Probabilistic Reasoning for Robustness in Automated Planning

NASA Technical Reports Server (NTRS)

Schaffer, Steven; Clement, Bradley; Chien, Steve

2007-01-01

A general-purpose computer program for planning the actions of a spacecraft or other complex system has been augmented by incorporating a subprogram that reasons about uncertainties in such continuous variables as times taken to perform tasks and amounts of resources to be consumed. This subprogram computes parametric probability distributions for time and resource variables on the basis of user-supplied models of actions and resources that they consume. The current system accepts bounded Gaussian distributions over action duration and resource use. The distributions are then combined during planning to determine the net probability distribution of each resource at any time point. In addition to a full combinatoric approach, several approximations for arriving at these combined distributions are available, including maximum-likelihood and pessimistic algorithms. Each such probability distribution can then be integrated to obtain a probability that execution of the plan under consideration would violate any constraints on the resource. The key idea is to use these probabilities of conflict to score potential plans and drive a search toward planning low-risk actions. An output plan provides a balance between the user s specified averseness to risk and other measures of optimality.

Evaluation of Mean and Variance Integrals without Integration

ERIC Educational Resources Information Center

Joarder, A. H.; Omar, M. H.

2007-01-01

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential…

Entropy Methods For Univariate Distributions in Decision Analysis

NASA Astrophysics Data System (ADS)

Abbas, Ali E.

2003-03-01

One of the most important steps in decision analysis practice is the elicitation of the decision-maker's belief about an uncertainty of interest in the form of a representative probability distribution. However, the probability elicitation process is a task that involves many cognitive and motivational biases. Alternatively, the decision-maker may provide other information about the distribution of interest, such as its moments, and the maximum entropy method can be used to obtain a full distribution subject to the given moment constraints. In practice however, decision makers cannot readily provide moments for the distribution, and are much more comfortable providing information about the fractiles of the distribution of interest or bounds on its cumulative probabilities. In this paper we present a graphical method to determine the maximum entropy distribution between upper and lower probability bounds and provide an interpretation for the shape of the maximum entropy distribution subject to fractile constraints, (FMED). We also discuss the problems with the FMED in that it is discontinuous and flat over each fractile interval. We present a heuristic approximation to a distribution if in addition to its fractiles, we also know it is continuous and work through full examples to illustrate the approach.

Path probability of stochastic motion: A functional approach

NASA Astrophysics Data System (ADS)

Hattori, Masayuki; Abe, Sumiyoshi

2016-06-01

The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.

Fragment size distribution in viscous bag breakup of a drop

NASA Astrophysics Data System (ADS)

Kulkarni, Varun; Bulusu, Kartik V.; Plesniak, Michael W.; Sojka, Paul E.

2015-11-01

In this study we examine the drop size distribution resulting from the fragmentation of a single drop in the presence of a continuous air jet. Specifically, we study the effect of Weber number, We, and Ohnesorge number, Oh on the disintegration process. The regime of breakup considered is observed between 12 <= We <= 16 for Oh <= 0.1. Experiments are conducted using phase Doppler anemometry. Both the number and volume fragment size probability distributions are plotted. The volume probability distribution revealed a bi-modal behavior with two distinct peaks: one corresponding to the rim fragments and the other to the bag fragments. This behavior was suppressed in the number probability distribution. Additionally, we employ an in-house particle detection code to isolate the rim fragment size distribution from the total probability distributions. Our experiments showed that the bag fragments are smaller in diameter and larger in number, while the rim fragments are larger in diameter and smaller in number. Furthermore, with increasing We for a given Ohwe observe a large number of small-diameter drops and small number of large-diameter drops. On the other hand, with increasing Oh for a fixed We the opposite is seen.

Robust approaches to quantification of margin and uncertainty for sparse data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hund, Lauren; Schroeder, Benjamin B.; Rumsey, Kelin

Characterizing the tails of probability distributions plays a key role in quantification of margins and uncertainties (QMU), where the goal is characterization of low probability, high consequence events based on continuous measures of performance. When data are collected using physical experimentation, probability distributions are typically fit using statistical methods based on the collected data, and these parametric distributional assumptions are often used to extrapolate about the extreme tail behavior of the underlying probability distribution. In this project, we character- ize the risk associated with such tail extrapolation. Specifically, we conducted a scaling study to demonstrate the large magnitude of themore » risk; then, we developed new methods for communicat- ing risk associated with tail extrapolation from unvalidated statistical models; lastly, we proposed a Bayesian data-integration framework to mitigate tail extrapolation risk through integrating ad- ditional information. We conclude that decision-making using QMU is a complex process that cannot be achieved using statistical analyses alone.« less

On the continuity of the stationary state distribution of DPCM

NASA Astrophysics Data System (ADS)

Naraghi-Pour, Morteza; Neuhoff, David L.

1990-03-01

Continuity and singularity properties of the stationary state distribution of differential pulse code modulation (DPCM) are explored. Two-level DPCM (i.e., delta modulation) operating on a first-order autoregressive source is considered, and it is shown that, when the magnitude of the DPCM prediciton coefficient is between zero and one-half, the stationary state distribution is singularly continuous; i.e., it is not discrete but concentrates on an uncountable set with a Lebesgue measure of zero. Consequently, it cannot be represented with a probability density function. For prediction coefficients with magnitude greater than or equal to one-half, the distribution is pure, i.e., either absolutely continuous and representable with a density function, or singular. This problem is compared to the well-known and still substantially unsolved problem of symmetric Bernoulli convolutions.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

Spatial Probability Distribution of Strata's Lithofacies and its Impacts on Land Subsidence in Huairou Emergency Water Resources Region of Beijing

NASA Astrophysics Data System (ADS)

Li, Y.; Gong, H.; Zhu, L.; Guo, L.; Gao, M.; Zhou, C.

2016-12-01

Continuous over-exploitation of groundwater causes dramatic drawdown, and leads to regional land subsidence in the Huairou Emergency Water Resources region, which is located in the up-middle part of the Chaobai river basin of Beijing. Owing to the spatial heterogeneity of strata's lithofacies of the alluvial fan, ground deformation has no significant positive correlation with groundwater drawdown, and one of the challenges ahead is to quantify the spatial distribution of strata's lithofacies. The transition probability geostatistics approach provides potential for characterizing the distribution of heterogeneous lithofacies in the subsurface. Combined the thickness of clay layer extracted from the simulation, with deformation field acquired from PS-InSAR technology, the influence of strata's lithofacies on land subsidence can be analyzed quantitatively. The strata's lithofacies derived from borehole data were generalized into four categories and their probability distribution in the observe space was mined by using the transition probability geostatistics, of which clay was the predominant compressible material. Geologically plausible realizations of lithofacies distribution were produced, accounting for complex heterogeneity in alluvial plain. At a particular probability level of more than 40 percent, the volume of clay defined was 55 percent of the total volume of strata's lithofacies. This level, equaling nearly the volume of compressible clay derived from the geostatistics, was thus chosen to represent the boundary between compressible and uncompressible material. The method incorporates statistical geological information, such as distribution proportions, average lengths and juxtaposition tendencies of geological types, mainly derived from borehole data and expert knowledge, into the Markov chain model of transition probability. Some similarities of patterns were indicated between the spatial distribution of deformation field and clay layer. In the area with roughly similar water table decline, locations in the subsurface having a higher probability for the existence of compressible material occur more than that in the location with a lower probability. Such estimate of spatial probability distribution is useful to analyze the uncertainty of land subsidence.

ON CONTINUOUS-REVIEW (S-1,S) INVENTORY POLICIES WITH STATE-DEPENDENT LEADTIMES,

DTIC Science & Technology

INVENTORY CONTROL, *REPLACEMENT THEORY), MATHEMATICAL MODELS, LEAD TIME , MANAGEMENT ENGINEERING, DISTRIBUTION FUNCTIONS, PROBABILITY, QUEUEING THEORY, COSTS, OPTIMIZATION, STATISTICAL PROCESSES, DIFFERENCE EQUATIONS

Target intersection probabilities for parallel-line and continuous-grid types of search

USGS Publications Warehouse

McCammon, R.B.

1977-01-01

The expressions for calculating the probability of intersection of hidden targets of different sizes and shapes for parallel-line and continuous-grid types of search can be formulated by vsing the concept of conditional probability. When the prior probability of the orientation of a widden target is represented by a uniform distribution, the calculated posterior probabilities are identical with the results obtained by the classic methods of probability. For hidden targets of different sizes and shapes, the following generalizations about the probability of intersection can be made: (1) to a first approximation, the probability of intersection of a hidden target is proportional to the ratio of the greatest dimension of the target (viewed in plane projection) to the minimum line spacing of the search pattern; (2) the shape of the hidden target does not greatly affect the probability of the intersection when the largest dimension of the target is small relative to the minimum spacing of the search pattern, (3) the probability of intersecting a target twice for a particular type of search can be used as a lower bound if there is an element of uncertainty of detection for a particular type of tool; (4) the geometry of the search pattern becomes more critical when the largest dimension of the target equals or exceeds the minimum spacing of the search pattern; (5) for elongate targets, the probability of intersection is greater for parallel-line search than for an equivalent continuous square-grid search when the largest dimension of the target is less than the minimum spacing of the search pattern, whereas the opposite is true when the largest dimension exceeds the minimum spacing; (6) the probability of intersection for nonorthogonal continuous-grid search patterns is not greatly different from the probability of intersection for the equivalent orthogonal continuous-grid pattern when the orientation of the target is unknown. The probability of intersection for an elliptically shaped target can be approximated by treating the ellipse as intermediate between a circle and a line. A search conducted along a continuous rectangular grid can be represented as intermediate between a search along parallel lines and along a continuous square grid. On this basis, an upper and lower bound for the probability of intersection of an elliptically shaped target for a continuous rectangular grid can be calculated. Charts have been constructed that permit the values for these probabilities to be obtained graphically. The use of conditional probability allows the explorationist greater flexibility in considering alternate search strategies for locating hidden targets. ?? 1977 Plenum Publishing Corp.

Probability distributions for multimeric systems.

PubMed

Albert, Jaroslav; Rooman, Marianne

2016-01-01

We propose a fast and accurate method of obtaining the equilibrium mono-modal joint probability distributions for multimeric systems. The method necessitates only two assumptions: the copy number of all species of molecule may be treated as continuous; and, the probability density functions (pdf) are well-approximated by multivariate skew normal distributions (MSND). Starting from the master equation, we convert the problem into a set of equations for the statistical moments which are then expressed in terms of the parameters intrinsic to the MSND. Using an optimization package on Mathematica, we minimize a Euclidian distance function comprising of a sum of the squared difference between the left and the right hand sides of these equations. Comparison of results obtained via our method with those rendered by the Gillespie algorithm demonstrates our method to be highly accurate as well as efficient.

Continuous-time quantum walks on star graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salimi, S.

2009-06-15

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K{sub 2} graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

In Defense of the Chi-Square Continuity Correction.

ERIC Educational Resources Information Center

Veldman, Donald J.; McNemar, Quinn

Published studies of the sampling distribution of chi-square with and without Yates' correction for continuity have been interpreted as discrediting the correction. Yates' correction actually produces a biased chi-square value which in turn yields a better estimate of the exact probability of the discrete event concerned when used in conjunction…

Probing the statistics of transport in the Hénon Map

NASA Astrophysics Data System (ADS)

Alus, O.; Fishman, S.; Meiss, J. D.

2016-09-01

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant "boundary circles." We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.

Statistics on continuous IBD data: Exact distribution evaluation for a pair of full(half)-sibs and a pair of a (great-) grandchild with a (great-) grandparent

PubMed Central

Stefanov, Valeri T

2002-01-01

Background Pairs of related individuals are widely used in linkage analysis. Most of the tests for linkage analysis are based on statistics associated with identity by descent (IBD) data. The current biotechnology provides data on very densely packed loci, and therefore, it may provide almost continuous IBD data for pairs of closely related individuals. Therefore, the distribution theory for statistics on continuous IBD data is of interest. In particular, distributional results which allow the evaluation of p-values for relevant tests are of importance. Results A technology is provided for numerical evaluation, with any given accuracy, of the cumulative probabilities of some statistics on continuous genome data for pairs of closely related individuals. In the case of a pair of full-sibs, the following statistics are considered: (i) the proportion of genome with 2 (at least 1) haplotypes shared identical-by-descent (IBD) on a chromosomal segment, (ii) the number of distinct pieces (subsegments) of a chromosomal segment, on each of which exactly 2 (at least 1) haplotypes are shared IBD. The natural counterparts of these statistics for the other relationships are also considered. Relevant Maple codes are provided for a rapid evaluation of the cumulative probabilities of such statistics. The genomic continuum model, with Haldane's model for the crossover process, is assumed. Conclusions A technology, together with relevant software codes for its automated implementation, are provided for exact evaluation of the distributions of relevant statistics associated with continuous genome data on closely related individuals. PMID:11996673

Exact joint density-current probability function for the asymmetric exclusion process.

PubMed

Depken, Martin; Stinchcombe, Robin

2004-07-23

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra. Copyright 2004 The American Physical Society

Assessment of Group Preferences and Group Uncertainty for Decision Making

DTIC Science & Technology

1976-06-01

the individ- uals. decision making , group judgments should be preferred to individual judgments if obtaining group judgments costs more. -26- -YI IV... decision making group . IV. A. 3. Aggregation using conjugate distribution. Arvther procedure for combining indivi(jai probability judgments into a group...statisticized group group decision making group judgment subjective probability Delphi method expected utility nominal group 20. ABSTRACT (Continue on

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Zhang; Chen, Wei

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

On computational Gestalt detection thresholds.

PubMed

Grompone von Gioi, Rafael; Jakubowicz, Jérémie

2009-01-01

The aim of this paper is to show some recent developments of computational Gestalt theory, as pioneered by Desolneux, Moisan and Morel. The new results allow to predict much more accurately the detection thresholds. This step is unavoidable if one wants to analyze visual detection thresholds in the light of computational Gestalt theory. The paper first recalls the main elements of computational Gestalt theory. It points out a precision issue in this theory, essentially due to the use of discrete probability distributions. It then proposes to overcome this issue by using continuous probability distributions and illustrates it on the meaningful alignment detector of Desolneux et al.

Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

DOE PAGES

Jiang, Zhang; Chen, Wei

2017-11-03

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work.

Probability analysis for consecutive-day maximum rainfall for Tiruchirapalli City (south India, Asia)

NASA Astrophysics Data System (ADS)

Sabarish, R. Mani; Narasimhan, R.; Chandhru, A. R.; Suribabu, C. R.; Sudharsan, J.; Nithiyanantham, S.

2017-05-01

In the design of irrigation and other hydraulic structures, evaluating the magnitude of extreme rainfall for a specific probability of occurrence is of much importance. The capacity of such structures is usually designed to cater to the probability of occurrence of extreme rainfall during its lifetime. In this study, an extreme value analysis of rainfall for Tiruchirapalli City in Tamil Nadu was carried out using 100 years of rainfall data. Statistical methods were used in the analysis. The best-fit probability distribution was evaluated for 1, 2, 3, 4 and 5 days of continuous maximum rainfall. The goodness of fit was evaluated using Chi-square test. The results of the goodness-of-fit tests indicate that log-Pearson type III method is the overall best-fit probability distribution for 1-day maximum rainfall and consecutive 2-, 3-, 4-, 5- and 6-day maximum rainfall series of Tiruchirapalli. To be reliable, the forecasted maximum rainfalls for the selected return periods are evaluated in comparison with the results of the plotting position.

Probabilistic self-organizing maps for continuous data.

PubMed

Lopez-Rubio, Ezequiel

2010-10-01

The original self-organizing feature map did not define any probability distribution on the input space. However, the advantages of introducing probabilistic methodologies into self-organizing map models were soon evident. This has led to a wide range of proposals which reflect the current emergence of probabilistic approaches to computational intelligence. The underlying estimation theories behind them derive from two main lines of thought: the expectation maximization methodology and stochastic approximation methods. Here, we present a comprehensive view of the state of the art, with a unifying perspective of the involved theoretical frameworks. In particular, we examine the most commonly used continuous probability distributions, self-organization mechanisms, and learning schemes. Special emphasis is given to the connections among them and their relative advantages depending on the characteristics of the problem at hand. Furthermore, we evaluate their performance in two typical applications of self-organizing maps: classification and visualization.

THE DISTRIBUTION OF ROUNDS FIRED IN STOCHASTIC DUELS

DTIC Science & Technology

This paper continues the development of the theory of Stochastic Duels to include the distribution of the number of rounds fired. Most generally...the duel between two contestants who fire at each other with constant kill probabilities per round is considered. The time between rounds fired may be...at the beginning of the duel may be limited and is a discrete random variable. Besides the distribution of rounds fired, its first two moments and

A Novel Multiobjective Evolutionary Algorithm Based on Regression Analysis

PubMed Central

Song, Zhiming; Wang, Maocai; Dai, Guangming; Vasile, Massimiliano

2015-01-01

As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m − 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m − 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper. PMID:25874246

Metabolic networks evolve towards states of maximum entropy production.

PubMed

Unrean, Pornkamol; Srienc, Friedrich

2011-11-01

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles. Copyright © 2011 Elsevier Inc. All rights reserved.

Survey and Introduction to Modern Martingale Theory (Stopping Times, Semi-Martingales and Stochastic Integration)

DTIC Science & Technology

1986-10-01

35 ~- 2.3.12. Remark: Let X. Y be the processes given in the example :after Lemma 2.3.3. Take the same probability space as in that example and...z(s) =zjO) + ’ A zis).1als) + ’~ zsMs 0O<s<t 0O<s<t 0<~ Fix n>1I; then if s Is a point of increase of a, (that is. if Aa(s)=Al). then ri(s) = q(s...Absolute Continuity and Singularity of Locally Absolutely Continuous Probability Distributions. I. Math USSR Sbornik Vol. 35 , No 5, 631-680. Kabanov

Robustness of quantum key distribution with discrete and continuous variables to channel noise

NASA Astrophysics Data System (ADS)

Lasota, Mikołaj; Filip, Radim; Usenko, Vladyslav C.

2017-06-01

We study the robustness of quantum key distribution protocols using discrete or continuous variables to the channel noise. We introduce the model of such noise based on coupling of the signal to a thermal reservoir, typical for continuous-variable quantum key distribution, to the discrete-variable case. Then we perform a comparison of the bounds on the tolerable channel noise between these two kinds of protocols using the same noise parametrization, in the case of implementation which is perfect otherwise. Obtained results show that continuous-variable protocols can exhibit similar robustness to the channel noise when the transmittance of the channel is relatively high. However, for strong loss discrete-variable protocols are superior and can overcome even the infinite-squeezing continuous-variable protocol while using limited nonclassical resources. The requirement on the probability of a single-photon production which would have to be fulfilled by a practical source of photons in order to demonstrate such superiority is feasible thanks to the recent rapid development in this field.

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

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.

Quantifying Mixed Uncertainties in Cyber Attacker Payoffs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatterjee, Samrat; Halappanavar, Mahantesh; Tipireddy, Ramakrishna

Representation and propagation of uncertainty in cyber attacker payoffs is a key aspect of security games. Past research has primarily focused on representing the defender’s beliefs about attacker payoffs as point utility estimates. More recently, within the physical security domain, attacker payoff uncertainties have been represented as Uniform and Gaussian probability distributions, and intervals. Within cyber-settings, continuous probability distributions may still be appropriate for addressing statistical (aleatory) uncertainties where the defender may assume that the attacker’s payoffs differ over time. However, systematic (epistemic) uncertainties may exist, where the defender may not have sufficient knowledge or there is insufficient information aboutmore » the attacker’s payoff generation mechanism. Such epistemic uncertainties are more suitably represented as probability boxes with intervals. In this study, we explore the mathematical treatment of such mixed payoff uncertainties.« less

High throughput nonparametric probability density estimation.

PubMed

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.

High throughput nonparametric probability density estimation

PubMed Central

Farmer, Jenny

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. PMID:29750803

Empirical likelihood-based confidence intervals for the sensitivity of a continuous-scale diagnostic test at a fixed level of specificity.

PubMed

Gengsheng Qin; Davis, Angela E; Jing, Bing-Yi

2011-06-01

For a continuous-scale diagnostic test, it is often of interest to find the range of the sensitivity of the test at the cut-off that yields a desired specificity. In this article, we first define a profile empirical likelihood ratio for the sensitivity of a continuous-scale diagnostic test and show that its limiting distribution is a scaled chi-square distribution. We then propose two new empirical likelihood-based confidence intervals for the sensitivity of the test at a fixed level of specificity by using the scaled chi-square distribution. Simulation studies are conducted to compare the finite sample performance of the newly proposed intervals with the existing intervals for the sensitivity in terms of coverage probability. A real example is used to illustrate the application of the recommended methods.

Optimal nonlinear filtering using the finite-volume method

NASA Astrophysics Data System (ADS)

Fox, Colin; Morrison, Malcolm E. K.; Norton, Richard A.; Molteno, Timothy C. A.

2018-01-01

Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.

Determining probability distribution of coherent integration time near 133 Hz and 1346 km in the Pacific Ocean.

PubMed

Spiesberger, John L

2013-02-01

The hypothesis tested is that internal gravity waves limit the coherent integration time of sound at 1346 km in the Pacific ocean at 133 Hz and a pulse resolution of 0.06 s. Six months of continuous transmissions at about 18 min intervals are examined. The source and receiver are mounted on the bottom of the ocean with timing governed by atomic clocks. Measured variability is only due to fluctuations in the ocean. A model for the propagation of sound through fluctuating internal waves is run without any tuning with data. Excellent resemblance is found between the model and data's probability distributions of integration time up to five hours.

Detection of anomalous events

DOEpatents

Ferragut, Erik M.; Laska, Jason A.; Bridges, Robert A.

2016-06-07

A system is described for receiving a stream of events and scoring the events based on anomalousness and maliciousness (or other classification). The system can include a plurality of anomaly detectors that together implement an algorithm to identify low-probability events and detect atypical traffic patterns. The anomaly detector provides for comparability of disparate sources of data (e.g., network flow data and firewall logs.) Additionally, the anomaly detector allows for regulatability, meaning that the algorithm can be user configurable to adjust a number of false alerts. The anomaly detector can be used for a variety of probability density functions, including normal Gaussian distributions, irregular distributions, as well as functions associated with continuous or discrete variables.

Ages of Records in Random Walks

NASA Astrophysics Data System (ADS)

Szabó, Réka; Vető, Bálint

2016-12-01

We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for k=1,2,ldots and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

On Probability Domains IV

NASA Astrophysics Data System (ADS)

Frič, Roman; Papčo, Martin

2017-12-01

Stressing a categorical approach, we continue our study of fuzzified domains of probability, in which classical random events are replaced by measurable fuzzy random events. In operational probability theory (S. Bugajski) classical random variables are replaced by statistical maps (generalized distribution maps induced by random variables) and in fuzzy probability theory (S. Gudder) the central role is played by observables (maps between probability domains). We show that to each of the two generalized probability theories there corresponds a suitable category and the two resulting categories are dually equivalent. Statistical maps and observables become morphisms. A statistical map can send a degenerated (pure) state to a non-degenerated one —a quantum phenomenon and, dually, an observable can map a crisp random event to a genuine fuzzy random event —a fuzzy phenomenon. The dual equivalence means that the operational probability theory and the fuzzy probability theory coincide and the resulting generalized probability theory has two dual aspects: quantum and fuzzy. We close with some notes on products and coproducts in the dual categories.

Probability elicitation to inform early health economic evaluations of new medical technologies: a case study in heart failure disease management.

PubMed

Cao, Qi; Postmus, Douwe; Hillege, Hans L; Buskens, Erik

2013-06-01

Early estimates of the commercial headroom available to a new medical device can assist producers of health technology in making appropriate product investment decisions. The purpose of this study was to illustrate how this quantity can be captured probabilistically by combining probability elicitation with early health economic modeling. The technology considered was a novel point-of-care testing device in heart failure disease management. First, we developed a continuous-time Markov model to represent the patients' disease progression under the current care setting. Next, we identified the model parameters that are likely to change after the introduction of the new device and interviewed three cardiologists to capture the probability distributions of these parameters. Finally, we obtained the probability distribution of the commercial headroom available per measurement by propagating the uncertainty in the model inputs to uncertainty in modeled outcomes. For a willingness-to-pay value of €10,000 per life-year, the median headroom available per measurement was €1.64 (interquartile range €0.05-€3.16) when the measurement frequency was assumed to be daily. In the subsequently conducted sensitivity analysis, this median value increased to a maximum of €57.70 for different combinations of the willingness-to-pay threshold and the measurement frequency. Probability elicitation can successfully be combined with early health economic modeling to obtain the probability distribution of the headroom available to a new medical technology. Subsequently feeding this distribution into a product investment evaluation method enables stakeholders to make more informed decisions regarding to which markets a currently available product prototype should be targeted. Copyright © 2013. Published by Elsevier Inc.

Geotechnical parameter spatial distribution stochastic analysis based on multi-precision information assimilation

NASA Astrophysics Data System (ADS)

Wang, C.; Rubin, Y.

2014-12-01

Spatial distribution of important geotechnical parameter named compression modulus Es contributes considerably to the understanding of the underlying geological processes and the adequate assessment of the Es mechanics effects for differential settlement of large continuous structure foundation. These analyses should be derived using an assimilating approach that combines in-situ static cone penetration test (CPT) with borehole experiments. To achieve such a task, the Es distribution of stratum of silty clay in region A of China Expo Center (Shanghai) is studied using the Bayesian-maximum entropy method. This method integrates rigorously and efficiently multi-precision of different geotechnical investigations and sources of uncertainty. Single CPT samplings were modeled as a rational probability density curve by maximum entropy theory. Spatial prior multivariate probability density function (PDF) and likelihood PDF of the CPT positions were built by borehole experiments and the potential value of the prediction point, then, preceding numerical integration on the CPT probability density curves, the posterior probability density curve of the prediction point would be calculated by the Bayesian reverse interpolation framework. The results were compared between Gaussian Sequential Stochastic Simulation and Bayesian methods. The differences were also discussed between single CPT samplings of normal distribution and simulated probability density curve based on maximum entropy theory. It is shown that the study of Es spatial distributions can be improved by properly incorporating CPT sampling variation into interpolation process, whereas more informative estimations are generated by considering CPT Uncertainty for the estimation points. Calculation illustrates the significance of stochastic Es characterization in a stratum, and identifies limitations associated with inadequate geostatistical interpolation techniques. This characterization results will provide a multi-precision information assimilation method of other geotechnical parameters.

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

A matrix contraction process

NASA Astrophysics Data System (ADS)

Wilkinson, Michael; Grant, John

2018-03-01

We consider a stochastic process in which independent identically distributed random matrices are multiplied and where the Lyapunov exponent of the product is positive. We continue multiplying the random matrices as long as the norm, ɛ, of the product is less than unity. If the norm is greater than unity we reset the matrix to a multiple of the identity and then continue the multiplication. We address the problem of determining the probability density function of the norm, \

Processor tradeoffs in distributed real-time systems

NASA Technical Reports Server (NTRS)

Krishna, C. M.; Shin, Kang G.; Bhandari, Inderpal S.

1987-01-01

The problem of the optimization of the design of real-time distributed systems is examined with reference to a class of computer architectures similar to the continuously reconfigurable multiprocessor flight control system structure, CM2FCS. Particular attention is given to the impact of processor replacement and the burn-in time on the probability of dynamic failure and mean cost. The solution is obtained numerically and interpreted in the context of real-time applications.

Some New Approaches to Multivariate Probability Distributions.

DTIC Science & Technology

1986-12-01

Krishnaiah (1977). The following example may serve as an illustration of this point. EXAMPLE 2. (Fre^*chet’s bivariate continuous distribution...the error in the theorem of "" Prakasa Rao (1974) and to Dr. P.R. Krishnaiah for his valuable comments on the initial draft, his monumental patience and...M. and Proschan, F. (1984). Nonparametric Concepts and Methods in Reliability, Handbook of Statistics, 4, 613-655, (eds. P.R. Krishnaiah and P.K

The utility of Bayesian predictive probabilities for interim monitoring of clinical trials

PubMed Central

Connor, Jason T.; Ayers, Gregory D; Alvarez, JoAnn

2014-01-01

Background Bayesian predictive probabilities can be used for interim monitoring of clinical trials to estimate the probability of observing a statistically significant treatment effect if the trial were to continue to its predefined maximum sample size. Purpose We explore settings in which Bayesian predictive probabilities are advantageous for interim monitoring compared to Bayesian posterior probabilities, p-values, conditional power, or group sequential methods. Results For interim analyses that address prediction hypotheses, such as futility monitoring and efficacy monitoring with lagged outcomes, only predictive probabilities properly account for the amount of data remaining to be observed in a clinical trial and have the flexibility to incorporate additional information via auxiliary variables. Limitations Computational burdens limit the feasibility of predictive probabilities in many clinical trial settings. The specification of prior distributions brings additional challenges for regulatory approval. Conclusions The use of Bayesian predictive probabilities enables the choice of logical interim stopping rules that closely align with the clinical decision making process. PMID:24872363

Combining Probability Distributions of Wind Waves and Sea Level Variations to Assess Return Periods of Coastal Floods

NASA Astrophysics Data System (ADS)

Leijala, U.; Bjorkqvist, J. V.; Pellikka, H.; Johansson, M. M.; Kahma, K. K.

2017-12-01

Predicting the behaviour of the joint effect of sea level and wind waves is of great significance due to the major impact of flooding events in densely populated coastal regions. As mean sea level rises, the effect of sea level variations accompanied by the waves will be even more harmful in the future. The main challenge when evaluating the effect of waves and sea level variations is that long time series of both variables rarely exist. Wave statistics are also highly location-dependent, thus requiring wave buoy measurements and/or high-resolution wave modelling. As an initial approximation of the joint effect, the variables may be treated as independent random variables, to achieve the probability distribution of their sum. We present results of a case study based on three probability distributions: 1) wave run-up constructed from individual wave buoy measurements, 2) short-term sea level variability based on tide gauge data, and 3) mean sea level projections based on up-to-date regional scenarios. The wave measurements were conducted during 2012-2014 on the coast of city of Helsinki located in the Gulf of Finland in the Baltic Sea. The short-term sea level distribution contains the last 30 years (1986-2015) of hourly data from Helsinki tide gauge, and the mean sea level projections are scenarios adjusted for the Gulf of Finland. Additionally, we present a sensitivity test based on six different theoretical wave height distributions representing different wave behaviour in relation to sea level variations. As these wave distributions are merged with one common sea level distribution, we can study how the different shapes of the wave height distribution affect the distribution of the sum, and which one of the components is dominating under different wave conditions. As an outcome of the method, we obtain a probability distribution of the maximum elevation of the continuous water mass, which enables a flexible tool for evaluating different risk levels in the current and future climate.

21 CFR 810.10 - Cease distribution and notification order.

Code of Federal Regulations, 2010 CFR

2010-04-01

... (CONTINUED) MEDICAL DEVICES MEDICAL DEVICE RECALL AUTHORITY Mandatory Medical Device Recall Procedures § 810... usual name of the device; (iii) The model, catalog, or product code numbers of the device; and (iv) The... opportunity to consult with the agency, FDA finds that there is a reasonable probability that a device...

21 CFR 810.10 - Cease distribution and notification order.

Code of Federal Regulations, 2011 CFR

2011-04-01

... (CONTINUED) MEDICAL DEVICES MEDICAL DEVICE RECALL AUTHORITY Mandatory Medical Device Recall Procedures § 810... usual name of the device; (iii) The model, catalog, or product code numbers of the device; and (iv) The... opportunity to consult with the agency, FDA finds that there is a reasonable probability that a device...

Modeling evaporation of Jet A, JP-7 and RP-1 drops at 1 to 15 bars

NASA Technical Reports Server (NTRS)

Harstad, K.; Bellan, J.

2003-01-01

A model describing the evaportion of an isolated drop of a multicomponent fuel containing hundreds of species has been developed. The model is based on Continuous Thermodynamics concepts wherein the composition of a fuel is statistically described using a Probability Distribution Function (PDF).

Stochastic transfer of polarized radiation in finite cloudy atmospheric media with reflective boundaries

NASA Astrophysics Data System (ADS)

Sallah, M.

2014-03-01

The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.

Joint analysis of air pollution in street canyons in St. Petersburg and Copenhagen

NASA Astrophysics Data System (ADS)

Genikhovich, E. L.; Ziv, A. D.; Iakovleva, E. A.; Palmgren, F.; Berkowicz, R.

The bi-annual data set of concentrations of several traffic-related air pollutants, measured continuously in street canyons in St. Petersburg and Copenhagen, is analysed jointly using different statistical techniques. Annual mean concentrations of NO 2, NO x and, especially, benzene are found systematically higher in St. Petersburg than in Copenhagen but for ozone the situation is opposite. In both cities probability distribution functions (PDFs) of concentrations and their daily or weekly extrema are fitted with the Weibull and double exponential distributions, respectively. Sample estimates of bi-variate distributions of concentrations, concentration roses, and probabilities of concentration of one pollutant being extreme given that another one reaches its extremum are presented in this paper as well as auto- and co-spectra. It is demonstrated that there is a reasonably high correlation between seasonally averaged concentrations of pollutants in St. Petersburg and Copenhagen.

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

NASA Astrophysics Data System (ADS)

Zhang, Hong; Li, Guo-Hua

2016-11-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).

A study of the application of power-spectral methods of generalized harmonic analysis to gust loads on airplanes

NASA Technical Reports Server (NTRS)

Press, Harry; Mazelsky, Bernard

1954-01-01

The applicability of some results from the theory of generalized harmonic analysis (or power-spectral analysis) to the analysis of gust loads on airplanes in continuous rough air is examined. The general relations for linear systems between power spectrums of a random input disturbance and an output response are used to relate the spectrum of airplane load in rough air to the spectrum of atmospheric gust velocity. The power spectrum of loads is shown to provide a measure of the load intensity in terms of the standard deviation (root mean square) of the load distribution for an airplane in flight through continuous rough air. For the case of a load output having a normal distribution, which appears from experimental evidence to apply to homogeneous rough air, the standard deviation is shown to describe the probability distribution of loads or the proportion of total time that the load has given values. Thus, for airplane in flight through homogeneous rough air, the probability distribution of loads may be determined from a power-spectral analysis. In order to illustrate the application of power-spectral analysis to gust-load analysis and to obtain an insight into the relations between loads and airplane gust-response characteristics, two selected series of calculations are presented. The results indicate that both methods of analysis yield results that are consistent to a first approximation.

Exploration properties of biased evanescent random walkers on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

We investigate the combined effects of bias and evanescence on the characteristics of random walks on a one-dimensional lattice. We calculate the time-dependent return probability, eventual return probability, conditional mean return time, and the time-dependent mean number of visited sites of biased immortal and evanescent discrete-time random walkers on a one-dimensional lattice. We then extend the calculations to the case of a continuous-time step-coupled biased evanescent random walk on a one-dimensional lattice with an exponential waiting time distribution.

A Comparative Study of Probability Collectives Based Multi-agent Systems and Genetic Algorithms

NASA Technical Reports Server (NTRS)

Huang, Chien-Feng; Wolpert, David H.; Bieniawski, Stefan; Strauss, Charles E. M.

2005-01-01

We compare Genetic Algorithms (GA's) with Probability Collectives (PC), a new framework for distributed optimization and control. In contrast to GA's, PC-based methods do not update populations of solutions. Instead they update an explicitly parameterized probability distribution p over the space of solutions. That updating of p arises as the optimization of a functional of p. The functional is chosen so that any p that optimizes it should be p peaked about good solutions. The PC approach works in both continuous and discrete problems. It does not suffer from the resolution limitation of the finite bit length encoding of parameters into GA alleles. It also has deep connections with both game theory and statistical physics. We review the PC approach using its motivation as the information theoretic formulation of bounded rationality for multi-agent systems. It is then compared with GA's on a diverse set of problems. To handle high dimensional surfaces, in the PC method investigated here p is restricted to a product distribution. Each distribution in that product is controlled by a separate agent. The test functions were selected for their difficulty using either traditional gradient descent or genetic algorithms. On those functions the PC-based approach significantly outperforms traditional GA's in both rate of descent, trapping in false minima, and long term optimization.

Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics with Level Set Transformation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hammond, Glenn Edward; Song, Xuehang; Ye, Ming

A new approach is developed to delineate the spatial distribution of discrete facies (geological units that have unique distributions of hydraulic, physical, and/or chemical properties) conditioned not only on direct data (measurements directly related to facies properties, e.g., grain size distribution obtained from borehole samples) but also on indirect data (observations indirectly related to facies distribution, e.g., hydraulic head and tracer concentration). Our method integrates for the first time ensemble data assimilation with traditional transition probability-based geostatistics. The concept of level set is introduced to build shape parameterization that allows transformation between discrete facies indicators and continuous random variables. Themore » spatial structure of different facies is simulated by indicator models using conditioning points selected adaptively during the iterative process of data assimilation. To evaluate the new method, a two-dimensional semi-synthetic example is designed to estimate the spatial distribution and permeability of two distinct facies from transient head data induced by pumping tests. The example demonstrates that our new method adequately captures the spatial pattern of facies distribution by imposing spatial continuity through conditioning points. The new method also reproduces the overall response in hydraulic head field with better accuracy compared to data assimilation with no constraints on spatial continuity on facies.« less

Bayesian probability of success for clinical trials using historical data

PubMed Central

Ibrahim, Joseph G.; Chen, Ming-Hui; Lakshminarayanan, Mani; Liu, Guanghan F.; Heyse, Joseph F.

2015-01-01

Developing sophisticated statistical methods for go/no-go decisions is crucial for clinical trials, as planning phase III or phase IV trials is costly and time consuming. In this paper, we develop a novel Bayesian methodology for determining the probability of success of a treatment regimen on the basis of the current data of a given trial. We introduce a new criterion for calculating the probability of success that allows for inclusion of covariates as well as allowing for historical data based on the treatment regimen, and patient characteristics. A new class of prior distributions and covariate distributions is developed to achieve this goal. The methodology is quite general and can be used with univariate or multivariate continuous or discrete data, and it generalizes Chuang-Stein’s work. This methodology will be invaluable for informing the scientist on the likelihood of success of the compound, while including the information of covariates for patient characteristics in the trial population for planning future pre-market or post-market trials. PMID:25339499

Bayesian probability of success for clinical trials using historical data.

