerce — The stationary point count (SPC) method is used to conduct reef fish surveys in the Hawaiian and Mariana Archipelagos, American Samoa, and the Pacific Remote Island...
National Oceanic and Atmospheric Administration, Department of Commerce — The stationary point count (SPC) method is used to conduct reef fish surveys in the Hawaiian and Mariana Archipelagos, American Samoa, and the Pacific Remote Island...
Inoue, N.
2017-12-01
The conditional probability of surface ruptures is affected by various factors, such as shallow material properties, process of earthquakes, ground motions and so on. Toda (2013) pointed out difference of the conditional probability of strike and reverse fault by considering the fault dip and width of seismogenic layer. This study evaluated conditional probability of surface rupture based on following procedures. Fault geometry was determined from the randomly generated magnitude based on The Headquarters for Earthquake Research Promotion (2017) method. If the defined fault plane was not saturated in the assumed width of the seismogenic layer, the fault plane depth was randomly provided within the seismogenic layer. The logistic analysis was performed to two data sets: surface displacement calculated by dislocation methods (Wang et al., 2003) from the defined source fault, the depth of top of the defined source fault. The estimated conditional probability from surface displacement indicated higher probability of reverse faults than that of strike faults, and this result coincides to previous similar studies (i.e. Kagawa et al., 2004; Kataoka and Kusakabe, 2005). On the contrary, the probability estimated from the depth of the source fault indicated higher probability of thrust faults than that of strike and reverse faults, and this trend is similar to the conditional probability of PFDHA results (Youngs et al., 2003; Moss and Ross, 2011). The probability of combined simulated results of thrust and reverse also shows low probability. The worldwide compiled reverse fault data include low fault dip angle earthquake. On the other hand, in the case of Japanese reverse fault, there is possibility that the conditional probability of reverse faults with less low dip angle earthquake shows low probability and indicates similar probability of strike fault (i.e. Takao et al., 2013). In the future, numerical simulation by considering failure condition of surface by the source
Probability concepts in quality risk management.
Claycamp, H Gregg
2012-01-01
Essentially any concept of risk is built on fundamental concepts of chance, likelihood, or probability. Although risk is generally a probability of loss of something of value, given that a risk-generating event will occur or has occurred, it is ironic that the quality risk management literature and guidelines on quality risk management tools are relatively silent on the meaning and uses of "probability." The probability concept is typically applied by risk managers as a combination of frequency-based calculation and a "degree of belief" meaning of probability. Probability as a concept that is crucial for understanding and managing risk is discussed through examples from the most general, scenario-defining and ranking tools that use probability implicitly to more specific probabilistic tools in risk management. A rich history of probability in risk management applied to other fields suggests that high-quality risk management decisions benefit from the implementation of more thoughtful probability concepts in both risk modeling and risk management. Essentially any concept of risk is built on fundamental concepts of chance, likelihood, or probability. Although "risk" generally describes a probability of loss of something of value, given that a risk-generating event will occur or has occurred, it is ironic that the quality risk management literature and guidelines on quality risk management methodologies and respective tools focus on managing severity but are relatively silent on the in-depth meaning and uses of "probability." Pharmaceutical manufacturers are expanding their use of quality risk management to identify and manage risks to the patient that might occur in phases of the pharmaceutical life cycle from drug development to manufacture, marketing to product discontinuation. A probability concept is typically applied by risk managers as a combination of data-based measures of probability and a subjective "degree of belief" meaning of probability. Probability as
Probability problems in seismic risk analysis and load combinations for nuclear power plants
International Nuclear Information System (INIS)
George, L.L.
1983-01-01
This workshop describes some probability problems in power plant reliability and maintenance analysis. The problems are seismic risk analysis, loss of load probability, load combinations, and load sharing. The seismic risk problem is to compute power plant reliability given an earthquake and the resulting risk. Component survival occurs if its peak random response to the earthquake does not exceed its strength. Power plant survival is a complicated Boolean function of component failures and survivals. The responses and strengths of components are dependent random processes, and the peak responses are maxima of random processes. The resulting risk is the expected cost of power plant failure
Recursive recovery of Markov transition probabilities from boundary value data
Energy Technology Data Exchange (ETDEWEB)
Patch, Sarah Kathyrn [Univ. of California, Berkeley, CA (United States)
1994-04-01
In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requires finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.
Probability of inadvertent operation of electrical components in harsh environments
International Nuclear Information System (INIS)
Knoll, A.
1989-01-01
Harsh environment, which means humidity and high temperature, may and will affect unsealed electrical components by causing leakage ground currents in ungrounded direct current systems. The concern in a nuclear power plant is that such harsh environment conditions could cause inadvertent operation of normally deenergized components, which may have a safety-related isolation function. Harsh environment is a common cause failure, and one way to approach the problem is to assume that all the unsealed electrical components will simultaneously and inadvertently energize as a result of the environmental common cause failure. This assumption is unrealistically conservative. Test results indicated that insulating resistences of any terminal block in harsh environments have a random distribution in the range of 1 to 270 kΩ, with a mean value ∼59 kΩ. The objective of this paper is to evaluate a realistic conditional failure probability for inadvertent operation of electrical components in harsh environments. This value will be used thereafter in probabilistic safety evaluations of harsh environment events and will replace both the overconservative common cause probability of 1 and the random failure probability used for mild environments
Transition probability spaces in loop quantum gravity
Guo, Xiao-Kan
2018-03-01
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.
Towards a Categorical Account of Conditional Probability
Directory of Open Access Journals (Sweden)
Robert Furber
2015-11-01
Full Text Available This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condition. The latter is a predicate in the logic of effect modules on this Kleisli category. This same approach can be transferred to the category of C*-algebras (with positive unital maps, whose predicate logic is also expressed in terms of effect modules. Conditional probabilities can again be expressed via a triangle-fill-in property. In the literature, there are several proposals for what quantum conditional probability should be, and also there are extra difficulties not present in the classical case. At this stage, we only describe quantum systems with classical parametrization.
UT Biomedical Informatics Lab (BMIL) probability wheel
Huang, Sheng-Cheng; Lee, Sara; Wang, Allen; Cantor, Scott B.; Sun, Clement; Fan, Kaili; Reece, Gregory P.; Kim, Min Soon; Markey, Mia K.
A probability wheel app is intended to facilitate communication between two people, an "investigator" and a "participant", about uncertainties inherent in decision-making. Traditionally, a probability wheel is a mechanical prop with two colored slices. A user adjusts the sizes of the slices to indicate the relative value of the probabilities assigned to them. A probability wheel can improve the adjustment process and attenuate the effect of anchoring bias when it is used to estimate or communicate probabilities of outcomes. The goal of this work was to develop a mobile application of the probability wheel that is portable, easily available, and more versatile. We provide a motivating example from medical decision-making, but the tool is widely applicable for researchers in the decision sciences.
A probability space for quantum models
Lemmens, L. F.
2017-06-01
A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.
Striatal activity is modulated by target probability.
Hon, Nicholas
2017-06-14
Target probability has well-known neural effects. In the brain, target probability is known to affect frontal activity, with lower probability targets producing more prefrontal activation than those that occur with higher probability. Although the effect of target probability on cortical activity is well specified, its effect on subcortical structures such as the striatum is less well understood. Here, I examined this issue and found that the striatum was highly responsive to target probability. This is consistent with its hypothesized role in the gating of salient information into higher-order task representations. The current data are interpreted in light of that fact that different components of the striatum are sensitive to different types of task-relevant information.