PubMed

Ibrahim, Joseph G; Chen, Ming-Hui; Lakshminarayanan, Mani; Liu, Guanghan F; Heyse, Joseph F

2015-01-30

Developing sophisticated statistical methods for go/no-go decisions is crucial for clinical trials, as planning phase III or phase IV trials is costly and time consuming. In this paper, we develop a novel Bayesian methodology for determining the probability of success of a treatment regimen on the basis of the current data of a given trial. We introduce a new criterion for calculating the probability of success that allows for inclusion of covariates as well as allowing for historical data based on the treatment regimen, and patient characteristics. A new class of prior distributions and covariate distributions is developed to achieve this goal. The methodology is quite general and can be used with univariate or multivariate continuous or discrete data, and it generalizes Chuang-Stein's work. This methodology will be invaluable for informing the scientist on the likelihood of success of the compound, while including the information of covariates for patient characteristics in the trial population for planning future pre-market or post-market trials. Copyright © 2014 John Wiley & Sons, Ltd.

Fingerprint Recognition with Identical Twin Fingerprints

PubMed Central

Yang, Xin; Tian, Jie

2012-01-01

Fingerprint recognition with identical twins is a challenging task due to the closest genetics-based relationship existing in the identical twins. Several pioneers have analyzed the similarity between twins' fingerprints. In this work we continue to investigate the topic of the similarity of identical twin fingerprints. Our study was tested based on a large identical twin fingerprint database that contains 83 twin pairs, 4 fingers per individual and six impressions per finger: 3984 (83*2*4*6) images. Compared to the previous work, our contributions are summarized as follows: (1) Two state-of-the-art fingerprint identification methods: P071 and VeriFinger 6.1 were used, rather than one fingerprint identification method in previous studies. (2) Six impressions per finger were captured, rather than just one impression, which makes the genuine distribution of matching scores more realistic. (3) A larger sample (83 pairs) was collected. (4) A novel statistical analysis, which aims at showing the probability distribution of the fingerprint types for the corresponding fingers of identical twins which have same fingerprint type, has been conducted. (5) A novel analysis, which aims at showing which finger from identical twins has higher probability of having same fingerprint type, has been conducted. Our results showed that: (a) A state-of-the-art automatic fingerprint verification system can distinguish identical twins without drastic degradation in performance. (b) The chance that the fingerprints have the same type from identical twins is 0.7440, comparing to 0.3215 from non-identical twins. (c) For the corresponding fingers of identical twins which have same fingerprint type, the probability distribution of five major fingerprint types is similar to the probability distribution for all the fingers' fingerprint type. (d) For each of four fingers of identical twins, the probability of having same fingerprint type is similar. PMID:22558204

Fingerprint recognition with identical twin fingerprints.

PubMed

Tao, Xunqiang; Chen, Xinjian; Yang, Xin; Tian, Jie

2012-01-01

Fingerprint recognition with identical twins is a challenging task due to the closest genetics-based relationship existing in the identical twins. Several pioneers have analyzed the similarity between twins' fingerprints. In this work we continue to investigate the topic of the similarity of identical twin fingerprints. Our study was tested based on a large identical twin fingerprint database that contains 83 twin pairs, 4 fingers per individual and six impressions per finger: 3984 (83*2*4*6) images. Compared to the previous work, our contributions are summarized as follows: (1) Two state-of-the-art fingerprint identification methods: P071 and VeriFinger 6.1 were used, rather than one fingerprint identification method in previous studies. (2) Six impressions per finger were captured, rather than just one impression, which makes the genuine distribution of matching scores more realistic. (3) A larger sample (83 pairs) was collected. (4) A novel statistical analysis, which aims at showing the probability distribution of the fingerprint types for the corresponding fingers of identical twins which have same fingerprint type, has been conducted. (5) A novel analysis, which aims at showing which finger from identical twins has higher probability of having same fingerprint type, has been conducted. Our results showed that: (a) A state-of-the-art automatic fingerprint verification system can distinguish identical twins without drastic degradation in performance. (b) The chance that the fingerprints have the same type from identical twins is 0.7440, comparing to 0.3215 from non-identical twins. (c) For the corresponding fingers of identical twins which have same fingerprint type, the probability distribution of five major fingerprint types is similar to the probability distribution for all the fingers' fingerprint type. (d) For each of four fingers of identical twins, the probability of having same fingerprint type is similar.

Bayesian functional integral method for inferring continuous data from discrete measurements.

PubMed

Heuett, William J; Miller, Bernard V; Racette, Susan B; Holloszy, John O; Chow, Carson C; Periwal, Vipul

2012-02-08

Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Role of conviction in nonequilibrium models of opinion formation

NASA Astrophysics Data System (ADS)

Crokidakis, Nuno; Anteneodo, Celia

2012-12-01

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value (±1 or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability p (1-p), a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a nonequilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point pc that depends on the distribution of the convictions, with the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).

Multi-objective possibilistic model for portfolio selection with transaction cost

NASA Astrophysics Data System (ADS)

Jana, P.; Roy, T. K.; Mazumder, S. K.

2009-06-01

In this paper, we introduce the possibilistic mean value and variance of continuous distribution, rather than probability distributions. We propose a multi-objective Portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation. For quantifying any potential return and risk, portfolio liquidity is taken into account and a multi-objective non-linear programming model for portfolio rebalancing with transaction cost is proposed. The models are illustrated with numerical examples.

Eliciting Subjective Probability Distributions on Continuous Variables

DTIC Science & Technology

1975-08-01

problems. Its stall memhers inclu.lc la.ultv an.! gn^M stiiilents liom many ot the Departments ami Schools ol the University. SSRI’s research activities...Mipporre.l in pa’t liom Iniversity tunds anil in part by \\arious ipamm ranee liom c\\tmiiel\\ basic to relatively applied. Most SSK1 i-rojects mix both

Pseudochemotaxis in inhomogeneous active Brownian systems

NASA Astrophysics Data System (ADS)

Vuijk, Hidde D.; Sharma, Abhinav; Mondal, Debasish; Sommer, Jens-Uwe; Merlitz, Holger

2018-04-01

We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active system. Moreover, for a continuously distributed profile, the activity gradient results in a drift of active particle up the gradient bearing resemblance to chemotaxis. Integrating out the orientational degrees of freedom, we derive an approximate Fokker-Planck equation and show that the theoretical predictions are in very good agreement with the Brownian dynamics simulations.

Quantum Theory of Wormholes

NASA Astrophysics Data System (ADS)

González-Díaz, Pedro F.

We re-explore the effects of multiply-connected wormholes on ordinary matter at low energies. It is obtained that the path integral that describes these effects is given in terms of a Planckian probability distribution for the Coleman α-parameters, rather than a classical Gaussian distribution law. This implies that the path integral over all low-energy fields with the wormhole effective interactions can no longer vary continuously, and that the quantities α2 are interpretable as the momenta of a quantum field. Using the new result that, rather than being given in terms of the Coleman-Hawking probability, the Euclidean action must equal negative entropy, the model predicts a very small but still nonzero cosmological constant and quite reasonable values for the pion and neutrino masses. The divergence problems of Euclidean quantum gravity are also discussed in the light of the above results.

Spatial estimation from remotely sensed data via empirical Bayes models

NASA Technical Reports Server (NTRS)

Hill, J. R.; Hinkley, D. V.; Kostal, H.; Morris, C. N.

1984-01-01

Multichannel satellite image data, available as LANDSAT imagery, are recorded as a multivariate time series (four channels, multiple passovers) in two spatial dimensions. The application of parametric empirical Bayes theory to classification of, and estimating the probability of, each crop type at each of a large number of pixels is considered. This theory involves both the probability distribution of imagery data, conditional on crop types, and the prior spatial distribution of crop types. For the latter Markov models indexed by estimable parameters are used. A broad outline of the general theory reveals several questions for further research. Some detailed results are given for the special case of two crop types when only a line transect is analyzed. Finally, the estimation of an underlying continuous process on the lattice is discussed which would be applicable to such quantities as crop yield.

Application of Bayesian Reliability Concepts to Cruise Missile Electronic Components

DTIC Science & Technology

1989-09-01

and contrast them with the more prevalent classical inference view. 3 II. literature Review Introduction This literature review will consider current ...events on the basis of whatever evidence is currently available. Then if additional evidence is subsequently obtained, the initial probabilities are...Chay contends there is no longer any need to approximate continuous prior distributions through discretization because current computer calculations

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

César Mansur Filho, Júlio; Dickman, Ronald

2011-05-01

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32 000 sites. The resulting estimates for critical exponents β, \\beta /\

Multi-hazard Assessment and Scenario Toolbox (MhAST): A Framework for Analyzing Compounding Effects of Multiple Hazards

NASA Astrophysics Data System (ADS)

Sadegh, M.; Moftakhari, H.; AghaKouchak, A.

2017-12-01

Many natural hazards are driven by multiple forcing variables, and concurrence/consecutive extreme events significantly increases risk of infrastructure/system failure. It is a common practice to use univariate analysis based upon a perceived ruling driver to estimate design quantiles and/or return periods of extreme events. A multivariate analysis, however, permits modeling simultaneous occurrence of multiple forcing variables. In this presentation, we introduce the Multi-hazard Assessment and Scenario Toolbox (MhAST) that comprehensively analyzes marginal and joint probability distributions of natural hazards. MhAST also offers a wide range of scenarios of return period and design levels and their likelihoods. Contribution of this study is four-fold: 1. comprehensive analysis of marginal and joint probability of multiple drivers through 17 continuous distributions and 26 copulas, 2. multiple scenario analysis of concurrent extremes based upon the most likely joint occurrence, one ruling variable, and weighted random sampling of joint occurrences with similar exceedance probabilities, 3. weighted average scenario analysis based on a expected event, and 4. uncertainty analysis of the most likely joint occurrence scenario using a Bayesian framework.

Examining Spillovers between Long and Short Repeated Prisoner's Dilemma Games Played in the Laboratory.

PubMed

Arechar, Antonio A; Kouchaki, Maryam; Rand, David G

2018-03-01

We had participants play two sets of repeated Prisoner's Dilemma (RPD) games, one with a large continuation probability and the other with a small continuation probability, as well as Dictator Games (DGs) before and after the RPDs. We find that, regardless of which is RPD set is played first, participants typically cooperate when the continuation probability is large and defect when the continuation probability is small. However, there is an asymmetry in behavior when transitioning from one continuation probability to the other. When switching from large to small, transient higher levels of cooperation are observed in the early games of the small continuation set. Conversely, when switching from small to large, cooperation is immediately high in the first game of the large continuation set. We also observe that response times increase when transitioning between sets of RPDs, except for altruistic participants transitioning into the set of RPDs with long continuation probabilities. These asymmetries suggest a bias in favor of cooperation. Finally, we examine the link between altruism and RPD play. We find that small continuation probability RPD play is correlated with giving in DGs played before and after the RPDs, whereas high continuation probability RPD play is not.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

a Probability-Based Statistical Method to Extract Water Body of TM Images with Missing Information

NASA Astrophysics Data System (ADS)

Lian, Shizhong; Chen, Jiangping; Luo, Minghai

2016-06-01

Water information cannot be accurately extracted using TM images because true information is lost in some images because of blocking clouds and missing data stripes, thereby water information cannot be accurately extracted. Water is continuously distributed in natural conditions; thus, this paper proposed a new method of water body extraction based on probability statistics to improve the accuracy of water information extraction of TM images with missing information. Different disturbing information of clouds and missing data stripes are simulated. Water information is extracted using global histogram matching, local histogram matching, and the probability-based statistical method in the simulated images. Experiments show that smaller Areal Error and higher Boundary Recall can be obtained using this method compared with the conventional methods.

Performance of toxicity probability interval based designs in contrast to the continual reassessment method

PubMed Central

Horton, Bethany Jablonski; Wages, Nolan A.; Conaway, Mark R.

2016-01-01

Toxicity probability interval designs have received increasing attention as a dose-finding method in recent years. In this study, we compared the two-stage, likelihood-based continual reassessment method (CRM), modified toxicity probability interval (mTPI), and the Bayesian optimal interval design (BOIN) in order to evaluate each method's performance in dose selection for Phase I trials. We use several summary measures to compare the performance of these methods, including percentage of correct selection (PCS) of the true maximum tolerable dose (MTD), allocation of patients to doses at and around the true MTD, and an accuracy index. This index is an efficiency measure that describes the entire distribution of MTD selection and patient allocation by taking into account the distance between the true probability of toxicity at each dose level and the target toxicity rate. The simulation study considered a broad range of toxicity curves and various sample sizes. When considering PCS, we found that CRM outperformed the two competing methods in most scenarios, followed by BOIN, then mTPI. We observed a similar trend when considering the accuracy index for dose allocation, where CRM most often outperformed both the mTPI and BOIN. These trends were more pronounced with increasing number of dose levels. PMID:27435150

On the use of posterior predictive probabilities and prediction uncertainty to tailor informative sampling for parasitological surveillance in livestock.

PubMed

Musella, Vincenzo; Rinaldi, Laura; Lagazio, Corrado; Cringoli, Giuseppe; Biggeri, Annibale; Catelan, Dolores

2014-09-15

Model-based geostatistics and Bayesian approaches are appropriate in the context of Veterinary Epidemiology when point data have been collected by valid study designs. The aim is to predict a continuous infection risk surface. Little work has been done on the use of predictive infection probabilities at farm unit level. In this paper we show how to use predictive infection probability and related uncertainty from a Bayesian kriging model to draw a informative samples from the 8794 geo-referenced sheep farms of the Campania region (southern Italy). Parasitological data come from a first cross-sectional survey carried out to study the spatial distribution of selected helminths in sheep farms. A grid sampling was performed to select the farms for coprological examinations. Faecal samples were collected for 121 sheep farms and the presence of 21 different helminths were investigated using the FLOTAC technique. The 21 responses are very different in terms of geographical distribution and prevalence of infection. The observed prevalence range is from 0.83% to 96.69%. The distributions of the posterior predictive probabilities for all the 21 parasites are very heterogeneous. We show how the results of the Bayesian kriging model can be used to plan a second wave survey. Several alternatives can be chosen depending on the purposes of the second survey: weight by posterior predictive probabilities, their uncertainty or combining both information. The proposed Bayesian kriging model is simple, and the proposed samping strategy represents a useful tool to address targeted infection control treatments and surbveillance campaigns. It is easily extendable to other fields of research. Copyright © 2014 Elsevier B.V. All rights reserved.

Examining Spillovers between Long and Short Repeated Prisoner’s Dilemma Games Played in the Laboratory

PubMed Central

Arechar, Antonio A.; Kouchaki, Maryam; Rand, David G.

2018-01-01

We had participants play two sets of repeated Prisoner’s Dilemma (RPD) games, one with a large continuation probability and the other with a small continuation probability, as well as Dictator Games (DGs) before and after the RPDs. We find that, regardless of which is RPD set is played first, participants typically cooperate when the continuation probability is large and defect when the continuation probability is small. However, there is an asymmetry in behavior when transitioning from one continuation probability to the other. When switching from large to small, transient higher levels of cooperation are observed in the early games of the small continuation set. Conversely, when switching from small to large, cooperation is immediately high in the first game of the large continuation set. We also observe that response times increase when transitioning between sets of RPDs, except for altruistic participants transitioning into the set of RPDs with long continuation probabilities. These asymmetries suggest a bias in favor of cooperation. Finally, we examine the link between altruism and RPD play. We find that small continuation probability RPD play is correlated with giving in DGs played before and after the RPDs, whereas high continuation probability RPD play is not. PMID:29809199

Metocean design parameter estimation for fixed platform based on copula functions

NASA Astrophysics Data System (ADS)

Zhai, Jinjin; Yin, Qilin; Dong, Sheng

2017-08-01

Considering the dependent relationship among wave height, wind speed, and current velocity, we construct novel trivariate joint probability distributions via Archimedean copula functions. Total 30-year data of wave height, wind speed, and current velocity in the Bohai Sea are hindcast and sampled for case study. Four kinds of distributions, namely, Gumbel distribution, lognormal distribution, Weibull distribution, and Pearson Type III distribution, are candidate models for marginal distributions of wave height, wind speed, and current velocity. The Pearson Type III distribution is selected as the optimal model. Bivariate and trivariate probability distributions of these environmental conditions are established based on four bivariate and trivariate Archimedean copulas, namely, Clayton, Frank, Gumbel-Hougaard, and Ali-Mikhail-Haq copulas. These joint probability models can maximize marginal information and the dependence among the three variables. The design return values of these three variables can be obtained by three methods: univariate probability, conditional probability, and joint probability. The joint return periods of different load combinations are estimated by the proposed models. Platform responses (including base shear, overturning moment, and deck displacement) are further calculated. For the same return period, the design values of wave height, wind speed, and current velocity obtained by the conditional and joint probability models are much smaller than those by univariate probability. Considering the dependence among variables, the multivariate probability distributions provide close design parameters to actual sea state for ocean platform design.

Models of multidimensional discrete distribution of probabilities of random variables in information systems

NASA Astrophysics Data System (ADS)

Gromov, Yu Yu; Minin, Yu V.; Ivanova, O. G.; Morozova, O. N.

2018-03-01

Multidimensional discrete distributions of probabilities of independent random values were received. Their one-dimensional distribution is widely used in probability theory. Producing functions of those multidimensional distributions were also received.

A PLUG-AND-PLAY ARCHITECTURE FOR PROBABILISTIC PROGRAMMING

DTIC Science & Technology

2017-04-01

programs that use discrete numerical distributions, but even then, the space of possible outcomes may be uncountable (as a solution can be infinite...also identify conditions guaranteeing that all possible outcomes are finite (and then the probability space is discrete ). 2.2.2 The PlogiQL...and not determined at runtime. Nevertheless, the PRAiSE team plans to extend their solution to support numerical (continuous or discrete

Evolution of Particle Size Distributions in Fragmentation Over Time

NASA Astrophysics Data System (ADS)

Charalambous, C. A.; Pike, W. T.

2013-12-01

We present a new model of fragmentation based on a probabilistic calculation of the repeated fracture of a particle population. The resulting continuous solution, which is in closed form, gives the evolution of fragmentation products from an initial block, through a scale-invariant power-law relationship to a final comminuted powder. Models for the fragmentation of particles have been developed separately in mainly two different disciplines: the continuous integro-differential equations of batch mineral grinding (Reid, 1965) and the fractal analysis of geophysics (Turcotte, 1986) based on a discrete model with a single probability of fracture. The first gives a time-dependent development of the particle-size distribution, but has resisted a closed-form solution, while the latter leads to the scale-invariant power laws, but with no time dependence. Bird (2009) recently introduced a bridge between these two approaches with a step-wise iterative calculation of the fragmentation products. The development of the particle-size distribution occurs with discrete steps: during each fragmentation event, the particles will repeatedly fracture probabilistically, cascading down the length scales to a final size distribution reached after all particles have failed to further fragment. We have identified this process as the equivalent to a sequence of trials for each particle with a fixed probability of fragmentation. Although the resulting distribution is discrete, it can be reformulated as a continuous distribution in maturity over time and particle size. In our model, Turcotte's power-law distribution emerges at a unique maturation index that defines a regime boundary. Up to this index, the fragmentation is in an erosional regime with the initial particle size setting the scaling. Fragmentation beyond this index is in a regime of comminution with rebreakage of the particles down to the size limit of fracture. The maturation index can increment continuously, for example under grinding conditions, or as discrete steps, such as with impact events. In both cases our model gives the energy associated with the fragmentation in terms of the developing surface area of the population. We show the agreement of our model to the evolution of particle size distributions associated with episodic and continuous fragmentation and how the evolution of some popular fractals may be represented using this approach. C. A. Charalambous and W. T. Pike (2013). Multi-Scale Particle Size Distributions of Mars, Moon and Itokawa based on a time-maturation dependent fragmentation model. Abstract Submitted to the AGU 46th Fall Meeting. Bird, N. R. A., Watts, C. W., Tarquis, A. M., & Whitmore, A. P. (2009). Modeling dynamic fragmentation of soil. Vadose Zone Journal, 8(1), 197-201. Reid, K. J. (1965). A solution to the batch grinding equation. Chemical Engineering Science, 20(11), 953-963. Turcotte, D. L. (1986). Fractals and fragmentation. Journal of Geophysical Research: Solid Earth 91(B2), 1921-1926.

A random walk rule for phase I clinical trials.

PubMed

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

1997-06-01

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

2dFLenS and KiDS: determining source redshift distributions with cross-correlations

NASA Astrophysics Data System (ADS)

Johnson, Andrew; Blake, Chris; Amon, Alexandra; Erben, Thomas; Glazebrook, Karl; Harnois-Deraps, Joachim; Heymans, Catherine; Hildebrandt, Hendrik; Joudaki, Shahab; Klaes, Dominik; Kuijken, Konrad; Lidman, Chris; Marin, Felipe A.; McFarland, John; Morrison, Christopher B.; Parkinson, David; Poole, Gregory B.; Radovich, Mario; Wolf, Christian

2017-03-01

We develop a statistical estimator to infer the redshift probability distribution of a photometric sample of galaxies from its angular cross-correlation in redshift bins with an overlapping spectroscopic sample. This estimator is a minimum-variance weighted quadratic function of the data: a quadratic estimator. This extends and modifies the methodology presented by McQuinn & White. The derived source redshift distribution is degenerate with the source galaxy bias, which must be constrained via additional assumptions. We apply this estimator to constrain source galaxy redshift distributions in the Kilo-Degree imaging survey through cross-correlation with the spectroscopic 2-degree Field Lensing Survey, presenting results first as a binned step-wise distribution in the range z < 0.8, and then building a continuous distribution using a Gaussian process model. We demonstrate the robustness of our methodology using mock catalogues constructed from N-body simulations, and comparisons with other techniques for inferring the redshift distribution.

USGS Methodology for Assessing Continuous Petroleum Resources

USGS Publications Warehouse

Charpentier, Ronald R.; Cook, Troy A.

2011-01-01

The U.S. Geological Survey (USGS) has developed a new quantitative methodology for assessing resources in continuous (unconventional) petroleum deposits. Continuous petroleum resources include shale gas, coalbed gas, and other oil and gas deposits in low-permeability ("tight") reservoirs. The methodology is based on an approach combining geologic understanding with well productivities. The methodology is probabilistic, with both input and output variables as probability distributions, and uses Monte Carlo simulation to calculate the estimates. The new methodology is an improvement of previous USGS methodologies in that it better accommodates the uncertainties in undrilled or minimally drilled deposits that must be assessed using analogs. The publication is a collection of PowerPoint slides with accompanying comments.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.

PubMed

Shalymov, Dmitry S; Fradkov, Alexander L

2016-01-01

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

PubMed Central

2016-01-01

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined. PMID:26997886

Statistical tests for whether a given set of independent, identically distributed draws comes from a specified probability density.

PubMed

Tygert, Mark

2010-09-21

We discuss several tests for determining whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly Kuiper's variant, which focus on discrepancies between the cumulative distribution function for the specified probability density and the empirical cumulative distribution function for the given set of i.i.d. draws. Unfortunately, variations in the probability density function often get smoothed over in the cumulative distribution function, making it difficult to detect discrepancies in regions where the probability density is small in comparison with its values in surrounding regions. We discuss tests without this deficiency, complementing the classical methods. The tests of the present paper are based on the plain fact that it is unlikely to draw a random number whose probability is small, provided that the draw is taken from the same distribution used in calculating the probability (thus, if we draw a random number whose probability is small, then we can be confident that we did not draw the number from the same distribution used in calculating the probability).

How extreme was the October 2015 flood in the Carolinas? An assessment of flood frequency analysis and distribution tails

NASA Astrophysics Data System (ADS)

Phillips, R. C.; Samadi, S. Z.; Meadows, M. E.

2018-07-01

This paper examines the frequency, distribution tails, and peak-over-threshold (POT) of extreme floods through analysis that centers on the October 2015 flooding in North Carolina (NC) and South Carolina (SC), United States (US). The most striking features of the October 2015 flooding were a short time to peak (Tp) and a multi-hour continuous flood peak which caused intensive and widespread damages to human lives, properties, and infrastructure. The 2015 flooding was produced by a sequence of intense rainfall events which originated from category 4 hurricane Joaquin over a period of four days. Here, the probability distribution and distribution parameters (i.e., location, scale, and shape) of floods were investigated by comparing the upper part of empirical distributions of the annual maximum flood (AMF) and POT with light- to heavy- theoretical tails: Fréchet, Pareto, Gumbel, Weibull, Beta, and Exponential. Specifically, four sets of U.S. Geological Survey (USGS) gauging data from the central Carolinas with record lengths from approximately 65-125 years were used. Analysis suggests that heavier-tailed distributions are in better agreement with the POT and somewhat AMF data than more often used exponential (light) tailed probability distributions. Further, the threshold selection and record length affect the heaviness of the tail and fluctuations of the parent distributions. The shape parameter and its evolution in the period of record play a critical and poorly understood role in determining the scaling of flood response to intense rainfall.

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

NASA Technical Reports Server (NTRS)

Chiu, J. Christine; Petty, Grant W.

2005-01-01

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

High-Speed Quantum Key Distribution Using Photonic Integrated Circuits

DTIC Science & Technology

2013-01-01

protocol [14] that uses energy-time entanglement of pairs of photons. We are employing the QPIC architecture to implement a novel high-dimensional disper...continuous Hilbert spaces using measures of the covariance matrix. Although we focus the discussion on a scheme employing entangled photon pairs...is the probability that parameter estimation fails [20]. The parameter ε̄ accounts for the accuracy of estimating the smooth min- entropy , which

Neuromorphic learning of continuous-valued mappings from noise-corrupted data. Application to real-time adaptive control

NASA Technical Reports Server (NTRS)

Troudet, Terry; Merrill, Walter C.

1990-01-01

The ability of feed-forward neural network architectures to learn continuous valued mappings in the presence of noise was demonstrated in relation to parameter identification and real-time adaptive control applications. An error function was introduced to help optimize parameter values such as number of training iterations, observation time, sampling rate, and scaling of the control signal. The learning performance depended essentially on the degree of embodiment of the control law in the training data set and on the degree of uniformity of the probability distribution function of the data that are presented to the net during sequence. When a control law was corrupted by noise, the fluctuations of the training data biased the probability distribution function of the training data sequence. Only if the noise contamination is minimized and the degree of embodiment of the control law is maximized, can a neural net develop a good representation of the mapping and be used as a neurocontroller. A multilayer net was trained with back-error-propagation to control a cart-pole system for linear and nonlinear control laws in the presence of data processing noise and measurement noise. The neurocontroller exhibited noise-filtering properties and was found to operate more smoothly than the teacher in the presence of measurement noise.

Diameter distribution in a Brazilian tropical dry forest domain: predictions for the stand and species.

PubMed

Lima, Robson B DE; Bufalino, Lina; Alves, Francisco T; Silva, José A A DA; Ferreira, Rinaldo L C

2017-01-01

Currently, there is a lack of studies on the correct utilization of continuous distributions for dry tropical forests. Therefore, this work aims to investigate the diameter structure of a brazilian tropical dry forest and to select suitable continuous distributions by means of statistic tools for the stand and the main species. Two subsets were randomly selected from 40 plots. Diameter at base height was obtained. The following functions were tested: log-normal; gamma; Weibull 2P and Burr. The best fits were selected by Akaike's information validation criterion. Overall, the diameter distribution of the dry tropical forest was better described by negative exponential curves and positive skewness. The forest studied showed diameter distributions with decreasing probability for larger trees. This behavior was observed for both the main species and the stand. The generalization of the function fitted for the main species show that the development of individual models is needed. The Burr function showed good flexibility to describe the diameter structure of the stand and the behavior of Mimosa ophthalmocentra and Bauhinia cheilantha species. For Poincianella bracteosa, Aspidosperma pyrifolium and Myracrodum urundeuva better fitting was obtained with the log-normal function.

Probability bounds analysis for nonlinear population ecology models.

PubMed

Enszer, Joshua A; Andrei Măceș, D; Stadtherr, Mark A

2015-09-01

Mathematical models in population ecology often involve parameters that are empirically determined and inherently uncertain, with probability distributions for the uncertainties not known precisely. Propagating such imprecise uncertainties rigorously through a model to determine their effect on model outputs can be a challenging problem. We illustrate here a method for the direct propagation of uncertainties represented by probability bounds though nonlinear, continuous-time, dynamic models in population ecology. This makes it possible to determine rigorous bounds on the probability that some specified outcome for a population is achieved, which can be a core problem in ecosystem modeling for risk assessment and management. Results can be obtained at a computational cost that is considerably less than that required by statistical sampling methods such as Monte Carlo analysis. The method is demonstrated using three example systems, with focus on a model of an experimental aquatic food web subject to the effects of contamination by ionic liquids, a new class of potentially important industrial chemicals. Copyright © 2015. Published by Elsevier Inc.

Investigation of Dielectric Breakdown Characteristics for Double-break Vacuum Interrupter and Dielectric Breakdown Probability Distribution in Vacuum Interrupter

NASA Astrophysics Data System (ADS)

Shioiri, Tetsu; Asari, Naoki; Sato, Junichi; Sasage, Kosuke; Yokokura, Kunio; Homma, Mitsutaka; Suzuki, Katsumi

To investigate the reliability of equipment of vacuum insulation, a study was carried out to clarify breakdown probability distributions in vacuum gap. Further, a double-break vacuum circuit breaker was investigated for breakdown probability distribution. The test results show that the breakdown probability distribution of the vacuum gap can be represented by a Weibull distribution using a location parameter, which shows the voltage that permits a zero breakdown probability. The location parameter obtained from Weibull plot depends on electrode area. The shape parameter obtained from Weibull plot of vacuum gap was 10∼14, and is constant irrespective non-uniform field factor. The breakdown probability distribution after no-load switching can be represented by Weibull distribution using a location parameter. The shape parameter after no-load switching was 6∼8.5, and is constant, irrespective of gap length. This indicates that the scatter of breakdown voltage was increased by no-load switching. If the vacuum circuit breaker uses a double break, breakdown probability at low voltage becomes lower than single-break probability. Although potential distribution is a concern in the double-break vacuum cuicuit breaker, its insulation reliability is better than that of the single-break vacuum interrupter even if the bias of the vacuum interrupter's sharing voltage is taken into account.

Modeling Invasion Dynamics with Spatial Random-Fitness Due to Micro-Environment

PubMed Central

Manem, V. S. K.; Kaveh, K.; Kohandel, M.; Sivaloganathan, S.

2015-01-01

Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous microenvironments for cellular systems that is reflected in the phenotypic heterogeneity within the system. In this paper, we study the effect of microenvironment on the invasive capability of species, or mutants, on structured grids (in particular, square lattices) under the influence of site-dependent random proliferation in addition to a migration potential. We discuss both continuous and discrete fitness distributions. Our results suggest that the invasion probability is negatively correlated with the variance of fitness distribution of mutants (for both advantageous and neutral mutants) in the absence of migration of both types of cells. A similar behaviour is observed even in the presence of a random fitness distribution of host cells in the system with neutral fitness rate. In the case of a bimodal distribution, we observe zero invasion probability until the system reaches a (specific) proportion of advantageous phenotypes. Also, we find that the migrative potential amplifies the invasion probability as the variance of fitness of mutants increases in the system, which is the exact opposite in the absence of migration. Our computational framework captures the harsh microenvironmental conditions through quenched random fitness distributions and migration of cells, and our analysis shows that they play an important role in the invasion dynamics of several biological systems such as bacterial micro-habitats, epithelial dysplasia, and metastasis. We believe that our results may lead to more experimental studies, which can in turn provide further insights into the role and impact of heterogeneous environments on invasion dynamics. PMID:26509572

Using a Betabinomial distribution to estimate the prevalence of adherence to physical activity guidelines among children and youth.

PubMed

Garriguet, Didier

2016-04-01

Estimates of the prevalence of adherence to physical activity guidelines in the population are generally the result of averaging individual probability of adherence based on the number of days people meet the guidelines and the number of days they are assessed. Given this number of active and inactive days (days assessed minus days active), the conditional probability of meeting the guidelines that has been used in the past is a Beta (1 + active days, 1 + inactive days) distribution assuming the probability p of a day being active is bounded by 0 and 1 and averages 50%. A change in the assumption about the distribution of p is required to better match the discrete nature of the data and to better assess the probability of adherence when the percentage of active days in the population differs from 50%. Using accelerometry data from the Canadian Health Measures Survey, the probability of adherence to physical activity guidelines is estimated using a conditional probability given the number of active and inactive days distributed as a Betabinomial(n, a + active days , β + inactive days) assuming that p is randomly distributed as Beta(a, β) where the parameters a and β are estimated by maximum likelihood. The resulting Betabinomial distribution is discrete. For children aged 6 or older, the probability of meeting physical activity guidelines 7 out of 7 days is similar to published estimates. For pre-schoolers, the Betabinomial distribution yields higher estimates of adherence to the guidelines than the Beta distribution, in line with the probability of being active on any given day. In estimating the probability of adherence to physical activity guidelines, the Betabinomial distribution has several advantages over the previously used Beta distribution. It is a discrete distribution and maximizes the richness of accelerometer data.

Timescales of isotropic and anisotropic cluster collapse

NASA Astrophysics Data System (ADS)

Bartelmann, M.; Ehlers, J.; Schneider, P.

1993-12-01

From a simple estimate for the formation time of galaxy clusters, Richstone et al. have recently concluded that the evidence for non-virialized structures in a large fraction of observed clusters points towards a high value for the cosmological density parameter Omega0. This conclusion was based on a study of the spherical collapse of density perturbations, assumed to follow a Gaussian probability distribution. In this paper, we extend their treatment in several respects: first, we argue that the collapse does not start from a comoving motion of the perturbation, but that the continuity equation requires an initial velocity perturbation directly related to the density perturbation. This requirement modifies the initial condition for the evolution equation and has the effect that the collapse proceeds faster than in the case where the initial velocity perturbation is set to zero; the timescale is reduced by a factor of up to approximately equal 0.5. Our results thus strengthens the conclusion of Richstone et al. for a high Omega0. In addition, we study the collapse of density fluctuations in the frame of the Zel'dovich approximation, using as starting condition the analytically known probability distribution of the eigenvalues of the deformation tensor, which depends only on the (Gaussian) width of the perturbation spectrum. Finally, we consider the anisotropic collapse of density perturbations dynamically, again with initial conditions drawn from the probability distribution of the deformation tensor. We find that in both cases of anisotropic collapse, in the Zel'dovich approximation and in the dynamical calculations, the resulting distribution of collapse times agrees remarkably well with the results from spherical collapse. We discuss this agreement and conclude that it is mainly due to the properties of the probability distribution for the eigenvalues of the Zel'dovich deformation tensor. Hence, the conclusions of Richstone et al. on the value of Omega0 can be verified and strengthened, even if a more general approach to the collapse of density perturbations is employed. A simple analytic formula for the cluster redshift distribution in an Einstein-deSitter universe is derived.

Testing for entanglement with periodic coarse graining

NASA Astrophysics Data System (ADS)

Tasca, D. S.; Rudnicki, Łukasz; Aspden, R. S.; Padgett, M. J.; Souto Ribeiro, P. H.; Walborn, S. P.

2018-04-01

Continuous-variable systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of ˜60 % relative to 7344 studied cases.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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

Nonparametric Density Estimation Based on Self-Organizing Incremental Neural Network for Large Noisy Data.

PubMed

Nakamura, Yoshihiro; Hasegawa, Osamu

2017-01-01

With the ongoing development and expansion of communication networks and sensors, massive amounts of data are continuously generated in real time from real environments. Beforehand, prediction of a distribution underlying such data is difficult; furthermore, the data include substantial amounts of noise. These factors make it difficult to estimate probability densities. To handle these issues and massive amounts of data, we propose a nonparametric density estimator that rapidly learns data online and has high robustness. Our approach is an extension of both kernel density estimation (KDE) and a self-organizing incremental neural network (SOINN); therefore, we call our approach KDESOINN. An SOINN provides a clustering method that learns about the given data as networks of prototype of data; more specifically, an SOINN can learn the distribution underlying the given data. Using this information, KDESOINN estimates the probability density function. The results of our experiments show that KDESOINN outperforms or achieves performance comparable to the current state-of-the-art approaches in terms of robustness, learning time, and accuracy.

Breakdown of the classical description of a local system.

PubMed

Kot, Eran; Grønbech-Jensen, Niels; Nielsen, Bo M; Neergaard-Nielsen, Jonas S; Polzik, Eugene S; Sørensen, Anders S

2012-06-08

We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig [Phys. Rev. A 83, 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature of the breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system described by the continuous canonical variables x and p, such as a mechanical or an electrical oscillator and a collective spin of a large ensemble.

Stochastic modelling of animal movement.

PubMed

Smouse, Peter E; Focardi, Stefano; Moorcroft, Paul R; Kie, John G; Forester, James D; Morales, Juan M

2010-07-27

Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal 'settling down', accomplished by including one or more focal points that attract the animal's movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.

General simulation algorithm for autocorrelated binary processes.

PubMed

Serinaldi, Francesco; Lombardo, Federico

2017-02-01

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.

Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions.

PubMed

Dinov, Ivo D; Siegrist, Kyle; Pearl, Dennis K; Kalinin, Alexandr; Christou, Nicolas

2016-06-01

Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome , which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols.

Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions

PubMed Central

Dinov, Ivo D.; Siegrist, Kyle; Pearl, Dennis K.; Kalinin, Alexandr; Christou, Nicolas

2015-01-01

Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome, which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols. PMID:27158191

A short note on the maximal point-biserial correlation under non-normality.

PubMed

Cheng, Ying; Liu, Haiyan

2016-11-01

The aim of this paper is to derive the maximal point-biserial correlation under non-normality. Several widely used non-normal distributions are considered, namely the uniform distribution, t-distribution, exponential distribution, and a mixture of two normal distributions. Results show that the maximal point-biserial correlation, depending on the non-normal continuous variable underlying the binary manifest variable, may not be a function of p (the probability that the dichotomous variable takes the value 1), can be symmetric or non-symmetric around p = .5, and may still lie in the range from -1.0 to 1.0. Therefore researchers should exercise caution when they interpret their sample point-biserial correlation coefficients based on popular beliefs that the maximal point-biserial correlation is always smaller than 1, and that the size of the correlation is always further restricted as p deviates from .5. © 2016 The British Psychological Society.

Outcome Probability versus Magnitude: When Waiting Benefits One at the Cost of the Other

PubMed Central

Young, Michael E.; Webb, Tara L.; Rung, Jillian M.; McCoy, Anthony W.