Defining Probability in Sex Offender Risk Assessment.
Elwood, Richard W
2016-12-01
There is ongoing debate and confusion over using actuarial scales to predict individuals' risk of sexual recidivism. Much of the debate comes from not distinguishing Frequentist from Bayesian definitions of probability. Much of the confusion comes from applying Frequentist probability to individuals' risk. By definition, only Bayesian probability can be applied to the single case. The Bayesian concept of probability resolves most of the confusion and much of the debate in sex offender risk assessment. Although Bayesian probability is well accepted in risk assessment generally, it has not been widely used to assess the risk of sex offenders. I review the two concepts of probability and show how the Bayesian view alone provides a coherent scheme to conceptualize individuals' risk of sexual recidivism.
Spatial probability aids visual stimulus discrimination
Directory of Open Access Journals (Sweden)
Michael Druker
2010-08-01
Full Text Available We investigated whether the statistical predictability of a target's location would influence how quickly and accurately it was classified. Recent results have suggested that spatial probability can be a cue for the allocation of attention in visual search. One explanation for probability cuing is spatial repetition priming. In our two experiments we used probability distributions that were continuous across the display rather than relying on a few arbitrary screen locations. This produced fewer spatial repeats and allowed us to dissociate the effect of a high probability location from that of short-term spatial repetition. The task required participants to quickly judge the color of a single dot presented on a computer screen. In Experiment 1, targets were more probable in an off-center hotspot of high probability that gradually declined to a background rate. Targets garnered faster responses if they were near earlier target locations (priming and if they were near the high probability hotspot (probability cuing. In Experiment 2, target locations were chosen on three concentric circles around fixation. One circle contained 80% of targets. The value of this ring distribution is that it allowed for a spatially restricted high probability zone in which sequentially repeated trials were not likely to be physically close. Participant performance was sensitive to the high-probability circle in addition to the expected effects of eccentricity and the distance to recent targets. These two experiments suggest that inhomogeneities in spatial probability can be learned and used by participants on-line and without prompting as an aid for visual stimulus discrimination and that spatial repetition priming is not a sufficient explanation for this effect. Future models of attention should consider explicitly incorporating the probabilities of targets locations and features.
Is probability of frequency too narrow?
International Nuclear Information System (INIS)
Martz, H.F.
1993-01-01
Modern methods of statistical data analysis, such as empirical and hierarchical Bayesian methods, should find increasing use in future Probabilistic Risk Assessment (PRA) applications. In addition, there will be a more formalized use of expert judgment in future PRAs. These methods require an extension of the probabilistic framework of PRA, in particular, the popular notion of probability of frequency, to consideration of frequency of frequency, frequency of probability, and probability of probability. The genesis, interpretation, and examples of these three extended notions are discussed
Internal Medicine residents use heuristics to estimate disease probability.
Phang, Sen Han; Ravani, Pietro; Schaefer, Jeffrey; Wright, Bruce; McLaughlin, Kevin
2015-01-01
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. We randomized 55 Internal Medicine residents to different versions of four clinical vignettes and asked them to estimate probabilities of target conditions. We manipulated the clinical data for each vignette to be consistent with either 1) using a representative heuristic, by adding non-discriminating prototypical clinical features of the target condition, or 2) using anchoring with adjustment heuristic, by providing a high or low anchor for the target condition. When presented with additional non-discriminating data the odds of diagnosing the target condition were increased (odds ratio (OR) 2.83, 95% confidence interval [1.30, 6.15], p = 0.009). Similarly, the odds of diagnosing the target condition were increased when a high anchor preceded the vignette (OR 2.04, [1.09, 3.81], p = 0.025). Our findings suggest that despite previous exposure to the use of Bayesian reasoning, residents use heuristics, such as the representative heuristic and anchoring with adjustment, to estimate probabilities. Potential reasons for attribute substitution include the relative cognitive ease of heuristics vs. Bayesian reasoning or perhaps residents in their clinical practice use gist traces rather than precise probability estimates when diagnosing.
[Inverse probability weighting (IPW) for evaluating and "correcting" selection bias].
Narduzzi, Silvia; Golini, Martina Nicole; Porta, Daniela; Stafoggia, Massimo; Forastiere, Francesco
2014-01-01
the Inverse probability weighting (IPW) is a methodology developed to account for missingness and selection bias caused by non-randomselection of observations, or non-random lack of some information in a subgroup of the population. to provide an overview of IPW methodology and an application in a cohort study of the association between exposure to traffic air pollution (nitrogen dioxide, NO₂) and 7-year children IQ. this methodology allows to correct the analysis by weighting the observations with the probability of being selected. The IPW is based on the assumption that individual information that can predict the probability of inclusion (non-missingness) are available for the entire study population, so that, after taking account of them, we can make inferences about the entire target population starting from the nonmissing observations alone.The procedure for the calculation is the following: firstly, we consider the entire population at study and calculate the probability of non-missing information using a logistic regression model, where the response is the nonmissingness and the covariates are its possible predictors.The weight of each subject is given by the inverse of the predicted probability. Then the analysis is performed only on the non-missing observations using a weighted model. IPW is a technique that allows to embed the selection process in the analysis of the estimates, but its effectiveness in "correcting" the selection bias depends on the availability of enough information, for the entire population, to predict the non-missingness probability. In the example proposed, the IPW application showed that the effect of exposure to NO2 on the area of verbal intelligence quotient of children is stronger than the effect showed from the analysis performed without regard to the selection processes.
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.
Independent random sampling methods
Martino, Luca; Míguez, Joaquín
2018-01-01
This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general-purpose approaches, which can be used to generate samples from arbitrary probability distributions, and tailored techniques, designed to efficiently address common real-world practical problems, are introduced and discussed in detail. In turn, the monograph presents fundamental results and methodologies in the field, elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples, which are discussed in detail in the text and supplemented with ready-to-run computer code. The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field, address the latest methods, and emphasize the li...
International Nuclear Information System (INIS)
Simonen, F.A.; Garnich, M.R.; Simonen, E.P.; Bian, S.H.; Nomura, K.K.; Anderson, W.E.; Pedersen, L.T.
1986-04-01
A fracture mechanics model was developed at the Pacific Northwest Laboratory (PNL) to predict the behavior of a reactor pressure vessel following a through-wall crack that occurs during a pressurized thermal shock (PTS) event. This study, which contributed to a US Nuclear Regulatory Commission (NRC) program to study PTS risk, was coordinated with the Integrated Pressurized Thermal Shock (IPTS) Program at Oak Ridge National Laboratory (ORNL). The PNL fracture mechanics model uses the critical transients and probabilities of through-wall cracks from the IPTS Program. The PNL model predicts the arrest, reinitiation, and direction of crack growth for a postulated through-wall crack and thereby predicts the mode of vessel failure. A Monte-Carlo type of computer code was written to predict the probabilities of the alternative failure modes. This code treats the fracture mechanics properties of the various welds and plates of a vessel as random variables. Plant-specific calculations were performed for the Oconee-1, Calvert Cliffs-1, and H.B. Robinson-2 reactor pressure vessels for the conditions of postulated transients. The model predicted that 50% or more of the through-wall axial cracks will turn to follow a circumferential weld. The predicted failure mode is a complete circumferential fracture of the vessel, which results in a potential vertically directed missile consisting of the upper head assembly. Missile arrest calculations for the three nuclear plants predict that such vertical missiles, as well as all potential horizontally directed fragmentation type missiles, will be confined to the vessel enclosre cavity. The PNL failure mode model is recommended for use in future evaluations of other plants, to determine the failure modes that are most probable for postulated PTS events
Hilário, M.; Hollander, den W.Th.F.; Sidoravicius, V.; Soares dos Santos, R.; Teixeira, A.
2014-01-01
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density ¿¿(0,8). At each step the random walk performs a nearest-neighbour jump, moving to
Predicting non-square 2D dice probabilities
Pender, G. A. T.; Uhrin, M.
2014-07-01
The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability. Indeed, it was considered by Newton in 1664 (Newton 1967 The Mathematical Papers of Issac Newton vol I (Cambridge: Cambridge University Press) pp 60-1). In this paper we make progress on the 2D problem (which can be realized in 3D by considering a long cuboid, or alternatively a rectangular cross-sectioned dreidel). For the two-dimensional case we suggest that the ratio of the probabilities of landing on each of the two sides is given by \\frac{\\sqrt{{{k}^{2}}+{{l}^{2}}}-k}{\\sqrt{{{k}^{2}}+{{l}^{2}}}-l}\\frac{arctan \\frac{l}{k}}{arctan \\frac{k}{l}} where k and l are the lengths of the two sides. We test this theory both experimentally and computationally, and find good agreement between our theory, experimental and computational results. Our theory is known, from its derivation, to be an approximation for particularly bouncy or ‘grippy’ surfaces where the die rolls through many revolutions before settling. On real surfaces we would expect (and we observe) that the true probability ratio for a 2D die is a somewhat closer to unity than predicted by our theory. This problem may also have wider relevance in the testing of physics engines.
Scale-invariant transition probabilities in free word association trajectories
Directory of Open Access Journals (Sweden)
Martin Elias Costa
2009-09-01
Full Text Available Free-word association has been used as a vehicle to understand the organization of human thoughts. The original studies relied mainly on qualitative assertions, yielding the widely intuitive notion that trajectories of word associations are structured, yet considerably more random than organized linguistic text. Here we set to determine a precise characterization of this space, generating a large number of word association trajectories in a web implemented game. We embedded the trajectories in the graph of word co-occurrences from a linguistic corpus. To constrain possible transport models we measured the memory loss and the cycling probability. These two measures could not be reconciled by a bounded diffusive model since the cycling probability was very high (16 % of order-2 cycles implying a majority of short-range associations whereas the memory loss was very rapid (converging to the asymptotic value in ∼ 7 steps which, in turn, forced a high fraction of long-range associations. We show that memory loss and cycling probabilities of free word association trajectories can be simultaneously accounted by a model in which transitions are determined by a scale invariant probability distribution.
International Nuclear Information System (INIS)
Reuss, J.D.; Misguich, J.H.
1993-02-01
The Campbell process is a stationary random process which can have various correlation functions, according to the choice of an elementary response function. The statistical properties of this process are presented. A numerical algorithm and a subroutine for generating such a process is built up and tested, for the physically interesting case of a Campbell process with Gaussian correlations. The (non-Gaussian) probability distribution appears to be similar to the Gamma distribution
Malarz, K.; Szvetelszky, Z.; Szekf, B.; Kulakowski, K.
2006-11-01
We consider the average probability X of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erd{õ}s and Rényi. In this theory, a network is characterized by two parameters: the size N and the link probability p. Our experimental data suggest three levels of social inclusion of friendship. The critical value pc, for which half of agents are informed, scales with the system size as N-gamma with gamma approx 0.68. Computer simulations show that the probability X varies with p as a sigmoidal curve. Influence of the correlations between neighbors is also evaluated: with increasing clustering coefficient C, X decreases.
Human Inferences about Sequences: A Minimal Transition Probability Model.
Directory of Open Access Journals (Sweden)
Florent Meyniel
2016-12-01
Full Text Available The brain constantly infers the causes of the inputs it receives and uses these inferences to generate statistical expectations about future observations. Experimental evidence for these expectations and their violations include explicit reports, sequential effects on reaction times, and mismatch or surprise signals recorded in electrophysiology and functional MRI. Here, we explore the hypothesis that the brain acts as a near-optimal inference device that constantly attempts to infer the time-varying matrix of transition probabilities between the stimuli it receives, even when those stimuli are in fact fully unpredictable. This parsimonious Bayesian model, with a single free parameter, accounts for a broad range of findings on surprise signals, sequential effects and the perception of randomness. Notably, it explains the pervasive asymmetry between repetitions and alternations encountered in those studies. Our analysis suggests that a neural machinery for inferring transition probabilities lies at the core of human sequence knowledge.
STADIC: a computer code for combining probability distributions
International Nuclear Information System (INIS)
Cairns, J.J.; Fleming, K.N.
1977-03-01
The STADIC computer code uses a Monte Carlo simulation technique for combining probability distributions. The specific function for combination of the input distribution is defined by the user by introducing the appropriate FORTRAN statements to the appropriate subroutine. The code generates a Monte Carlo sampling from each of the input distributions and combines these according to the user-supplied function to provide, in essence, a random sampling of the combined distribution. When the desired number of samples is obtained, the output routine calculates the mean, standard deviation, and confidence limits for the resultant distribution. This method of combining probability distributions is particularly useful in cases where analytical approaches are either too difficult or undefined
Probability of Grounding and Collision Events
DEFF Research Database (Denmark)
Pedersen, Preben Terndrup
1996-01-01
To quantify the risks involved in ship traffic, rational criteria for collision and grounding accidents are developed. This implies that probabilities as well as inherent consequences can be analysed and assessed. The presnt paper outlines a method for evaluation of the probability of ship...
Probability of Grounding and Collision Events
DEFF Research Database (Denmark)
Pedersen, Preben Terndrup
1996-01-01
To quantify the risks involved in ship traffic, rational criteria for collision and grounding accidents have to be developed. This implies that probabilities as well as inherent consequences have to be analyzed and assessed.The present notes outline a method for evaluation of the probability...
Introducing Disjoint and Independent Events in Probability.
Kelly, I. W.; Zwiers, F. W.
Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…
Selected papers on probability and statistics
2009-01-01
This volume contains translations of papers that originally appeared in the Japanese journal Sūgaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.
Collective probabilities algorithm for surface hopping calculations
International Nuclear Information System (INIS)
Bastida, Adolfo; Cruz, Carlos; Zuniga, Jose; Requena, Alberto
2003-01-01
General equations that transition probabilities of the hopping algorithms in surface hopping calculations must obey to assure the equality between the average quantum and classical populations are derived. These equations are solved for two particular cases. In the first it is assumed that probabilities are the same for all trajectories and that the number of hops is kept to a minimum. These assumptions specify the collective probabilities (CP) algorithm, for which the transition probabilities depend on the average populations for all trajectories. In the second case, the probabilities for each trajectory are supposed to be completely independent of the results from the other trajectories. There is, then, a unique solution of the general equations assuring that the transition probabilities are equal to the quantum population of the target state, which is referred to as the independent probabilities (IP) algorithm. The fewest switches (FS) algorithm developed by Tully is accordingly understood as an approximate hopping algorithm which takes elements from the accurate CP and IP solutions. A numerical test of all these hopping algorithms is carried out for a one-dimensional two-state problem with two avoiding crossings which shows the accuracy and computational efficiency of the collective probabilities algorithm proposed, the limitations of the FS algorithm and the similarity between the results offered by the IP algorithm and those obtained with the Ehrenfest method
Examples of Neutrosophic Probability in Physics
Directory of Open Access Journals (Sweden)
Fu Yuhua
2015-01-01
Full Text Available This paper re-discusses the problems of the so-called “law of nonconservation of parity” and “accelerating expansion of the universe”, and presents the examples of determining Neutrosophic Probability of the experiment of Chien-Shiung Wu et al in 1957, and determining Neutrosophic Probability of accelerating expansion of the partial universe.