2014-01-01

Using a continuous impulsivity and risk platform (CIRP) that was constructed using a video game engine, choice was assessed under conditions in which waiting produced a continuously increasing probability of an outcome with a continuously decreasing magnitude (Experiment 1) or a continuously increasing magnitude of an outcome with a continuously decreasing probability (Experiment 2). Performance in both experiments reflected a greater desire for a higher probability even though the corresponding wait times produced substantive decreases in overall performance. These tendencies are considered to principally reflect hyperbolic discounting of probability, power discounting of magnitude, and the mathematical consequences of different response rates. Behavior in the CIRP is compared and contrasted with that in the Balloon Analogue Risk Task (BART). PMID:24892657

Random Partition Distribution Indexed by Pairwise Information

PubMed Central

Dahl, David B.; Day, Ryan; Tsai, Jerry W.

2017-01-01

We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for flexible Bayesian modeling. A defining feature of the distribution is that it allocates probability among partitions within a given number of subsets, but it does not shift probability among sets of partitions with different numbers of subsets. Our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant. The distribution of the number of subsets (and its moments) is available in closed-form and is not a function of the similarities. Our formulation has an explicit probability mass function (with a tractable normalizing constant) so the full suite of MCMC methods may be used for posterior inference. We compare our distribution with several existing partition distributions, showing that our formulation has attractive properties. We provide three demonstrations to highlight the features and relative performance of our distribution. PMID:29276318

Use of collateral information to improve LANDSAT classification accuracies

NASA Technical Reports Server (NTRS)

Strahler, A. H. (Principal Investigator)

1981-01-01

Methods to improve LANDSAT classification accuracies were investigated including: (1) the use of prior probabilities in maximum likelihood classification as a methodology to integrate discrete collateral data with continuously measured image density variables; (2) the use of the logit classifier as an alternative to multivariate normal classification that permits mixing both continuous and categorical variables in a single model and fits empirical distributions of observations more closely than the multivariate normal density function; and (3) the use of collateral data in a geographic information system as exercised to model a desired output information layer as a function of input layers of raster format collateral and image data base layers.

Speech processing using conditional observable maximum likelihood continuity mapping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hogden, John; Nix, David

A computer implemented method enables the recognition of speech and speech characteristics. Parameters are initialized of first probability density functions that map between the symbols in the vocabulary of one or more sequences of speech codes that represent speech sounds and a continuity map. Parameters are also initialized of second probability density functions that map between the elements in the vocabulary of one or more desired sequences of speech transcription symbols and the continuity map. The parameters of the probability density functions are then trained to maximize the probabilities of the desired sequences of speech-transcription symbols. A new sequence ofmore » speech codes is then input to the continuity map having the trained first and second probability function parameters. A smooth path is identified on the continuity map that has the maximum probability for the new sequence of speech codes. The probability of each speech transcription symbol for each input speech code can then be output.« less

The consistency service of the ATLAS Distributed Data Management system

NASA Astrophysics Data System (ADS)

Serfon, Cédric; Garonne, Vincent; ATLAS Collaboration

2011-12-01

With the continuously increasing volume of data produced by ATLAS and stored on the WLCG sites, the probability of data corruption or data losses, due to software and hardware failures is increasing. In order to ensure the consistency of all data produced by ATLAS a Consistency Service has been developed as part of the DQ2 Distributed Data Management system. This service is fed by the different ATLAS tools, i.e. the analysis tools, production tools, DQ2 site services or by site administrators that report corrupted or lost files. It automatically corrects the errors reported and informs the users in case of irrecoverable file loss.

Strong regularities in world wide web surfing

PubMed

Huberman; Pirolli; Pitkow; Lukose

1998-04-03

One of the most common modes of accessing information in the World Wide Web is surfing from one document to another along hyperlinks. Several large empirical studies have revealed common patterns of surfing behavior. A model that assumes that users make a sequence of decisions to proceed to another page, continuing as long as the value of the current page exceeds some threshold, yields the probability distribution for the number of pages that a user visits within a given Web site. This model was verified by comparing its predictions with detailed measurements of surfing patterns. The model also explains the observed Zipf-like distributions in page hits observed at Web sites.

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

PubMed Central

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity. PMID:27010993

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.

PubMed

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.

Birth/birth-death processes and their computable transition probabilities with biological applications.

PubMed

Ho, Lam Si Tung; Xu, Jason; Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2018-03-01

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

Changes in tropical precipitation cluster size distributions under global warming

NASA Astrophysics Data System (ADS)

Neelin, J. D.; Quinn, K. M.

2016-12-01

The total amount of precipitation integrated across a tropical storm or other precipitation feature (contiguous clusters of precipitation exceeding a minimum rain rate) is a useful measure of the aggregate size of the disturbance. To establish baseline behavior in current climate, the probability distribution of cluster sizes from multiple satellite retrievals and National Center for Environmental Prediction (NCEP) reanalysis is compared to those from Coupled Model Intercomparison Project (CMIP5) models and the Geophysical Fluid Dynamics Laboratory high-resolution atmospheric model (HIRAM-360 and -180). With the caveat that a minimum rain rate threshold is important in the models (which tend to overproduce low rain rates), the models agree well with observations in leading properties. In particular, scale-free power law ranges in which the probability drops slowly with increasing cluster size are well modeled, followed by a rapid drop in probability of the largest clusters above a cutoff scale. Under the RCP 8.5 global warming scenario, the models indicate substantial increases in probability (up to an order of magnitude) of the largest clusters by the end of century. For models with continuous time series of high resolution output, there is substantial spread on when these probability increases for the largest precipitation clusters should be detectable, ranging from detectable within the observational period to statistically significant trends emerging only in the second half of the century. Examination of NCEP reanalysis and SSMI/SSMIS series of satellite retrievals from 1979 to present does not yield reliable evidence of trends at this time. The results suggest improvements in inter-satellite calibration of the SSMI/SSMIS retrievals could aid future detection.

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

PubMed

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.

The global impact distribution of Near-Earth objects

NASA Astrophysics Data System (ADS)

Rumpf, Clemens; Lewis, Hugh G.; Atkinson, Peter M.

2016-02-01

Asteroids that could collide with the Earth are listed on the publicly available Near-Earth object (NEO) hazard web sites maintained by the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The impact probability distribution of 69 potentially threatening NEOs from these lists that produce 261 dynamically distinct impact instances, or Virtual Impactors (VIs), were calculated using the Asteroid Risk Mitigation and Optimization Research (ARMOR) tool in conjunction with OrbFit. ARMOR projected the impact probability of each VI onto the surface of the Earth as a spatial probability distribution. The projection considers orbit solution accuracy and the global impact probability. The method of ARMOR is introduced and the tool is validated against two asteroid-Earth collision cases with objects 2008 TC3 and 2014 AA. In the analysis, the natural distribution of impact corridors is contrasted against the impact probability distribution to evaluate the distributions' conformity with the uniform impact distribution assumption. The distribution of impact corridors is based on the NEO population and orbital mechanics. The analysis shows that the distribution of impact corridors matches the common assumption of uniform impact distribution and the result extends the evidence base for the uniform assumption from qualitative analysis of historic impact events into the future in a quantitative way. This finding is confirmed in a parallel analysis of impact points belonging to a synthetic population of 10,006 VIs. Taking into account the impact probabilities introduced significant variation into the results and the impact probability distribution, consequently, deviates markedly from uniformity. The concept of impact probabilities is a product of the asteroid observation and orbit determination technique and, thus, represents a man-made component that is largely disconnected from natural processes. It is important to consider impact probabilities because such information represents the best estimate of where an impact might occur.

Ecology of nonnative Siberian prawn (Palaemon modestus) in the lower Snake River, Washington, USA

USGS Publications Warehouse

Erhardt, John M.; Tiffan, Kenneth F.

2016-01-01

We assessed the abundance, distribution, and ecology of the nonnative Siberian prawn Palaemon modestus in the lower Snake River, Washington, USA. Analysis of prawn passage abundance at three Snake River dams showed that populations are growing at exponential rates, especially at Little Goose Dam where over 464,000 prawns were collected in 2015. Monthly beam trawling during 2011–2013 provided information on prawn abundance and distribution in Lower Granite and Little Goose Reservoirs. Zero-inflated regression predicted that the probability of prawn presence increased with decreasing water velocity and increasing depth. Negative binomial models predicted higher catch rates of prawns in deeper water and in closer proximity to dams. Temporally, prawn densities decreased slightly in the summer, likely due to the mortality of older individuals, and then increased in autumn and winter with the emergence and recruitment of young of the year. Seasonal length frequencies showed that distinct juvenile and adult size classes exist throughout the year, suggesting prawns live from 1 to 2 years and may be able to reproduce multiple times during their life. Most juvenile prawns become reproductive adults in 1 year, and peak reproduction occurs from late July through October. Mean fecundity (189 eggs) and reproductive output (11.9 %) are similar to that in their native range. The current use of deep habitats by prawns likely makes them unavailable to most predators in the reservoirs. The distribution and role of Siberian prawns in the lower Snake River food web will probably continue to change as the population grows and warrants continued monitoring and investigation.

Kolmogorov-Smirnov test for spatially correlated data

USGS Publications Warehouse

Olea, R.A.; Pawlowsky-Glahn, V.

2009-01-01

The Kolmogorov-Smirnov test is a convenient method for investigating whether two underlying univariate probability distributions can be regarded as undistinguishable from each other or whether an underlying probability distribution differs from a hypothesized distribution. Application of the test requires that the sample be unbiased and the outcomes be independent and identically distributed, conditions that are violated in several degrees by spatially continuous attributes, such as topographical elevation. A generalized form of the bootstrap method is used here for the purpose of modeling the distribution of the statistic D of the Kolmogorov-Smirnov test. The innovation is in the resampling, which in the traditional formulation of bootstrap is done by drawing from the empirical sample with replacement presuming independence. The generalization consists of preparing resamplings with the same spatial correlation as the empirical sample. This is accomplished by reading the value of unconditional stochastic realizations at the sampling locations, realizations that are generated by simulated annealing. The new approach was tested by two empirical samples taken from an exhaustive sample closely following a lognormal distribution. One sample was a regular, unbiased sample while the other one was a clustered, preferential sample that had to be preprocessed. Our results show that the p-value for the spatially correlated case is always larger that the p-value of the statistic in the absence of spatial correlation, which is in agreement with the fact that the information content of an uncorrelated sample is larger than the one for a spatially correlated sample of the same size. ?? Springer-Verlag 2008.

On the distribution of interspecies correlation for Markov models of character evolution on Yule trees.

PubMed

Mulder, Willem H; Crawford, Forrest W

2015-01-07

Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule process, in which new species are "born" from existing lineages at a constant rate. Recent work has illuminated some of the structural properties of Yule trees, but it remains mostly unknown how these properties affect sequence and trait patterns observed at the tips of the phylogenetic tree. Understanding the interplay between speciation and mutation under simple models of evolution is essential for deriving valid phylogenetic inference methods and gives insight into the optimal design of phylogenetic studies. In this work, we derive the probability distribution of interspecies covariance under Brownian motion and Ornstein-Uhlenbeck models of phenotypic change on a Yule tree. We compute the probability distribution of the number of mutations shared between two randomly chosen taxa in a Yule tree under discrete Markov mutation models. Our results suggest summary measures of phylogenetic information content, illuminate the correlation between site patterns in sequences or traits of related organisms, and provide heuristics for experimental design and reconstruction of phylogenetic trees. Copyright © 2014 Elsevier Ltd. All rights reserved.

Distributed agile software development for the SKA

NASA Astrophysics Data System (ADS)

Wicenec, Andreas; Parsons, Rebecca; Kitaeff, Slava; Vinsen, Kevin; Wu, Chen; Nelson, Paul; Reed, David

2012-09-01

The SKA software will most probably be developed by many groups distributed across the globe and coming from dierent backgrounds, like industries and research institutions. The SKA software subsystems will have to cover a very wide range of dierent areas, but still they have to react and work together like a single system to achieve the scientic goals and satisfy the challenging data ow requirements. Designing and developing such a system in a distributed fashion requires proper tools and the setup of an environment to allow for ecient detection and tracking of interface and integration issues in particular in a timely way. Agile development can provide much faster feedback mechanisms and also much tighter collaboration between the customer (scientist) and the developer. Continuous integration and continuous deployment on the other hand can provide much faster feedback of integration issues from the system level to the subsystem developers. This paper describes the results obtained from trialing a potential SKA development environment based on existing science software development processes like ALMA, the expected distribution of the groups potentially involved in the SKA development and experience gained in the development of large scale commercial software projects.

Precipitation Cluster Distributions: Current Climate Storm Statistics and Projected Changes Under Global Warming

NASA Astrophysics Data System (ADS)

Quinn, Kevin Martin

The total amount of precipitation integrated across a precipitation cluster (contiguous precipitating grid cells exceeding a minimum rain rate) is a useful measure of the aggregate size of the disturbance, expressed as the rate of water mass lost or latent heat released, i.e. the power of the disturbance. Probability distributions of cluster power are examined during boreal summer (May-September) and winter (January-March) using satellite-retrieved rain rates from the Tropical Rainfall Measuring Mission (TRMM) 3B42 and Special Sensor Microwave Imager and Sounder (SSM/I and SSMIS) programs, model output from the High Resolution Atmospheric Model (HIRAM, roughly 0.25-0.5 0 resolution), seven 1-2° resolution members of the Coupled Model Intercomparison Project Phase 5 (CMIP5) experiment, and National Center for Atmospheric Research Large Ensemble (NCAR LENS). Spatial distributions of precipitation-weighted centroids are also investigated in observations (TRMM-3B42) and climate models during winter as a metric for changes in mid-latitude storm tracks. Observed probability distributions for both seasons are scale-free from the smallest clusters up to a cutoff scale at high cluster power, after which the probability density drops rapidly. When low rain rates are excluded by choosing a minimum rain rate threshold in defining clusters, the models accurately reproduce observed cluster power statistics and winter storm tracks. Changes in behavior in the tail of the distribution, above the cutoff, are important for impacts since these quantify the frequency of the most powerful storms. End-of-century cluster power distributions and storm track locations are investigated in these models under a "business as usual" global warming scenario. The probability of high cluster power events increases by end-of-century across all models, by up to an order of magnitude for the highest-power events for which statistics can be computed. For the three models in the suite with continuous time series of high resolution output, there is substantial variability on when these probability increases for the most powerful precipitation clusters become detectable, ranging from detectable within the observational period to statistically significant trends emerging only after 2050. A similar analysis of National Centers for Environmental Prediction (NCEP) Reanalysis 2 and SSM/I-SSMIS rain rate retrievals in the recent observational record does not yield reliable evidence of trends in high-power cluster probabilities at this time. Large impacts to mid-latitude storm tracks are projected over the West Coast and eastern North America, with no less than 8 of the 9 models examined showing large increases by end-of-century in the probability density of the most powerful storms, ranging up to a factor of 6.5 in the highest range bin for which historical statistics are computed. However, within these regional domains, there is considerable variation among models in pinpointing exactly where the largest increases will occur.

Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry-Mather Theory

NASA Astrophysics Data System (ADS)

Lopes, Artur O.; Neumann, Adriana

2015-05-01

In the present paper, we consider a family of continuous time symmetric random walks indexed by , . For each the matching random walk take values in the finite set of states ; notice that is a subset of , where is the unitary circle. The infinitesimal generator of such chain is denoted by . The stationary probability for such process converges to the uniform distribution on the circle, when . Here we want to study other natural measures, obtained via a limit on , that are concentrated on some points of . We will disturb this process by a potential and study for each the perturbed stationary measures of this new process when . We disturb the system considering a fixed potential and we will denote by the restriction of to . Then, we define a non-stochastic semigroup generated by the matrix , where is the infinifesimal generator of . From the continuous time Perron's Theorem one can normalized such semigroup, and, then we get another stochastic semigroup which generates a continuous time Markov Chain taking values on . This new chain is called the continuous time Gibbs state associated to the potential , see (Lopes et al. in J Stat Phys 152:894-933, 2013). The stationary probability vector for such Markov Chain is denoted by . We assume that the maximum of is attained in a unique point of , and from this will follow that . Thus, here, our main goal is to analyze the large deviation principle for the family , when . The deviation function , which is defined on , will be obtained from a procedure based on fixed points of the Lax-Oleinik operator and Aubry-Mather theory. In order to obtain the associated Lax-Oleinik operator we use the Varadhan's Lemma for the process . For a careful analysis of the problem we present full details of the proof of the Large Deviation Principle, in the Skorohod space, for such family of Markov Chains, when . Finally, we compute the entropy of the invariant probabilities on the Skorohod space associated to the Markov Chains we analyze.

Bayes to the Rescue: Continuous Positive Airway Pressure Has Less Mortality Than High-Flow Oxygen.

PubMed

Modesto I Alapont, Vicent; Khemani, Robinder G; Medina, Alberto; Del Villar Guerra, Pablo; Molina Cambra, Alfred

2017-02-01

The merits of high-flow nasal cannula oxygen versus bubble continuous positive airway pressure are debated in children with pneumonia, with suggestions that randomized controlled trials are needed. In light of a previous randomized controlled trial showing a trend for lower mortality with bubble continuous positive airway pressure, we sought to determine the probability that a new randomized controlled trial would find high-flow nasal cannula oxygen superior to bubble continuous positive airway pressure through a "robust" Bayesian analysis. Sample data were extracted from the trial by Chisti et al, and requisite to "robust" Bayesian analysis, we specified three prior distributions to represent clinically meaningful assumptions. These priors (reference, pessimistic, and optimistic) were used to generate three scenarios to represent the range of possible hypotheses. 1) "Reference": we believe bubble continuous positive airway pressure and high-flow nasal cannula oxygen are equally effective with the same uninformative reference priors; 2) "Sceptic on high-flow nasal cannula oxygen": we believe that bubble continuous positive airway pressure is better than high-flow nasal cannula oxygen (bubble continuous positive airway pressure has an optimistic prior and high-flow nasal cannula oxygen has a pessimistic prior); and 3) "Enthusiastic on high-flow nasal cannula oxygen": we believe that high-flow nasal cannula oxygen is better than bubble continuous positive airway pressure (high-flow nasal cannula oxygen has an optimistic prior and bubble continuous positive airway pressure has a pessimistic prior). Finally, posterior empiric Bayesian distributions were obtained through 100,000 Markov Chain Monte Carlo simulations. In all three scenarios, there was a high probability for more death from high-flow nasal cannula oxygen compared with bubble continuous positive airway pressure (reference, 0.98; sceptic on high-flow nasal cannula oxygen, 0.982; enthusiastic on high-flow nasal cannula oxygen, 0.742). The posterior 95% credible interval on the difference in mortality identified a future randomized controlled trial would be extremely unlikely to find a mortality benefit for high-flow nasal cannula oxygen over bubble continuous positive airway pressure, regardless of the scenario. Interpreting these findings using the "range of practical equivalence" framework would recommend rejecting the hypothesis that high-flow nasal cannula oxygen is superior to bubble continuous positive airway pressure for these children. For children younger than 5 years with pneumonia, high-flow nasal cannula oxygen has higher mortality than bubble continuous positive airway pressure. A future randomized controlled trial in this population is unlikely to find high-flow nasal cannula oxygen superior to bubble continuous positive airway pressure.

Modeling Evaporation of Drops of Different Kerosenes

NASA Technical Reports Server (NTRS)

Bellan, Josette; Harstad, Kenneth

2007-01-01

A mathematical model describes the evaporation of drops of a hydrocarbon liquid composed of as many as hundreds of chemical species. The model is intended especially for application to any of several types of kerosenes commonly used as fuels. The concept of continuous thermodynamics, according to which the chemical composition of the evaporating multicomponent liquid is described by use of a probability distribution function (PDF). However, the present model is more generally applicable than is its immediate predecessor.

Characterization of Sensory-Motor Behavior Under Cognitive Load Using a New Statistical Platform for Studies of Embodied Cognition

PubMed Central

Ryu, Jihye; Torres, Elizabeth B.

2018-01-01

The field of enacted/embodied cognition has emerged as a contemporary attempt to connect the mind and body in the study of cognition. However, there has been a paucity of methods that enable a multi-layered approach tapping into different levels of functionality within the nervous systems (e.g., continuously capturing in tandem multi-modal biophysical signals in naturalistic settings). The present study introduces a new theoretical and statistical framework to characterize the influences of cognitive demands on biophysical rhythmic signals harnessed from deliberate, spontaneous and autonomic activities. In this study, nine participants performed a basic pointing task to communicate a decision while they were exposed to different levels of cognitive load. Within these decision-making contexts, we examined the moment-by-moment fluctuations in the peak amplitude and timing of the biophysical time series data (e.g., continuous waveforms extracted from hand kinematics and heart signals). These spike-trains data offered high statistical power for personalized empirical statistical estimation and were well-characterized by a Gamma process. Our approach enabled the identification of different empirically estimated families of probability distributions to facilitate inference regarding the continuous physiological phenomena underlying cognitively driven decision-making. We found that the same pointing task revealed shifts in the probability distribution functions (PDFs) of the hand kinematic signals under study and were accompanied by shifts in the signatures of the heart inter-beat-interval timings. Within the time scale of an experimental session, marked changes in skewness and dispersion of the distributions were tracked on the Gamma parameter plane with 95% confidence. The results suggest that traditional theoretical assumptions of stationarity and normality in biophysical data from the nervous systems are incongruent with the true statistical nature of empirical data. This work offers a unifying platform for personalized statistical inference that goes far beyond those used in conventional studies, often assuming a “one size fits all model” on data drawn from discrete events such as mouse clicks, and observations that leave out continuously co-occurring spontaneous activity taking place largely beneath awareness. PMID:29681805

Continuation rates and reasons for discontinuation of intra-uterine device in three provinces of Pakistan: results of a 24-month prospective client follow-up.

PubMed

Hameed, Waqas; Azmat, Syed Khurram; Ishaque, Muhammad; Hussain, Wajahat; Munroe, Erik; Mustafa, Ghulam; Khan, Omar Farooq; Abbas, Ghazunfer; Ali, Safdar; Asghar, Qaiser Jamshaid; Ali, Sajid; Ahmed, Aftab; Hamza, Hasan Bin

2015-11-25

Long-acting reversible contraceptives, such as the intrauterine device (IUD), remain underutilised in Pakistan with high discontinuation rates. Based on a 24-month prospective client follow-up (nested within a larger quasi-experimental study), this paper presents the comparison of two intervention models, one using private mid-level providers branded as "Suraj" and the other using community midwives (CMWs) of Maternal Newborn and Child Health Programme, for method continuation among IUD users. Moreover, determinants of IUD continuation and the reasons for discontinuation, and switching behaviour were studied within each arm. A total of 1,163 IUD users, 824 from Suraj and 339 from the CMW model, were enrolled in this 24-month prospective client follow-up. Participants were followed-up by female community mobilisers physically every second month to ascertain continued IUD usage and to collect information on associated factors, switching behaviour, reasons for discontinuation, and pregnancy occurrence. The probabilities of IUD continuation and the risk factors for discontinuation were estimated by life table analysis and Cox proportional-hazard techniques, respectively. The cumulative probabilities of IUD continuation at 24 months in Suraj and CMW models were 82% and 80%, respectively. The difference between the two intervention areas was not significant. The probability distributions of IUD continuation were also similar in both interventions (Log rank test: χ(2) = 0.06, df = 1, P = 0.81; Breslow test: χ(2) = 0.6, df = 1, P = 0.44). Health concerns (Suraj = 57.1%, CMW = 38.7%) and pregnancy desire (Suraj = 29.3%, CMW = 40.3%) were reported as the most prominent reasons for IUD discontinuation in both intervention arms. IUD discontinuation was significantly associated with place of residence in Suraj and with age (15-25 years) in the CMW model. CMWs and private providers are equally capable of providing quality IUD services and ensuring higher method continuation. Pakistan's National Maternal Newborn and Child Health programme should consider training CMWs and providing IUDs through them. Moreover, private sector mid-level providers could be engaged in promoting the use of IUDs.

Adaptive Quadrature Detection for Multicarrier Continuous-Variable Quantum Key Distribution

NASA Astrophysics Data System (ADS)

Gyongyosi, Laszlo; Imre, Sandor

2015-03-01

We propose the adaptive quadrature detection for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD scheme uses Gaussian subcarrier continuous variables for the information conveying and Gaussian sub-channels for the transmission. The proposed multicarrier detection scheme dynamically adapts to the sub-channel conditions using a corresponding statistics which is provided by our sophisticated sub-channel estimation procedure. The sub-channel estimation phase determines the transmittance coefficients of the sub-channels, which information are used further in the adaptive quadrature decoding process. We define the technique called subcarrier spreading to estimate the transmittance conditions of the sub-channels with a theoretical error-minimum in the presence of a Gaussian noise. We introduce the terms of single and collective adaptive quadrature detection. We also extend the results for a multiuser multicarrier CVQKD scenario. We prove the achievable error probabilities, the signal-to-noise ratios, and quantify the attributes of the framework. The adaptive detection scheme allows to utilize the extra resources of multicarrier CVQKD and to maximize the amount of transmittable information. This work was partially supported by the GOP-1.1.1-11-2012-0092 (Secure quantum key distribution between two units on optical fiber network) project sponsored by the EU and European Structural Fund, and by the COST Action MP1006.

Nonadditive entropies yield probability distributions with biases not warranted by the data.

PubMed

Pressé, Steve; Ghosh, Kingshuk; Lee, Julian; Dill, Ken A

2013-11-01

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

THE SEMIGROUP OF METRIC MEASURE SPACES AND ITS INFINITELY DIVISIBLE PROBABILITY MEASURES

PubMed Central

EVANS, STEVEN N.; MOLCHANOV, ILYA

2015-01-01

A metric measure space is a complete, separable metric space equipped with a probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second. The resulting set of equivalence classes can be metrized with the Gromov–Prohorov metric of Greven, Pfaffelhuber and Winter. We consider the natural binary operation ⊞ on this space that takes two metric measure spaces and forms their Cartesian product equipped with the sum of the two metrics and the product of the two probability measures. We show that the metric measure spaces equipped with this operation form a cancellative, commutative, Polish semigroup with a translation invariant metric. There is an explicit family of continuous semicharacters that is extremely useful for, inter alia, establishing that there are no infinitely divisible elements and that each element has a unique factorization into prime elements. We investigate the interaction between the semigroup structure and the natural action of the positive real numbers on this space that arises from scaling the metric. For example, we show that for any given positive real numbers a, b, c the trivial space is the only space that satisfies a ⊞ b = c . We establish that there is no analogue of the law of large numbers: if X1, X2, … is an identically distributed independent sequence of random spaces, then no subsequence of 1n⊞k=1nXk converges in distribution unless each Xk is almost surely equal to the trivial space. We characterize the infinitely divisible probability measures and the Lévy processes on this semigroup, characterize the stable probability measures and establish a counterpart of the LePage representation for the latter class. PMID:28065980

The minimum area requirements (MAR) for giant panda: an empirical study

PubMed Central

Qing, Jing; Yang, Zhisong; He, Ke; Zhang, Zejun; Gu, Xiaodong; Yang, Xuyu; Zhang, Wen; Yang, Biao; Qi, Dunwu; Dai, Qiang

2016-01-01

Habitat fragmentation can reduce population viability, especially for area-sensitive species. The Minimum Area Requirements (MAR) of a population is the area required for the population’s long-term persistence. In this study, the response of occupancy probability of giant pandas against habitat patch size was studied in five of the six mountain ranges inhabited by giant panda, which cover over 78% of the global distribution of giant panda habitat. The probability of giant panda occurrence was positively associated with habitat patch area, and the observed increase in occupancy probability with patch size was higher than that due to passive sampling alone. These results suggest that the giant panda is an area-sensitive species. The MAR for giant panda was estimated to be 114.7 km2 based on analysis of its occupancy probability. Giant panda habitats appear more fragmented in the three southern mountain ranges, while they are large and more continuous in the other two. Establishing corridors among habitat patches can mitigate habitat fragmentation, but expanding habitat patch sizes is necessary in mountain ranges where fragmentation is most intensive. PMID:27929520

The minimum area requirements (MAR) for giant panda: an empirical study.

PubMed

Qing, Jing; Yang, Zhisong; He, Ke; Zhang, Zejun; Gu, Xiaodong; Yang, Xuyu; Zhang, Wen; Yang, Biao; Qi, Dunwu; Dai, Qiang

2016-12-08

Habitat fragmentation can reduce population viability, especially for area-sensitive species. The Minimum Area Requirements (MAR) of a population is the area required for the population's long-term persistence. In this study, the response of occupancy probability of giant pandas against habitat patch size was studied in five of the six mountain ranges inhabited by giant panda, which cover over 78% of the global distribution of giant panda habitat. The probability of giant panda occurrence was positively associated with habitat patch area, and the observed increase in occupancy probability with patch size was higher than that due to passive sampling alone. These results suggest that the giant panda is an area-sensitive species. The MAR for giant panda was estimated to be 114.7 km 2 based on analysis of its occupancy probability. Giant panda habitats appear more fragmented in the three southern mountain ranges, while they are large and more continuous in the other two. Establishing corridors among habitat patches can mitigate habitat fragmentation, but expanding habitat patch sizes is necessary in mountain ranges where fragmentation is most intensive.

ProbOnto: ontology and knowledge base of probability distributions.

PubMed

Swat, Maciej J; Grenon, Pierre; Wimalaratne, Sarala

2016-09-01

Probability distributions play a central role in mathematical and statistical modelling. The encoding, annotation and exchange of such models could be greatly simplified by a resource providing a common reference for the definition of probability distributions. Although some resources exist, no suitably detailed and complex ontology exists nor any database allowing programmatic access. ProbOnto, is an ontology-based knowledge base of probability distributions, featuring more than 80 uni- and multivariate distributions with their defining functions, characteristics, relationships and re-parameterization formulas. It can be used for model annotation and facilitates the encoding of distribution-based models, related functions and quantities. http://probonto.org mjswat@ebi.ac.uk Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.

Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach.

PubMed

Duarte Queirós, Sílvio M; Crokidakis, Nuno; Soares-Pinto, Diogo O

2009-07-01

The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter tau<3 to each site. For tau<5/3, such distributions, which are basically Student-t and r distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a alpha-stable Lévy distribution with alpha=(3-tau)/(tau-1). For every value of tau, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz (tau=2) which is accompanied with a divergent free energy per spin (at zero temperature).

PRODIGEN: visualizing the probability landscape of stochastic gene regulatory networks in state and time space.

PubMed

Ma, Chihua; Luciani, Timothy; Terebus, Anna; Liang, Jie; Marai, G Elisabeta

2017-02-15

Visualizing the complex probability landscape of stochastic gene regulatory networks can further biologists' understanding of phenotypic behavior associated with specific genes. We present PRODIGEN (PRObability DIstribution of GEne Networks), a web-based visual analysis tool for the systematic exploration of probability distributions over simulation time and state space in such networks. PRODIGEN was designed in collaboration with bioinformaticians who research stochastic gene networks. The analysis tool combines in a novel way existing, expanded, and new visual encodings to capture the time-varying characteristics of probability distributions: spaghetti plots over one dimensional projection, heatmaps of distributions over 2D projections, enhanced with overlaid time curves to display temporal changes, and novel individual glyphs of state information corresponding to particular peaks. We demonstrate the effectiveness of the tool through two case studies on the computed probabilistic landscape of a gene regulatory network and of a toggle-switch network. Domain expert feedback indicates that our visual approach can help biologists: 1) visualize probabilities of stable states, 2) explore the temporal probability distributions, and 3) discover small peaks in the probability landscape that have potential relation to specific diseases.

Comparision of the different probability distributions for earthquake hazard assessment in the North Anatolian Fault Zone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yilmaz, Şeyda, E-mail: seydayilmaz@ktu.edu.tr; Bayrak, Erdem, E-mail: erdmbyrk@gmail.com; Bayrak, Yusuf, E-mail: bayrak@ktu.edu.tr

In this study we examined and compared the three different probabilistic distribution methods for determining the best suitable model in probabilistic assessment of earthquake hazards. We analyzed a reliable homogeneous earthquake catalogue between a time period 1900-2015 for magnitude M ≥ 6.0 and estimated the probabilistic seismic hazard in the North Anatolian Fault zone (39°-41° N 30°-40° E) using three distribution methods namely Weibull distribution, Frechet distribution and three-parameter Weibull distribution. The distribution parameters suitability was evaluated Kolmogorov-Smirnov (K-S) goodness-of-fit test. We also compared the estimated cumulative probability and the conditional probabilities of occurrence of earthquakes for different elapsed timemore » using these three distribution methods. We used Easyfit and Matlab software to calculate these distribution parameters and plotted the conditional probability curves. We concluded that the Weibull distribution method was the most suitable than other distribution methods in this region.« less

Multivariate normal maximum likelihood with both ordinal and continuous variables, and data missing at random.

PubMed

Pritikin, Joshua N; Brick, Timothy R; Neale, Michael C

2018-04-01

A novel method for the maximum likelihood estimation of structural equation models (SEM) with both ordinal and continuous indicators is introduced using a flexible multivariate probit model for the ordinal indicators. A full information approach ensures unbiased estimates for data missing at random. Exceeding the capability of prior methods, up to 13 ordinal variables can be included before integration time increases beyond 1 s per row. The method relies on the axiom of conditional probability to split apart the distribution of continuous and ordinal variables. Due to the symmetry of the axiom, two similar methods are available. A simulation study provides evidence that the two similar approaches offer equal accuracy. A further simulation is used to develop a heuristic to automatically select the most computationally efficient approach. Joint ordinal continuous SEM is implemented in OpenMx, free and open-source software.

Incorporating Skew into RMS Surface Roughness Probability Distribution

NASA Technical Reports Server (NTRS)

Stahl, Mark T.; Stahl, H. Philip.

2013-01-01

The standard treatment of RMS surface roughness data is the application of a Gaussian probability distribution. This handling of surface roughness ignores the skew present in the surface and overestimates the most probable RMS of the surface, the mode. Using experimental data we confirm the Gaussian distribution overestimates the mode and application of an asymmetric distribution provides a better fit. Implementing the proposed asymmetric distribution into the optical manufacturing process would reduce the polishing time required to meet surface roughness specifications.

Violation of continuous-variable Einstein-Podolsky-Rosen steering with discrete measurements.

PubMed

Schneeloch, James; Dixon, P Ben; Howland, Gregory A; Broadbent, Curtis J; Howell, John C

2013-03-29

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.

Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

NASA Astrophysics Data System (ADS)

Schneeloch, James; Dixon, P. Ben; Howland, Gregory A.; Broadbent, Curtis J.; Howell, John C.

2013-03-01

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.

Mesoscopic description of random walks on combs

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Iomin, Alexander; Campos, Daniel; Horsthemke, Werner

2015-12-01

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.

The Estimation of Tree Posterior Probabilities Using Conditional Clade Probability Distributions

PubMed Central

Larget, Bret

2013-01-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample. [Bayesian phylogenetics; conditional clade distributions; improved accuracy; posterior probabilities of trees.] PMID:23479066

The Effect of Velocity Correlation on the Spatial Evolution of Breakthrough Curves in Heterogeneous Media

NASA Astrophysics Data System (ADS)

Massoudieh, A.; Dentz, M.; Le Borgne, T.

2017-12-01

In heterogeneous media, the velocity distribution and the spatial correlation structure of velocity for solute particles determine the breakthrough curves and how they evolve as one moves away from the solute source. The ability to predict such evolution can help relating the spatio-statistical hydraulic properties of the media to the transport behavior and travel time distributions. While commonly used non-local transport models such as anomalous dispersion and classical continuous time random walk (CTRW) can reproduce breakthrough curve successfully by adjusting the model parameter values, they lack the ability to relate model parameters to the spatio-statistical properties of the media. This in turns limits the transferability of these models. In the research to be presented, we express concentration or flux of solutes as a distribution over their velocity. We then derive an integrodifferential equation that governs the evolution of the particle distribution over velocity at given times and locations for a particle ensemble, based on a presumed velocity correlation structure and an ergodic cross-sectional velocity distribution. This way, the spatial evolution of breakthrough curves away from the source is predicted based on cross-sectional velocity distribution and the connectivity, which is expressed by the velocity transition probability density. The transition probability is specified via a copula function that can help construct a joint distribution with a given correlation and given marginal velocities. Using this approach, we analyze the breakthrough curves depending on the velocity distribution and correlation properties. The model shows how the solute transport behavior evolves from ballistic transport at small spatial scales to Fickian dispersion at large length scales relative to the velocity correlation length.

Vertical changes in the probability distribution of downward irradiance within the near-surface ocean under sunny conditions

NASA Astrophysics Data System (ADS)

Gernez, Pierre; Stramski, Dariusz; Darecki, Miroslaw

2011-07-01

Time series measurements of fluctuations in underwater downward irradiance, Ed, within the green spectral band (532 nm) show that the probability distribution of instantaneous irradiance varies greatly as a function of depth within the near-surface ocean under sunny conditions. Because of intense light flashes caused by surface wave focusing, the near-surface probability distributions are highly skewed to the right and are heavy tailed. The coefficients of skewness and excess kurtosis at depths smaller than 1 m can exceed 3 and 20, respectively. We tested several probability models, such as lognormal, Gumbel, Fréchet, log-logistic, and Pareto, which are potentially suited to describe the highly skewed heavy-tailed distributions. We found that the models cannot approximate with consistently good accuracy the high irradiance values within the right tail of the experimental distribution where the probability of these values is less than 10%. This portion of the distribution corresponds approximately to light flashes with Ed > 1.5?, where ? is the time-averaged downward irradiance. However, the remaining part of the probability distribution covering all irradiance values smaller than the 90th percentile can be described with a reasonable accuracy (i.e., within 20%) with a lognormal model for all 86 measurements from the top 10 m of the ocean included in this analysis. As the intensity of irradiance fluctuations decreases with depth, the probability distribution tends toward a function symmetrical around the mean like the normal distribution. For the examined data set, the skewness and excess kurtosis assumed values very close to zero at a depth of about 10 m.

Predicting the probability of slip in gait: methodology and distribution study.

PubMed

Gragg, Jared; Yang, James

2016-01-01

The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.

Integrated-Circuit Pseudorandom-Number Generator

NASA Technical Reports Server (NTRS)

Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur

1992-01-01

Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.

Bivariate normal, conditional and rectangular probabilities: A computer program with applications

NASA Technical Reports Server (NTRS)

Swaroop, R.; Brownlow, J. D.; Ashwworth, G. R.; Winter, W. R.

1980-01-01

Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.