Eliciting Subjective Probabilities with Binary Lotteries
DEFF Research Database (Denmark)
Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd
objective probabilities. Drawing a sample from the same subject population, we find evidence that the binary lottery procedure induces linear utility in a subjective probability elicitation task using the Quadratic Scoring Rule. We also show that the binary lottery procedure can induce direct revelation...
Probability Issues in without Replacement Sampling
Joarder, A. H.; Al-Sabah, W. S.
2007-01-01
Sampling without replacement is an important aspect in teaching conditional probabilities in elementary statistics courses. Different methods proposed in different texts for calculating probabilities of events in this context are reviewed and their relative merits and limitations in applications are pinpointed. An alternative representation of…
Some open problems in noncommutative probability
International Nuclear Information System (INIS)
Kruszynski, P.
1981-01-01
A generalization of probability measures to non-Boolean structures is discussed. The starting point of the theory is the Gleason theorem about the form of measures on closed subspaces of a Hilbert space. The problems are formulated in terms of probability on lattices of projections in arbitrary von Neumann algebras. (Auth.)
Probability: A Matter of Life and Death
Hassani, Mehdi; Kippen, Rebecca; Mills, Terence
2016-01-01
Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…
Teaching Probability: A Socio-Constructivist Perspective
Sharma, Sashi
2015-01-01
There is a considerable and rich literature on students' misconceptions in probability. However, less attention has been paid to the development of students' probabilistic thinking in the classroom. This paper offers a sequence, grounded in socio-constructivist perspective for teaching probability.
Stimulus Probability Effects in Absolute Identification
Kent, Christopher; Lamberts, Koen
2016-01-01
This study investigated the effect of stimulus presentation probability on accuracy and response times in an absolute identification task. Three schedules of presentation were used to investigate the interaction between presentation probability and stimulus position within the set. Data from individual participants indicated strong effects of…
Against All Odds: When Logic Meets Probability
van Benthem, J.; Katoen, J.-P.; Langerak, R.; Rensink, A.
2017-01-01
This paper is a light walk along interfaces between logic and probability, triggered by a chance encounter with Ed Brinksma. It is not a research paper, or a literature survey, but a pointer to issues. I discuss both direct combinations of logic and probability and structured ways in which logic can
The probability of the false vacuum decay
International Nuclear Information System (INIS)
Kiselev, V.; Selivanov, K.
1983-01-01
The closed expession for the probability of the false vacuum decay in (1+1) dimensions is given. The probability of false vacuum decay is expessed as the product of exponential quasiclassical factor and a functional determinant of the given form. The method for calcutation of this determinant is developed and a complete answer for (1+1) dimensions is given
The transition probabilities of the reciprocity model
Snijders, T.A.B.
1999-01-01
The reciprocity model is a continuous-time Markov chain model used for modeling longitudinal network data. A new explicit expression is derived for its transition probability matrix. This expression can be checked relatively easily. Some properties of the transition probabilities are given, as well
Probability numeracy and health insurance purchase
Dillingh, Rik; Kooreman, Peter; Potters, Jan
2016-01-01
This paper provides new field evidence on the role of probability numeracy in health insurance purchase. Our regression results, based on rich survey panel data, indicate that the expenditure on two out of three measures of health insurance first rises with probability numeracy and then falls again.
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.
The enigma of probability and physics
International Nuclear Information System (INIS)
Mayants, L.
1984-01-01
This volume contains a coherent exposition of the elements of two unique sciences: probabilistics (science of probability) and probabilistic physics (application of probabilistics to physics). Proceeding from a key methodological principle, it starts with the disclosure of the true content of probability and the interrelation between probability theory and experimental statistics. This makes is possible to introduce a proper order in all the sciences dealing with probability and, by conceiving the real content of statistical mechanics and quantum mechanics in particular, to construct both as two interconnected domains of probabilistic physics. Consistent theories of kinetics of physical transformations, decay processes, and intramolecular rearrangements are also outlined. The interrelation between the electromagnetic field, photons, and the theoretically discovered subatomic particle 'emon' is considered. Numerous internal imperfections of conventional probability theory, statistical physics, and quantum physics are exposed and removed - quantum physics no longer needs special interpretation. EPR, Bohm, and Bell paradoxes are easily resolved, among others. (Auth.)
Optimizing Probability of Detection Point Estimate Demonstration
Koshti, Ajay M.
2017-01-01
Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.
Alternative probability theories for cognitive psychology.
Narens, Louis
2014-01-01
Various proposals for generalizing event spaces for probability functions have been put forth in the mathematical, scientific, and philosophic literatures. In cognitive psychology such generalizations are used for explaining puzzling results in decision theory and for modeling the influence of context effects. This commentary discusses proposals for generalizing probability theory to event spaces that are not necessarily boolean algebras. Two prominent examples are quantum probability theory, which is based on the set of closed subspaces of a Hilbert space, and topological probability theory, which is based on the set of open sets of a topology. Both have been applied to a variety of cognitive situations. This commentary focuses on how event space properties can influence probability concepts and impact cognitive modeling. Copyright © 2013 Cognitive Science Society, Inc.
Determination of the probability for radioactive materials on properties in Monticello, Utah
International Nuclear Information System (INIS)
Wilson, M.J.; Crutcher, J.W.; Halford, D.K.
1991-01-01
The former uranium mill site at Monticello, Utah, is a surplus facility subject to clean-up under the Surplus Facilities Management Program (SFMP). Surrounding properties contaminated with mill site material are also subject to cleanup, and are referred to as Monticello Vicinity Properties (MVP). The Pollutant Assessments Group (PAG) of Oak Ridge National Laboratory (ORNL), Grand Junction, Colorado (GJ), was directed by the US Department of Energy (DOE) in July 1988 to assess the radiological condition of properties in Monticello, Utah. Since the Monticello activities are on the National Priority List, extra measures to identify potentially contaminated properties were undertaken. Thus, the likelihood that a random property could contain radioactive materials became a concern to the DOE. The objective of this study was to determine the probability that a vicinity property not addressed under the MVP project could contain Monticello mill-related residual radioactive material in excess of the DOE guidelines. Results suggest approximately 20% of the properties in the Monticello area contain Monticello mill-related residual radioactive material in excess of the DOE guidelines. This suggested that further designation measures be taken prior to the close of the designation phase. A public relations effort that included a property-owner mailing effort, public posting, and newspaper advertisement was one measure taken to ensure that most properties were assessed. As a consequence of this study, DOE directed that radiological screening surveys be conducted on the entirety of the Monticello area
Nilsson, Håkan; Juslin, Peter; Winman, Anders
2016-01-01
Costello and Watts (2014) present a model assuming that people's knowledge of probabilities adheres to probability theory, but that their probability judgments are perturbed by a random noise in the retrieval from memory. Predictions for the relationships between probability judgments for constituent events and their disjunctions and conjunctions, as well as for sums of such judgments were derived from probability theory. Costello and Watts (2014) report behavioral data showing that subjective probability judgments accord with these predictions. Based on the finding that subjective probability judgments follow probability theory, Costello and Watts (2014) conclude that the results imply that people's probability judgments embody the rules of probability theory and thereby refute theories of heuristic processing. Here, we demonstrate the invalidity of this conclusion by showing that all of the tested predictions follow straightforwardly from an account assuming heuristic probability integration (Nilsson, Winman, Juslin, & Hansson, 2009). We end with a discussion of a number of previous findings that harmonize very poorly with the predictions by the model suggested by Costello and Watts (2014). (c) 2015 APA, all rights reserved).
International Nuclear Information System (INIS)
Shimada, Yoshio
2000-01-01
It is anticipated that the change of frequency of surveillance tests, preventive maintenance or parts replacement of safety related components may cause the change of component failure probability and result in the change of core damage probability. It is also anticipated that the change is different depending on the initiating event frequency or the component types. This study assessed the change of core damage probability using simplified PSA model capable of calculating core damage probability in a short time period, which is developed by the US NRC to process accident sequence precursors, when various component's failure probability is changed between 0 and 1, or Japanese or American initiating event frequency data are used. As a result of the analysis, (1) It was clarified that frequency of surveillance test, preventive maintenance or parts replacement of motor driven pumps (high pressure injection pumps, residual heat removal pumps, auxiliary feedwater pumps) should be carefully changed, since the core damage probability's change is large, when the base failure probability changes toward increasing direction. (2) Core damage probability change is insensitive to surveillance test frequency change, since the core damage probability change is small, when motor operated valves and turbine driven auxiliary feed water pump failure probability changes around one figure. (3) Core damage probability change is small, when Japanese failure probability data are applied to emergency diesel generator, even if failure probability changes one figure from the base value. On the other hand, when American failure probability data is applied, core damage probability increase is large, even if failure probability changes toward increasing direction. Therefore, when Japanese failure probability data is applied, core damage probability change is insensitive to surveillance tests frequency change etc. (author)
On Field Size and Success Probability in Network Coding
DEFF Research Database (Denmark)
Geil, Hans Olav; Matsumoto, Ryutaroh; Thomsen, Casper
2008-01-01
Using tools from algebraic geometry and Gröbner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network...... coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix....
Front Probability, NOAA GOES Imager, 0.05 degrees, Western Hemisphere, EXPERIMENTAL
National Oceanic and Atmospheric Administration, Department of Commerce — The data indicates the probability of oceanic sea surface temperature fronts off the California coast. They were created using remote sensing sea surface temperature...
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
Failure probability analysis of optical grid
Zhong, Yaoquan; Guo, Wei; Sun, Weiqiang; Jin, Yaohui; Hu, Weisheng
2008-11-01
Optical grid, the integrated computing environment based on optical network, is expected to be an efficient infrastructure to support advanced data-intensive grid applications. In optical grid, the faults of both computational and network resources are inevitable due to the large scale and high complexity of the system. With the optical network based distributed computing systems extensive applied in the processing of data, the requirement of the application failure probability have been an important indicator of the quality of application and an important aspect the operators consider. This paper will present a task-based analysis method of the application failure probability in optical grid. Then the failure probability of the entire application can be quantified, and the performance of reducing application failure probability in different backup strategies can be compared, so that the different requirements of different clients can be satisfied according to the application failure probability respectively. In optical grid, when the application based DAG (directed acyclic graph) is executed in different backup strategies, the application failure probability and the application complete time is different. This paper will propose new multi-objective differentiated services algorithm (MDSA). New application scheduling algorithm can guarantee the requirement of the failure probability and improve the network resource utilization, realize a compromise between the network operator and the application submission. Then differentiated services can be achieved in optical grid.
Multipartite nonlocality and random measurements
de Rosier, Anna; Gruca, Jacek; Parisio, Fernando; Vértesi, Tamás; Laskowski, Wiesław
2017-07-01
We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness of genuine multipartite entanglement.
Uncertainty about probability: a decision analysis perspective
International Nuclear Information System (INIS)
Howard, R.A.
1988-01-01
The issue of how to think about uncertainty about probability is framed and analyzed from the viewpoint of a decision analyst. The failure of nuclear power plants is used as an example. The key idea is to think of probability as describing a state of information on an uncertain event, and to pose the issue of uncertainty in this quantity as uncertainty about a number that would be definitive: it has the property that you would assign it as the probability if you knew it. Logical consistency requires that the probability to assign to a single occurrence in the absence of further information be the mean of the distribution of this definitive number, not the medium as is sometimes suggested. Any decision that must be made without the benefit of further information must also be made using the mean of the definitive number's distribution. With this formulation, they find further that the probability of r occurrences in n exchangeable trials will depend on the first n moments of the definitive number's distribution. In making decisions, the expected value of clairvoyance on the occurrence of the event must be at least as great as that on the definitive number. If one of the events in question occurs, then the increase in probability of another such event is readily computed. This means, in terms of coin tossing, that unless one is absolutely sure of the fairness of a coin, seeing a head must increase the probability of heads, in distinction to usual thought. A numerical example for nuclear power shows that the failure of one plant of a group with a low probability of failure can significantly increase the probability that must be assigned to failure of a second plant in the group
Probability of misclassifying biological elements in surface waters.
Loga, Małgorzata; Wierzchołowska-Dziedzic, Anna
2017-11-24
Measurement uncertainties are inherent to assessment of biological indices of water bodies. The effect of these uncertainties on the probability of misclassification of ecological status is the subject of this paper. Four Monte-Carlo (M-C) models were applied to simulate the occurrence of random errors in the measurements of metrics corresponding to four biological elements of surface waters: macrophytes, phytoplankton, phytobenthos, and benthic macroinvertebrates. Long series of error-prone measurement values of these metrics, generated by M-C models, were used to identify cases in which values of any of the four biological indices lay outside of the "true" water body class, i.e., outside the class assigned from the actual physical measurements. Fraction of such cases in the M-C generated series was used to estimate the probability of misclassification. The method is particularly useful for estimating the probability of misclassification of the ecological status of surface water bodies in the case of short sequences of measurements of biological indices. The results of the Monte-Carlo simulations show a relatively high sensitivity of this probability to measurement errors of the river macrophyte index (MIR) and high robustness to measurement errors of the benthic macroinvertebrate index (MMI). The proposed method of using Monte-Carlo models to estimate the probability of misclassification has significant potential for assessing the uncertainty of water body status reported to the EC by the EU member countries according to WFD. The method can be readily applied also in risk assessment of water management decisions before adopting the status dependent corrective actions.
Probability an introduction with statistical applications
Kinney, John J
2014-01-01
Praise for the First Edition""This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory."" - The StatisticianThoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, h
Dependency models and probability of joint events
International Nuclear Information System (INIS)
Oerjasaeter, O.
1982-08-01
Probabilistic dependencies between components/systems are discussed with reference to a broad classification of potential failure mechanisms. Further, a generalized time-dependency model, based on conditional probabilities for estimation of the probability of joint events and event sequences is described. The applicability of this model is clarified/demonstrated by various examples. It is concluded that the described model of dependency is a useful tool for solving a variety of practical problems concerning the probability of joint events and event sequences where common cause and time-dependent failure mechanisms are involved. (Auth.)