Assessment of source probabilities for potential tsunamis affecting the U.S. Atlantic coast

USGS Publications Warehouse

Geist, E.L.; Parsons, T.

2009-01-01

Estimating the likelihood of tsunamis occurring along the U.S. Atlantic coast critically depends on knowledge of tsunami source probability. We review available information on both earthquake and landslide probabilities from potential sources that could generate local and transoceanic tsunamis. Estimating source probability includes defining both size and recurrence distributions for earthquakes and landslides. For the former distribution, source sizes are often distributed according to a truncated or tapered power-law relationship. For the latter distribution, sources are often assumed to occur in time according to a Poisson process, simplifying the way tsunami probabilities from individual sources can be aggregated. For the U.S. Atlantic coast, earthquake tsunami sources primarily occur at transoceanic distances along plate boundary faults. Probabilities for these sources are constrained from previous statistical studies of global seismicity for similar plate boundary types. In contrast, there is presently little information constraining landslide probabilities that may generate local tsunamis. Though there is significant uncertainty in tsunami source probabilities for the Atlantic, results from this study yield a comparative analysis of tsunami source recurrence rates that can form the basis for future probabilistic analyses.

Multinomial mixture model with heterogeneous classification probabilities

USGS Publications Warehouse

Holland, M.D.; Gray, B.R.

2011-01-01

Royle and Link (Ecology 86(9):2505-2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data. ?? 2010 Springer Science+Business Media, LLC.

A blueprint for demonstrating quantum supremacy with superconducting qubits

NASA Astrophysics Data System (ADS)

Neill, C.; Roushan, P.; Kechedzhi, K.; Boixo, S.; Isakov, S. V.; Smelyanskiy, V.; Megrant, A.; Chiaro, B.; Dunsworth, A.; Arya, K.; Barends, R.; Burkett, B.; Chen, Y.; Chen, Z.; Fowler, A.; Foxen, B.; Giustina, M.; Graff, R.; Jeffrey, E.; Huang, T.; Kelly, J.; Klimov, P.; Lucero, E.; Mutus, J.; Neeley, M.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Neven, H.; Martinis, J. M.

2018-04-01

A key step toward demonstrating a quantum system that can address difficult problems in physics and chemistry will be performing a computation beyond the capabilities of any classical computer, thus achieving so-called quantum supremacy. In this study, we used nine superconducting qubits to demonstrate a promising path toward quantum supremacy. By individually tuning the qubit parameters, we were able to generate thousands of distinct Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert space. As the number of qubits increases, the system continues to explore the exponentially growing number of states. Extending these results to a system of 50 qubits has the potential to address scientific questions that are beyond the capabilities of any classical computer.

Positive phase space distributions and uncertainty relations

NASA Technical Reports Server (NTRS)

Kruger, Jan

1993-01-01

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Adaptive hybrid simulations for multiscale stochastic reaction networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

Monthly streamflow forecasting based on hidden Markov model and Gaussian Mixture Regression

NASA Astrophysics Data System (ADS)

Liu, Yongqi; Ye, Lei; Qin, Hui; Hong, Xiaofeng; Ye, Jiajun; Yin, Xingli

2018-06-01

Reliable streamflow forecasts can be highly valuable for water resources planning and management. In this study, we combined a hidden Markov model (HMM) and Gaussian Mixture Regression (GMR) for probabilistic monthly streamflow forecasting. The HMM is initialized using a kernelized K-medoids clustering method, and the Baum-Welch algorithm is then executed to learn the model parameters. GMR derives a conditional probability distribution for the predictand given covariate information, including the antecedent flow at a local station and two surrounding stations. The performance of HMM-GMR was verified based on the mean square error and continuous ranked probability score skill scores. The reliability of the forecasts was assessed by examining the uniformity of the probability integral transform values. The results show that HMM-GMR obtained reasonably high skill scores and the uncertainty spread was appropriate. Different HMM states were assumed to be different climate conditions, which would lead to different types of observed values. We demonstrated that the HMM-GMR approach can handle multimodal and heteroscedastic data.

[Observation of animal behavior by revolving activity cage method: A new automatic measuring and recording system of motor activity of a mouse by means of revolving activity cage is presented (author's transl)].

PubMed

Nakamura, K

1978-09-01

With this system, several parameters can be recorded continuously over several months without exterior stimuli. Time per revolution is counted and punched into the paper tape as binary coded numbers, and the number of revolutions and the frequency of "passage" in a given time are printed out on a rolled paper by a digital recorder. "Passage" is defined as one revolving trial without a pause over a fixed time (criterion time) and used as a behavioral unit of "stop and go". The raw data on the paper tape are processed and analyzed with a general-purpose computer. It was confirmed that when a mouse became well accustomed to the revolving activity cage, the time per revolution followed the law of exponential distribution probability, while the length of passage (i.e. the number of revolutions per revolving trial) followed that of geometrical distribution probability. The revolving activity of mice treated with single subcutaneous injection of methamphetamine was examined using these parameters.

A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems

DOE PAGES

Kouri, Drew Philip

2017-12-19

In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robustmore » optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.« less

The proton and helium anomalies in the light of the Myriad model

NASA Astrophysics Data System (ADS)

Salati, Pierre; Génolini, Yoann; Serpico, Pasquale; Taillet, Richard

2017-03-01

A hardening of the proton and helium fluxes is observed above a few hundreds of GeV/nuc. The distribution of local sources of primary cosmic rays has been suggested as a potential solution to this puzzling behavior. Some authors even claim that a single source is responsible for the observed anomalies. But how probable these explanations are? To answer that question, our current description of cosmic ray Galactic propagation needs to be replaced by the Myriad model. In the former approach, sources of protons and helium nuclei are treated as a jelly continuously spread over space and time. A more accurate description is provided by the Myriad model where sources are considered as point-like events. This leads to a probabilistic derivation of the fluxes of primary species, and opens the possibility that larger-than-average values may be observed at the Earth. For a long time though, a major obstacle has been the infinite variance associated to the probability distribution function which the fluxes follow. Several suggestions have been made to cure this problem but none is entirely satisfactory. We go a step further here and solve the infinite variance problem of the Myriad model by making use of the generalized central limit theorem. We find that primary fluxes are distributed according to a stable law with heavy tail, well-known to financial analysts. The probability that the proton and helium anomalies are sourced by local SNR can then be calculated. The p-values associated to the CREAM measurements turn out to be small, unless somewhat unrealistic propagation parameters are assumed.

A new general method for the assessment of the molecular-weight distribution of polydisperse preparations. Its application to an intestinal epithelial glycoprotein and two dextran samples, and comparison with a monodisperse glycoprotein

PubMed Central

Gibbons, Richard A.; Dixon, Stephen N.; Pocock, David H.

1973-01-01

A specimen of intestinal glycoprotein isolated from the pig and two samples of dextran, all of which are polydisperse (that is, the preparations may be regarded as consisting of a continuous distribution of molecular weights), have been examined in the ultracentrifuge under meniscus-depletion conditions at equilibrium. They are compared with each other and with a glycoprotein from Cysticercus tenuicollis cyst fluid which is almost monodisperse. The quantity c−⅓ (c=concentration) is plotted against ξ (the reduced radius); this plot is linear when the molecular-weight distribution approximates to the `most probable', i.e. when Mn:Mw:Mz: M(z+1)....... is as 1:2:3:4: etc. The use of this plot, and related procedures, to evaluate qualitatively and semi-quantitatively molecular-weight distribution functions where they can be realistically approximated to Schulz distributions is discussed. The theoretical basis is given in an Appendix. PMID:4778265

Modeling the probability distribution of peak discharge for infiltrating hillslopes

NASA Astrophysics Data System (ADS)

Baiamonte, Giorgio; Singh, Vijay P.

2017-07-01

Hillslope response plays a fundamental role in the prediction of peak discharge at the basin outlet. The peak discharge for the critical duration of rainfall and its probability distribution are needed for designing urban infrastructure facilities. This study derives the probability distribution, denoted as GABS model, by coupling three models: (1) the Green-Ampt model for computing infiltration, (2) the kinematic wave model for computing discharge hydrograph from the hillslope, and (3) the intensity-duration-frequency (IDF) model for computing design rainfall intensity. The Hortonian mechanism for runoff generation is employed for computing the surface runoff hydrograph. Since the antecedent soil moisture condition (ASMC) significantly affects the rate of infiltration, its effect on the probability distribution of peak discharge is investigated. Application to a watershed in Sicily, Italy, shows that with the increase of probability, the expected effect of ASMC to increase the maximum discharge diminishes. Only for low values of probability, the critical duration of rainfall is influenced by ASMC, whereas its effect on the peak discharge seems to be less for any probability. For a set of parameters, the derived probability distribution of peak discharge seems to be fitted by the gamma distribution well. Finally, an application to a small watershed, with the aim to test the possibility to arrange in advance the rational runoff coefficient tables to be used for the rational method, and a comparison between peak discharges obtained by the GABS model with those measured in an experimental flume for a loamy-sand soil were carried out.

Reconciling Streamflow Uncertainty Estimation and River Bed Morphology Dynamics. Insights from a Probabilistic Assessment of Streamflow Uncertainties Using a Reliability Diagram

NASA Astrophysics Data System (ADS)

Morlot, T.; Mathevet, T.; Perret, C.; Favre Pugin, A. C.

2014-12-01

Streamflow uncertainty estimation has recently received a large attention in the literature. A dynamic rating curve assessment method has been introduced (Morlot et al., 2014). This dynamic method allows to compute a rating curve for each gauging and a continuous streamflow time-series, while calculating streamflow uncertainties. Streamflow uncertainty takes into account many sources of uncertainty (water level, rating curve interpolation and extrapolation, gauging aging, etc.) and produces an estimated distribution of streamflow for each days. In order to caracterise streamflow uncertainty, a probabilistic framework has been applied on a large sample of hydrometric stations of the Division Technique Générale (DTG) of Électricité de France (EDF) hydrometric network (>250 stations) in France. A reliability diagram (Wilks, 1995) has been constructed for some stations, based on the streamflow distribution estimated for a given day and compared to a real streamflow observation estimated via a gauging. To build a reliability diagram, we computed the probability of an observed streamflow (gauging), given the streamflow distribution. Then, the reliability diagram allows to check that the distribution of probabilities of non-exceedance of the gaugings follows a uniform law (i.e., quantiles should be equipropables). Given the shape of the reliability diagram, the probabilistic calibration is caracterised (underdispersion, overdispersion, bias) (Thyer et al., 2009). In this paper, we present case studies where reliability diagrams have different statistical properties for different periods. Compared to our knowledge of river bed morphology dynamic of these hydrometric stations, we show how reliability diagram gives us invaluable information on river bed movements, like a continuous digging or backfilling of the hydraulic control due to erosion or sedimentation processes. Hence, the careful analysis of reliability diagrams allows to reconcile statistics and long-term river bed morphology processes. This knowledge improves our real-time management of hydrometric stations, given a better caracterisation of erosion/sedimentation processes and the stability of hydrometric station hydraulic control.

Measurement of the top quark mass using template methods on dilepton events in p anti-p collisions at s**(1/2) = 1.96-TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abulencia, A.; Acosta, D.; Adelman, Jahred A.

2006-02-01

The authors describe a measurement of the top quark mass from events produced in p{bar p} collisions at a center-of-mass energy of 1.96 TeV, using the Collider Detector at Fermilab. They identify t{bar t} candidates where both W bosons from the top quarks decay into leptons (e{nu}, {mu}{nu}, or {tau}{nu}) from a data sample of 360 pb{sup -1}. The top quark mass is reconstructed in each event separately by three different methods, which draw upon simulated distributions of the neutrino pseudorapidity, t{bar t} longitudinal momentum, or neutrino azimuthal angle in order to extract probability distributions for the top quark mass.more » For each method, representative mass distributions, or templates, are constructed from simulated samples of signal and background events, and parameterized to form continuous probability density functions. A likelihood fit incorporating these parameterized templates is then performed on the data sample masses in order to derive a final top quark mass. Combining the three template methods, taking into account correlations in their statistical and systematic uncertainties, results in a top quark mass measurement of 170.1 {+-} 6.0(stat.) {+-} 4.1(syst.) GeV/c{sup 2}.« less

A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

NASA Astrophysics Data System (ADS)

Wang, Q. J.; Robertson, D. E.; Chiew, F. H. S.

2009-05-01

Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box-Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño-Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box-Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data-handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

NASA Astrophysics Data System (ADS)

Chen, Yen-Luan; Chang, Chin-Chih; Sheu, Dwan-Fang

2016-04-01

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.

Continuity equation for probability as a requirement of inference over paths

NASA Astrophysics Data System (ADS)

González, Diego; Díaz, Daniela; Davis, Sergio

2016-09-01

Local conservation of probability, expressed as the continuity equation, is a central feature of non-equilibrium Statistical Mechanics. In the existing literature, the continuity equation is always motivated by heuristic arguments with no derivation from first principles. In this work we show that the continuity equation is a logical consequence of the laws of probability and the application of the formalism of inference over paths for dynamical systems. That is, the simple postulate that a system moves continuously through time following paths implies the continuity equation. The translation between the language of dynamical paths to the usual representation in terms of probability densities of states is performed by means of an identity derived from Bayes' theorem. The formalism presented here is valid independently of the nature of the system studied: it is applicable to physical systems and also to more abstract dynamics such as financial indicators, population dynamics in ecology among others.

Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction

NASA Technical Reports Server (NTRS)

Cohen, A. C.

1971-01-01

A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.

Determinants of ante-partum depression: a multicenter study.

PubMed

Balestrieri, Matteo; Matteo, Balestrieri; Isola, Miriam; Miriam, Isola; Bisoffi, Giulia; Giulia, Bisoffi; Calò, Salvatore; Salvatore, Calò; Conforti, Anita; Anita, Conforti; Driul, Lorenza; Lorenza, Driul; Marchesoni, Diego; Diego, Marchesoni; Petrosemolo, Paola; Paola, Petrosemolo; Rossi, Michela; Michela, Rossi; Zito, Adriana; Adriana, Zito; Zorzenone, Stefania; Stefania, Zorzenone; Di Sciascio, Guido; Guido, Di Sciascio; Leone, Roberto; Roberto, Leone; Bellantuono, Cesario; Cesario, Bellantuono

2012-12-01

Ante-partum depression (APD) is usually defined as a non-psychotic depressive episode of mild to moderate severity, beginning in or extending into pregnancy. APD has received less attention than postpartum depression. This is a cross-sectional study carried out in the Obstetrics and Gynaecology (OG) departments of four different general hospitals in Italy. Women attending consecutively the OG departments for their first ultrasound examination were asked to fill in the Edinburgh Postnatal Depression Scale (EPDS) in its Italian validated version. We used the total scores of the EPDS as a continuous variable for univariate and linear regression analyses; in accordance with the literature, the item analysis of EPDS was carried out by classifying the sample as women with "no depression" (scores 0-9), "possible depression" (scores 10-12), "probable depression" (scores 13+) and "probable APD" (scores 15+). The number of women recruited was 1,608. The EPDS assessment classified 10.9 % of the women as possibly depressed, 8.3 % as probably depressed and 4.7 % probably affected from an APD. EPDS score distribution was associated with nationality (higher scores for foreigners), cohabitation (higher scores for women living with friends or in a community), occupation (higher scores for housewives), past episodes of depression and use of herbal drugs. Non-depressed women had significantly lower values on all ten items as compared with depressed women, however, the pattern of item distribution on the EPDS scale remained similar across depression severity groups. In all four groups item 4 (anxious depression) attained the highest scores, while item 10 (suicidality) attained the lowest scores.

The coalescent of a sample from a binary branching process.

PubMed

Lambert, Amaury

2018-04-25

At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth-death process. Stop this process at time T>0. It is known that the tree spanned by the N tips alive at time T of the tree thus obtained (called a reduced tree or coalescent tree) is a coalescent point process (CPP), which basically means that the depths of interior nodes are independent and identically distributed (iid). Now select each of the N tips independently with probability y (Bernoulli sample). It is known that the tree generated by the selected tips, which we will call the Bernoulli sampled CPP, is again a CPP. Now instead, select exactly k tips uniformly at random among the N tips (a k-sample). We show that the tree generated by the selected tips is a mixture of Bernoulli sampled CPPs with the same parent CPP, over some explicit distribution of the sampling probability y. An immediate consequence is that the genealogy of a k-sample can be obtained by the realization of k random variables, first the random sampling probability Y and then the k-1 node depths which are iid conditional on Y=y. Copyright © 2018. Published by Elsevier Inc.

Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Ocean: Observations and Approximations

NASA Astrophysics Data System (ADS)

Lozovatsky, I.; Fernando, H. J. S.; Planella-Morato, J.; Liu, Zhiyu; Lee, J.-H.; Jinadasa, S. U. P.

2017-10-01

The probability distribution of turbulent kinetic energy dissipation rate in stratified ocean usually deviates from the classic lognormal distribution that has been formulated for and often observed in unstratified homogeneous layers of atmospheric and oceanic turbulence. Our measurements of vertical profiles of micro-scale shear, collected in the East China Sea, northern Bay of Bengal, to the south and east of Sri Lanka, and in the Gulf Stream region, show that the probability distributions of the dissipation rate ɛ˜r in the pycnoclines (r ˜ 1.4 m is the averaging scale) can be successfully modeled by the Burr (type XII) probability distribution. In weakly stratified boundary layers, lognormal distribution of ɛ˜r is preferable, although the Burr is an acceptable alternative. The skewness Skɛ and the kurtosis Kɛ of the dissipation rate appear to be well correlated in a wide range of Skɛ and Kɛ variability.

Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition

NASA Astrophysics Data System (ADS)

Roy, Bappaditya; Santra, S. B.

2018-05-01

A random growth lattice filling model of percolation with a touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty lattice sites and clusters are grown from these nucleation centers with a growth probability g. For a given g (), the system passes through a critical point during the growth process where the transition from a disconnected to a connected phase occurs. The model is found to exhibit second order continuous percolation transitions as ordinary percolation for whereas for it exhibits weak first order discontinuous percolation transitions. The continuous transitions are characterized by estimating the values of the critical exponents associated with the order parameter fluctuation and the fractal dimension of the spanning cluster over the whole range of g. The discontinuous transitions, however, are characterized by a compact spanning cluster, lattice size independent fluctuation of the order parameter per lattice, departure from power law scaling in the cluster size distribution and weak bimodal distribution of the order parameter. The nature of transitions are further confirmed by studying the Binder cumulant. Instead of a sharp tricritical point, a tricritical region is found to occur for 0.5  <  g  <  0.8 within which the values of the critical exponents change continuously until the crossover from continuous to discontinuous transition is completed.

Evaluation of the Three Parameter Weibull Distribution Function for Predicting Fracture Probability in Composite Materials

DTIC Science & Technology

1978-03-01

for the risk of rupture for a unidirectionally laminat - ed composite subjected to pure bending. (5D This equation can be simplified further by use of...C EVALUATION OF THE THREE PARAMETER WEIBULL DISTRIBUTION FUNCTION FOR PREDICTING FRACTURE PROBABILITY IN COMPOSITE MATERIALS. THESIS / AFIT/GAE...EVALUATION OF THE THREE PARAMETER WE1BULL DISTRIBUTION FUNCTION FOR PREDICTING FRACTURE PROBABILITY IN COMPOSITE MATERIALS THESIS Presented

Gaussification and entanglement distillation of continuous-variable systems: a unifying picture.

PubMed

Campbell, Earl T; Eisert, Jens

2012-01-13

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.

Global behavior analysis for stochastic system of 1,3-PD continuous fermentation

NASA Astrophysics Data System (ADS)

Zhu, Xi; Kliemann, Wolfgang; Li, Chunfa; Feng, Enmin; Xiu, Zhilong

2017-12-01

Global behavior for stochastic system of continuous fermentation in glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae is analyzed in this paper. This bioprocess cannot avoid the stochastic perturbation caused by internal and external disturbance which reflect on the growth rate. These negative factors can limit and degrade the achievable performance of controlled systems. Based on multiplicity phenomena, the equilibriums and bifurcations of the deterministic system are analyzed. Then, a stochastic model is presented by a bounded Markov diffusion process. In order to analyze the global behavior, we compute the control sets for the associated control system. The probability distributions of relative supports are also computed. The simulation results indicate that how the disturbed biosystem tend to stationary behavior globally.

The structure of water around the compressibility minimum

DOE PAGES

L. B. Skinner; Benmore, C. J.; Parise, J.; ...

2014-12-03

Here we present diffraction data that yield the oxygen-oxygen pair distribution function, gOO(r) over the range 254.2–365.9 K. The running O-O coordination number, which represents the integral of the pair distribution function as a function of radial distance, is found to exhibit an isosbestic point at 3.30(5) Å. The probability of finding an oxygen atom surrounding another oxygen at this distance is therefore shown to be independent of temperature and corresponds to an O-O coordination number of 4.3(2). Moreover, the experimental data also show a continuous transition associated with the second peak position in gOO(r) concomitant with the compressibility minimummore » at 319 K.« less

A Compendium of Wind Statistics and Models for the NASA Space Shuttle and Other Aerospace Vehicle Programs

NASA Technical Reports Server (NTRS)

Smith, O. E.; Adelfang, S. I.

1998-01-01

The wind profile with all of its variations with respect to altitude has been, is now, and will continue to be important for aerospace vehicle design and operations. Wind profile databases and models are used for the vehicle ascent flight design for structural wind loading, flight control systems, performance analysis, and launch operations. This report presents the evolution of wind statistics and wind models from the empirical scalar wind profile model established for the Saturn Program through the development of the vector wind profile model used for the Space Shuttle design to the variations of this wind modeling concept for the X-33 program. Because wind is a vector quantity, the vector wind models use the rigorous mathematical probability properties of the multivariate normal probability distribution. When the vehicle ascent steering commands (ascent guidance) are wind biased to the wind profile measured on the day-of-launch, ascent structural wind loads are reduced and launch probability is increased. This wind load alleviation technique is recommended in the initial phase of vehicle development. The vehicle must fly through the largest load allowable versus altitude to achieve its mission. The Gumbel extreme value probability distribution is used to obtain the probability of exceeding (or not exceeding) the load allowable. The time conditional probability function is derived from the Gumbel bivariate extreme value distribution. This time conditional function is used for calculation of wind loads persistence increments using 3.5-hour Jimsphere wind pairs. These increments are used to protect the commit-to-launch decision. Other topics presented include the Shuttle Shuttle load-response to smoothed wind profiles, a new gust model, and advancements in wind profile measuring systems. From the lessons learned and knowledge gained from past vehicle programs, the development of future launch vehicles can be accelerated. However, new vehicle programs by their very nature will require specialized support for new databases and analyses for wind, atmospheric parameters (pressure, temperature, and density versus altitude), and weather. It is for this reason that project managers are encouraged to collaborate with natural environment specialists early in the conceptual design phase. Such action will give the lead time necessary to meet the natural environment design and operational requirements, and thus, reduce development costs.

Bivariate extreme value distributions

NASA Technical Reports Server (NTRS)

Elshamy, M.

1992-01-01

In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.

Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2017-02-01

The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of description of physical phenomena. In general there are no reasons to expect that properties of ontic states are approachable through our measurements. There is a gap between ontic and epistemic descriptions, cf. also with 't Hooft [49,50] and G G. Groessing et al. [51]. In general the presence of such a gap also implies unapproachability of the probabilistic ontic states, i.e., probability distributions on the space of ontic states. De Broglie [28] called such probability distributions hidden probabilities and distinguished them sharply from probability distributions of measurements outcomes, see also Lochak [29]. (The latter distributions are described by the quantum formalism.)This ontic-epistemic approach based on the combination of two descriptive levels for natural phenomena is closely related to the old Bild conception which was originated in the works of Hertz. Later it was heavily explored by Schrödinger in the quantum domain, see, e.g., [8,11] for detailed analysis. According to Hertz one cannot expect to construct a complete theoretical model based explicitly on observable quantities. The complete theoretical model can contain quantities which are unapproachable for external measurement inspection. For example, Hertz by trying to create a mechanical model for Maxwell's electromagnetism invented hidden masses. The main distinguishing property of a theoretical model (in contrast to an observational model) is the continuity of description, i.e., the absence of gaps in description. From this viewpoint, the quantum mechanical description is not continuous: there is a gap between premeasurement dynamics and the measurement outcome. QM cannot say anything what happens in the process of measurement, this is the well known measurement problem of QM [32], cf. [52,53]. Continuity of description is closely related to causality. However, here we cannot go in more detail, see [8,11].The important question is about interrelation between two levels of description, ontic-epistemic (or theoretical-observational). In the introduction we have already cited Schrödinger who emphasized the possible complexity of this interrelation. In particular, in general there is no reason to expect a straightforward coupling of the form, cf. [9,10]:

Reliable gain-scheduled control of discrete-time systems and its application to CSTR model

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, Y.

2016-10-01

This paper is focused on reliable gain-scheduled controller design for a class of discrete-time systems with randomly occurring nonlinearities and actuator fault. Further, the nonlinearity in the system model is assumed to occur randomly according to a Bernoulli distribution with measurable time-varying probability in real time. The main purpose of this paper is to design a gain-scheduled controller by implementing a probability-dependent Lyapunov function and linear matrix inequality (LMI) approach such that the closed-loop discrete-time system is stochastically stable for all admissible randomly occurring nonlinearities. The existence conditions for the reliable controller is formulated in terms of LMI constraints. Finally, the proposed reliable gain-scheduled control scheme is applied on continuously stirred tank reactor model to demonstrate the effectiveness and applicability of the proposed design technique.

Eruption probabilities for the Lassen Volcanic Center and regional volcanism, northern California, and probabilities for large explosive eruptions in the Cascade Range

USGS Publications Warehouse

Nathenson, Manuel; Clynne, Michael A.; Muffler, L.J. Patrick

2012-01-01

Chronologies for eruptive activity of the Lassen Volcanic Center and for eruptions from the regional mafic vents in the surrounding area of the Lassen segment of the Cascade Range are here used to estimate probabilities of future eruptions. For the regional mafic volcanism, the ages of many vents are known only within broad ranges, and two models are developed that should bracket the actual eruptive ages. These chronologies are used with exponential, Weibull, and mixed-exponential probability distributions to match the data for time intervals between eruptions. For the Lassen Volcanic Center, the probability of an eruption in the next year is 1.4x10-4 for the exponential distribution and 2.3x10-4 for the mixed exponential distribution. For the regional mafic vents, the exponential distribution gives a probability of an eruption in the next year of 6.5x10-4, but the mixed exponential distribution indicates that the current probability, 12,000 years after the last event, could be significantly lower. For the exponential distribution, the highest probability is for an eruption from a regional mafic vent. Data on areas and volumes of lava flows and domes of the Lassen Volcanic Center and of eruptions from the regional mafic vents provide constraints on the probable sizes of future eruptions. Probabilities of lava-flow coverage are similar for the Lassen Volcanic Center and for regional mafic vents, whereas the probable eruptive volumes for the mafic vents are generally smaller. Data have been compiled for large explosive eruptions (>≈ 5 km3 in deposit volume) in the Cascade Range during the past 1.2 m.y. in order to estimate probabilities of eruption. For erupted volumes >≈5 km3, the rate of occurrence since 13.6 ka is much higher than for the entire period, and we use these data to calculate the annual probability of a large eruption at 4.6x10-4. For erupted volumes ≥10 km3, the rate of occurrence has been reasonably constant from 630 ka to the present, giving more confidence in the estimate, and we use those data to calculate the annual probability of a large eruption in the next year at 1.4x10-5.

Burst wait time simulation of CALIBAN reactor at delayed super-critical state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humbert, P.; Authier, N.; Richard, B.

2012-07-01

In the past, the super prompt critical wait time probability distribution was measured on CALIBAN fast burst reactor [4]. Afterwards, these experiments were simulated with a very good agreement by solving the non-extinction probability equation [5]. Recently, the burst wait time probability distribution has been measured at CEA-Valduc on CALIBAN at different delayed super-critical states [6]. However, in the delayed super-critical case the non-extinction probability does not give access to the wait time distribution. In this case it is necessary to compute the time dependent evolution of the full neutron count number probability distribution. In this paper we present themore » point model deterministic method used to calculate the probability distribution of the wait time before a prescribed count level taking into account prompt neutrons and delayed neutron precursors. This method is based on the solution of the time dependent adjoint Kolmogorov master equations for the number of detections using the generating function methodology [8,9,10] and inverse discrete Fourier transforms. The obtained results are then compared to the measurements and Monte-Carlo calculations based on the algorithm presented in [7]. (authors)« less

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

NASA Astrophysics Data System (ADS)

Malakar, Kanaya; Jemseena, V.; Kundu, Anupam; Vijay Kumar, K.; Sabhapandit, Sanjib; Majumdar, Satya N.; Redner, S.; Dhar, Abhishek

2018-04-01

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady-state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady-state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain with an absorbing boundary condition at the origin. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verification of our analytical results.

Fitness Probability Distribution of Bit-Flip Mutation.

PubMed

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

Directional Migration of Recirculating Lymphocytes through Lymph Nodes via Random Walks

PubMed Central

Thomas, Niclas; Matejovicova, Lenka; Srikusalanukul, Wichat; Shawe-Taylor, John; Chain, Benny

2012-01-01

Naive T lymphocytes exhibit extensive antigen-independent recirculation between blood and lymph nodes, where they may encounter dendritic cells carrying cognate antigen. We examine how long different T cells may spend in an individual lymph node by examining data from long term cannulation of blood and efferent lymphatics of a single lymph node in the sheep. We determine empirically the distribution of transit times of migrating T cells by applying the Least Absolute Shrinkage & Selection Operator () or regularised to fit experimental data describing the proportion of labelled infused cells in blood and efferent lymphatics over time. The optimal inferred solution reveals a distribution with high variance and strong skew. The mode transit time is typically between 10 and 20 hours, but a significant number of cells spend more than 70 hours before exiting. We complement the empirical machine learning based approach by modelling lymphocyte passage through the lymph node . On the basis of previous two photon analysis of lymphocyte movement, we optimised distributions which describe the transit times (first passage times) of discrete one dimensional and continuous (Brownian) three dimensional random walks with drift. The optimal fit is obtained when drift is small, i.e. the ratio of probabilities of migrating forward and backward within the node is close to one. These distributions are qualitatively similar to the inferred empirical distribution, with high variance and strong skew. In contrast, an optimised normal distribution of transit times (symmetrical around mean) fitted the data poorly. The results demonstrate that the rapid recirculation of lymphocytes observed at a macro level is compatible with predominantly randomised movement within lymph nodes, and significant probabilities of long transit times. We discuss how this pattern of migration may contribute to facilitating interactions between low frequency T cells and antigen presenting cells carrying cognate antigen. PMID:23028891

The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

ERIC Educational Resources Information Center

Conant, Darcy Lynn

2013-01-01

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

DOE PAGES

Ye, Xin; Garikapati, Venu M.; You, Daehyun; ...

2017-11-08

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basismore » of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.« less

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ye, Xin; Garikapati, Venu M.; You, Daehyun

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basismore » of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.« less

Probability distributions of the electroencephalogram envelope of preterm infants.

PubMed

Saji, Ryoya; Hirasawa, Kyoko; Ito, Masako; Kusuda, Satoshi; Konishi, Yukuo; Taga, Gentaro

2015-06-01

To determine the stationary characteristics of electroencephalogram (EEG) envelopes for prematurely born (preterm) infants and investigate the intrinsic characteristics of early brain development in preterm infants. Twenty neurologically normal sets of EEGs recorded in infants with a post-conceptional age (PCA) range of 26-44 weeks (mean 37.5 ± 5.0 weeks) were analyzed. Hilbert transform was applied to extract the envelope. We determined the suitable probability distribution of the envelope and performed a statistical analysis. It was found that (i) the probability distributions for preterm EEG envelopes were best fitted by lognormal distributions at 38 weeks PCA or less, and by gamma distributions at 44 weeks PCA; (ii) the scale parameter of the lognormal distribution had positive correlations with PCA as well as a strong negative correlation with the percentage of low-voltage activity; (iii) the shape parameter of the lognormal distribution had significant positive correlations with PCA; (iv) the statistics of mode showed significant linear relationships with PCA, and, therefore, it was considered a useful index in PCA prediction. These statistics, including the scale parameter of the lognormal distribution and the skewness and mode derived from a suitable probability distribution, may be good indexes for estimating stationary nature in developing brain activity in preterm infants. The stationary characteristics, such as discontinuity, asymmetry, and unimodality, of preterm EEGs are well indicated by the statistics estimated from the probability distribution of the preterm EEG envelopes. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Factors affecting continued use of ceramic water purifiers distributed to tsunami-affected communities in Sri Lanka.

PubMed

Casanova, Lisa M; Walters, Adam; Naghawatte, Ajith; Sobsey, Mark D

2012-11-01

There is little information about continued use of point-of-use technologies after disaster relief efforts. After the 2004 tsunami, the Red Cross distributed ceramic water filters in Sri Lanka. This study determined factors associated with filter disuse and evaluate the quality of household drinking water. A cross-sectional survey of water sources and treatment, filter use and household characteristics was administered by in-person oral interview, and household water quality was tested. Multivariable logistic regression was used to model probability of filter non-use. At the time of survey, 24% of households (107/452) did not use filters; the most common reason given was breakage (42%). The most common household water sources were taps and wells. Wells were used by 45% of filter users and 28% of non-users. Of households with taps, 75% had source water Escherichia coli in the lowest World Health Organisation risk category (<1/100 ml), vs. only 30% of households reporting wells did. Tap households were approximately four times more likely to discontinue filter use than well households. After 2 years, 24% of households were non-users. The main factors were breakage and household water source; households with taps were more likely to stop use than households with wells. Tap water users also had higher-quality source water, suggesting that disuse is not necessarily negative and monitoring of water quality can aid decision-making about continued use. To promote continued use, disaster recovery filter distribution efforts must be joined with capacity building for long-term water monitoring, supply chains and local production. © 2012 Blackwell Publishing Ltd.

A quantum heuristic algorithm for the traveling salesman problem

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Ryu, Junghee; Lee, Changhyoup; Yoo, Seokwon; Lim, James; Lee, Jinhyoung

2012-12-01

We propose a quantum heuristic algorithm to solve the traveling salesman problem by generalizing the Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with the cheapest costs reaching almost to unity. These conditions are characterized by the statistical properties of tour costs and are shown to be automatically satisfied in the large-number limit of cities. In particular for a continuous distribution of the tours along the cost, we show that the quantum heuristic algorithm exhibits a quadratic speedup compared to its classical heuristic algorithm.

Probabilistic measures of persistence and extinction in measles (meta)populations.

PubMed

Gunning, Christian E; Wearing, Helen J

2013-08-01

Persistence and extinction are fundamental processes in ecological systems that are difficult to accurately measure due to stochasticity and incomplete observation. Moreover, these processes operate on multiple scales, from individual populations to metapopulations. Here, we examine an extensive new data set of measles case reports and associated demographics in pre-vaccine era US cities, alongside a classic England & Wales data set. We first infer the per-population quasi-continuous distribution of log incidence. We then use stochastic, spatially implicit metapopulation models to explore the frequency of rescue events and apparent extinctions. We show that, unlike critical community size, the inferred distributions account for observational processes, allowing direct comparisons between metapopulations. The inferred distributions scale with population size. We use these scalings to estimate extinction boundary probabilities. We compare these predictions with measurements in individual populations and random aggregates of populations, highlighting the importance of medium-sized populations in metapopulation persistence. © 2013 John Wiley & Sons Ltd/CNRS.

Understanding poisson regression.

PubMed

Hayat, Matthew J; Higgins, Melinda

2014-04-01

Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes. Copyright 2014, SLACK Incorporated.

Flood Frequency Curves - Use of information on the likelihood of extreme floods

NASA Astrophysics Data System (ADS)

Faber, B.

2011-12-01

Investment in the infrastructure that reduces flood risk for flood-prone communities must incorporate information on the magnitude and frequency of flooding in that area. Traditionally, that information has been a probability distribution of annual maximum streamflows developed from the historical gaged record at a stream site. Practice in the United States fits a Log-Pearson type3 distribution to the annual maximum flows of an unimpaired streamflow record, using the method of moments to estimate distribution parameters. The procedure makes the assumptions that annual peak streamflow events are (1) independent, (2) identically distributed, and (3) form a representative sample of the overall probability distribution. Each of these assumptions can be challenged. We rarely have enough data to form a representative sample, and therefore must compute and display the uncertainty in the estimated flood distribution. But, is there a wet/dry cycle that makes precipitation less than independent between successive years? Are the peak flows caused by different types of events from different statistical populations? How does the watershed or climate changing over time (non-stationarity) affect the probability distribution floods? Potential approaches to avoid these assumptions vary from estimating trend and shift and removing them from early data (and so forming a homogeneous data set), to methods that estimate statistical parameters that vary with time. A further issue in estimating a probability distribution of flood magnitude (the flood frequency curve) is whether a purely statistical approach can accurately capture the range and frequency of floods that are of interest. A meteorologically-based analysis produces "probable maximum precipitation" (PMP) and subsequently a "probable maximum flood" (PMF) that attempts to describe an upper bound on flood magnitude in a particular watershed. This analysis can help constrain the upper tail of the probability distribution, well beyond the range of gaged data or even historical or paleo-flood data, which can be very important in risk analyses performed for flood risk management and dam and levee safety studies.

Transitional probabilities count more than frequency, but might not be used for memorization.

PubMed

Endress, Ansgar D; Langus, Alan

2017-02-01

Learners often need to extract recurring items from continuous sequences, in both vision and audition. The best-known example is probably found in word-learning, where listeners have to determine where words start and end in fluent speech. This could be achieved through universal and experience-independent statistical mechanisms, for example by relying on Transitional Probabilities (TPs). Further, these mechanisms might allow learners to store items in memory. However, previous investigations have yielded conflicting evidence as to whether a sensitivity to TPs is diagnostic of the memorization of recurring items. Here, we address this issue in the visual modality. Participants were familiarized with a continuous sequence of visual items (i.e., arbitrary or everyday symbols), and then had to choose between (i) high-TP items that appeared in the sequence, (ii) high-TP items that did not appear in the sequence, and (iii) low-TP items that appeared in the sequence. Items matched in TPs but differing in (chunk) frequency were much harder to discriminate than items differing in TPs (with no significant sensitivity to chunk frequency), and learners preferred unattested high-TP items over attested low-TP items. Contrary to previous claims, these results cannot be explained on the basis of the similarity of the test items. Learners thus weigh within-item TPs higher than the frequency of the chunks, even when the TP differences are relatively subtle. We argue that these results are problematic for distributional clustering mechanisms that analyze continuous sequences, and provide supporting computational results. We suggest that the role of TPs might not be to memorize items per se, but rather to prepare learners to memorize recurring items once they are presented in subsequent learning situations with richer cues. Copyright © 2016 Elsevier Inc. All rights reserved.