Handbook of probability theory and applications
Rudas, Tamas
2008-01-01
""This is a valuable reference guide for readers interested in gaining a basic understanding of probability theory or its applications in problem solving in the other disciplines.""-CHOICEProviding cutting-edge perspectives and real-world insights into the greater utility of probability and its applications, the Handbook of Probability offers an equal balance of theory and direct applications in a non-technical, yet comprehensive, format. Editor Tamás Rudas and the internationally-known contributors present the material in a manner so that researchers of vari
Probabilities on Streams and Reflexive Games
Directory of Open Access Journals (Sweden)
Andrew Schumann
2014-01-01
Full Text Available Probability measures on streams (e.g. on hypernumbers and p-adic numbers have been defined. It was shown that these probabilities can be used for simulations of reflexive games. In particular, it can be proved that Aumann's agreement theorem does not hold for these probabilities. Instead of this theorem, there is a statement that is called the reflexion disagreement theorem. Based on this theorem, probabilistic and knowledge conditions can be defined for reflexive games at various reflexion levels up to the infinite level. (original abstract
Concept of probability in statistical physics
Guttmann, Y M
1999-01-01
Foundational issues in statistical mechanics and the more general question of how probability is to be understood in the context of physical theories are both areas that have been neglected by philosophers of physics. This book fills an important gap in the literature by providing a most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics. The book explores both subjectivist and objectivist accounts of probability, and takes full measure of work in the foundations of probability theory, in statistical mechanics, and in mathematical theory. It will be of particular interest to philosophers of science, physicists and mathematicians interested in foundational issues, and also to historians of science.
Computation of the Complex Probability Function
Energy Technology Data Exchange (ETDEWEB)
Trainer, Amelia Jo [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ledwith, Patrick John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-08-22
The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the n^{th} degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.
Pre-aggregation for Probability Distributions
DEFF Research Database (Denmark)
Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach
Motivated by the increasing need to analyze complex uncertain multidimensional data (e.g., in order to optimize and personalize location-based services), this paper proposes novel types of {\\em probabilistic} OLAP queries that operate on aggregate values that are probability distributions...... and the techniques to process these queries. The paper also presents the methods for computing the probability distributions, which enables pre-aggregation, and for using the pre-aggregated distributions for further aggregation. In order to achieve good time and space efficiency, the methods perform approximate...... multidimensional data analysis that is considered in this paper (i.e., approximate processing of probabilistic OLAP queries over probability distributions)....
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....
Modeling experiments using quantum and Kolmogorov probability
International Nuclear Information System (INIS)
Hess, Karl
2008-01-01
Criteria are presented that permit a straightforward partition of experiments into sets that can be modeled using both quantum probability and the classical probability framework of Kolmogorov. These new criteria concentrate on the operational aspects of the experiments and lead beyond the commonly appreciated partition by relating experiments to commuting and non-commuting quantum operators as well as non-entangled and entangled wavefunctions. In other words the space of experiments that can be understood using classical probability is larger than usually assumed. This knowledge provides advantages for areas such as nanoscience and engineering or quantum computation.
Keren, G.; Teigen, K.H.
2001-01-01
This article presents a framework for lay people's internal representations of probabilities, which supposedly reflect the strength of underlying dispositions, or propensities, associated with the predicted event. From this framework, we derive the probability-outcome correspondence principle, which
Quantum randomness and unpredictability
Energy Technology Data Exchange (ETDEWEB)
Jaeger, Gregg [Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA (United States)
2017-06-15
Quantum mechanics is a physical theory supplying probabilities corresponding to expectation values for measurement outcomes. Indeed, its formalism can be constructed with measurement as a fundamental process, as was done by Schwinger, provided that individual measurements outcomes occur in a random way. The randomness appearing in quantum mechanics, as with other forms of randomness, has often been considered equivalent to a form of indeterminism. Here, it is argued that quantum randomness should instead be understood as a form of unpredictability because, amongst other things, indeterminism is not a necessary condition for randomness. For concreteness, an explication of the randomness of quantum mechanics as the unpredictability of quantum measurement outcomes is provided. Finally, it is shown how this view can be combined with the recently introduced view that the very appearance of individual quantum measurement outcomes can be grounded in the Plenitude principle of Leibniz, a principle variants of which have been utilized in physics by Dirac and Gell-Mann in relation to the fundamental processes. This move provides further support to Schwinger's ''symbolic'' derivation of quantum mechanics from measurement. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Roulaud, M; Durand-Zaleski, I; Ingrand, P; Serrie, A; Diallo, B; Peruzzi, P; Hieu, P D; Voirin, J; Raoul, S; Page, P; Fontaine, D; Lantéri-Minet, M; Blond, S; Buisset, N; Cuny, E; Cadenne, M; Caire, F; Ranoux, D; Mertens, P; Naous, H; Simon, E; Emery, E; Gadan, B; Regis, J; Sol, J-C; Béraud, G; Debiais, F; Durand, G; Guetarni Ging, F; Prévost, A; Brandet, C; Monlezun, O; Delmotte, A; d'Houtaud, S; Bataille, B; Rigoard, P
2015-03-01
Many studies have demonstrated the efficacy of spinal cord stimulation (SCS) for chronic neuropathic radicular pain over recent decades, but despite global favourable outcomes in failed back surgery syndrome (FBSS) with leg pain, the back pain component remains poorly controlled by neurostimulation. Technological and scientific progress has led to the development of new SCS leads, comprising a multicolumn design and a greater number of contacts. The efficacy of multicolumn SCS lead configurations for the treatment of the back pain component of FBSS has recently been suggested by pilot studies. However, a randomized controlled trial must be conducted to confirm the efficacy of new generation multicolumn SCS. Évaluation médico-économique de la STImulation MEdullaire mulTi-colonnes (ESTIMET) is a multicentre, randomized study designed to compare the clinical efficacy and health economics aspects of mono- vs. multicolumn SCS lead programming in FBSS patients with radicular pain and significant back pain. FBSS patients with a radicular pain VAS score≥50mm, associated with a significant back pain component were recruited in 14 centres in France and implanted with multicolumn SCS. Before the lead implantation procedure, they were 1:1 randomized to monocolumn SCS (group 1) or multicolumn SCS (group 2). Programming was performed using only one column for group 1 and full use of the 3 columns for group 2. Outcome assessment was performed at baseline (pre-implantation), and 1, 3, 6 and 12months post-implantation. The primary outcome measure was a reduction of the severity of low back pain (bVAS reduction≥50%) at the 6-month visit. Additional outcome measures were changes in global pain, leg pain, paraesthesia coverage mapping, functional capacities, quality of life, neuropsychological aspects, patient satisfaction and healthcare resource consumption. Trial recruitment started in May 2012. As of September 2013, all 14 study centres have been initiated and 112
Modelling the probability of building fires
Directory of Open Access Journals (Sweden)
Vojtěch Barták
2014-12-01
Full Text Available Systematic spatial risk analysis plays a crucial role in preventing emergencies.In the Czech Republic, risk mapping is currently based on the risk accumulationprinciple, area vulnerability, and preparedness levels of Integrated Rescue Systemcomponents. Expert estimates are used to determine risk levels for individualhazard types, while statistical modelling based on data from actual incidents andtheir possible causes is not used. Our model study, conducted in cooperation withthe Fire Rescue Service of the Czech Republic as a model within the Liberec andHradec Králové regions, presents an analytical procedure leading to the creation ofbuilding fire probability maps based on recent incidents in the studied areas andon building parameters. In order to estimate the probability of building fires, aprediction model based on logistic regression was used. Probability of fire calculatedby means of model parameters and attributes of specific buildings can subsequentlybe visualized in probability maps.