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution

PubMed Central

Dinov, Ivo D.; Kamino, Scott; Bhakhrani, Bilal; Christou, Nicolas

2014-01-01

Summary Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students’ understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference. PMID:25419016

Technology-enhanced Interactive Teaching of Marginal, Joint and Conditional Probabilities: The Special Case of Bivariate Normal Distribution.

PubMed

Dinov, Ivo D; Kamino, Scott; Bhakhrani, Bilal; Christou, Nicolas

2013-01-01

Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students' understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference.

Structural changes and fluctuations of proteins. I. A statistical thermodynamic model.

PubMed

Ikegami, A

1977-01-01

A general theory of the structural changes and fluctuations of proteins has been proposed based on statistical thermodynamic considerations at the chain level. The "structure" of protein was assumed to be characterized by the state of secondary bonds between unique pairs of specific sites on peptide chains. Every secondary bond changes between the bonded and unbonded states by thermal agitation and the "structure" is continuously fluctuating. The free energy of the "structural state" that is defined by the fraction of secondary bonds in the bonded state has been expressed by the bond energy, the cooperative interaction between bonds, the mixing entropy of bonds, and the entropy of polypeptide chains. The most probable "structural state" can be simply determined by graphical analysis and the effect of temperature or solvent composition on it is discussed. The temperature dependence of the free energy, the probability distribution of structural states and the specific heat have been calculted for two examples of structural change. The theory predicts two different types of structural changes from the ordered to disorderd state, a "structured transition" and a "gradual structural change" with rising temperature. In the "structural transition", the probability distribution has two maxima in the temperature range of transition. In the "gradual structural change", the probabilty distribution has only one maximum during the change. A considerable fraction of secondary bonds is in the unbounded state and is always fluctuating even in the ordered state at room temperature. Such structural flucutations in a single protein molecule have been discussed quantitatively. The theory is extended to include small molecules which bind to the protein molecule and affect the structural state. The changes of structural state caused by specific and non-specific binding and allosteric effects are explained in a unified manner.

Cost-effective solutions to maintaining smart grid reliability

NASA Astrophysics Data System (ADS)

Qin, Qiu

As the aging power systems are increasingly working closer to the capacity and thermal limits, maintaining an sufficient reliability has been of great concern to the government agency, utility companies and users. This dissertation focuses on improving the reliability of transmission and distribution systems. Based on the wide area measurements, multiple model algorithms are developed to diagnose transmission line three-phase short to ground faults in the presence of protection misoperations. The multiple model algorithms utilize the electric network dynamics to provide prompt and reliable diagnosis outcomes. Computational complexity of the diagnosis algorithm is reduced by using a two-step heuristic. The multiple model algorithm is incorporated into a hybrid simulation framework, which consist of both continuous state simulation and discrete event simulation, to study the operation of transmission systems. With hybrid simulation, line switching strategy for enhancing the tolerance to protection misoperations is studied based on the concept of security index, which involves the faulted mode probability and stability coverage. Local measurements are used to track the generator state and faulty mode probabilities are calculated in the multiple model algorithms. FACTS devices are considered as controllers for the transmission system. The placement of FACTS devices into power systems is investigated with a criterion of maintaining a prescribed level of control reconfigurability. Control reconfigurability measures the small signal combined controllability and observability of a power system with an additional requirement on fault tolerance. For the distribution systems, a hierarchical framework, including a high level recloser allocation scheme and a low level recloser placement scheme, is presented. The impacts of recloser placement on the reliability indices is analyzed. Evaluation of reliability indices in the placement process is carried out via discrete event simulation. The reliability requirements are described with probabilities and evaluated from the empirical distributions of reliability indices.

Framework for cascade size calculations on random networks

NASA Astrophysics Data System (ADS)

Burkholz, Rebekka; Schweitzer, Frank

2018-04-01

We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary degree distribution, degree-degree correlations, and, in case of threshold models, for arbitrary threshold distribution. With our approach, we shift the perspective from the known branching process approximations to the iterative update of suitable probability distributions. Such distributions are key to capture cascade dynamics that involve possibly continuous quantities and that depend on the cascade history, e.g., if load is accumulated over time. As a proof of concept, we provide two examples: (a) Constant load models that cover many of the analytically tractable casacade models, and, as a highlight, (b) a fiber bundle model that was not tractable by branching process approximations before. Our derivations cover the whole cascade dynamics, not only their steady state. This allows us to include interventions in time or further model complexity in the analysis.

Mathematical Model to estimate the wind power using four-parameter Burr distribution

NASA Astrophysics Data System (ADS)

Liu, Sanming; Wang, Zhijie; Pan, Zhaoxu

2018-03-01

When the real probability of wind speed in the same position needs to be described, the four-parameter Burr distribution is more suitable than other distributions. This paper introduces its important properties and characteristics. Also, the application of the four-parameter Burr distribution in wind speed prediction is discussed, and the expression of probability distribution of output power of wind turbine is deduced.

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations

NASA Astrophysics Data System (ADS)

Bhattacharjee, J. K.; Kirkpatrick, T. R.; Sengers, J. V.

2018-04-01

Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.

Methods to elicit probability distributions from experts: a systematic review of reported practice in health technology assessment.

PubMed

Grigore, Bogdan; Peters, Jaime; Hyde, Christopher; Stein, Ken

2013-11-01

Elicitation is a technique that can be used to obtain probability distribution from experts about unknown quantities. We conducted a methodology review of reports where probability distributions had been elicited from experts to be used in model-based health technology assessments. Databases including MEDLINE, EMBASE and the CRD database were searched from inception to April 2013. Reference lists were checked and citation mapping was also used. Studies describing their approach to the elicitation of probability distributions were included. Data was abstracted on pre-defined aspects of the elicitation technique. Reports were critically appraised on their consideration of the validity, reliability and feasibility of the elicitation exercise. Fourteen articles were included. Across these studies, the most marked features were heterogeneity in elicitation approach and failure to report key aspects of the elicitation method. The most frequently used approaches to elicitation were the histogram technique and the bisection method. Only three papers explicitly considered the validity, reliability and feasibility of the elicitation exercises. Judged by the studies identified in the review, reports of expert elicitation are insufficient in detail and this impacts on the perceived usability of expert-elicited probability distributions. In this context, the wider credibility of elicitation will only be improved by better reporting and greater standardisation of approach. Until then, the advantage of eliciting probability distributions from experts may be lost.

Computer simulation of random variables and vectors with arbitrary probability distribution laws

NASA Technical Reports Server (NTRS)

Bogdan, V. M.

1981-01-01

Assume that there is given an arbitrary n-dimensional probability distribution F. A recursive construction is found for a sequence of functions x sub 1 = f sub 1 (U sub 1, ..., U sub n), ..., x sub n = f sub n (U sub 1, ..., U sub n) such that if U sub 1, ..., U sub n are independent random variables having uniform distribution over the open interval (0,1), then the joint distribution of the variables x sub 1, ..., x sub n coincides with the distribution F. Since uniform independent random variables can be well simulated by means of a computer, this result allows one to simulate arbitrary n-random variables if their joint probability distribution is known.

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

Bartram, Bart W.; Vaughan, Frank R.; Englehart, Richard W., Dr.

1991-01-01

The use of a radioisotope thermoelectric generator fueled with plutonium-238 dioxide on the Space Shuttle-launched Ulysses mission implies some level of risk due to potential accidents. This paper describes the method used to quantify risks in the Ulysses mission Final Safety Analysis Report prepared for the U.S. Department of Energy. The starting point for the analysis described herein is following input of source term probability distributions from the General Electric Company. A Monte Carlo technique is used to develop probability distributions of radiological consequences for a range of accident scenarios thoughout the mission. Factors affecting radiological consequences are identified, the probability distribution of the effect of each factor determined, and the functional relationship among all the factors established. The probability distributions of all the factor effects are then combined using a Monte Carlo technique. The results of the analysis are presented in terms of complementary cumulative distribution functions (CCDF) by mission sub-phase, phase, and the overall mission. The CCDFs show the total probability that consequences (calculated health effects) would be equal to or greater than a given value.

Force Density Function Relationships in 2-D Granular Media

NASA Technical Reports Server (NTRS)

Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.

2004-01-01

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

An evaluation of procedures to estimate monthly precipitation probabilities

NASA Astrophysics Data System (ADS)

Legates, David R.

1991-01-01

Many frequency distributions have been used to evaluate monthly precipitation probabilities. Eight of these distributions (including Pearson type III, extreme value, and transform normal probability density functions) are comparatively examined to determine their ability to represent accurately variations in monthly precipitation totals for global hydroclimatological analyses. Results indicate that a modified version of the Box-Cox transform-normal distribution more adequately describes the 'true' precipitation distribution than does any of the other methods. This assessment was made using a cross-validation procedure for a global network of 253 stations for which at least 100 years of monthly precipitation totals were available.

q-Gaussian distributions of leverage returns, first stopping times, and default risk valuations

NASA Astrophysics Data System (ADS)

Katz, Yuri A.; Tian, Li

2013-10-01

We study the probability distributions of daily leverage returns of 520 North American industrial companies that survive de-listing during the financial crisis, 2006-2012. We provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of q-Gaussian distributions with the Tsallis entropic parameter within the interval 1

Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form

USGS Publications Warehouse

Greenwood, J. Arthur; Landwehr, J. Maciunas; Matalas, N.C.; Wallis, J.R.

1979-01-01

Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.

Univariate Probability Distributions

ERIC Educational Resources Information Center

Leemis, Lawrence M.; Luckett, Daniel J.; Powell, Austin G.; Vermeer, Peter E.

2012-01-01

We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the probability density function and cumulative distribution…

A probability space for quantum models

NASA Astrophysics Data System (ADS)

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.

Weak Measurement and Quantum Smoothing of a Superconducting Qubit

NASA Astrophysics Data System (ADS)

Tan, Dian

In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix rho(t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix rho(t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [rho(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix rho(t) with only diagonal elements in a given basis |n〉 may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal rho(t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.

Quantization of high dimensional Gaussian vector using permutation modulation with application to information reconciliation in continuous variable QKD

NASA Astrophysics Data System (ADS)

Daneshgaran, Fred; Mondin, Marina; Olia, Khashayar

This paper is focused on the problem of Information Reconciliation (IR) for continuous variable Quantum Key Distribution (QKD). The main problem is quantization and assignment of labels to the samples of the Gaussian variables observed at Alice and Bob. Trouble is that most of the samples, assuming that the Gaussian variable is zero mean which is de-facto the case, tend to have small magnitudes and are easily disturbed by noise. Transmission over longer and longer distances increases the losses corresponding to a lower effective Signal-to-Noise Ratio (SNR) exasperating the problem. Quantization over higher dimensions is advantageous since it allows for fractional bit per sample accuracy which may be needed at very low SNR conditions whereby the achievable secret key rate is significantly less than one bit per sample. In this paper, we propose to use Permutation Modulation (PM) for quantization of Gaussian vectors potentially containing thousands of samples. PM is applied to the magnitudes of the Gaussian samples and we explore the dependence of the sign error probability on the magnitude of the samples. At very low SNR, we may transmit the entire label of the PM code from Bob to Alice in Reverse Reconciliation (RR) over public channel. The side information extracted from this label can then be used by Alice to characterize the sign error probability of her individual samples. Forward Error Correction (FEC) coding can be used by Bob on each subset of samples with similar sign error probability to aid Alice in error correction. This can be done for different subsets of samples with similar sign error probabilities leading to an Unequal Error Protection (UEP) coding paradigm.

Metabolomics variable selection and classification in the presence of observations below the detection limit using an extension of ERp.

PubMed

van Reenen, Mari; Westerhuis, Johan A; Reinecke, Carolus J; Venter, J Hendrik

2017-02-02

ERp is a variable selection and classification method for metabolomics data. ERp uses minimized classification error rates, based on data from a control and experimental group, to test the null hypothesis of no difference between the distributions of variables over the two groups. If the associated p-values are significant they indicate discriminatory variables (i.e. informative metabolites). The p-values are calculated assuming a common continuous strictly increasing cumulative distribution under the null hypothesis. This assumption is violated when zero-valued observations can occur with positive probability, a characteristic of GC-MS metabolomics data, disqualifying ERp in this context. This paper extends ERp to address two sources of zero-valued observations: (i) zeros reflecting the complete absence of a metabolite from a sample (true zeros); and (ii) zeros reflecting a measurement below the detection limit. This is achieved by allowing the null cumulative distribution function to take the form of a mixture between a jump at zero and a continuous strictly increasing function. The extended ERp approach is referred to as XERp. XERp is no longer non-parametric, but its null distributions depend only on one parameter, the true proportion of zeros. Under the null hypothesis this parameter can be estimated by the proportion of zeros in the available data. XERp is shown to perform well with regard to bias and power. To demonstrate the utility of XERp, it is applied to GC-MS data from a metabolomics study on tuberculosis meningitis in infants and children. We find that XERp is able to provide an informative shortlist of discriminatory variables, while attaining satisfactory classification accuracy for new subjects in a leave-one-out cross-validation context. XERp takes into account the distributional structure of data with a probability mass at zero without requiring any knowledge of the detection limit of the metabolomics platform. XERp is able to identify variables that discriminate between two groups by simultaneously extracting information from the difference in the proportion of zeros and shifts in the distributions of the non-zero observations. XERp uses simple rules to classify new subjects and a weight pair to adjust for unequal sample sizes or sensitivity and specificity requirements.

FORSPAN Model Users Guide

USGS Publications Warehouse

Klett, T.R.; Charpentier, Ronald R.

2003-01-01

The USGS FORSPAN model is designed for the assessment of continuous accumulations of crude oil, natural gas, and natural gas liquids (collectively called petroleum). Continuous (also called ?unconventional?) accumulations have large spatial dimensions and lack well defined down-dip petroleum/water contacts. Oil and natural gas therefore are not localized by buoyancy in water in these accumulations. Continuous accumulations include ?tight gas reservoirs,? coalbed gas, oil and gas in shale, oil and gas in chalk, and shallow biogenic gas. The FORSPAN model treats a continuous accumulation as a collection of petroleumcontaining cells for assessment purposes. Each cell is capable of producing oil or gas, but the cells may vary significantly from one another in their production (and thus economic) characteristics. The potential additions to reserves from continuous petroleum resources are calculated by statistically combining probability distributions of the estimated number of untested cells having the potential for additions to reserves with the estimated volume of oil and natural gas that each of the untested cells may potentially produce (total recovery). One such statistical method for combination of number of cells with total recovery, used by the USGS, is called ACCESS.

Identifying Changes in the Probability of High Temperature, High Humidity Heat Wave Events

NASA Astrophysics Data System (ADS)

Ballard, T.; Diffenbaugh, N. S.

2016-12-01

Understanding how heat waves will respond to climate change is critical for adequate planning and adaptation. While temperature is the primary determinant of heat wave severity, humidity has been shown to play a key role in heat wave intensity with direct links to human health and safety. Here we investigate the individual contributions of temperature and specific humidity to extreme heat wave conditions in recent decades. Using global NCEP-DOE Reanalysis II daily data, we identify regional variability in the joint probability distribution of humidity and temperature. We also identify a statistically significant positive trend in humidity over the eastern U.S. during heat wave events, leading to an increased probability of high humidity, high temperature events. The extent to which we can expect this trend to continue under climate change is complicated due to variability between CMIP5 models, in particular among projections of humidity. However, our results support the notion that heat wave dynamics are characterized by more than high temperatures alone, and understanding and quantifying the various components of the heat wave system is crucial for forecasting future impacts.

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

NASA Astrophysics Data System (ADS)

Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.

2018-09-01

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

Derivation of Failure Rates and Probability of Failures for the International Space Station Probabilistic Risk Assessment Study

NASA Technical Reports Server (NTRS)

Vitali, Roberto; Lutomski, Michael G.

2004-01-01

National Aeronautics and Space Administration s (NASA) International Space Station (ISS) Program uses Probabilistic Risk Assessment (PRA) as part of its Continuous Risk Management Process. It is used as a decision and management support tool to not only quantify risk for specific conditions, but more importantly comparing different operational and management options to determine the lowest risk option and provide rationale for management decisions. This paper presents the derivation of the probability distributions used to quantify the failure rates and the probability of failures of the basic events employed in the PRA model of the ISS. The paper will show how a Bayesian approach was used with different sources of data including the actual ISS on orbit failures to enhance the confidence in results of the PRA. As time progresses and more meaningful data is gathered from on orbit failures, an increasingly accurate failure rate probability distribution for the basic events of the ISS PRA model can be obtained. The ISS PRA has been developed by mapping the ISS critical systems such as propulsion, thermal control, or power generation into event sequences diagrams and fault trees. The lowest level of indenture of the fault trees was the orbital replacement units (ORU). The ORU level was chosen consistently with the level of statistically meaningful data that could be obtained from the aerospace industry and from the experts in the field. For example, data was gathered for the solenoid valves present in the propulsion system of the ISS. However valves themselves are composed of parts and the individual failure of these parts was not accounted for in the PRA model. In other words the failure of a spring within a valve was considered a failure of the valve itself.

Regional probability distribution of the annual reference evapotranspiration and its effective parameters in Iran

NASA Astrophysics Data System (ADS)

Khanmohammadi, Neda; Rezaie, Hossein; Montaseri, Majid; Behmanesh, Javad

2017-10-01

The reference evapotranspiration (ET0) plays an important role in water management plans in arid or semi-arid countries such as Iran. For this reason, the regional analysis of this parameter is important. But, ET0 process is affected by several meteorological parameters such as wind speed, solar radiation, temperature and relative humidity. Therefore, the effect of distribution type of effective meteorological variables on ET0 distribution was analyzed. For this purpose, the regional probability distribution of the annual ET0 and its effective parameters were selected. Used data in this research was recorded data at 30 synoptic stations of Iran during 1960-2014. Using the probability plot correlation coefficient (PPCC) test and the L-moment method, five common distributions were compared and the best distribution was selected. The results of PPCC test and L-moment diagram indicated that the Pearson type III distribution was the best probability distribution for fitting annual ET0 and its four effective parameters. The results of RMSE showed that the ability of the PPCC test and L-moment method for regional analysis of reference evapotranspiration and its effective parameters was similar. The results also showed that the distribution type of the parameters which affected ET0 values can affect the distribution of reference evapotranspiration.

On Applying the Prognostic Performance Metrics

NASA Technical Reports Server (NTRS)

Saxena, Abhinav; Celaya, Jose; Saha, Bhaskar; Saha, Sankalita; Goebel, Kai

2009-01-01

Prognostics performance evaluation has gained significant attention in the past few years. As prognostics technology matures and more sophisticated methods for prognostic uncertainty management are developed, a standardized methodology for performance evaluation becomes extremely important to guide improvement efforts in a constructive manner. This paper is in continuation of previous efforts where several new evaluation metrics tailored for prognostics were introduced and were shown to effectively evaluate various algorithms as compared to other conventional metrics. Specifically, this paper presents a detailed discussion on how these metrics should be interpreted and used. Several shortcomings identified, while applying these metrics to a variety of real applications, are also summarized along with discussions that attempt to alleviate these problems. Further, these metrics have been enhanced to include the capability of incorporating probability distribution information from prognostic algorithms as opposed to evaluation based on point estimates only. Several methods have been suggested and guidelines have been provided to help choose one method over another based on probability distribution characteristics. These approaches also offer a convenient and intuitive visualization of algorithm performance with respect to some of these new metrics like prognostic horizon and alpha-lambda performance, and also quantify the corresponding performance while incorporating the uncertainty information.

Probabilistic reasoning in data analysis.

PubMed

Sirovich, Lawrence

2011-09-20

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on probabilistic reasoning in the analysis of biological data. General probabilistic frameworks are introduced, and a number of standard probability distributions are described using simple intuitive ideas. Particular attention is focused on random arrivals that are independent of prior history (Markovian events), with an emphasis on waiting times, Poisson processes, and Poisson probability distributions. The use of these various probability distributions is applied to biomedical problems, including several classic experimental studies.

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Work probability distribution and tossing a biased coin

NASA Astrophysics Data System (ADS)

Saha, Arnab; Bhattacharjee, Jayanta K.; Chakraborty, Sagar

2011-01-01

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for the Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modeling other physical phenomena where rare events play an important role.

Influence of pitting defects on quality of high power laser light field

NASA Astrophysics Data System (ADS)

Ren, Huan; Zhang, Lin; Yang, Yi; Shi, Zhendong; Ma, Hua; Jiang, Hongzhen; Chen, Bo; Yang, XiaoYu; Zheng, Wanguo; Zhu, Rihong

2018-01-01

With the split-step-Fourier-transform method for solving the nonlinear paraxial wave equation, the intensity distribution of the light field when the pits diameter or depth change is obtained by using numerical simulation, include the intensity distribution inside optical element, the beam near-field, the different distances behind the element and the beam far-field. Results show that with the increase of pits diameter or depth, the light field peak intensity and the contrast inside of element corresponding enhancement. The contrast of the intensity distribution of the rear surface of the element will increase slightly. The peak intensity produced by a specific location element downstream of thermal effect will continue to increase, the damage probability in optics placed here is greatly increased. For the intensity distribution of the far-field, increase the pitting diameter or depth will cause the focal spot intensity distribution changes, and the energy of the spectrum center region increase constantly. This work provide a basis for quantitative design and inspection for pitting defects, which provides a reference for the design of optical path arrangement.

Hybrid computer technique yields random signal probability distributions

NASA Technical Reports Server (NTRS)

Cameron, W. D.

1965-01-01

Hybrid computer determines the probability distributions of instantaneous and peak amplitudes of random signals. This combined digital and analog computer system reduces the errors and delays of manual data analysis.

Fast Reliability Assessing Method for Distribution Network with Distributed Renewable Energy Generation

NASA Astrophysics Data System (ADS)

Chen, Fan; Huang, Shaoxiong; Ding, Jinjin; Ding, Jinjin; Gao, Bo; Xie, Yuguang; Wang, Xiaoming

2018-01-01

This paper proposes a fast reliability assessing method for distribution grid with distributed renewable energy generation. First, the Weibull distribution and the Beta distribution are used to describe the probability distribution characteristics of wind speed and solar irradiance respectively, and the models of wind farm, solar park and local load are built for reliability assessment. Then based on power system production cost simulation probability discretization and linearization power flow, a optimal power flow objected with minimum cost of conventional power generation is to be resolved. Thus a reliability assessment for distribution grid is implemented fast and accurately. The Loss Of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) are selected as the reliability index, a simulation for IEEE RBTS BUS6 system in MATLAB indicates that the fast reliability assessing method calculates the reliability index much faster with the accuracy ensured when compared with Monte Carlo method.

40 CFR Appendix C to Part 191 - Guidance for Implementation of Subpart B

Code of Federal Regulations, 2014 CFR

2014-07-01

... that the remaining probability distribution of cumulative releases would not be significantly changed... with § 191.13 into a “complementary cumulative distribution function” that indicates the probability of... distribution function for each disposal system considered. The Agency assumes that a disposal system can be...

40 CFR Appendix C to Part 191 - Guidance for Implementation of Subpart B

Code of Federal Regulations, 2011 CFR

2011-07-01

... that the remaining probability distribution of cumulative releases would not be significantly changed... with § 191.13 into a “complementary cumulative distribution function” that indicates the probability of... distribution function for each disposal system considered. The Agency assumes that a disposal system can be...

Correlated continuous time random walk and option pricing

NASA Astrophysics Data System (ADS)

Lv, Longjin; Xiao, Jianbin; Fan, Liangzhong; Ren, Fuyao

2016-04-01

In this paper, we study a correlated continuous time random walk (CCTRW) with averaged waiting time, whose probability density function (PDF) is proved to follow stretched Gaussian distribution. Then, we apply this process into option pricing problem. Supposing the price of the underlying is driven by this CCTRW, we find this model captures the subdiffusive characteristic of financial markets. By using the mean self-financing hedging strategy, we obtain the closed-form pricing formulas for a European option with and without transaction costs, respectively. At last, comparing the obtained model with the classical Black-Scholes model, we find the price obtained in this paper is higher than that obtained from the Black-Scholes model. A empirical analysis is also introduced to confirm the obtained results can fit the real data well.

A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall

NASA Astrophysics Data System (ADS)

Lombardo, F.; Volpi, E.; Koutsoyiannis, D.; Serinaldi, F.

2017-06-01

Generating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.

Pseudo Bayes Estimates for Test Score Distributions and Chained Equipercentile Equating. Research Report. ETS RR-09-47

ERIC Educational Resources Information Center

Moses, Tim; Oh, Hyeonjoo J.

2009-01-01

Pseudo Bayes probability estimates are weighted averages of raw and modeled probabilities; these estimates have been studied primarily in nonpsychometric contexts. The purpose of this study was to evaluate pseudo Bayes probability estimates as applied to the estimation of psychometric test score distributions and chained equipercentile equating…

Variability of daily UV index in Jokioinen, Finland, in 1995-2015

NASA Astrophysics Data System (ADS)

Heikkilä, A.; Uusitalo, K.; Kärhä, P.; Vaskuri, A.; Lakkala, K.; Koskela, T.

2017-02-01

UV Index is a measure for UV radiation harmful for the human skin, developed and used to promote the sun awareness and protection of people. Monitoring programs conducted around the world have produced a number of long-term time series of UV irradiance. One of the longest time series of solar spectral UV irradiance in Europe has been obtained from the continuous measurements of Brewer #107 spectrophotometer in Jokioinen (lat. 60°44'N, lon. 23°30'E), Finland, over the years 1995-2015. We have used descriptive statistics and estimates of cumulative distribution functions, quantiles and probability density functions in the analysis of the time series of daily UV Index maxima. Seasonal differences in the estimated distributions and in the trends of the estimated quantiles are found.

Applications of Genomic Selection in Breeding Wheat for Rust Resistance.

PubMed

Ornella, Leonardo; González-Camacho, Juan Manuel; Dreisigacker, Susanne; Crossa, Jose

2017-01-01

There are a lot of methods developed to predict untested phenotypes in schemes commonly used in genomic selection (GS) breeding. The use of GS for predicting disease resistance has its own particularities: (a) most populations shows additivity in quantitative adult plant resistance (APR); (b) resistance needs effective combinations of major and minor genes; and (c) phenotype is commonly expressed in ordinal categorical traits, whereas most parametric applications assume that the response variable is continuous and normally distributed. Machine learning methods (MLM) can take advantage of examples (data) that capture characteristics of interest from an unknown underlying probability distribution (i.e., data-driven). We introduce some state-of-the-art MLM capable to predict rust resistance in wheat. We also present two parametric R packages for the reader to be able to compare.

Visualizing Big Data Outliers through Distributed Aggregation.

PubMed

Wilkinson, Leland

2017-08-29

Visualizing outliers in massive datasets requires statistical pre-processing in order to reduce the scale of the problem to a size amenable to rendering systems like D3, Plotly or analytic systems like R or SAS. This paper presents a new algorithm, called hdoutliers, for detecting multidimensional outliers. It is unique for a) dealing with a mixture of categorical and continuous variables, b) dealing with big-p (many columns of data), c) dealing with big-n (many rows of data), d) dealing with outliers that mask other outliers, and e) dealing consistently with unidimensional and multidimensional datasets. Unlike ad hoc methods found in many machine learning papers, hdoutliers is based on a distributional model that allows outliers to be tagged with a probability. This critical feature reduces the likelihood of false discoveries.

Failure probability under parameter uncertainty.

PubMed

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.

Comparison of three-parameter probability distributions for representing annual extreme and partial duration precipitation series

NASA Astrophysics Data System (ADS)

Wilks, Daniel S.

1993-10-01

Performance of 8 three-parameter probability distributions for representing annual extreme and partial duration precipitation data at stations in the northeastern and southeastern United States is investigated. Particular attention is paid to fidelity on the right tail, through use of a bootstrap procedure simulating extrapolation on the right tail beyond the data. It is found that the beta-κ distribution best describes the extreme right tail of annual extreme series, and the beta-P distribution is best for the partial duration data. The conventionally employed two-parameter Gumbel distribution is found to substantially underestimate probabilities associated with the larger precipitation amounts for both annual extreme and partial duration data. Fitting the distributions using left-censored data did not result in improved fits to the right tail.

Combining state-and-transition simulations and species distribution models to anticipate the effects of climate change

USGS Publications Warehouse

Miller, Brian W.; Frid, Leonardo; Chang, Tony; Piekielek, N. B.; Hansen, Andrew J.; Morisette, Jeffrey T.

2015-01-01

State-and-transition simulation models (STSMs) are known for their ability to explore the combined effects of multiple disturbances, ecological dynamics, and management actions on vegetation. However, integrating the additional impacts of climate change into STSMs remains a challenge. We address this challenge by combining an STSM with species distribution modeling (SDM). SDMs estimate the probability of occurrence of a given species based on observed presence and absence locations as well as environmental and climatic covariates. Thus, in order to account for changes in habitat suitability due to climate change, we used SDM to generate continuous surfaces of species occurrence probabilities. These data were imported into ST-Sim, an STSM platform, where they dictated the probability of each cell transitioning between alternate potential vegetation types at each time step. The STSM was parameterized to capture additional processes of vegetation growth and disturbance that are relevant to a keystone species in the Greater Yellowstone Ecosystem—whitebark pine (Pinus albicaulis). We compared historical model runs against historical observations of whitebark pine and a key disturbance agent (mountain pine beetle, Dendroctonus ponderosae), and then projected the simulation into the future. Using this combination of correlative and stochastic simulation models, we were able to reproduce historical observations and identify key data gaps. Results indicated that SDMs and STSMs are complementary tools, and combining them is an effective way to account for the anticipated impacts of climate change, biotic interactions, and disturbances, while also allowing for the exploration of management options.

A blueprint for demonstrating quantum supremacy with superconducting qubits.

PubMed

Neill, C; Roushan, P; Kechedzhi, K; Boixo, S; Isakov, S V; Smelyanskiy, V; Megrant, A; Chiaro, B; Dunsworth, A; Arya, K; Barends, R; Burkett, B; Chen, Y; Chen, Z; Fowler, A; Foxen, B; Giustina, M; Graff, R; Jeffrey, E; Huang, T; Kelly, J; Klimov, P; Lucero, E; Mutus, J; Neeley, M; Quintana, C; Sank, D; Vainsencher, A; Wenner, J; White, T C; Neven, H; Martinis, J M

2018-04-13

A key step toward demonstrating a quantum system that can address difficult problems in physics and chemistry will be performing a computation beyond the capabilities of any classical computer, thus achieving so-called quantum supremacy. In this study, we used nine superconducting qubits to demonstrate a promising path toward quantum supremacy. By individually tuning the qubit parameters, we were able to generate thousands of distinct Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert space. As the number of qubits increases, the system continues to explore the exponentially growing number of states. Extending these results to a system of 50 qubits has the potential to address scientific questions that are beyond the capabilities of any classical computer. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Solutions of burnt-bridge models for molecular motor transport.

PubMed

Morozov, Alexander Yu; Pronina, Ekaterina; Kolomeisky, Anatoly B; Artyomov, Maxim N

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called "bridges"), is investigated theoretically by analyzing discrete-state stochastic "burnt-bridge" models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed ("burned") with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander; Pronina, Ekaterina; Kolomeisky, Anatoly; Artyomov, Maxim

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability p, creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of p<1 a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Solutions of burnt-bridge models for molecular motor transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander Yu.; Pronina, Ekaterina; Kolomeisky, Anatoly B.; Artyomov, Maxim N.

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called “bridges”), is investigated theoretically by analyzing discrete-state stochastic “burnt-bridge” models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (“burned”) with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

The estimation of tree posterior probabilities using conditional clade probability distributions.

PubMed

Larget, Bret

2013-07-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample.

Mutually cooperative epidemics on power-law networks

NASA Astrophysics Data System (ADS)

Cui, Peng-Bi; Colaiori, Francesca; Castellano, Claudio

2017-08-01

The spread of an infectious disease can, in some cases, promote the propagation of other pathogens favoring violent outbreaks, which cause a discontinuous transition to an endemic state. The topology of the contact network plays a crucial role in these cooperative dynamics. We consider a susceptible-infected-removed-type model with two mutually cooperative pathogens: An individual already infected with one disease has an increased probability of getting infected by the other. We present a heterogeneous mean-field theoretical approach to the coinfection dynamics on generic uncorrelated power-law degree-distributed networks and validate its results by means of numerical simulations. We show that, when the second moment of the degree distribution is finite, the epidemic transition is continuous for low cooperativity, while it is discontinuous when cooperativity is sufficiently high. For scale-free networks, i.e., topologies with diverging second moment, the transition is instead always continuous. In this way we clarify the effect of heterogeneity and system size on the nature of the transition, and we validate the physical interpretation about the origin of the discontinuity.

A non-gaussian model of continuous atmospheric turbulence for use in aircraft design

NASA Technical Reports Server (NTRS)

Reeves, P. M.; Joppa, R. G.; Ganzer, V. M.

1976-01-01

A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.

Probability Analysis of the Wave-Slamming Pressure Values of the Horizontal Deck with Elastic Support

NASA Astrophysics Data System (ADS)

Zuo, Weiguang; Liu, Ming; Fan, Tianhui; Wang, Pengtao

2018-06-01

This paper presents the probability distribution of the slamming pressure from an experimental study of regular wave slamming on an elastically supported horizontal deck. The time series of the slamming pressure during the wave impact were first obtained through statistical analyses on experimental data. The exceeding probability distribution of the maximum slamming pressure peak and distribution parameters were analyzed, and the results show that the exceeding probability distribution of the maximum slamming pressure peak accords with the three-parameter Weibull distribution. Furthermore, the range and relationships of the distribution parameters were studied. The sum of the location parameter D and the scale parameter L was approximately equal to 1.0, and the exceeding probability was more than 36.79% when the random peak was equal to the sample average during the wave impact. The variation of the distribution parameters and slamming pressure under different model conditions were comprehensively presented, and the parameter values of the Weibull distribution of wave-slamming pressure peaks were different due to different test models. The parameter values were found to decrease due to the increased stiffness of the elastic support. The damage criterion of the structure model caused by the wave impact was initially discussed, and the structure model was destroyed when the average slamming time was greater than a certain value during the duration of the wave impact. The conclusions of the experimental study were then described.

On the inequivalence of the CH and CHSH inequalities due to finite statistics

NASA Astrophysics Data System (ADS)

Renou, M. O.; Rosset, D.; Martin, A.; Gisin, N.

2017-06-01

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.

Confidence as Bayesian Probability: From Neural Origins to Behavior.

PubMed

Meyniel, Florent; Sigman, Mariano; Mainen, Zachary F

2015-10-07

Research on confidence spreads across several sub-fields of psychology and neuroscience. Here, we explore how a definition of confidence as Bayesian probability can unify these viewpoints. This computational view entails that there are distinct forms in which confidence is represented and used in the brain, including distributional confidence, pertaining to neural representations of probability distributions, and summary confidence, pertaining to scalar summaries of those distributions. Summary confidence is, normatively, derived or "read out" from distributional confidence. Neural implementations of readout will trade off optimality versus flexibility of routing across brain systems, allowing confidence to serve diverse cognitive functions. Copyright © 2015 Elsevier Inc. All rights reserved.

Exact probability distribution functions for Parrondo's games

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Saakian, David B.; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

Exact probability distribution functions for Parrondo's games.

PubMed

Zadourian, Rubina; Saakian, David B; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

What Can Quantum Optics Say about Computational Complexity Theory?

NASA Astrophysics Data System (ADS)

Rahimi-Keshari, Saleh; Lund, Austin P.; Ralph, Timothy C.

2015-02-01

Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPPNP complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output.

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

Schiappacasse, Enrico D.; Fewster, Christopher J.; Ford, L. H.

2018-01-01

Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we study a specific operator that contributes to the stress-energy tensor of a massless scalar field in Minkowski spacetime, namely, the normal ordered square of the time derivative of the field. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lend additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.

Measurements of gas hydrate formation probability distributions on a quasi-free water droplet

NASA Astrophysics Data System (ADS)

Maeda, Nobuo

2014-06-01

A High Pressure Automated Lag Time Apparatus (HP-ALTA) can measure gas hydrate formation probability distributions from water in a glass sample cell. In an HP-ALTA gas hydrate formation originates near the edges of the sample cell and gas hydrate films subsequently grow across the water-guest gas interface. It would ideally be desirable to be able to measure gas hydrate formation probability distributions of a single water droplet or mist that is freely levitating in a guest gas, but this is technically challenging. The next best option is to let a water droplet sit on top of a denser, immiscible, inert, and wall-wetting hydrophobic liquid to avoid contact of a water droplet with the solid walls. Here we report the development of a second generation HP-ALTA which can measure gas hydrate formation probability distributions of a water droplet which sits on a perfluorocarbon oil in a container that is coated with 1H,1H,2H,2H-Perfluorodecyltriethoxysilane. It was found that the gas hydrate formation probability distributions of such a quasi-free water droplet were significantly lower than those of water in a glass sample cell.

Muscle categorization using PDF estimation and Naive Bayes classification.

PubMed

Adel, Tameem M; Smith, Benn E; Stashuk, Daniel W

2012-01-01

The structure of motor unit potentials (MUPs) and their times of occurrence provide information about the motor units (MUs) that created them. As such, electromyographic (EMG) data can be used to categorize muscles as normal or suffering from a neuromuscular disease. Using pattern discovery (PD) allows clinicians to understand the rationale underlying a certain muscle characterization; i.e. it is transparent. Discretization is required in PD, which leads to some loss in accuracy. In this work, characterization techniques that are based on estimating probability density functions (PDFs) for each muscle category are implemented. Characterization probabilities of each motor unit potential train (MUPT) are obtained from these PDFs and then Bayes rule is used to aggregate the MUPT characterization probabilities to calculate muscle level probabilities. Even though this technique is not as transparent as PD, its accuracy is higher than the discrete PD. Ultimately, the goal is to use a technique that is based on both PDFs and PD and make it as transparent and as efficient as possible, but first it was necessary to thoroughly assess how accurate a fully continuous approach can be. Using gaussian PDF estimation achieved improvements in muscle categorization accuracy over PD and further improvements resulted from using feature value histograms to choose more representative PDFs; for instance, using log-normal distribution to represent skewed histograms.