Encounter Probability of Individual Wave Height
DEFF Research Database (Denmark)
Liu, Z.; Burcharth, H. F.
1998-01-01
wave height corresponding to a certain exceedence probability within a structure lifetime (encounter probability), based on the statistical analysis of long-term extreme significant wave height. Then the design individual wave height is calculated as the expected maximum individual wave height...... associated with the design significant wave height, with the assumption that the individual wave heights follow the Rayleigh distribution. However, the exceedence probability of such a design individual wave height within the structure lifetime is unknown. The paper presents a method for the determination...... of the design individual wave height corresponding to an exceedence probability within the structure lifetime, given the long-term extreme significant wave height. The method can also be applied for estimation of the number of relatively large waves for fatigue analysis of constructions....
Predicting binary choices from probability phrase meanings.
Wallsten, Thomas S; Jang, Yoonhee
2008-08-01
The issues of how individuals decide which of two events is more likely and of how they understand probability phrases both involve judging relative likelihoods. In this study, we investigated whether derived scales representing probability phrase meanings could be used within a choice model to predict independently observed binary choices. If they can, this simultaneously provides support for our model and suggests that the phrase meanings are measured meaningfully. The model assumes that, when deciding which of two events is more likely, judges take a single sample from memory regarding each event and respond accordingly. The model predicts choice probabilities by using the scaled meanings of individually selected probability phrases as proxies for confidence distributions associated with sampling from memory. Predictions are sustained for 34 of 41 participants but, nevertheless, are biased slightly low. Sequential sampling models improve the fit. The results have both theoretical and applied implications.
Certainties and probabilities of the IPCC
International Nuclear Information System (INIS)
2004-01-01
Based on an analysis of information about the climate evolution, simulations of a global warming and the snow coverage monitoring of Meteo-France, the IPCC presented its certainties and probabilities concerning the greenhouse effect. (A.L.B.)
The probability factor in establishing causation
International Nuclear Information System (INIS)
Hebert, J.
1988-01-01
This paper discusses the possibilities and limitations of methods using the probability factor in establishing the causal link between bodily injury, whether immediate or delayed, and the nuclear incident presumed to have caused it (NEA) [fr
Characteristic length of the knotting probability revisited
International Nuclear Information System (INIS)
Uehara, Erica; Deguchi, Tetsuo
2015-01-01
We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of impermeable cylindrical segments corresponds to the screening length of double-stranded DNA surrounded by counter ions. For the model we evaluate the probability for a generated SAP with N segments having a given knot K through simulation. We call it the knotting probability of a knot K with N segments for the SAP model. We show that when N is large the most significant factor in the knotting probability is given by the exponentially decaying part exp(−N/N K ), where the estimates of parameter N K are consistent with the same value for all the different knots we investigated. We thus call it the characteristic length of the knotting probability. We give formulae expressing the characteristic length as a function of the cylindrical radius r ex , i.e. the screening length of double-stranded DNA. (paper)
Probability of Survival Decision Aid (PSDA)
National Research Council Canada - National Science Library
Xu, Xiaojiang; Amin, Mitesh; Santee, William R
2008-01-01
A Probability of Survival Decision Aid (PSDA) is developed to predict survival time for hypothermia and dehydration during prolonged exposure at sea in both air and water for a wide range of environmental conditions...
Probability and statistics with integrated software routines
Deep, Ronald
2005-01-01
Probability & Statistics with Integrated Software Routines is a calculus-based treatment of probability concurrent with and integrated with statistics through interactive, tailored software applications designed to enhance the phenomena of probability and statistics. The software programs make the book unique.The book comes with a CD containing the interactive software leading to the Statistical Genie. The student can issue commands repeatedly while making parameter changes to observe the effects. Computer programming is an excellent skill for problem solvers, involving design, prototyping, data gathering, testing, redesign, validating, etc, all wrapped up in the scientific method.See also: CD to accompany Probability and Stats with Integrated Software Routines (0123694698)* Incorporates more than 1,000 engaging problems with answers* Includes more than 300 solved examples* Uses varied problem solving methods
Pre-Aggregation with Probability Distributions
DEFF Research Database (Denmark)
Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach
2006-01-01
Motivated by the increasing need to analyze complex, uncertain multidimensional data this paper proposes probabilistic OLAP queries that are computed using probability distributions rather than atomic values. The paper describes how to create probability distributions from base data, and how...... the distributions can be subsequently used in pre-aggregation. Since the probability distributions can become large, we show how to achieve good time and space efficiency by approximating the distributions. We present the results of several experiments that demonstrate the effectiveness of our methods. The work...... is motivated with a real-world case study, based on our collaboration with a leading Danish vendor of location-based services. This paper is the first to consider the approximate processing of probabilistic OLAP queries over probability distributions....
Probability of spent fuel transportation accidents
International Nuclear Information System (INIS)
McClure, J.D.
1981-07-01
The transported volume of spent fuel, incident/accident experience and accident environment probabilities were reviewed in order to provide an estimate of spent fuel accident probabilities. In particular, the accident review assessed the accident experience for large casks of the type that could transport spent (irradiated) nuclear fuel. This review determined that since 1971, the beginning of official US Department of Transportation record keeping for accidents/incidents, there has been one spent fuel transportation accident. This information, coupled with estimated annual shipping volumes for spent fuel, indicated an estimated annual probability of a spent fuel transport accident of 5 x 10 -7 spent fuel accidents per mile. This is consistent with ordinary truck accident rates. A comparison of accident environments and regulatory test environments suggests that the probability of truck accidents exceeding regulatory test for impact is approximately 10 -9 /mile
Sampling, Probability Models and Statistical Reasoning Statistical
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Sampling, Probability Models and Statistical Reasoning Statistical Inference. Mohan Delampady V R Padmawar. General Article Volume 1 Issue 5 May 1996 pp 49-58 ...
Imprecise Probability Methods for Weapons UQ
Energy Technology Data Exchange (ETDEWEB)
Picard, Richard Roy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vander Wiel, Scott Alan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-13
Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.
Escape and transmission probabilities in cylindrical geometry
International Nuclear Information System (INIS)
Bjerke, M.A.
1980-01-01
An improved technique for the generation of escape and transmission probabilities in cylindrical geometry was applied to the existing resonance cross section processing code ROLAIDS. The algorithm of Hwang and Toppel, [ANL-FRA-TM-118] (with modifications) was employed. The probabilities generated were found to be as accurate as those given by the method previously applied in ROLAIDS, while requiring much less computer core storage and CPU time
Probability and statistics for computer science
Johnson, James L
2011-01-01
Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: ""to present the mathematical analysis underlying probability results"" Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra in an appendix Mathematical interludes (in each chapter) which examine mathematical techniques in the context of probabilistic or statistical importance Numerous section exercises, summaries, historical notes, and Further Readings for reinforcem
Collision Probabilities for Finite Cylinders and Cuboids
Energy Technology Data Exchange (ETDEWEB)
Carlvik, I
1967-05-15
Analytical formulae have been derived for the collision probabilities of homogeneous finite cylinders and cuboids. The formula for the finite cylinder contains double integrals, and the formula for the cuboid only single integrals. Collision probabilities have been calculated by means of the formulae and compared with values obtained by other authors. It was found that the calculations using the analytical formulae are much quicker and give higher accuracy than Monte Carlo calculations.
Probability distributions for Markov chain based quantum walks
Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.
2018-01-01
We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.
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.
{sup 134}Cs emission probabilities determination by gamma spectrometry
Energy Technology Data Exchange (ETDEWEB)
Almeida, M.C.M. de, E-mail: candida@cnen.gov.br [Comissão Nacional de Energia Nuclear (DINOR/CNEN), Riode Janeiro, RJ (Brazil); Poledna, R.; Delgado, J.U.; Silva, R.L.; Araujo, M.T.; Silva, C.J. da [Instituto de Radioproteção e Dosimetria (LNMRI/IRD/CNEN-RJ), Rio de Janeiro, RJ (Brazil)
2017-07-01
The National Laboratory for Ionizing Radiation Metrology (LNMRI/IRD/CNEN) of Rio de Janeiro performed primary and secondary standardization of different radionuclides reaching satisfactory uncertainties. A solution of {sup 134}Cs radionuclide was purchased from commercial supplier to emission probabilities determination of some of its energies. {sup 134}Cs is a beta gamma emitter with 754 days of half-life. This radionuclide is used as standard in environmental, water and food control. It is also important to germanium detector calibration.The gamma emission probabilities (Pγ) were determined mainly for some energies of the {sup 134}Cs by efficiency curve method and the Pγ absolute uncertainties obtained were below 1% (k=1). (author)
Perceptions of randomized security schedules.
Scurich, Nicholas; John, Richard S
2014-04-01
Security of infrastructure is a major concern. Traditional security schedules are unable to provide omnipresent coverage; consequently, adversaries can exploit predictable vulnerabilities to their advantage. Randomized security schedules, which randomly deploy security measures, overcome these limitations, but public perceptions of such schedules have not been examined. In this experiment, participants were asked to make a choice between attending a venue that employed a traditional (i.e., search everyone) or a random (i.e., a probability of being searched) security schedule. The absolute probability of detecting contraband was manipulated (i.e., 1/10, 1/4, 1/2) but equivalent between the two schedule types. In general, participants were indifferent to either security schedule, regardless of the probability of detection. The randomized schedule was deemed more convenient, but the traditional schedule was considered fairer and safer. There were no differences between traditional and random schedule in terms of perceived effectiveness or deterrence. Policy implications for the implementation and utilization of randomized schedules are discussed. © 2013 Society for Risk Analysis.
Subjective randomness as statistical inference.
Griffiths, Thomas L; Daniels, Dylan; Austerweil, Joseph L; Tenenbaum, Joshua B
2018-06-01
Some events seem more random than others. For example, when tossing a coin, a sequence of eight heads in a row does not seem very random. Where do these intuitions about randomness come from? We argue that subjective randomness can be understood as the result of a statistical inference assessing the evidence that an event provides for having been produced by a random generating process. We show how this account provides a link to previous work relating randomness to algorithmic complexity, in which random events are those that cannot be described by short computer programs. Algorithmic complexity is both incomputable and too general to capture the regularities that people can recognize, but viewing randomness as statistical inference provides two paths to addressing these problems: considering regularities generated by simpler computing machines, and restricting the set of probability distributions that characterize regularity. Building on previous work exploring these different routes to a more restricted notion of randomness, we define strong quantitative models of human randomness judgments that apply not just to binary sequences - which have been the focus of much of the previous work on subjective randomness - but also to binary matrices and spatial clustering. Copyright © 2018 Elsevier Inc. All rights reserved.
SCRAED - Simple and Complex Random Assignment in Experimental Designs
Alferes, Valentim R.
2009-01-01
SCRAED is a package of 37 self-contained SPSS syntax files that performs simple and complex random assignment in experimental designs. For between-subjects designs, SCRAED includes simple random assignment (no restrictions, forced equal sizes, forced unequal sizes, and unequal probabilities), block random assignment (simple and generalized blocks), and stratified random assignment (no restrictions, forced equal sizes, forced unequal sizes, and unequal probabilities). For within-subject...
Modelling the Probability of Landslides Impacting Road Networks
Taylor, F. E.; Malamud, B. D.
2012-04-01
During a landslide triggering event, the threat of landslides blocking roads poses a risk to logistics, rescue efforts and communities dependant on those road networks. Here we present preliminary results of a stochastic model we have developed to evaluate the probability of landslides intersecting a simple road network during a landslide triggering event and apply simple network indices to measure the state of the road network in the affected region. A 4000 x 4000 cell array with a 5 m x 5 m resolution was used, with a pre-defined simple road network laid onto it, and landslides 'randomly' dropped onto it. Landslide areas (AL) were randomly selected from a three-parameter inverse gamma probability density function, consisting of a power-law decay of about -2.4 for medium and large values of AL and an exponential rollover for small values of AL; the rollover (maximum probability) occurs at about AL = 400 m2 This statistical distribution was chosen based on three substantially complete triggered landslide inventories recorded in existing literature. The number of landslide areas (NL) selected for each triggered event iteration was chosen to have an average density of 1 landslide km-2, i.e. NL = 400 landslide areas chosen randomly for each iteration, and was based on several existing triggered landslide event inventories. A simple road network was chosen, in a 'T' shape configuration, with one road 1 x 4000 cells (5 m x 20 km) in a 'T' formation with another road 1 x 2000 cells (5 m x 10 km). The landslide areas were then randomly 'dropped' over the road array and indices such as the location, size (ABL) and number of road blockages (NBL) recorded. This process was performed 500 times (iterations) in a Monte-Carlo type simulation. Initial results show that for a landslide triggering event with 400 landslides over a 400 km2 region, the number of road blocks per iteration, NBL,ranges from 0 to 7. The average blockage area for the 500 iterations (A¯ BL) is about 3000 m
Left passage probability of Schramm-Loewner Evolution
Najafi, M. N.
2013-06-01
SLE(κ,ρ⃗) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE(κ,ρ⃗) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case κ=2 and hρ=0 in which hρ is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from ξ0 and conditioned by a change of boundary conditions at x0, we find that this probability depends significantly on the factor x0-ξ0. We also present the perturbative general solution for large x0. As a prototype, we apply this formalism to SLE(κ,κ-6) which governs the curves that start from and end on the real axis.
Culture and Probability Judgment Accuracy: The Influence of Holistic Reasoning.
Lechuga, Julia; Wiebe, John S
2011-08-01
A well-established phenomenon in the judgment and decision-making tradition is the overconfidence one places in the amount of knowledge that one possesses. Overconfidence or probability judgment accuracy varies not only individually but also across cultures. However, research efforts to explain cross-cultural variations in the overconfidence phenomenon have seldom been made. In Study 1, the authors compared the probability judgment accuracy of U.S. Americans (N = 108) and Mexican participants (N = 100). In Study 2, they experimentally primed culture by randomly assigning English/Spanish bilingual Mexican Americans (N = 195) to response language. Results of both studies replicated the cross-cultural variation of probability judgment accuracy previously observed in other cultural groups. U.S. Americans displayed less overconfidence when compared to Mexicans. These results were then replicated in bilingual participants, when culture was experimentally manipulated with language priming. Holistic reasoning did not account for the cross-cultural variation of overconfidence. Suggestions for future studies are discussed.