Geographic Expansion of Lyme Disease in Michigan, 2000-2014.

PubMed

Lantos, Paul M; Tsao, Jean; Nigrovic, Lise E; Auwaerter, Paul G; Fowler, Vance G; Ruffin, Felicia; Foster, Erik; Hickling, Graham

2017-01-01

Most Lyme disease cases in the Midwestern United States are reported in Minnesota and Wisconsin. In recent years, however, a widening geographic extent of Lyme disease has been noted with evidence of expansion eastwards into Michigan and neighboring states with historically low incidence rates. We collected confirmed and probable cases of Lyme disease from 2000 through 2014 from the Michigan Department of Health and Human Services, entering them in a geographic information system. We performed spatial focal cluster analyses to characterize Lyme disease expansion. We compared the distribution of human cases with recent Ixodes scapularis tick distribution studies. Lyme disease cases in both the Upper and Lower Peninsulas of Michigan expanded more than 5-fold over the study period. Although increases were seen throughout the Upper Peninsula, the Lower Peninsula particularly expanded along the Indiana border north along the eastern shore of Lake Michigan. Human cases corresponded to a simultaneous expansion in established I scapularis tick populations. The geographic distribution of Lyme disease cases significantly expanded in Michigan between 2000 and 2014, particularly northward along the Lake Michigan shore. If such dynamic trends continue, Michigan-and possibly neighboring areas of Indiana, Ohio, and Ontario, Canada-can expect a continued increase in Lyme disease cases. © The Author 2017. Published by Oxford University Press on behalf of Infectious Diseases Society of America.

Adaptive Sequential Monte Carlo for Multiple Changepoint Analysis

DOE PAGES

Heard, Nicholas A.; Turcotte, Melissa J. M.

2016-05-21

Process monitoring and control requires detection of structural changes in a data stream in real time. This paper introduces an efficient sequential Monte Carlo algorithm designed for learning unknown changepoints in continuous time. The method is intuitively simple: new changepoints for the latest window of data are proposed by conditioning only on data observed since the most recent estimated changepoint, as these observations carry most of the information about the current state of the process. The proposed method shows improved performance over the current state of the art. Another advantage of the proposed algorithm is that it can be mademore » adaptive, varying the number of particles according to the apparent local complexity of the target changepoint probability distribution. This saves valuable computing time when changes in the changepoint distribution are negligible, and enables re-balancing of the importance weights of existing particles when a significant change in the target distribution is encountered. The plain and adaptive versions of the method are illustrated using the canonical continuous time changepoint problem of inferring the intensity of an inhomogeneous Poisson process, although the method is generally applicable to any changepoint problem. Performance is demonstrated using both conjugate and non-conjugate Bayesian models for the intensity. Lastly, appendices to the article are available online, illustrating the method on other models and applications.« less

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

PubMed Central

Crawford, Forrest W.; Suchard, Marc A.

2011-01-01

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λn and a particle dies with instantaneous rate μn. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics. PMID:21984359

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

Bartram, Bart W.; Vaughan, Frank R.; Englehart, Richard W.

An account is given of the method used to quantify the risks accruing to the use of a radioisotope thermoelectric generator fueled by Pu-238 dioxide aboard the Space Shuttle-launched Ulysses mission. After using a Monte Carlo technique to develop probability distributions for the radiological consequences of a range of accident scenarios throughout the mission, factors affecting those consequences are identified in conjunction with their probability distributions. The functional relationship among all the factors is then established, and probability distributions for all factor effects are combined by means of a Monte Carlo technique.

Score distributions of gapped multiple sequence alignments down to the low-probability tail

NASA Astrophysics Data System (ADS)

Fieth, Pascal; Hartmann, Alexander K.

2016-08-01

Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the biologically relevant high-scoring region, where the probabilities are exponentially small. For gapless local alignments of infinitely long sequences this distribution is known analytically to follow a Gumbel distribution. Distributions for gapped local alignments and global alignments of finite lengths can only be obtained numerically. To obtain result for the small-probability region, specific statistical mechanics-based rare-event algorithms can be applied. In previous studies, this was achieved for pairwise alignments. They showed that, contrary to results from previous simple sampling studies, strong deviations from the Gumbel distribution occur in case of finite sequence lengths. Here we extend the studies to multiple sequence alignments with gaps, which are much more relevant for practical applications in molecular biology. We study the distributions of scores over a large range of the support, reaching probabilities as small as 10-160, for global and local (sum-of-pair scores) multiple alignments. We find that even after suitable rescaling, eliminating the sequence-length dependence, the distributions for multiple alignment differ from the pairwise alignment case. Furthermore, we also show that the previously discussed Gaussian correction to the Gumbel distribution needs to be refined, also for the case of pairwise alignments.

Contrasting patterns of population history and seed-mediated gene flow in two endemic Costa Rican oak species.

PubMed

Rodríguez-Correa, Hernando; Oyama, Ken; Quesada, Mauricio; Fuchs, Eric J; González-Rodríguez, Antonio

2018-03-02

Lower Central America is an important area to study recent population history and diversification of Neotropical species due to its complex and dynamic geology and climate. Phylogeographic studies in this region are few in comparison with other regions and even less for tree species. The aim of the present study was to characterize the phylogeographic structure in two partially co-distributed endemic oak species (Quercus costaricensis and Q. bumelioides) of the Costa Rican mountains using chloroplast short sequence repeats (cpSSRs), and to test for the effect of geological and palaeoclimatic processes on their population history. Genetic diversity and structure, haplotype networks, patterns of seed-mediated gene flow and historical demography were estimated for both species. Results suggested contrasting patterns. Quercus costaricensis exhibited high values of genetic diversity, a marked phylogeographic structure, a north-to-south genetic diversity gradient and evidence of a demographic expansion during the Quaternary. Quercus bumelioides did not show significant genetic structure and the haplotype network and historical demography estimates suggested a recent population expansion probably during the Pleistocene-Holocene transition. Phylogeographic structure of Q. costaricensis seems to be related to Pleistocene altitudinal migration due to its higher altitudinal distribution. Meanwhile, historical seed-mediated gene flow through the lower altitudinal distribution of Q. bumelioides may have promoted the homogenization of genetic variation. Population expansion and stable availability of suitable climatic areas in both species probably indicate that palaeoclimatic changes promoted downwards altitudinal migration and formation of continuous forests allowing oak species to expand their distribution into the Panamanian mountains during glacial stages.

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

PubMed

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

Site occupancy models with heterogeneous detection probabilities

USGS Publications Warehouse

Royle, J. Andrew

2006-01-01

Models for estimating the probability of occurrence of a species in the presence of imperfect detection are important in many ecological disciplines. In these ?site occupancy? models, the possibility of heterogeneity in detection probabilities among sites must be considered because variation in abundance (and other factors) among sampled sites induces variation in detection probability (p). In this article, I develop occurrence probability models that allow for heterogeneous detection probabilities by considering several common classes of mixture distributions for p. For any mixing distribution, the likelihood has the general form of a zero-inflated binomial mixture for which inference based upon integrated likelihood is straightforward. A recent paper by Link (2003, Biometrics 59, 1123?1130) demonstrates that in closed population models used for estimating population size, different classes of mixture distributions are indistinguishable from data, yet can produce very different inferences about population size. I demonstrate that this problem can also arise in models for estimating site occupancy in the presence of heterogeneous detection probabilities. The implications of this are discussed in the context of an application to avian survey data and the development of animal monitoring programs.

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Yupeng, E-mail: yupeng@ualberta.ca; Deutsch, Clayton V.

2012-06-15

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells.more » In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.« less

Modeling highway travel time distribution with conditional probability models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oliveira Neto, Francisco Moraes; Chin, Shih-Miao; Hwang, Ho-Ling

ABSTRACT Under the sponsorship of the Federal Highway Administration's Office of Freight Management and Operations, the American Transportation Research Institute (ATRI) has developed performance measures through the Freight Performance Measures (FPM) initiative. Under this program, travel speed information is derived from data collected using wireless based global positioning systems. These telemetric data systems are subscribed and used by trucking industry as an operations management tool. More than one telemetric operator submits their data dumps to ATRI on a regular basis. Each data transmission contains truck location, its travel time, and a clock time/date stamp. Data from the FPM program providesmore » a unique opportunity for studying the upstream-downstream speed distributions at different locations, as well as different time of the day and day of the week. This research is focused on the stochastic nature of successive link travel speed data on the continental United States Interstates network. Specifically, a method to estimate route probability distributions of travel time is proposed. This method uses the concepts of convolution of probability distributions and bivariate, link-to-link, conditional probability to estimate the expected distributions for the route travel time. Major contribution of this study is the consideration of speed correlation between upstream and downstream contiguous Interstate segments through conditional probability. The established conditional probability distributions, between successive segments, can be used to provide travel time reliability measures. This study also suggests an adaptive method for calculating and updating route travel time distribution as new data or information is added. This methodology can be useful to estimate performance measures as required by the recent Moving Ahead for Progress in the 21st Century Act (MAP 21).« less

Probability of success for phase III after exploratory biomarker analysis in phase II.

PubMed

Götte, Heiko; Kirchner, Marietta; Sailer, Martin Oliver

2017-05-01

The probability of success or average power describes the potential of a future trial by weighting the power with a probability distribution of the treatment effect. The treatment effect estimate from a previous trial can be used to define such a distribution. During the development of targeted therapies, it is common practice to look for predictive biomarkers. The consequence is that the trial population for phase III is often selected on the basis of the most extreme result from phase II biomarker subgroup analyses. In such a case, there is a tendency to overestimate the treatment effect. We investigate whether the overestimation of the treatment effect estimate from phase II is transformed into a positive bias for the probability of success for phase III. We simulate a phase II/III development program for targeted therapies. This simulation allows to investigate selection probabilities and allows to compare the estimated with the true probability of success. We consider the estimated probability of success with and without subgroup selection. Depending on the true treatment effects, there is a negative bias without selection because of the weighting by the phase II distribution. In comparison, selection increases the estimated probability of success. Thus, selection does not lead to a bias in probability of success if underestimation due to the phase II distribution and overestimation due to selection cancel each other out. We recommend to perform similar simulations in practice to get the necessary information about the risk and chances associated with such subgroup selection designs. Copyright © 2017 John Wiley & Sons, Ltd.

General formulation of long-range degree correlations in complex networks

NASA Astrophysics Data System (ADS)

Fujiki, Yuka; Takaguchi, Taro; Yakubo, Kousuke

2018-06-01

We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One joint and four conditional probability distributions are introduced to fully describe long-range degree correlations with respect to degrees k and k' of two nodes and shortest path length l between them. We present general relations among these probability distributions and clarify the relevance to nearest-neighbor degree correlations. Unlike nearest-neighbor correlations, some of these probability distributions are meaningful only in finite-size networks. Furthermore, as a baseline to determine the existence of intrinsic long-range degree correlations in a network other than inevitable correlations caused by the finite-size effect, the functional forms of these probability distributions for random networks are analytically evaluated within a mean-field approximation. The utility of our argument is demonstrated by applying it to real-world networks.

Stochastic analysis of particle movement over a dune bed

USGS Publications Warehouse

Lee, Baum K.; Jobson, Harvey E.

1977-01-01

Stochastic models are available that can be used to predict the transport and dispersion of bed-material sediment particles in an alluvial channel. These models are based on the proposition that the movement of a single bed-material sediment particle consists of a series of steps of random length separated by rest periods of random duration and, therefore, application of the models requires a knowledge of the probability distributions of the step lengths, the rest periods, the elevation of particle deposition, and the elevation of particle erosion. The procedure was tested by determining distributions from bed profiles formed in a large laboratory flume with a coarse sand as the bed material. The elevation of particle deposition and the elevation of particle erosion can be considered to be identically distributed, and their distribution can be described by either a ' truncated Gaussian ' or a ' triangular ' density function. The conditional probability distribution of the rest period given the elevation of particle deposition closely followed the two-parameter gamma distribution. The conditional probability distribution of the step length given the elevation of particle erosion and the elevation of particle deposition also closely followed the two-parameter gamma density function. For a given flow, the scale and shape parameters describing the gamma probability distributions can be expressed as functions of bed-elevation. (Woodard-USGS)

Using type IV Pearson distribution to calculate the probabilities of underrun and overrun of lists of multiple cases.

PubMed

Wang, Jihan; Yang, Kai

2014-07-01

An efficient operating room needs both little underutilised and overutilised time to achieve optimal cost efficiency. The probabilities of underrun and overrun of lists of cases can be estimated by a well defined duration distribution of the lists. To propose a method of predicting the probabilities of underrun and overrun of lists of cases using Type IV Pearson distribution to support case scheduling. Six years of data were collected. The first 5 years of data were used to fit distributions and estimate parameters. The data from the last year were used as testing data to validate the proposed methods. The percentiles of the duration distribution of lists of cases were calculated by Type IV Pearson distribution and t-distribution. Monte Carlo simulation was conducted to verify the accuracy of percentiles defined by the proposed methods. Operating rooms in John D. Dingell VA Medical Center, United States, from January 2005 to December 2011. Differences between the proportion of lists of cases that were completed within the percentiles of the proposed duration distribution of the lists and the corresponding percentiles. Compared with the t-distribution, the proposed new distribution is 8.31% (0.38) more accurate on average and 14.16% (0.19) more accurate in calculating the probabilities at the 10th and 90th percentiles of the distribution, which is a major concern of operating room schedulers. The absolute deviations between the percentiles defined by Type IV Pearson distribution and those from Monte Carlo simulation varied from 0.20  min (0.01) to 0.43  min (0.03). Operating room schedulers can rely on the most recent 10 cases with the same combination of surgeon and procedure(s) for distribution parameter estimation to plan lists of cases. Values are mean (SEM). The proposed Type IV Pearson distribution is more accurate than t-distribution to estimate the probabilities of underrun and overrun of lists of cases. However, as not all the individual case durations followed log-normal distributions, there was some deviation from the true duration distribution of the lists.

A tool for simulating collision probabilities of animals with marine renewable energy devices.

PubMed

Schmitt, Pál; Culloch, Ross; Lieber, Lilian; Molander, Sverker; Hammar, Linus; Kregting, Louise

2017-01-01

The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time). Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.

Lognormal Approximations of Fault Tree Uncertainty Distributions.

PubMed

El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

2018-01-26

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

Quantum key distribution without the wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations of the Hilbert space version of quantum key distribution, but are based upon a general nonclassical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution; this is a purely algebraic property of the quantum logic and represents the transition probability between the outcomes of two consecutive quantum measurements.

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations.

Probability distributions of hydraulic conductivity for the hydrogeologic units of the Death Valley regional ground-water flow system, Nevada and California

USGS Publications Warehouse

Belcher, Wayne R.; Sweetkind, Donald S.; Elliott, Peggy E.

2002-01-01

The use of geologic information such as lithology and rock properties is important to constrain conceptual and numerical hydrogeologic models. This geologic information is difficult to apply explicitly to numerical modeling and analyses because it tends to be qualitative rather than quantitative. This study uses a compilation of hydraulic-conductivity measurements to derive estimates of the probability distributions for several hydrogeologic units within the Death Valley regional ground-water flow system, a geologically and hydrologically complex region underlain by basin-fill sediments, volcanic, intrusive, sedimentary, and metamorphic rocks. Probability distributions of hydraulic conductivity for general rock types have been studied previously; however, this study provides more detailed definition of hydrogeologic units based on lithostratigraphy, lithology, alteration, and fracturing and compares the probability distributions to the aquifer test data. Results suggest that these probability distributions can be used for studies involving, for example, numerical flow modeling, recharge, evapotranspiration, and rainfall runoff. These probability distributions can be used for such studies involving the hydrogeologic units in the region, as well as for similar rock types elsewhere. Within the study area, fracturing appears to have the greatest influence on the hydraulic conductivity of carbonate bedrock hydrogeologic units. Similar to earlier studies, we find that alteration and welding in the Tertiary volcanic rocks greatly influence hydraulic conductivity. As alteration increases, hydraulic conductivity tends to decrease. Increasing degrees of welding appears to increase hydraulic conductivity because welding increases the brittleness of the volcanic rocks, thus increasing the amount of fracturing.

Universal Inverse Power-Law Distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter-Annual Variability of Indian and USA Region Rainfall

NASA Astrophysics Data System (ADS)

Selvam, A. M.

2017-01-01

Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference to possible prediction of climate change. Model concepts, if correct, rule out unambiguously, linear trends in climate. Climate change will only be manifested as increase or decrease in the natural variability. However, more stringent tests of model concepts and predictions are required before applications to such an important issue as climate change. Observations and simulations with climate models show that precipitation extremes intensify in response to a warming climate (O'Gorman in Curr Clim Change Rep 1:49-59, 2015).

Bayesian alternative to the ISO-GUM's use of the Welch Satterthwaite formula

NASA Astrophysics Data System (ADS)

Kacker, Raghu N.

2006-02-01

In certain disciplines, uncertainty is traditionally expressed as an interval about an estimate for the value of the measurand. Development of such uncertainty intervals with a stated coverage probability based on the International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) requires a description of the probability distribution for the value of the measurand. The ISO-GUM propagates the estimates and their associated standard uncertainties for various input quantities through a linear approximation of the measurement equation to determine an estimate and its associated standard uncertainty for the value of the measurand. This procedure does not yield a probability distribution for the value of the measurand. The ISO-GUM suggests that under certain conditions motivated by the central limit theorem the distribution for the value of the measurand may be approximated by a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite (W-S) formula. The approximate t-distribution may then be used to develop an uncertainty interval with a stated coverage probability for the value of the measurand. We propose an approximate normal distribution based on a Bayesian uncertainty as an alternative to the t-distribution based on the W-S formula. A benefit of the approximate normal distribution based on a Bayesian uncertainty is that it greatly simplifies the expression of uncertainty by eliminating altogether the need for calculating effective degrees of freedom from the W-S formula. In the special case where the measurand is the difference between two means, each evaluated from statistical analyses of independent normally distributed measurements with unknown and possibly unequal variances, the probability distribution for the value of the measurand is known to be a Behrens-Fisher distribution. We compare the performance of the approximate normal distribution based on a Bayesian uncertainty and the approximate t-distribution based on the W-S formula with respect to the Behrens-Fisher distribution. The approximate normal distribution is simpler and better in this case. A thorough investigation of the relative performance of the two approximate distributions would require comparison for a range of measurement equations by numerical methods.

Does Litter Size Variation Affect Models of Terrestrial Carnivore Extinction Risk and Management?

PubMed Central

Devenish-Nelson, Eleanor S.; Stephens, Philip A.; Harris, Stephen; Soulsbury, Carl; Richards, Shane A.

2013-01-01

Background Individual variation in both survival and reproduction has the potential to influence extinction risk. Especially for rare or threatened species, reliable population models should adequately incorporate demographic uncertainty. Here, we focus on an important form of demographic stochasticity: variation in litter sizes. We use terrestrial carnivores as an example taxon, as they are frequently threatened or of economic importance. Since data on intraspecific litter size variation are often sparse, it is unclear what probability distribution should be used to describe the pattern of litter size variation for multiparous carnivores. Methodology/Principal Findings We used litter size data on 32 terrestrial carnivore species to test the fit of 12 probability distributions. The influence of these distributions on quasi-extinction probabilities and the probability of successful disease control was then examined for three canid species – the island fox Urocyon littoralis, the red fox Vulpes vulpes, and the African wild dog Lycaon pictus. Best fitting probability distributions differed among the carnivores examined. However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small. Importantly, however, the outcomes of demographic models were generally robust to the distribution used. Conclusion/Significance These results provide reassurance for those using demographic modelling for the management of less studied carnivores in which litter size variation is estimated using data from species with similar reproductive attributes. PMID:23469140

Does litter size variation affect models of terrestrial carnivore extinction risk and management?

PubMed

Devenish-Nelson, Eleanor S; Stephens, Philip A; Harris, Stephen; Soulsbury, Carl; Richards, Shane A

2013-01-01

Individual variation in both survival and reproduction has the potential to influence extinction risk. Especially for rare or threatened species, reliable population models should adequately incorporate demographic uncertainty. Here, we focus on an important form of demographic stochasticity: variation in litter sizes. We use terrestrial carnivores as an example taxon, as they are frequently threatened or of economic importance. Since data on intraspecific litter size variation are often sparse, it is unclear what probability distribution should be used to describe the pattern of litter size variation for multiparous carnivores. We used litter size data on 32 terrestrial carnivore species to test the fit of 12 probability distributions. The influence of these distributions on quasi-extinction probabilities and the probability of successful disease control was then examined for three canid species - the island fox Urocyon littoralis, the red fox Vulpes vulpes, and the African wild dog Lycaon pictus. Best fitting probability distributions differed among the carnivores examined. However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small. Importantly, however, the outcomes of demographic models were generally robust to the distribution used. These results provide reassurance for those using demographic modelling for the management of less studied carnivores in which litter size variation is estimated using data from species with similar reproductive attributes.

Neighbor-Dependent Ramachandran Probability Distributions of Amino Acids Developed from a Hierarchical Dirichlet Process Model

PubMed Central

Mitra, Rajib; Jordan, Michael I.; Dunbrack, Roland L.

2010-01-01

Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1) input data size and criteria for structure inclusion (resolution, R-factor, etc.); 2) filtering of suspect conformations and outliers using B-factors or other features; 3) secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included); 4) the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5) whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately) have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp. PMID:20442867

Probabilistic analysis of preload in the abutment screw of a dental implant complex.

PubMed

Guda, Teja; Ross, Thomas A; Lang, Lisa A; Millwater, Harry R

2008-09-01

Screw loosening is a problem for a percentage of implants. A probabilistic analysis to determine the cumulative probability distribution of the preload, the probability of obtaining an optimal preload, and the probabilistic sensitivities identifying important variables is lacking. The purpose of this study was to examine the inherent variability of material properties, surface interactions, and applied torque in an implant system to determine the probability of obtaining desired preload values and to identify the significant variables that affect the preload. Using software programs, an abutment screw was subjected to a tightening torque and the preload was determined from finite element (FE) analysis. The FE model was integrated with probabilistic analysis software. Two probabilistic analysis methods (advanced mean value and Monte Carlo sampling) were applied to determine the cumulative distribution function (CDF) of preload. The coefficient of friction, elastic moduli, Poisson's ratios, and applied torque were modeled as random variables and defined by probability distributions. Separate probability distributions were determined for the coefficient of friction in well-lubricated and dry environments. The probabilistic analyses were performed and the cumulative distribution of preload was determined for each environment. A distinct difference was seen between the preload probability distributions generated in a dry environment (normal distribution, mean (SD): 347 (61.9) N) compared to a well-lubricated environment (normal distribution, mean (SD): 616 (92.2) N). The probability of obtaining a preload value within the target range was approximately 54% for the well-lubricated environment and only 0.02% for the dry environment. The preload is predominately affected by the applied torque and coefficient of friction between the screw threads and implant bore at lower and middle values of the preload CDF, and by the applied torque and the elastic modulus of the abutment screw at high values of the preload CDF. Lubrication at the threaded surfaces between the abutment screw and implant bore affects the preload developed in the implant complex. For the well-lubricated surfaces, only approximately 50% of implants will have preload values within the generally accepted range. This probability can be improved by applying a higher torque than normally recommended or a more closely controlled torque than typically achieved. It is also suggested that materials with higher elastic moduli be used in the manufacture of the abutment screw to achieve a higher preload.

Comparative analysis through probability distributions of a data set

NASA Astrophysics Data System (ADS)

Cristea, Gabriel; Constantinescu, Dan Mihai

2018-02-01

In practice, probability distributions are applied in such diverse fields as risk analysis, reliability engineering, chemical engineering, hydrology, image processing, physics, market research, business and economic research, customer support, medicine, sociology, demography etc. This article highlights important aspects of fitting probability distributions to data and applying the analysis results to make informed decisions. There are a number of statistical methods available which can help us to select the best fitting model. Some of the graphs display both input data and fitted distributions at the same time, as probability density and cumulative distribution. The goodness of fit tests can be used to determine whether a certain distribution is a good fit. The main used idea is to measure the "distance" between the data and the tested distribution, and compare that distance to some threshold values. Calculating the goodness of fit statistics also enables us to order the fitted distributions accordingly to how good they fit to data. This particular feature is very helpful for comparing the fitted models. The paper presents a comparison of most commonly used goodness of fit tests as: Kolmogorov-Smirnov, Anderson-Darling, and Chi-Squared. A large set of data is analyzed and conclusions are drawn by visualizing the data, comparing multiple fitted distributions and selecting the best model. These graphs should be viewed as an addition to the goodness of fit tests.

SIMULATED HUMAN ERROR PROBABILITY AND ITS APPLICATION TO DYNAMIC HUMAN FAILURE EVENTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herberger, Sarah M.; Boring, Ronald L.

Abstract Objectives: Human reliability analysis (HRA) methods typically analyze human failure events (HFEs) at the overall task level. For dynamic HRA, it is important to model human activities at the subtask level. There exists a disconnect between dynamic subtask level and static task level that presents issues when modeling dynamic scenarios. For example, the SPAR-H method is typically used to calculate the human error probability (HEP) at the task level. As demonstrated in this paper, quantification in SPAR-H does not translate to the subtask level. Methods: Two different discrete distributions were generated for each SPAR-H Performance Shaping Factor (PSF) tomore » define the frequency of PSF levels. The first distribution was a uniform, or uninformed distribution that assumed the frequency of each PSF level was equally likely. The second non-continuous distribution took the frequency of PSF level as identified from an assessment of the HERA database. These two different approaches were created to identify the resulting distribution of the HEP. The resulting HEP that appears closer to the known distribution, a log-normal centered on 1E-3, is the more desirable. Each approach then has median, average and maximum HFE calculations applied. To calculate these three values, three events, A, B and C are generated from the PSF level frequencies comprised of subtasks. The median HFE selects the median PSF level from each PSF and calculates HEP. The average HFE takes the mean PSF level, and the maximum takes the maximum PSF level. The same data set of subtask HEPs yields starkly different HEPs when aggregated to the HFE level in SPAR-H. Results: Assuming that each PSF level in each HFE is equally likely creates an unrealistic distribution of the HEP that is centered at 1. Next the observed frequency of PSF levels was applied with the resulting HEP behaving log-normally with a majority of the values under 2.5% HEP. The median, average and maximum HFE calculations did yield different answers for the HFE. The HFE maximum grossly over estimates the HFE, while the HFE distribution occurs less than HFE median, and greater than HFE average. Conclusions: Dynamic task modeling can be perused through the framework of SPAR-H. Identification of distributions associated with each PSF needs to be defined, and may change depending upon the scenario. However it is very unlikely that each PSF level is equally likely as the resulting HEP distribution is strongly centered at 100%, which is unrealistic. Other distributions may need to be identified for PSFs, to facilitate the transition to dynamic task modeling. Additionally discrete distributions need to be exchanged for continuous so that simulations for the HFE can further advance. This paper provides a method to explore dynamic subtask to task translation and provides examples of the process using the SPAR-H method.« less

Impact of temporal probability in 4D dose calculation for lung tumors.

PubMed

Rouabhi, Ouided; Ma, Mingyu; Bayouth, John; Xia, Junyi

2015-11-08

The purpose of this study was to evaluate the dosimetric uncertainty in 4D dose calculation using three temporal probability distributions: uniform distribution, sinusoidal distribution, and patient-specific distribution derived from the patient respiratory trace. Temporal probability, defined as the fraction of time a patient spends in each respiratory amplitude, was evaluated in nine lung cancer patients. Four-dimensional computed tomography (4D CT), along with deformable image registration, was used to compute 4D dose incorporating the patient's respiratory motion. First, the dose of each of 10 phase CTs was computed using the same planning parameters as those used in 3D treatment planning based on the breath-hold CT. Next, deformable image registration was used to deform the dose of each phase CT to the breath-hold CT using the deformation map between the phase CT and the breath-hold CT. Finally, the 4D dose was computed by summing the deformed phase doses using their corresponding temporal probabilities. In this study, 4D dose calculated from the patient-specific temporal probability distribution was used as the ground truth. The dosimetric evaluation matrix included: 1) 3D gamma analysis, 2) mean tumor dose (MTD), 3) mean lung dose (MLD), and 4) lung V20. For seven out of nine patients, both uniform and sinusoidal temporal probability dose distributions were found to have an average gamma passing rate > 95% for both the lung and PTV regions. Compared with 4D dose calculated using the patient respiratory trace, doses using uniform and sinusoidal distribution showed a percentage difference on average of -0.1% ± 0.6% and -0.2% ± 0.4% in MTD, -0.2% ± 1.9% and -0.2% ± 1.3% in MLD, 0.09% ± 2.8% and -0.07% ± 1.8% in lung V20, -0.1% ± 2.0% and 0.08% ± 1.34% in lung V10, 0.47% ± 1.8% and 0.19% ± 1.3% in lung V5, respectively. We concluded that four-dimensional dose computed using either a uniform or sinusoidal temporal probability distribution can approximate four-dimensional dose computed using the patient-specific respiratory trace.

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

NASA Astrophysics Data System (ADS)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.

Net present value probability distributions from decline curve reserves estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simpson, D.E.; Huffman, C.H.; Thompson, R.S.

1995-12-31

This paper demonstrates how reserves probability distributions can be used to develop net present value (NPV) distributions. NPV probability distributions were developed from the rate and reserves distributions presented in SPE 28333. This real data study used practicing engineer`s evaluations of production histories. Two approaches were examined to quantify portfolio risk. The first approach, the NPV Relative Risk Plot, compares the mean NPV with the NPV relative risk ratio for the portfolio. The relative risk ratio is the NPV standard deviation (a) divided the mean ({mu}) NPV. The second approach, a Risk - Return Plot, is a plot of themore » {mu} discounted cash flow rate of return (DCFROR) versus the {sigma} for the DCFROR distribution. This plot provides a risk-return relationship for comparing various portfolios. These methods may help evaluate property acquisition and divestiture alternatives and assess the relative risk of a suite of wells or fields for bank loans.« less

Optimal random search for a single hidden target.

PubMed

Snider, Joseph

2011-01-01

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

Use of passive ambient ozone (O3) samplers in vegetation effects assessment

USGS Publications Warehouse

Krupa, S.; Nosal, M.; Peterson, D.L.

2001-01-01

A stochastistic, Weibull probability model was developed and verified to simulate the underlying frequency distributions of hourly ozone (O3) concentrations (exposure dynamics) using the single, weekly mean values obtained from a passive (sodium nitrite absorbent) sampler. The simulation was based on the data derived from a co-located continuous monitor. Although at the moment the model output may be considered as being specific to the elevation and location of the study site, the results were extremely good. This effort for the approximation of the O3 exposure dynamics can be extended to other sites with similar data sets and in developing a generalized understanding of the stochastic O3 exposure-plant response relationships, conferring measurable benefits to the future use of passive O3 samplers, in the absence of continuous monitoring. Copyright ?? 2000 Elsevier Science Ltd.

Multi-scale Characterization and Modeling of Surface Slope Probability Distribution for ~20-km Diameter Lunar Craters

NASA Astrophysics Data System (ADS)

Mahanti, P.; Robinson, M. S.; Boyd, A. K.

2013-12-01

Craters ~20-km diameter and above significantly shaped the lunar landscape. The statistical nature of the slope distribution on their walls and floors dominate the overall slope distribution statistics for the lunar surface. Slope statistics are inherently useful for characterizing the current topography of the surface, determining accurate photometric and surface scattering properties, and in defining lunar surface trafficability [1-4]. Earlier experimental studies on the statistical nature of lunar surface slopes were restricted either by resolution limits (Apollo era photogrammetric studies) or by model error considerations (photoclinometric and radar scattering studies) where the true nature of slope probability distribution was not discernible at baselines smaller than a kilometer[2,3,5]. Accordingly, historical modeling of lunar surface slopes probability distributions for applications such as in scattering theory development or rover traversability assessment is more general in nature (use of simple statistical models such as the Gaussian distribution[1,2,5,6]). With the advent of high resolution, high precision topographic models of the Moon[7,8], slopes in lunar craters can now be obtained at baselines as low as 6-meters allowing unprecedented multi-scale (multiple baselines) modeling possibilities for slope probability distributions. Topographic analysis (Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) 2-m digital elevation models (DEM)) of ~20-km diameter Copernican lunar craters revealed generally steep slopes on interior walls (30° to 36°, locally exceeding 40°) over 15-meter baselines[9]. In this work, we extend the analysis from a probability distribution modeling point-of-view with NAC DEMs to characterize the slope statistics for the floors and walls for the same ~20-km Copernican lunar craters. The difference in slope standard deviations between the Gaussian approximation and the actual distribution (2-meter sampling) was computed over multiple scales. This slope analysis showed that local slope distributions are non-Gaussian for both crater walls and floors. Over larger baselines (~100 meters), crater wall slope probability distributions do approximate Gaussian distributions better, but have long distribution tails. Crater floor probability distributions however, were always asymmetric (for the baseline scales analyzed) and less affected by baseline scale variations. Accordingly, our results suggest that use of long tailed probability distributions (like Cauchy) and a baseline-dependant multi-scale model can be more effective in describing the slope statistics for lunar topography. Refrences: [1]Moore, H.(1971), JGR,75(11) [2]Marcus, A. H.(1969),JGR,74 (22).[3]R.J. Pike (1970),U.S. Geological Survey Working Paper [4]N. C. Costes, J. E. Farmer and E. B. George (1972),NASA Technical Report TR R-401 [5]M. N. Parker and G. L. Tyler(1973), Radio Science, 8(3),177-184 [6]Alekseev, V. A.et al (1968), Soviet Astronomy, Vol. 11, p.860 [7]Burns et al. (2012) Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XXXIX-B4, 483-488.[8]Smith et al. (2010) GRL 37, L18204, DOI: 10.1029/2010GL043751. [9]Wagner R., Robinson, M., Speyerer E., Mahanti, P., LPSC 2013, #2924.

Development and application of an empirical probability distribution for the prediction error of re-entry body maximum dynamic pressure

NASA Technical Reports Server (NTRS)

Lanzi, R. James; Vincent, Brett T.

1993-01-01

The relationship between actual and predicted re-entry maximum dynamic pressure is characterized using a probability density function and a cumulative distribution function derived from sounding rocket flight data. This paper explores the properties of this distribution and demonstrates applications of this data with observed sounding rocket re-entry body damage characteristics to assess probabilities of sustaining various levels of heating damage. The results from this paper effectively bridge the gap existing in sounding rocket reentry analysis between the known damage level/flight environment relationships and the predicted flight environment.

Probability and the changing shape of response distributions for orientation.

PubMed

Anderson, Britt

2014-11-18

Spatial attention and feature-based attention are regarded as two independent mechanisms for biasing the processing of sensory stimuli. Feature attention is held to be a spatially invariant mechanism that advantages a single feature per sensory dimension. In contrast to the prediction of location independence, I found that participants were able to report the orientation of a briefly presented visual grating better for targets defined by high probability conjunctions of features and locations even when orientations and locations were individually uniform. The advantage for high-probability conjunctions was accompanied by changes in the shape of the response distributions. High-probability conjunctions had error distributions that were not normally distributed but demonstrated increased kurtosis. The increase in kurtosis could be explained as a change in the variances of the component tuning functions that comprise a population mixture. By changing the mixture distribution of orientation-tuned neurons, it is possible to change the shape of the discrimination function. This prompts the suggestion that attention may not "increase" the quality of perceptual processing in an absolute sense but rather prioritizes some stimuli over others. This results in an increased number of highly accurate responses to probable targets and, simultaneously, an increase in the number of very inaccurate responses. © 2014 ARVO.

Vector wind and vector wind shear models 0 to 27 km altitude for Cape Kennedy, Florida, and Vandenberg AFB, California

NASA Technical Reports Server (NTRS)

Smith, O. E.

1976-01-01

The techniques are presented to derive several statistical wind models. The techniques are from the properties of the multivariate normal probability function. Assuming that the winds can be considered as bivariate normally distributed, then (1) the wind components and conditional wind components are univariate normally distributed, (2) the wind speed is Rayleigh distributed, (3) the conditional distribution of wind speed given a wind direction is Rayleigh distributed, and (4) the frequency of wind direction can be derived. All of these distributions are derived from the 5-sample parameter of wind for the bivariate normal distribution. By further assuming that the winds at two altitudes are quadravariate normally distributed, then the vector wind shear is bivariate normally distributed and the modulus of the vector wind shear is Rayleigh distributed. The conditional probability of wind component shears given a wind component is normally distributed. Examples of these and other properties of the multivariate normal probability distribution function as applied to Cape Kennedy, Florida, and Vandenberg AFB, California, wind data samples are given. A technique to develop a synthetic vector wind profile model of interest to aerospace vehicle applications is presented.

Joint probabilities and quantum cognition

NASA Astrophysics Data System (ADS)

de Barros, J. Acacio

2012-12-01

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.

Major and trace element distribution in soil and sediments from the Egyptian central Nile Valley

NASA Astrophysics Data System (ADS)

Badawy, W. M.; Ghanim, E. H.; Duliu, O. G.; El Samman, H.; Frontasyeva, M. V.

2017-07-01

The distributions of 32 major and trace elements in 72 surface soil and sediment samples collected from the Asyut to Cairo Nile river section were determined by epithermal neutron activation analysis and compared with corresponding data for the Upper Continental Crust, North American Shale Composite, Average Soil and Average Sediment as well as suspended sediments from Congo and Upper Niger Rivers, in order to establish to which extent the Nile sedimentary material can be related to similar material all over the world as well as to local geology. Their relative distributions indicate the presence of detrital material of igneous origin, most probably resulting from weathering of the Ethiopian Highlands and transported by the Blue Nile, the Nile main tributary. The distributions of nickel, zinc, and arsenic contents suggest that the lower part of the Nile and its surroundings including the Nile Delta is not seriously polluted with heavy metals, so that, in spite of a human activity, which lasted four millennia, the Nile River continues to be less affected by any anthropogenic contamination.

Modelling the stochastic nature of the available coefficient of friction at footwear-floor interfaces.

PubMed

Gragg, Jared; Klose, Ellison; Yang, James

2017-07-01

The available coefficient of friction (ACOF) is a measure of the friction available between two surfaces, which for human gait would be the footwear-floor interface. It is often compared to the required coefficient of friction (RCOF) to determine the likelihood of a slip in gait. Both the ACOF and RCOF are stochastic by nature meaning that neither should be represented by a deterministic value, such as the sample mean. Previous research has determined that the RCOF can be modelled well by either the normal or lognormal distributions, but previous research aimed at determining an appropriate distribution for the ACOF was inconclusive. This study focuses on modelling the stochastic nature of the ACOF by fitting eight continuous probability distributions to ACOF data for six scenarios. In addition, the data were used to study the effect that a simple housekeeping action such as sweeping could have on the ACOF. Practitioner Summary: Previous research aimed at determining an appropriate distribution for the ACOF was inconclusive. The study addresses this issue as well as looking at the effect that an act such as sweeping has on the ACOF.

Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks.

PubMed

Zhuang, Jiancang; Ogata, Yosihiko

2006-04-01

The space-time epidemic-type aftershock sequence model is a stochastic branching process in which earthquake activity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to certain rules. This paper gives the probability distributions associated with the largest event in a cluster and their properties for all three cases when the process is subcritical, critical, and supercritical. One of the direct uses of these probability distributions is to evaluate the probability of an earthquake to be a foreshock, and magnitude distributions of foreshocks and nonforeshock earthquakes. To verify these theoretical results, the Japan Meteorological Agency earthquake catalog is analyzed. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15%. When the differences between background events and triggered event in the behavior of triggering children are considered, a background event has a probability about 8% to be a foreshock. This probability decreases when the magnitude of the background event increases. These results, obtained from a complicated clustering model, where the characteristics of background events and triggered events are different, are consistent with the results obtained in [Ogata, Geophys. J. Int. 127, 17 (1996)] by using the conventional single-linked cluster declustering method.

Comparison of the efficiency between two sampling plans for aflatoxins analysis in maize

PubMed Central

Mallmann, Adriano Olnei; Marchioro, Alexandro; Oliveira, Maurício Schneider; Rauber, Ricardo Hummes; Dilkin, Paulo; Mallmann, Carlos Augusto

2014-01-01

Variance and performance of two sampling plans for aflatoxins quantification in maize were evaluated. Eight lots of maize were sampled using two plans: manual, using sampling spear for kernels; and automatic, using a continuous flow to collect milled maize. Total variance and sampling, preparation, and analysis variance were determined and compared between plans through multifactor analysis of variance. Four theoretical distribution models were used to compare aflatoxins quantification distributions in eight maize lots. The acceptance and rejection probabilities for a lot under certain aflatoxin concentration were determined using variance and the information on the selected distribution model to build the operational characteristic curves (OC). Sampling and total variance were lower at the automatic plan. The OC curve from the automatic plan reduced both consumer and producer risks in comparison to the manual plan. The automatic plan is more efficient than the manual one because it expresses more accurately the real aflatoxin contamination in maize. PMID:24948911

Estimation of the diagnostic threshold accounting for decision costs and sampling uncertainty.

PubMed

Skaltsa, Konstantina; Jover, Lluís; Carrasco, Josep Lluís

2010-10-01

Medical diagnostic tests are used to classify subjects as non-diseased or diseased. The classification rule usually consists of classifying subjects using the values of a continuous marker that is dichotomised by means of a threshold. Here, the optimum threshold estimate is found by minimising a cost function that accounts for both decision costs and sampling uncertainty. The cost function is optimised either analytically in a normal distribution setting or empirically in a free-distribution setting when the underlying probability distributions of diseased and non-diseased subjects are unknown. Inference of the threshold estimates is based on approximate analytically standard errors and bootstrap-based approaches. The performance of the proposed methodology is assessed by means of a simulation study, and the sample size required for a given confidence interval precision and sample size ratio is also calculated. Finally, a case example based on previously published data concerning the diagnosis of Alzheimer's patients is provided in order to illustrate the procedure.

Adaptive Detector Arrays for Optical Communications Receivers

NASA Technical Reports Server (NTRS)

Vilnrotter, V.; Srinivasan, M.

2000-01-01

The structure of an optimal adaptive array receiver for ground-based optical communications is described and its performance investigated. Kolmogorov phase screen simulations are used to model the sample functions of the focal-plane signal distribution due to turbulence and to generate realistic spatial distributions of the received optical field. This novel array detector concept reduces interference from background radiation by effectively assigning higher confidence levels at each instant of time to those detector elements that contain significant signal energy and suppressing those that do not. A simpler suboptimum structure that replaces the continuous weighting function of the optimal receiver by a hard decision on the selection of the signal detector elements also is described and evaluated. Approximations and bounds to the error probability are derived and compared with the exact calculations and receiver simulation results. It is shown that, for photon-counting receivers observing Poisson-distributed signals, performance improvements of approximately 5 dB can be obtained over conventional single-detector photon-counting receivers, when operating in high background environments.

Dissociating error-based and reinforcement-based loss functions during sensorimotor learning

PubMed Central

McGregor, Heather R.; Mohatarem, Ayman

2017-01-01

It has been proposed that the sensorimotor system uses a loss (cost) function to evaluate potential movements in the presence of random noise. Here we test this idea in the context of both error-based and reinforcement-based learning. In a reaching task, we laterally shifted a cursor relative to true hand position using a skewed probability distribution. This skewed probability distribution had its mean and mode separated, allowing us to dissociate the optimal predictions of an error-based loss function (corresponding to the mean of the lateral shifts) and a reinforcement-based loss function (corresponding to the mode). We then examined how the sensorimotor system uses error feedback and reinforcement feedback, in isolation and combination, when deciding where to aim the hand during a reach. We found that participants compensated differently to the same skewed lateral shift distribution depending on the form of feedback they received. When provided with error feedback, participants compensated based on the mean of the skewed noise. When provided with reinforcement feedback, participants compensated based on the mode. Participants receiving both error and reinforcement feedback continued to compensate based on the mean while repeatedly missing the target, despite receiving auditory, visual and monetary reinforcement feedback that rewarded hitting the target. Our work shows that reinforcement-based and error-based learning are separable and can occur independently. Further, when error and reinforcement feedback are in conflict, the sensorimotor system heavily weights error feedback over reinforcement feedback. PMID:28753634

Dissociating error-based and reinforcement-based loss functions during sensorimotor learning.

PubMed

Cashaback, Joshua G A; McGregor, Heather R; Mohatarem, Ayman; Gribble, Paul L

2017-07-01

It has been proposed that the sensorimotor system uses a loss (cost) function to evaluate potential movements in the presence of random noise. Here we test this idea in the context of both error-based and reinforcement-based learning. In a reaching task, we laterally shifted a cursor relative to true hand position using a skewed probability distribution. This skewed probability distribution had its mean and mode separated, allowing us to dissociate the optimal predictions of an error-based loss function (corresponding to the mean of the lateral shifts) and a reinforcement-based loss function (corresponding to the mode). We then examined how the sensorimotor system uses error feedback and reinforcement feedback, in isolation and combination, when deciding where to aim the hand during a reach. We found that participants compensated differently to the same skewed lateral shift distribution depending on the form of feedback they received. When provided with error feedback, participants compensated based on the mean of the skewed noise. When provided with reinforcement feedback, participants compensated based on the mode. Participants receiving both error and reinforcement feedback continued to compensate based on the mean while repeatedly missing the target, despite receiving auditory, visual and monetary reinforcement feedback that rewarded hitting the target. Our work shows that reinforcement-based and error-based learning are separable and can occur independently. Further, when error and reinforcement feedback are in conflict, the sensorimotor system heavily weights error feedback over reinforcement feedback.

Does Breast Cancer Drive the Building of Survival Probability Models among States? An Assessment of Goodness of Fit for Patient Data from SEER Registries

PubMed

Khan, Hafiz; Saxena, Anshul; Perisetti, Abhilash; Rafiq, Aamrin; Gabbidon, Kemesha; Mende, Sarah; Lyuksyutova, Maria; Quesada, Kandi; Blakely, Summre; Torres, Tiffany; Afesse, Mahlet

2016-12-01

Background: Breast cancer is a worldwide public health concern and is the most prevalent type of cancer in women in the United States. This study concerned the best fit of statistical probability models on the basis of survival times for nine state cancer registries: California, Connecticut, Georgia, Hawaii, Iowa, Michigan, New Mexico, Utah, and Washington. Materials and Methods: A probability random sampling method was applied to select and extract records of 2,000 breast cancer patients from the Surveillance Epidemiology and End Results (SEER) database for each of the nine state cancer registries used in this study. EasyFit software was utilized to identify the best probability models by using goodness of fit tests, and to estimate parameters for various statistical probability distributions that fit survival data. Results: Statistical analysis for the summary of statistics is reported for each of the states for the years 1973 to 2012. Kolmogorov-Smirnov, Anderson-Darling, and Chi-squared goodness of fit test values were used for survival data, the highest values of goodness of fit statistics being considered indicative of the best fit survival model for each state. Conclusions: It was found that California, Connecticut, Georgia, Iowa, New Mexico, and Washington followed the Burr probability distribution, while the Dagum probability distribution gave the best fit for Michigan and Utah, and Hawaii followed the Gamma probability distribution. These findings highlight differences between states through selected sociodemographic variables and also demonstrate probability modeling differences in breast cancer survival times. The results of this study can be used to guide healthcare providers and researchers for further investigations into social and environmental factors in order to reduce the occurrence of and mortality due to breast cancer. Creative Commons Attribution License

Role of the site of synaptic competition and the balance of learning forces for Hebbian encoding of probabilistic Markov sequences

PubMed Central

Bouchard, Kristofer E.; Ganguli, Surya; Brainard, Michael S.

2015-01-01

The majority of distinct sensory and motor events occur as temporally ordered sequences with rich probabilistic structure. Sequences can be characterized by the probability of transitioning from the current state to upcoming states (forward probability), as well as the probability of having transitioned to the current state from previous states (backward probability). Despite the prevalence of probabilistic sequencing of both sensory and motor events, the Hebbian mechanisms that mold synapses to reflect the statistics of experienced probabilistic sequences are not well understood. Here, we show through analytic calculations and numerical simulations that Hebbian plasticity (correlation, covariance, and STDP) with pre-synaptic competition can develop synaptic weights equal to the conditional forward transition probabilities present in the input sequence. In contrast, post-synaptic competition can develop synaptic weights proportional to the conditional backward probabilities of the same input sequence. We demonstrate that to stably reflect the conditional probability of a neuron's inputs and outputs, local Hebbian plasticity requires balance between competitive learning forces that promote synaptic differentiation and homogenizing learning forces that promote synaptic stabilization. The balance between these forces dictates a prior over the distribution of learned synaptic weights, strongly influencing both the rate at which structure emerges and the entropy of the final distribution of synaptic weights. Together, these results demonstrate a simple correspondence between the biophysical organization of neurons, the site of synaptic competition, and the temporal flow of information encoded in synaptic weights by Hebbian plasticity while highlighting the utility of balancing learning forces to accurately encode probability distributions, and prior expectations over such probability distributions. PMID:26257637

Tips and Tricks for Successful Application of Statistical Methods to Biological Data.

PubMed

Schlenker, Evelyn

2016-01-01

This chapter discusses experimental design and use of statistics to describe characteristics of data (descriptive statistics) and inferential statistics that test the hypothesis posed by the investigator. Inferential statistics, based on probability distributions, depend upon the type and distribution of the data. For data that are continuous, randomly and independently selected, as well as normally distributed more powerful parametric tests such as Student's t test and analysis of variance (ANOVA) can be used. For non-normally distributed or skewed data, transformation of the data (using logarithms) may normalize the data allowing use of parametric tests. Alternatively, with skewed data nonparametric tests can be utilized, some of which rely on data that are ranked prior to statistical analysis. Experimental designs and analyses need to balance between committing type 1 errors (false positives) and type 2 errors (false negatives). For a variety of clinical studies that determine risk or benefit, relative risk ratios (random clinical trials and cohort studies) or odds ratios (case-control studies) are utilized. Although both use 2 × 2 tables, their premise and calculations differ. Finally, special statistical methods are applied to microarray and proteomics data, since the large number of genes or proteins evaluated increase the likelihood of false discoveries. Additional studies in separate samples are used to verify microarray and proteomic data. Examples in this chapter and references are available to help continued investigation of experimental designs and appropriate data analysis.

Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability.

PubMed

van Albada, S J; Robinson, P A

2007-04-15

Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are often used. Box-Cox transformations or ad hoc methods are sometimes used for parameters for which no transformation is known to approximate normality. However, these methods do not always give good agreement with the Gaussian. A transformation is discussed that maps probability distributions as closely as possible to the normal distribution, with exact agreement for continuous distributions. To illustrate, the transformation is applied to a theoretical distribution, and to quantitative electroencephalographic (qEEG) measures from repeat recordings of 32 subjects which are highly non-normal. Agreement with the Gaussian was better than using logarithmic, logit, or Box-Cox transformations. Since normal data have previously been shown to have better test-retest reliability than non-normal data under fairly general circumstances, the implications of our transformation for the test-retest reliability of parameters were investigated. Reliability was shown to improve with the transformation, where the improvement was comparable to that using Box-Cox. An advantage of the general transformation is that it does not require laborious optimization over a range of parameters or a case-specific choice of form.

Distribution functions of probabilistic automata

NASA Technical Reports Server (NTRS)

Vatan, F.

2001-01-01

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

A method to deconvolve stellar rotational velocities II. The probability distribution function via Tikhonov regularization

NASA Astrophysics Data System (ADS)

Christen, Alejandra; Escarate, Pedro; Curé, Michel; Rial, Diego F.; Cassetti, Julia

2016-10-01

Aims: Knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. Because we measure the projected rotational speed v sin I, we need to solve an ill-posed problem given by a Fredholm integral of the first kind to recover the "true" rotational velocity distribution. Methods: After discretization of the Fredholm integral we apply the Tikhonov regularization method to obtain directly the probability distribution function for stellar rotational velocities. We propose a simple and straightforward procedure to determine the Tikhonov parameter. We applied Monte Carlo simulations to prove that the Tikhonov method is a consistent estimator and asymptotically unbiased. Results: This method is applied to a sample of cluster stars. We obtain confidence intervals using a bootstrap method. Our results are in close agreement with those obtained using the Lucy method for recovering the probability density distribution of rotational velocities. Furthermore, Lucy estimation lies inside our confidence interval. Conclusions: Tikhonov regularization is a highly robust method that deconvolves the rotational velocity probability density function from a sample of v sin I data directly without the need for any convergence criteria.

Quantitative assessment of building fire risk to life safety.

PubMed

Guanquan, Chu; Jinhua, Sun

2008-06-01

This article presents a quantitative risk assessment framework for evaluating fire risk to life safety. Fire risk is divided into two parts: probability and corresponding consequence of every fire scenario. The time-dependent event tree technique is used to analyze probable fire scenarios based on the effect of fire protection systems on fire spread and smoke movement. To obtain the variation of occurrence probability with time, Markov chain is combined with a time-dependent event tree for stochastic analysis on the occurrence probability of fire scenarios. To obtain consequences of every fire scenario, some uncertainties are considered in the risk analysis process. When calculating the onset time to untenable conditions, a range of fires are designed based on different fire growth rates, after which uncertainty of onset time to untenable conditions can be characterized by probability distribution. When calculating occupant evacuation time, occupant premovement time is considered as a probability distribution. Consequences of a fire scenario can be evaluated according to probability distribution of evacuation time and onset time of untenable conditions. Then, fire risk to life safety can be evaluated based on occurrence probability and consequences of every fire scenario. To express the risk assessment method in detail, a commercial building is presented as a case study. A discussion compares the assessment result of the case study with fire statistics.

Competing risk models in reliability systems, an exponential distribution model with Bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

The exponential distribution is the most widely used reliability analysis. This distribution is very suitable for representing the lengths of life of many cases and is available in a simple statistical form. The characteristic of this distribution is a constant hazard rate. The exponential distribution is the lower rank of the Weibull distributions. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability analysis using Bayesian analysis approach and presenting their analytic methods. The cases are limited to the models with independent causes of failure. A non-informative prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.

Pores-scale hydrodynamics in a progressively bio-clogged three-dimensional porous medium: 3D particle tracking experiments and stochastic transport modelling

NASA Astrophysics Data System (ADS)

Morales, V. L.; Carrel, M.; Dentz, M.; Derlon, N.; Morgenroth, E.; Holzner, M.

2017-12-01

Biofilms are ubiquitous bacterial communities growing in various porous media including soils, trickling and sand filters and are relevant for applications such as the degradation of pollutants for bioremediation, waste water or drinking water production purposes. By their development, biofilms dynamically change the structure of porous media, increasing the heterogeneity of the pore network and the non-Fickian or anomalous dispersion. In this work, we use an experimental approach to investigate the influence of biofilm growth on pore scale hydrodynamics and transport processes and propose a correlated continuous time random walk model capturing these observations. We perform three-dimensional particle tracking velocimetry at four different time points from 0 to 48 hours of biofilm growth. The biofilm growth notably impacts pore-scale hydrodynamics, as shown by strong increase of the average velocity and in tailing of Lagrangian velocity probability density functions. Additionally, the spatial correlation length of the flow increases substantially. This points at the formation of preferential flow pathways and stagnation zones, which ultimately leads to an increase of anomalous transport in the porous media considered, characterized by non-Fickian scaling of mean-squared displacements and non-Gaussian distributions of the displacement probability density functions. A gamma distribution provides a remarkable approximation of the bulk and the high tail of the Lagrangian pore-scale velocity magnitude, indicating a transition from a parallel pore arrangement towards a more serial one. Finally, a correlated continuous time random walk based on a stochastic relation velocity model accurately reproduces the observations and could be used to predict transport beyond the time scales accessible to the experiment.

On probability-possibility transformations

NASA Technical Reports Server (NTRS)

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.

Theoretical size distribution of fossil taxa: analysis of a null model.

PubMed

Reed, William J; Hughes, Barry D

2007-03-22

This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family.

Newton/Poisson-Distribution Program

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Scheuer, Ernest M.

1990-01-01

NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles for X(sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Program written in C.

Solvable continuous-time random walk model of the motion of tracer particles through porous media.

PubMed

Fouxon, Itzhak; Holzner, Markus

2016-08-01

We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Formulation of a correlated variables methodology for assessment of continuous gas resources with an application to the Woodford play, Arkoma Basin, eastern Oklahoma

USGS Publications Warehouse

Olea, R.A.; Houseknecht, D.W.; Garrity, C.P.; Cook, T.A.

2011-01-01

Shale gas is a form of continuous unconventional hydrocarbon accumulation whose resource estimation is unfeasible through the inference of pore volume. Under these circumstances, the usual approach is to base the assessment on well productivity through estimated ultimate recovery (EUR). Unconventional resource assessments that consider uncertainty are typically done by applying analytical procedures based on classical statistics theory that ignores geographical location, does not take into account spatial correlation, and assumes independence of EUR from other variables that may enter into the modeling. We formulate a new, more comprehensive approach based on sequential simulation to test methodologies known to be capable of more fully utilizing the data and overcoming unrealistic simplifications. Theoretical requirements demand modeling of EUR as areal density instead of well EUR. The new experimental methodology is illustrated by evaluating a gas play in the Woodford Shale in the Arkoma Basin of Oklahoma. Differently from previous assessments, we used net thickness and vitrinite reflectance as secondary variables correlated to cell EUR. In addition to the traditional probability distribution for undiscovered resources, the new methodology provides maps of EUR density and maps with probabilities to reach any given cell EUR, which are useful to visualize geographical variations in prospectivity.

Probability theory for 3-layer remote sensing radiative transfer model: univariate case.

PubMed

Ben-David, Avishai; Davidson, Charles E

2012-04-23

A probability model for a 3-layer radiative transfer model (foreground layer, cloud layer, background layer, and an external source at the end of line of sight) has been developed. The 3-layer model is fundamentally important as the primary physical model in passive infrared remote sensing. The probability model is described by the Johnson family of distributions that are used as a fit for theoretically computed moments of the radiative transfer model. From the Johnson family we use the SU distribution that can address a wide range of skewness and kurtosis values (in addition to addressing the first two moments, mean and variance). In the limit, SU can also describe lognormal and normal distributions. With the probability model one can evaluate the potential for detecting a target (vapor cloud layer), the probability of observing thermal contrast, and evaluate performance (receiver operating characteristics curves) in clutter-noise limited scenarios. This is (to our knowledge) the first probability model for the 3-layer remote sensing geometry that treats all parameters as random variables and includes higher-order statistics. © 2012 Optical Society of America

Sampling probability distributions of lesions in mammograms

NASA Astrophysics Data System (ADS)

Looney, P.; Warren, L. M.; Dance, D. R.; Young, K. C.

2015-03-01

One approach to image perception studies in mammography using virtual clinical trials involves the insertion of simulated lesions into normal mammograms. To facilitate this, a method has been developed that allows for sampling of lesion positions across the cranio-caudal and medio-lateral radiographic projections in accordance with measured distributions of real lesion locations. 6825 mammograms from our mammography image database were segmented to find the breast outline. The outlines were averaged and smoothed to produce an average outline for each laterality and radiographic projection. Lesions in 3304 mammograms with malignant findings were mapped on to a standardised breast image corresponding to the average breast outline using piecewise affine transforms. A four dimensional probability distribution function was found from the lesion locations in the cranio-caudal and medio-lateral radiographic projections for calcification and noncalcification lesions. Lesion locations sampled from this probability distribution function were mapped on to individual mammograms using a piecewise affine transform which transforms the average outline to the outline of the breast in the mammogram. The four dimensional probability distribution function was validated by comparing it to the two dimensional distributions found by considering each radiographic projection and laterality independently. The correlation of the location of the lesions sampled from the four dimensional probability distribution function across radiographic projections was shown to match the correlation of the locations of the original mapped lesion locations. The current system has been implemented as a web-service on a server using the Python Django framework. The server performs the sampling, performs the mapping and returns the results in a javascript object notation format.

Automated classification of mouse pup isolation syllables: from cluster analysis to an Excel-based "mouse pup syllable classification calculator".

PubMed

Grimsley, Jasmine M S; Gadziola, Marie A; Wenstrup, Jeffrey J

2012-01-01

Mouse pups vocalize at high rates when they are cold or isolated from the nest. The proportions of each syllable type produced carry information about disease state and are being used as behavioral markers for the internal state of animals. Manual classifications of these vocalizations identified 10 syllable types based on their spectro-temporal features. However, manual classification of mouse syllables is time consuming and vulnerable to experimenter bias. This study uses an automated cluster analysis to identify acoustically distinct syllable types produced by CBA/CaJ mouse pups, and then compares the results to prior manual classification methods. The cluster analysis identified two syllable types, based on their frequency bands, that have continuous frequency-time structure, and two syllable types featuring abrupt frequency transitions. Although cluster analysis computed fewer syllable types than manual classification, the clusters represented well the probability distributions of the acoustic features within syllables. These probability distributions indicate that some of the manually classified syllable types are not statistically distinct. The characteristics of the four classified clusters were used to generate a Microsoft Excel-based mouse syllable classifier that rapidly categorizes syllables, with over a 90% match, into the syllable types determined by cluster analysis.

Assessment of food intake input distributions for use in probabilistic exposure assessments of food additives.

PubMed

Gilsenan, M B; Lambe, J; Gibney, M J

2003-11-01

A key component of a food chemical exposure assessment using probabilistic analysis is the selection of the most appropriate input distribution to represent exposure variables. The study explored the type of parametric distribution that could be used to model variability in food consumption data likely to be included in a probabilistic exposure assessment of food additives. The goodness-of-fit of a range of continuous distributions to observed data of 22 food categories expressed as average daily intakes among consumers from the North-South Ireland Food Consumption Survey was assessed using the BestFit distribution fitting program. The lognormal distribution was most commonly accepted as a plausible parametric distribution to represent food consumption data when food intakes were expressed as absolute intakes (16/22 foods) and as intakes per kg body weight (18/22 foods). Results from goodness-of-fit tests were accompanied by lognormal probability plots for a number of food categories. The influence on food additive intake of using a lognormal distribution to model food consumption input data was assessed by comparing modelled intake estimates with observed intakes. Results from the present study advise some level of caution about the use of a lognormal distribution as a mode of input for food consumption data in probabilistic food additive exposure assessments and the results highlight the need for further research in this area.

The living Drake equation of the Tau Zero Foundation

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2011-03-01

The living Drake equation is our statistical generalization of the Drake equation such that it can take into account any number of factors. This new result opens up the possibility to enrich the equation by inserting more new factors as long as the scientific learning increases. The adjective "Living" refers just to this continuous enrichment of the Drake equation and is the goal of a new research project that the Tau Zero Foundation has entrusted to this author as the discoverer of the statistical Drake equation described hereafter. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be arbitrarily distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov form of the CLT, or the Lindeberg form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the lognormal distribution. Then, the mean value, standard deviation, mode, median and all the moments of this lognormal N can be derived from the means and standard deviations of the seven input random variables. In fact, the seven factors in the ordinary Drake equation now become seven independent positive random variables. The probability distribution of each random variable may be arbitrary. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) distance between any two neighbouring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, this distance now becomes a new random variable. We derive the relevant probability density function, apparently previously unknown (dubbed "Maccone distribution" by Paul Davies). Data Enrichment Principle. It should be noticed that any positive number of random variables in the statistical Drake equation is compatible with the CLT. So, our generalization allows for many more factors to be added in the future as long as more refined scientific knowledge about each factor will be known to the scientists. This capability to make room for more future factors in the statistical Drake equation we call the "Data Enrichment Principle", and regard as the key to more profound, future results in Astrobiology and SETI.

How to model a negligible probability under the WTO sanitary and phytosanitary agreement?

PubMed

Powell, Mark R

2013-06-01

Since the 1997 EC--Hormones decision, World Trade Organization (WTO) Dispute Settlement Panels have wrestled with the question of what constitutes a negligible risk under the Sanitary and Phytosanitary Agreement. More recently, the 2010 WTO Australia--Apples Panel focused considerable attention on the appropriate quantitative model for a negligible probability in a risk assessment. The 2006 Australian Import Risk Analysis for Apples from New Zealand translated narrative probability statements into quantitative ranges. The uncertainty about a "negligible" probability was characterized as a uniform distribution with a minimum value of zero and a maximum value of 10(-6) . The Australia - Apples Panel found that the use of this distribution would tend to overestimate the likelihood of "negligible" events and indicated that a triangular distribution with a most probable value of zero and a maximum value of 10⁻⁶ would correct the bias. The Panel observed that the midpoint of the uniform distribution is 5 × 10⁻⁷ but did not consider that the triangular distribution has an expected value of 3.3 × 10⁻⁷. Therefore, if this triangular distribution is the appropriate correction, the magnitude of the bias found by the Panel appears modest. The Panel's detailed critique of the Australian risk assessment, and the conclusions of the WTO Appellate Body about the materiality of flaws found by the Panel, may have important implications for the standard of review for risk assessments under the WTO SPS Agreement. © 2012 Society for Risk Analysis.

Fourier Method for Calculating Fission Chain Neutron Multiplicity Distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chambers, David H.; Chandrasekaran, Hema; Walston, Sean E.

Here, a new way of utilizing the fast Fourier transform is developed to compute the probability distribution for a fission chain to create n neutrons. We then extend this technique to compute the probability distributions for detecting n neutrons. Lastly, our technique can be used for fission chains initiated by either a single neutron inducing a fission or by the spontaneous fission of another isotope.

Fourier Method for Calculating Fission Chain Neutron Multiplicity Distributions

DOE PAGES

Chambers, David H.; Chandrasekaran, Hema; Walston, Sean E.

2017-03-27

Here, a new way of utilizing the fast Fourier transform is developed to compute the probability distribution for a fission chain to create n neutrons. We then extend this technique to compute the probability distributions for detecting n neutrons. Lastly, our technique can be used for fission chains initiated by either a single neutron inducing a fission or by the spontaneous fission of another isotope.

Teaching Uncertainties

ERIC Educational Resources Information Center

Duerdoth, Ian

2009-01-01

The subject of uncertainties (sometimes called errors) is traditionally taught (to first-year science undergraduates) towards the end of a course on statistics that defines probability as the limit of many trials, and discusses probability distribution functions and the Gaussian distribution. We show how to introduce students to the concepts of…

Detecting background changes in environments with dynamic foreground by separating probability distribution function mixtures using Pearson's method of moments

NASA Astrophysics Data System (ADS)

Jenkins, Colleen; Jordan, Jay; Carlson, Jeff

2007-02-01

This paper presents parameter estimation techniques useful for detecting background changes in a video sequence with extreme foreground activity. A specific application of interest is automated detection of the covert placement of threats (e.g., a briefcase bomb) inside crowded public facilities. We propose that a histogram of pixel intensity acquired from a fixed mounted camera over time for a series of images will be a mixture of two Gaussian functions: the foreground probability distribution function and background probability distribution function. We will use Pearson's Method of Moments to separate the two probability distribution functions. The background function can then be "remembered" and changes in the background can be detected. Subsequent comparisons of background estimates are used to detect changes. Changes are flagged to alert security forces to the presence and location of potential threats. Results are presented that indicate the significant potential for robust parameter estimation techniques as applied to video surveillance.

p-adic stochastic hidden variable model

NASA Astrophysics Data System (ADS)

Khrennikov, Andrew

1998-03-01

We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P(U,λ), U=A,A',B,B', are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics. A frequency definition of p-adic probability is quite similar to the ordinary frequency definition of probability. p-adic frequency probability is defined as the limit of relative frequencies νn but in the p-adic metric. We study a model with p-adic stochastics on the level of the hidden variables description. But, of course, responses of macroapparatuses have to be described by ordinary stochastics. Thus our model describes a mixture of p-adic stochastics of the microworld and ordinary stochastics of macroapparatuses. In this model probabilities for physical observables are the ordinary probabilities. At the same time Bell's inequality is violated.

Stationary properties of maximum-entropy random walks.

PubMed

Dixit, Purushottam D

2015-10-01

Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraints affect ME-inferred state probabilities remains unknown. To that end, we derive the transition probabilities and the stationary distribution of a maximum path entropy Markov process subject to state- and path-dependent constraints. A main finding is that the stationary distribution over states differs significantly from the Boltzmann distribution and reflects a competition between path multiplicity and imposed constraints. We illustrate our results with particle diffusion on a two-dimensional landscape. Connections with the path integral approach to diffusion are discussed.

Fire frequency, area burned, and severity: A quantitative approach to defining a normal fire year

USGS Publications Warehouse

Lutz, J.A.; Key, C.H.; Kolden, C.A.; Kane, J.T.; van Wagtendonk, J.W.

2011-01-01

Fire frequency, area burned, and fire severity are important attributes of a fire regime, but few studies have quantified the interrelationships among them in evaluating a fire year. Although area burned is often used to summarize a fire season, burned area may not be well correlated with either the number or ecological effect of fires. Using the Landsat data archive, we examined all 148 wildland fires (prescribed fires and wildfires) >40 ha from 1984 through 2009 for the portion of the Sierra Nevada centered on Yosemite National Park, California, USA. We calculated mean fire frequency and mean annual area burned from a combination of field- and satellite-derived data. We used the continuous probability distribution of the differenced Normalized Burn Ratio (dNBR) values to describe fire severity. For fires >40 ha, fire frequency, annual area burned, and cumulative severity were consistent in only 13 of 26 years (50 %), but all pair-wise comparisons among these fire regime attributes were significant. Borrowing from long-established practice in climate science, we defined "fire normals" to be the 26 year means of fire frequency, annual area burned, and the area under the cumulative probability distribution of dNBR. Fire severity normals were significantly lower when they were aggregated by year compared to aggregation by area. Cumulative severity distributions for each year were best modeled with Weibull functions (all 26 years, r2 ??? 0.99; P < 0.001). Explicit modeling of the cumulative severity distributions may allow more comprehensive modeling of climate-severity and area-severity relationships. Together, the three metrics of number of fires, size of fires, and severity of fires provide land managers with a more comprehensive summary of a given fire year than any single metric.

Estimation and prediction of maximum daily rainfall at Sagar Island using best fit probability models

NASA Astrophysics Data System (ADS)

Mandal, S.; Choudhury, B. U.

2015-07-01

Sagar Island, setting on the continental shelf of Bay of Bengal, is one of the most vulnerable deltas to the occurrence of extreme rainfall-driven climatic hazards. Information on probability of occurrence of maximum daily rainfall will be useful in devising risk management for sustaining rainfed agrarian economy vis-a-vis food and livelihood security. Using six probability distribution models and long-term (1982-2010) daily rainfall data, we studied the probability of occurrence of annual, seasonal and monthly maximum daily rainfall (MDR) in the island. To select the best fit distribution models for annual, seasonal and monthly time series based on maximum rank with minimum value of test statistics, three statistical goodness of fit tests, viz. Kolmogorove-Smirnov test (K-S), Anderson Darling test ( A 2 ) and Chi-Square test ( X 2) were employed. The fourth probability distribution was identified from the highest overall score obtained from the three goodness of fit tests. Results revealed that normal probability distribution was best fitted for annual, post-monsoon and summer seasons MDR, while Lognormal, Weibull and Pearson 5 were best fitted for pre-monsoon, monsoon and winter seasons, respectively. The estimated annual MDR were 50, 69, 86, 106 and 114 mm for return periods of 2, 5, 10, 20 and 25 years, respectively. The probability of getting an annual MDR of >50, >100, >150, >200 and >250 mm were estimated as 99, 85, 40, 12 and 03 % level of exceedance, respectively. The monsoon, summer and winter seasons exhibited comparatively higher probabilities (78 to 85 %) for MDR of >100 mm and moderate probabilities (37 to 46 %) for >150 mm. For different recurrence intervals, the percent probability of MDR varied widely across intra- and inter-annual periods. In the island, rainfall anomaly can pose a climatic threat to the sustainability of agricultural production and thus needs adequate adaptation and mitigation measures.

Quasi-probabilities in conditioned quantum measurement and a geometric/statistical interpretation of Aharonov's weak value

NASA Astrophysics Data System (ADS)

Lee, Jaeha; Tsutsui, Izumi

2017-05-01

We show that the joint behavior of an arbitrary pair of (generally noncommuting) quantum observables can be described by quasi-probabilities, which are an extended version of the standard probabilities used for describing the outcome of measurement for a single observable. The physical situations that require these quasi-probabilities arise when one considers quantum measurement of an observable conditioned by some other variable, with the notable example being the weak measurement employed to obtain Aharonov's weak value. Specifically, we present a general prescription for the construction of quasi-joint probability (QJP) distributions associated with a given combination of observables. These QJP distributions are introduced in two complementary approaches: one from a bottom-up, strictly operational construction realized by examining the mathematical framework of the conditioned measurement scheme, and the other from a top-down viewpoint realized by applying the results of the spectral theorem for normal operators and their Fourier transforms. It is then revealed that, for a pair of simultaneously measurable observables, the QJP distribution reduces to the unique standard joint probability distribution of the pair, whereas for a noncommuting pair there exists an inherent indefiniteness in the choice of such QJP distributions, admitting a multitude of candidates that may equally be used for describing the joint behavior of the pair. In the course of our argument, we find that the QJP distributions furnish the space of operators in the underlying Hilbert space with their characteristic geometric structures such that the orthogonal projections and inner products of observables can be given statistical interpretations as, respectively, “conditionings” and “correlations”. The weak value Aw for an observable A is then given a geometric/statistical interpretation as either the orthogonal projection of A onto the subspace generated by another observable B, or equivalently, as the conditioning of A given B with respect to the QJP distribution under consideration.

Two Universality Properties Associated with the Monkey Model of Zipf's Law

NASA Astrophysics Data System (ADS)

Perline, Richard; Perline, Ron

2016-03-01

The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size increases and the letter probabilities are specified as the spacings from a random division of the unit interval for any distribution with a bounded density function on $[0,1]$; and (2), on a logarithmic scale the version of the model with a finite word length cutoff and unequal letter probabilities is approximately normally distributed in the part of the distribution away from the tails. The first property is proved using a remarkably general limit theorem for the logarithm of sample spacings from Shao and Hahn, and the second property follows from Anscombe's central limit theorem for a random number of i.i.d. random variables. The finite word length model leads to a hybrid Zipf-lognormal mixture distribution closely related to work in other areas.

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.

1983-01-01

Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Computer routines for probability distributions, random numbers, and related functions

USGS Publications Warehouse

Kirby, W.H.

1980-01-01

Use of previously codes and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main programs. The probability distributions provided include the beta, chisquare, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F tests. Other mathematical functions include the Bessel function I (subzero), gamma and log-gamma functions, error functions and exponential integral. Auxiliary services include sorting and printer plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)

Universal laws of human society's income distribution

NASA Astrophysics Data System (ADS)

Tao, Yong

2015-10-01

General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will provide a powerful support for the hypothesis of equal probability, then the principle of maximum entropy is available in a just and equilibrium economy so that an income distribution will occur spontaneously (with the largest probability). Remarkably, some scholars have observed such an income distribution in some democratic countries, e.g. USA. This result implies that the hypothesis of equal probability may be only suitable for some "fair" systems (economic or physical systems). From this meaning, the non-equilibrium systems may be "unfair" so that the hypothesis of equal probability is unavailable.

Polynomial chaos representation of databases on manifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. Themore » method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.« less

Gravitational lensing, time delay, and gamma-ray bursts

NASA Technical Reports Server (NTRS)

Mao, Shude

1992-01-01

The probability distributions of time delay in gravitational lensing by point masses and isolated galaxies (modeled as singular isothermal spheres) are studied. For point lenses (all with the same mass) the probability distribution is broad, and with a peak at delta(t) of about 50 S; for singular isothermal spheres, the probability distribution is a rapidly decreasing function with increasing time delay, with a median delta(t) equals about 1/h month, and its behavior depends sensitively on the luminosity function of galaxies. The present simplified calculation is particularly relevant to the gamma-ray bursts if they are of cosmological origin. The frequency of 'recurrent' bursts due to gravitational lensing by galaxies is probably between 0.05 and 0.4 percent. Gravitational lensing can be used as a test of the cosmological origin of gamma-ray bursts.

PDF turbulence modeling and DNS

NASA Technical Reports Server (NTRS)

Hsu, A. T.

1992-01-01

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Atom counting in HAADF STEM using a statistical model-based approach: methodology, possibilities, and inherent limitations.

PubMed

De Backer, A; Martinez, G T; Rosenauer, A; Van Aert, S

2013-11-01

In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total scattered intensity scales with the number of atoms per atom column. These intensities are quantitatively determined using model-based statistical parameter estimation theory. The distribution describing the probability that intensity values are generated by atomic columns containing a specific number of atoms is inferred on the basis of the experimental scattered intensities. Finally, the number of atoms per atom column is quantified using this estimated probability distribution. The number of atom columns available in the observed STEM image, the number of components in the estimated probability distribution, the width of the components of the probability distribution, and the typical shape of a criterion to assess the number of components in the probability distribution directly affect the accuracy and precision with which the number of atoms in a particular atom column can be estimated. It is shown that single atom sensitivity is feasible taking the latter aspects into consideration. © 2013 Elsevier B.V. All rights reserved.

Theoretical size distribution of fossil taxa: analysis of a null model

PubMed Central

Reed, William J; Hughes, Barry D

2007-01-01

Background This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. Model New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. Conclusion The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family. PMID:17376249

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lopez-Ruiz, R.; Nagy, A.; Romera, E.

A two-parameter family of complexity measures C-tilde{sup ({alpha},{beta})} based on the Renyi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the Lopez-Ruiz-Mancini-Calbet complexity, which is recovered for {alpha}=1 and {beta}=2. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, {alpha} or {beta}, goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator, andmore » square well.« less

Closed-form solutions of performability. [in computer systems

NASA Technical Reports Server (NTRS)

Meyer, J. F.

1982-01-01

It is noted that if computing system performance is degradable then system evaluation must deal simultaneously with aspects of both performance and reliability. One approach is the evaluation of a system's performability which, relative to a specified performance variable Y, generally requires solution of the probability distribution function of Y. The feasibility of closed-form solutions of performability when Y is continuous are examined. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. Employing an approximate decomposition of the model, it is shown that a closed-form solution can indeed be obtained.

Repelling, binding, and oscillating of two-particle discrete-time quantum walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Qinghao; Li, Zhi-Jian, E-mail: zjli@sxu.edu.cn

In this paper, we investigate the effects of particle–particle interaction and static force on the propagation of probability distribution in two-particle discrete-time quantum walk, where the interaction and static force are expressed as a collision phase and a linear position-dependent phase, respectively. It is found that the interaction can lead to boson repelling and fermion binding. The static force also induces Bloch oscillation and results in a continuous transition from boson bunching to fermion anti-bunching. The interplays of particle–particle interaction, quantum interference, and Bloch oscillation provide a versatile framework to study and simulate many-particle physics via quantum walks.

Surveillance and Datalink Communication Performance Analysis for Distributed Separation Assurance System Architectures

NASA Technical Reports Server (NTRS)

Chung, William W.; Linse, Dennis J.; Alaverdi, Omeed; Ifarraguerri, Carlos; Seifert, Scott C.; Salvano, Dan; Calender, Dale

2012-01-01

This study investigates the effects of two technical enablers: Automatic Dependent Surveillance - Broadcast (ADS-B) and digital datalink communication, of the Federal Aviation Administration s Next Generation Air Transportation System (NextGen) under two separation assurance (SA) system architectures: ground-based SA and airborne SA, on overall separation assurance performance. Datalink performance such as successful reception probability in both surveillance and communication messages, and surveillance accuracy are examined in various operational conditions. Required SA performance is evaluated as a function of subsystem performance, using availability, continuity, and integrity metrics to establish overall required separation assurance performance, under normal and off-nominal conditions.

Maximum entropy approach to statistical inference for an ocean acoustic waveguide.

PubMed

Knobles, D P; Sagers, J D; Koch, R A

2012-02-01

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America

Shallow slip amplification and enhanced tsunami hazard unravelled by dynamic simulations of mega-thrust earthquakes

PubMed Central

Murphy, S.; Scala, A.; Herrero, A.; Lorito, S.; Festa, G.; Trasatti, E.; Tonini, R.; Romano, F.; Molinari, I.; Nielsen, S.

2016-01-01

The 2011 Tohoku earthquake produced an unexpected large amount of shallow slip greatly contributing to the ensuing tsunami. How frequent are such events? How can they be efficiently modelled for tsunami hazard? Stochastic slip models, which can be computed rapidly, are used to explore the natural slip variability; however, they generally do not deal specifically with shallow slip features. We study the systematic depth-dependence of slip along a thrust fault with a number of 2D dynamic simulations using stochastic shear stress distributions and a geometry based on the cross section of the Tohoku fault. We obtain a probability density for the slip distribution, which varies both with depth, earthquake size and whether the rupture breaks the surface. We propose a method to modify stochastic slip distributions according to this dynamically-derived probability distribution. This method may be efficiently applied to produce large numbers of heterogeneous slip distributions for probabilistic tsunami hazard analysis. Using numerous M9 earthquake scenarios, we demonstrate that incorporating the dynamically-derived probability distribution does enhance the conditional probability of exceedance of maximum estimated tsunami wave heights along the Japanese coast. This technique for integrating dynamic features in stochastic models can be extended to any subduction zone and faulting style. PMID:27725733

A discussion on the origin of quantum probabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holik, Federico, E-mail: olentiev2@gmail.com; Departamento de Matemática - Ciclo Básico Común, Universidad de Buenos Aires - Pabellón III, Ciudad Universitaria, Buenos Aires; Sáenz, Manuel

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case). -- Highlights: •Several recent works use a derivation similar to that of R.T. Cox to obtain quantum probabilities. •We apply Cox’s method to the lattice of subspaces of the Hilbert space. •We obtain a derivationmore » of quantum probabilities which includes mixed states. •The method presented in this work is susceptible to generalization. •It includes quantum mechanics and classical mechanics as particular cases.« less

Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.

PubMed

Takemura, Kazuhisa; Murakami, Hajime

2016-01-01

A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

Hybrid Approaches and Industrial Applications of Pattern Recognition,

DTIC Science & Technology

1980-10-01

emphasized that the probability distribution in (9) is correct only under the assumption that P( wIx ) is known exactly. In practice this assumption will...sufficient precision. The alternative would be to take the probability distribution of estimates of P( wix ) into account in the analysis. However, from the

Generalized Success-Breeds-Success Principle Leading to Time-Dependent Informetric Distributions.

ERIC Educational Resources Information Center

Egghe, Leo; Rousseau, Ronald

1995-01-01

Reformulates the success-breeds-success (SBS) principle in informetrics in order to generate a general theory of source-item relationships. Topics include a time-dependent probability, a new model for the expected probability that is compared with the SBS principle with exact combinatorial calculations, classical frequency distributions, and…

Back to Normal! Gaussianizing posterior distributions for cosmological probes

NASA Astrophysics Data System (ADS)

Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.

2014-05-01

We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.

Random Walks on Homeo( S 1)

NASA Astrophysics Data System (ADS)

Malicet, Dominique

2017-12-01

In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo ( S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν}. We prove that under the only condition that there is no probability measure invariant by {ν}-almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk ( g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.

The beta distribution: A statistical model for world cloud cover

NASA Technical Reports Server (NTRS)

Falls, L. W.

1973-01-01

Much work has been performed in developing empirical global cloud cover models. This investigation was made to determine an underlying theoretical statistical distribution to represent worldwide cloud cover. The beta distribution with probability density function is given to represent the variability of this random variable. It is shown that the beta distribution possesses the versatile statistical characteristics necessary to assume the wide variety of shapes exhibited by cloud cover. A total of 160 representative empirical cloud cover distributions were investigated and the conclusion was reached that this study provides sufficient statical evidence to accept the beta probability distribution as the underlying model for world cloud cover.

Gas Hydrate Formation Probability Distributions: The Effect of Shear and Comparisons with Nucleation Theory.

PubMed

May, Eric F; Lim, Vincent W; Metaxas, Peter J; Du, Jianwei; Stanwix, Paul L; Rowland, Darren; Johns, Michael L; Haandrikman, Gert; Crosby, Daniel; Aman, Zachary M

2018-03-13

Gas hydrate formation is a stochastic phenomenon of considerable significance for any risk-based approach to flow assurance in the oil and gas industry. In principle, well-established results from nucleation theory offer the prospect of predictive models for hydrate formation probability in industrial production systems. In practice, however, heuristics are relied on when estimating formation risk for a given flowline subcooling or when quantifying kinetic hydrate inhibitor (KHI) performance. Here, we present statistically significant measurements of formation probability distributions for natural gas hydrate systems under shear, which are quantitatively compared with theoretical predictions. Distributions with over 100 points were generated using low-mass, Peltier-cooled pressure cells, cycled in temperature between 40 and -5 °C at up to 2 K·min -1 and analyzed with robust algorithms that automatically identify hydrate formation and initial growth rates from dynamic pressure data. The application of shear had a significant influence on the measured distributions: at 700 rpm mass-transfer limitations were minimal, as demonstrated by the kinetic growth rates observed. The formation probability distributions measured at this shear rate had mean subcoolings consistent with theoretical predictions and steel-hydrate-water contact angles of 14-26°. However, the experimental distributions were substantially wider than predicted, suggesting that phenomena acting on macroscopic length scales are responsible for much of the observed stochastic formation. Performance tests of a KHI provided new insights into how such chemicals can reduce the risk of hydrate blockage in flowlines. Our data demonstrate that the KHI not only reduces the probability of formation (by both shifting and sharpening the distribution) but also reduces hydrate growth rates by a factor of 2.

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

NASA Astrophysics Data System (ADS)

Witteveen, Jeroen A. S.; Bijl, Hester

2009-10-01

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

The planet crossing asteroid survey: Progress in the analysis of populations and terrestrial-planet cratering rates

NASA Technical Reports Server (NTRS)

Helin, E. F.; Dunbar, R. S.

1984-01-01

The Planet-Crossing Asteroid Survey (PCAS) is making steady progress toward the accumulation of the data required to make improved estimates of the populations and cratering rates which can be compared with the existing record of impact events. The PCAS is the chief source of new objects on which to base these calculations over the past decade, and is an integral part of the continuing refinement of the estimates used in planetological applications. An adjunct effort to determine albedo statistics from photometry of UCAS plates is being pursued as well, to better define the magnitude frequency distributions of asteroids. This will improve the quality of the population and collision probability calculations. The survey effort continues to discover new asteroids whose orbital characteristics may reveal the origin and evolution mechanisms reponsible for the transport of the planet-crossing asteroids to the inner solar system.

Efficient quantum walk on a quantum processor

PubMed Central

Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

2016-01-01

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471

Continuous-Variable Instantaneous Quantum Computing is Hard to Sample.

PubMed

Douce, T; Markham, D; Kashefi, E; Diamanti, E; Coudreau, T; Milman, P; van Loock, P; Ferrini, G

2017-02-17

Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

Potential Use of a Bayesian Network for Discriminating Flash Type from Future GOES-R Geostationary Lightning Mapper (GLM) data

NASA Technical Reports Server (NTRS)

Solakiewiz, Richard; Koshak, William

2008-01-01

Continuous monitoring of the ratio of cloud flashes to ground flashes may provide a better understanding of thunderstorm dynamics, intensification, and evolution, and it may be useful in severe weather warning. The National Lighting Detection Network TM (NLDN) senses ground flashes with exceptional detection efficiency and accuracy over most of the continental United States. A proposed Geostationary Lightning Mapper (GLM) aboard the Geostationary Operational Environmental Satellite (GOES-R) will look at the western hemisphere, and among the lightning data products to be made available will be the fundamental optical flash parameters for both cloud and ground flashes: radiance, area, duration, number of optical groups, and number of optical events. Previous studies have demonstrated that the optical flash parameter statistics of ground and cloud lightning, which are observable from space, are significantly different. This study investigates a Bayesian network methodology for discriminating lightning flash type (ground or cloud) using the lightning optical data and ancillary GOES-R data. A Directed Acyclic Graph (DAG) is set up with lightning as a "root" and data observed by GLM as the "leaves." This allows for a direct calculation of the joint probability distribution function for the lighting type and radiance, area, etc. Initially, the conditional probabilities that will be required can be estimated from the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) together with NLDN data. Directly manipulating the joint distribution will yield the conditional probability that a lightning flash is a ground flash given the evidence, which consists of the observed lightning optical data [and possibly cloud data retrieved from the GOES-R Advanced Baseline Imager (ABI) in a more mature Bayesian network configuration]. Later, actual GLM and NLDN data can be used to refine the estimates of the conditional probabilities used in the model; i.e., the Bayesian network is a learning network. Methods for efficient calculation of the conditional probabilities (e.g., an algorithm using junction trees), finding data conflicts, goodness of fit, and dealing with missing data will also be addressed.

Chance-Constrained Guidance With Non-Convex Constraints

NASA Technical Reports Server (NTRS)

Ono, Masahiro

2011-01-01

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

Quantum work in the Bohmian framework

NASA Astrophysics Data System (ADS)

Sampaio, R.; Suomela, S.; Ala-Nissila, T.; Anders, J.; Philbin, T. G.

2018-01-01

At nonzero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterized by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase-space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterization of the dynamics of quantum systems, including the measurement process.

Applying the log-normal distribution to target detection

NASA Astrophysics Data System (ADS)

Holst, Gerald C.

1992-09-01

Holst and Pickard experimentally determined that MRT responses tend to follow a log-normal distribution. The log normal distribution appeared reasonable because nearly all visual psychological data is plotted on a logarithmic scale. It has the additional advantage that it is bounded to positive values; an important consideration since probability of detection is often plotted in linear coordinates. Review of published data suggests that the log-normal distribution may have universal applicability. Specifically, the log-normal distribution obtained from MRT tests appears to fit the target transfer function and the probability of detection of rectangular targets.

Efficient entanglement distillation without quantum memory.

PubMed

Abdelkhalek, Daniela; Syllwasschy, Mareike; Cerf, Nicolas J; Fiurášek, Jaromír; Schnabel, Roman

2016-05-31

Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.

Efficient entanglement distillation without quantum memory

PubMed Central

Abdelkhalek, Daniela; Syllwasschy, Mareike; Cerf, Nicolas J.; Fiurášek, Jaromír; Schnabel, Roman

2016-01-01

Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution. PMID:27241946

Crystal gazing. Part 2: Implications of advanced in digital data storage technology

NASA Technical Reports Server (NTRS)

Wells, D. C.

1984-01-01

During the next 5-10 years it is likely that the bit density available in digital mass storage systems (magnetic tapes, optical and magnetic disks) will be increased to such an extent that it will greatly exceed that of the conventional photographic emulsions like IIIaJ which are used in astronomy. These developments imply that it will soon be advantageous for astronomers to use microdensitometers to completely digitize all photographic plates soon after they are developed. Distribution of digital copies of sky surveys and the contents of plate vaults will probably become feasible within ten years. Copies of other astronomical archieves (e.g., Space Telescope) could also be distributed with the same techniques. The implications for designers of future microdensitometers are: (1) there will be a continuing need for precision digitization of large-format photographic imagery, and (2) that the need for real-time analysis of the output of microdensitometers will decrease.

Evaluation of statistical distributions to analyze the pollution of Cd and Pb in urban runoff.

PubMed

Toranjian, Amin; Marofi, Safar

2017-05-01

Heavy metal pollution in urban runoff causes severe environmental damage. Identification of these pollutants and their statistical analysis is necessary to provide management guidelines. In this study, 45 continuous probability distribution functions were selected to fit the Cd and Pb data in the runoff events of an urban area during October 2014-May 2015. The sampling was conducted from the outlet of the city basin during seven precipitation events. For evaluation and ranking of the functions, we used the goodness of fit Kolmogorov-Smirnov and Anderson-Darling tests. The results of Cd analysis showed that Hyperbolic Secant, Wakeby and Log-Pearson 3 are suitable for frequency analysis of the event mean concentration (EMC), the instantaneous concentration series (ICS) and instantaneous concentration of each event (ICEE), respectively. In addition, the LP3, Wakeby and Generalized Extreme Value functions were chosen for the EMC, ICS and ICEE related to Pb contamination.

Tsunami Size Distributions at Far-Field Locations from Aggregated Earthquake Sources

NASA Astrophysics Data System (ADS)

Geist, E. L.; Parsons, T.

2015-12-01

The distribution of tsunami amplitudes at far-field tide gauge stations is explained by aggregating the probability of tsunamis derived from individual subduction zones and scaled by their seismic moment. The observed tsunami amplitude distributions of both continental (e.g., San Francisco) and island (e.g., Hilo) stations distant from subduction zones are examined. Although the observed probability distributions nominally follow a Pareto (power-law) distribution, there are significant deviations. Some stations exhibit varying degrees of tapering of the distribution at high amplitudes and, in the case of the Hilo station, there is a prominent break in slope on log-log probability plots. There are also differences in the slopes of the observed distributions among stations that can be significant. To explain these differences we first estimate seismic moment distributions of observed earthquakes for major subduction zones. Second, regression models are developed that relate the tsunami amplitude at a station to seismic moment at a subduction zone, correcting for epicentral distance. The seismic moment distribution is then transformed to a site-specific tsunami amplitude distribution using the regression model. Finally, a mixture distribution is developed, aggregating the transformed tsunami distributions from all relevant subduction zones. This mixture distribution is compared to the observed distribution to assess the performance of the method described above. This method allows us to estimate the largest tsunami that can be expected in a given time period at a station.

Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities

USGS Publications Warehouse

Asquith, William H.; Kiang, Julie E.; Cohn, Timothy A.

2017-07-17

The U.S. Geological Survey (USGS), in cooperation with the U.S. Nuclear Regulatory Commission, has investigated statistical methods for probabilistic flood hazard assessment to provide guidance on very low annual exceedance probability (AEP) estimation of peak-streamflow frequency and the quantification of corresponding uncertainties using streamgage-specific data. The term “very low AEP” implies exceptionally rare events defined as those having AEPs less than about 0.001 (or 1 × 10–3 in scientific notation or for brevity 10–3). Such low AEPs are of great interest to those involved with peak-streamflow frequency analyses for critical infrastructure, such as nuclear power plants. Flood frequency analyses at streamgages are most commonly based on annual instantaneous peak streamflow data and a probability distribution fit to these data. The fitted distribution provides a means to extrapolate to very low AEPs. Within the United States, the Pearson type III probability distribution, when fit to the base-10 logarithms of streamflow, is widely used, but other distribution choices exist. The USGS-PeakFQ software, implementing the Pearson type III within the Federal agency guidelines of Bulletin 17B (method of moments) and updates to the expected moments algorithm (EMA), was specially adapted for an “Extended Output” user option to provide estimates at selected AEPs from 10–3 to 10–6. Parameter estimation methods, in addition to product moments and EMA, include L-moments, maximum likelihood, and maximum product of spacings (maximum spacing estimation). This study comprehensively investigates multiple distributions and parameter estimation methods for two USGS streamgages (01400500 Raritan River at Manville, New Jersey, and 01638500 Potomac River at Point of Rocks, Maryland). The results of this study specifically involve the four methods for parameter estimation and up to nine probability distributions, including the generalized extreme value, generalized log-normal, generalized Pareto, and Weibull. Uncertainties in streamflow estimates for corresponding AEP are depicted and quantified as two primary forms: quantile (aleatoric [random sampling] uncertainty) and distribution-choice (epistemic [model] uncertainty). Sampling uncertainties of a given distribution are relatively straightforward to compute from analytical or Monte Carlo-based approaches. Distribution-choice uncertainty stems from choices of potentially applicable probability distributions for which divergence among the choices increases as AEP decreases. Conventional goodness-of-fit statistics, such as Cramér-von Mises, and L-moment ratio diagrams are demonstrated in order to hone distribution choice. The results generally show that distribution choice uncertainty is larger than sampling uncertainty for very low AEP values.

Polynomial probability distribution estimation using the method of moments

PubMed Central

Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation. PMID:28394949

Polynomial probability distribution estimation using the method of moments.

PubMed

Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

The Spiral of Life

NASA Astrophysics Data System (ADS)

Cajiao Vélez, F.; Kamiński, J. Z.; Krajewska, K.

2018-04-01

High-energy photoionization driven by short and circularly-polarized laser pulses is studied in the framework of the relativistic strong-field approximation. The saddle-point analysis of the integrals defining the probability amplitude is used to determine the general properties of the probability distributions. Additionally, an approximate solution to the saddle-point equation is derived. This leads to the concept of the three-dimensional spiral of life in momentum space, around which the ionization probability distribution is maximum. We demonstrate that such spiral is also obtained from a classical treatment.

Count data, detection probabilities, and the demography, dynamics, distribution, and decline of amphibians.

PubMed

Schmidt, Benedikt R

2003-08-01

The evidence for amphibian population declines is based on count data that were not adjusted for detection probabilities. Such data are not reliable even when collected using standard methods. The formula C = Np (where C is a count, N the true parameter value, and p is a detection probability) relates count data to demography, population size, or distributions. With unadjusted count data, one assumes a linear relationship between C and N and that p is constant. These assumptions are unlikely to be met in studies of amphibian populations. Amphibian population data should be based on methods that account for detection probabilities.

Bayesian data analysis tools for atomic physics

NASA Astrophysics Data System (ADS)

Trassinelli, Martino

2017-10-01

We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested_fit to calculate the different probability distributions and other related quantities. Nested_fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.

Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

NASA Astrophysics Data System (ADS)

Batac, Rene C.; Paguirigan, Antonino A., Jr.; Tarun, Anjali B.; Longjas, Anthony G.

2017-04-01

We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around -1. 6, consistent with the expectations of the Gutenberg-Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004-0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquake-generating regions.

Projecting Future Sea Level Rise for Water Resources Planning in California

NASA Astrophysics Data System (ADS)

Anderson, J.; Kao, K.; Chung, F.

2008-12-01

Sea level rise is one of the major concerns for the management of California's water resources. Higher water levels and salinity intrusion into the Sacramento-San Joaquin Delta could affect water supplies, water quality, levee stability, and aquatic and terrestrial flora and fauna species and their habitat. Over the 20th century, sea levels near San Francisco Bay increased by over 0.6ft. Some tidal gauge and satellite data indicate that rates of sea level rise are accelerating. Sea levels are expected to continue to rise due to increasing air temperatures causing thermal expansion of the ocean and melting of land-based ice such as ice on Greenland and in southeastern Alaska. For water planners, two related questions are raised on the uncertainty of future sea levels. First, what is the expected sea level at a specific point in time in the future, e.g., what is the expected sea level in 2050? Second, what is the expected point of time in the future when sea levels will exceed a certain height, e.g., what is the expected range of time when the sea level rises by one foot? To address these two types of questions, two factors are considered: (1) long term sea level rise trend, and (2) local extreme sea level fluctuations. A two-step approach will be used to develop sea level rise projection guidelines for decision making that takes both of these factors into account. The first step is developing global sea level rise probability distributions for the long term trends. The second step will extend the approach to take into account the effects of local astronomical tides, changes in atmospheric pressure, wind stress, floods, and the El Niño/Southern Oscillation. In this paper, the development of the first step approach is presented. To project the long term sea level rise trend, one option is to extend the current rate of sea level rise into the future. However, since recent data indicate rates of sea level rise are accelerating, methods for estimating sea level rise that account for this acceleration are needed. One such method is an empirical relationship between air temperatures and global sea levels. The air temperature-sea level rise relationship was applied to the 12 climate change projections selected by the California Climate Action Team to estimate future sea levels. The 95% confidence level developed from the historical data was extrapolated to estimate the uncertainties in the future projections. To create sea level rise trend probability distributions, a lognormal probability distribution and a generalized extreme value probability distribution are used. Parameter estimations for these distributions are subjective and inevitably involve uncertainties, which will be improved as more research is conducted in this area.

Characterising RNA secondary structure space using information entropy

PubMed Central

2013-01-01

Comparative methods for RNA secondary structure prediction use evolutionary information from RNA alignments to increase prediction accuracy. The model is often described in terms of stochastic context-free grammars (SCFGs), which generate a probability distribution over secondary structures. It is, however, unclear how this probability distribution changes as a function of the input alignment. As prediction programs typically only return a single secondary structure, better characterisation of the underlying probability space of RNA secondary structures is of great interest. In this work, we show how to efficiently compute the information entropy of the probability distribution over RNA secondary structures produced for RNA alignments by a phylo-SCFG, and implement it for the PPfold model. We also discuss interpretations and applications of this quantity, including how it can clarify reasons for low prediction reliability scores. PPfold and its source code are available from http://birc.au.dk/software/ppfold/. PMID:23368905

The probability distribution of side-chain conformations in [Leu] and [Met]enkephalin determines the potency and selectivity to mu and delta opiate receptors.

PubMed

Nielsen, Bjørn G; Jensen, Morten Ø; Bohr, Henrik G

2003-01-01

The structure of enkephalin, a small neuropeptide with five amino acids, has been simulated on computers using molecular dynamics. Such simulations exhibit a few stable conformations, which also have been identified experimentally. The simulations provide the possibility to perform cluster analysis in the space defined by potentially pharmacophoric measures such as dihedral angles, side-chain orientation, etc. By analyzing the statistics of the resulting clusters, the probability distribution of the side-chain conformations may be determined. These probabilities allow us to predict the selectivity of [Leu]enkephalin and [Met]enkephalin to the known mu- and delta-type opiate receptors to which they bind as agonists. Other plausible consequences of these probability distributions are discussed in relation to the way in which they may influence the dynamics of the synapse. Copyright 2003 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 71: 577-592, 2003

Exact probability distribution function for the volatility of cumulative production

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Klümper, Andreas

2018-04-01

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in Lafond et al. (2017), which addressed the effects of normally distributed noise in the production process. Due to its wide applicability in industrial and technological activities we present here the mathematical foundation for an arbitrary distribution function of the process, which we expect will pave the future research on forecasting of the production process.

Statistics of intensity in adaptive-optics images and their usefulness for detection and photometry of exoplanets.

PubMed

Gladysz, Szymon; Yaitskova, Natalia; Christou, Julian C

2010-11-01

This paper is an introduction to the problem of modeling the probability density function of adaptive-optics speckle. We show that with the modified Rician distribution one cannot describe the statistics of light on axis. A dual solution is proposed: the modified Rician distribution for off-axis speckle and gamma-based distribution for the core of the point spread function. From these two distributions we derive optimal statistical discriminators between real sources and quasi-static speckles. In the second part of the paper the morphological difference between the two probability density functions is used to constrain a one-dimensional, "blind," iterative deconvolution at the position of an exoplanet. Separation of the probability density functions of signal and speckle yields accurate differential photometry in our simulations of the SPHERE planet finder instrument.

Small-Scale Spatio-Temporal Distribution of Bactrocera minax (Enderlein) (Diptera: Tephritidae) Using Probability Kriging.

PubMed

Wang, S Q; Zhang, H Y; Li, Z L

2016-10-01

Understanding spatio-temporal distribution of pest in orchards can provide important information that could be used to design monitoring schemes and establish better means for pest control. In this study, the spatial and temporal distribution of Bactrocera minax (Enderlein) (Diptera: Tephritidae) was assessed, and activity trends were evaluated by using probability kriging. Adults of B. minax were captured in two successive occurrences in a small-scale citrus orchard by using food bait traps, which were placed both inside and outside the orchard. The weekly spatial distribution of B. minax within the orchard and adjacent woods was examined using semivariogram parameters. The edge concentration was discovered during the most weeks in adult occurrence, and the population of the adults aggregated with high probability within a less-than-100-m-wide band on both of the sides of the orchard and the woods. The sequential probability kriged maps showed that the adults were estimated in the marginal zone with higher probability, especially in the early and peak stages. The feeding, ovipositing, and mating behaviors of B. minax are possible explanations for these spatio-temporal patterns. Therefore, spatial arrangement and distance to the forest edge of traps or spraying spot should be considered to enhance pest control on B. minax in small-scale orchards.

Logistic and linear regression model documentation for statistical relations between continuous real-time and discrete water-quality constituents in the Kansas River, Kansas, July 2012 through June 2015

USGS Publications Warehouse

Foster, Guy M.; Graham, Jennifer L.

2016-04-06

The Kansas River is a primary source of drinking water for about 800,000 people in northeastern Kansas. Source-water supplies are treated by a combination of chemical and physical processes to remove contaminants before distribution. Advanced notification of changing water-quality conditions and cyanobacteria and associated toxin and taste-and-odor compounds provides drinking-water treatment facilities time to develop and implement adequate treatment strategies. The U.S. Geological Survey (USGS), in cooperation with the Kansas Water Office (funded in part through the Kansas State Water Plan Fund), and the City of Lawrence, the City of Topeka, the City of Olathe, and Johnson County Water One, began a study in July 2012 to develop statistical models at two Kansas River sites located upstream from drinking-water intakes. Continuous water-quality monitors have been operated and discrete-water quality samples have been collected on the Kansas River at Wamego (USGS site number 06887500) and De Soto (USGS site number 06892350) since July 2012. Continuous and discrete water-quality data collected during July 2012 through June 2015 were used to develop statistical models for constituents of interest at the Wamego and De Soto sites. Logistic models to continuously estimate the probability of occurrence above selected thresholds were developed for cyanobacteria, microcystin, and geosmin. Linear regression models to continuously estimate constituent concentrations were developed for major ions, dissolved solids, alkalinity, nutrients (nitrogen and phosphorus species), suspended sediment, indicator bacteria (Escherichia coli, fecal coliform, and enterococci), and actinomycetes bacteria. These models will be used to provide real-time estimates of the probability that cyanobacteria and associated compounds exceed thresholds and of the concentrations of other water-quality constituents in the Kansas River. The models documented in this report are useful for characterizing changes in water-quality conditions through time, characterizing potentially harmful cyanobacterial events, and indicating changes in water-quality conditions that may affect drinking-water treatment processes.

The Detection of Signals in Impulsive Noise.

DTIC Science & Technology

1983-06-01

ASSI FICATION/ DOWN GRADING SCHEOUL1E * I1S. DISTRIBUTION STATEMENT (of th0i0 Rhport) Approved for Public Release; Distribucion Unlimited * 17...has a symmetric distribution, sgn(x i) will be -1 with probability 1/2 and +1 with probability 1/2. Considering the sum of observations as 0 binomial

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diwaker, E-mail: diwakerphysics@gmail.com; Chakraborty, Aniruddha

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy

NASA Astrophysics Data System (ADS)

Salama, Paul

2008-02-01

Multi-photon microscopy has provided biologists with unprecedented opportunities for high resolution imaging deep into tissues. Unfortunately deep tissue multi-photon microscopy images are in general noisy since they are acquired at low photon counts. To aid in the analysis and segmentation of such images it is sometimes necessary to initially enhance the acquired images. One way to enhance an image is to find the maximum a posteriori (MAP) estimate of each pixel comprising an image, which is achieved by finding a constrained least squares estimate of the unknown distribution. In arriving at the distribution it is assumed that the noise is Poisson distributed, the true but unknown pixel values assume a probability mass function over a finite set of non-negative values, and since the observed data also assumes finite values because of low photon counts, the sum of the probabilities of the observed pixel values (obtained from the histogram of the acquired pixel values) is less than one. Experimental results demonstrate that it is possible to closely estimate the unknown probability mass function with these assumptions.

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

NASA Astrophysics Data System (ADS)

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.

A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.

On Orbital Elements of Extrasolar Planetary Candidates and Spectroscopic Binaries

NASA Technical Reports Server (NTRS)

Stepinski, T. F.; Black, D. C.

2001-01-01

We estimate probability densities of orbital elements, periods, and eccentricities, for the population of extrasolar planetary candidates (EPC) and, separately, for the population of spectroscopic binaries (SB) with solar-type primaries. We construct empirical cumulative distribution functions (CDFs) in order to infer probability distribution functions (PDFs) for orbital periods and eccentricities. We also derive a joint probability density for period-eccentricity pairs in each population. Comparison of respective distributions reveals that in all cases EPC and SB populations are, in the context of orbital elements, indistinguishable from each other to a high degree of statistical significance. Probability densities of orbital periods in both populations have P(exp -1) functional form, whereas the PDFs of eccentricities can he best characterized as a Gaussian with a mean of about 0.35 and standard deviation of about 0.2 turning into a flat distribution at small values of eccentricity. These remarkable similarities between EPC and SB must be taken into account by theories aimed at explaining the origin of extrasolar planetary candidates, and constitute an important clue us to their ultimate nature.

Steady-state distributions of probability fluxes on complex networks

NASA Astrophysics Data System (ADS)

Chełminiak, Przemysław; Kurzyński, Michał

2017-02-01

We consider a simple model of the Markovian stochastic dynamics on complex networks to examine the statistical properties of the probability fluxes. The additional transition, called hereafter a gate, powered by the external constant force breaks a detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge to the Gaussian distribution. By virtue of the stationary fluctuation theorem, its standard deviation depends directly on the square root of the mean flux. In turn, the nonlinear relation between the mean flux and the external force, which provides the key result of the present study, allows us to calculate the two parameters that entirely characterize the Gaussian distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of computer simulations are widely discussed in terms of the rigorous theoretical predictions.

Diagnostic assessment without cut-offs: application of serology for the modelling of bovine digital dermatitis infection.

PubMed

Vink, W D; Jones, G; Johnson, W O; Brown, J; Demirkan, I; Carter, S D; French, N P

2009-11-15

Bovine digital dermatitis (BDD) is an epidermitis which is a leading cause of infectious lameness. The only recognized diagnostic test is foot inspection, which is a labour-intensive procedure. There is no universally recognized, standardized lesion scoring system. As small lesions are easily missed, foot inspection has limited diagnostic sensitivity. Furthermore, interpretation is subjective, and prone to observer bias. Serology is more convenient to carry out and is potentially a more sensitive indicator of infection. By carrying out 20 serological assays using lesion-associated Treponema spp. isolates, three serogroups were identified. The reliability of the tests was established by assessing the level of agreement and the concordance correlation coefficient. Subsequently, an ELISA suitable for routine use was developed. The benchmark of diagnostic test validation is conventionally the determination of the key test parameters, sensitivity and specificity. This requires the imposition of a cut-off point. For serological assays with outcomes on a continuous scale, the degree by which the test result differs from this cut-off is disregarded. Bayesian statistical methodology has been developed which enables the assay result also to be interpreted on a continuous scale, thereby optimizing the information inherent in the test. Using a cross-sectional study dataset carried out on 8 representative dairy farms in the UK, the probability of infection, P(I), of each individual animal was estimated in the absence of a 'Gold Standard' by modelling I as a latent variable which was determined by lesion status, L as well as serology, S. Covariate data (foot hygiene score and age) were utilized to estimate P(L) when no lesion inspection was performed. Informative prior distributions were elicited where possible. The model was utilized for predictive inference, by computing estimates of P(I) and P(L) independently of the data. A more detailed and informative analysis of the farm-level distribution of infection could thus be performed. Also, biases associated with the subjective interpretation of lesion status were minimized. Model outputs showed that young stock were unlikely to be infected, whereas cows tended to have high or low probabilities of being infected. Estimates of probability of infection were considerably higher for animals with lesions than for those without. Associations were identified between both covariates and probability of infection in cows, but not in the young stock. Under the condition that the model assumptions are valid for the larger population, the results of this work can be generalized by predictive inference.

Time-dependent landslide probability mapping

USGS Publications Warehouse

Campbell, Russell H.; Bernknopf, Richard L.; ,

1993-01-01

Case studies where time of failure is known for rainfall-triggered debris flows can be used to estimate the parameters of a hazard model in which the probability of failure is a function of time. As an example, a time-dependent function for the conditional probability of a soil slip is estimated from independent variables representing hillside morphology, approximations of material properties, and the duration and rate of rainfall. If probabilities are calculated in a GIS (geomorphic information system ) environment, the spatial distribution of the result for any given hour can be displayed on a map. Although the probability levels in this example are uncalibrated, the method offers a potential for evaluating different physical models and different earth-science variables by comparing the map distribution of predicted probabilities with inventory maps for different areas and different storms. If linked with spatial and temporal socio-economic variables, this method could be used for short-term risk assessment.

Generalized Wishart Mixtures for Unsupervised Classification of PolSAR Data

NASA Astrophysics Data System (ADS)

Li, Lan; Chen, Erxue; Li, Zengyuan

2013-01-01

This paper presents an unsupervised clustering algorithm based upon the expectation maximization (EM) algorithm for finite mixture modelling, using the complex wishart probability density function (PDF) for the probabilities. The mixture model enables to consider heterogeneous thematic classes which could not be better fitted by the unimodal wishart distribution. In order to make it fast and robust to calculate, we use the recently proposed generalized gamma distribution (GΓD) for the single polarization intensity data to make the initial partition. Then we use the wishart probability density function for the corresponding sample covariance matrix to calculate the posterior class probabilities for each pixel. The posterior class probabilities are used for the prior probability estimates of each class and weights for all class parameter updates. The proposed method is evaluated and compared with the wishart H-Alpha-A classification. Preliminary results show that the proposed method has better performance.

Oil spill contamination probability in the southeastern Levantine basin.

PubMed

Goldman, Ron; Biton, Eli; Brokovich, Eran; Kark, Salit; Levin, Noam

2015-02-15

Recent gas discoveries in the eastern Mediterranean Sea led to multiple operations with substantial economic interest, and with them there is a risk of oil spills and their potential environmental impacts. To examine the potential spatial distribution of this threat, we created seasonal maps of the probability of oil spill pollution reaching an area in the Israeli coastal and exclusive economic zones, given knowledge of its initial sources. We performed simulations of virtual oil spills using realistic atmospheric and oceanic conditions. The resulting maps show dominance of the alongshore northerly current, which causes the high probability areas to be stretched parallel to the coast, increasing contamination probability downstream of source points. The seasonal westerly wind forcing determines how wide the high probability areas are, and may also restrict these to a small coastal region near source points. Seasonal variability in probability distribution, oil state, and pollution time is also discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Probability density function of non-reactive solute concentration in heterogeneous porous formations.

PubMed

Bellin, Alberto; Tonina, Daniele

2007-10-30

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.

The distribution and modeling of nitrate transport in the Carson Valley alluvial aquifer, Douglas County, Nevada

USGS Publications Warehouse

Naranjo, Ramon C.; Welborn, Toby L.; Rosen, Michael R.

2013-01-01

The distribution of nitrate as nitrogen (referred to herein as nitrate-N) concentrations in groundwater was determined by collecting more than 200 samples from 8 land-use categories: single family residential, multifamily residential, rural (including land use for agriculture), vacant land, commercial, industrial, utilities, and unclassified. Nitrate-N concentrations ranged from below detection (less than 0.05 milligrams per liter) to 18 milligrams per liter. The results of nitrate-N concentrations that were sampled from three wells equalled or exceeded the maximum contaminant level of 10 milligrams per liter set by the U.S. Environmental Protection Agency. Nitrate-N concentrations in sampled wells showed a positive correlation between elevated nitrate-N concentrations and the percentage of single-family land use and septic-system density. Wells sampled in other land-use categories did not have any correlation to nitrate-N concentrations. In areas with greater than 50-percent single-family land use, nitrate-N concentrations were two times greater than in areas with less than 50 percent single-family land use. Nitrate-N concentrations in groundwater near septic systems that had been used more than 20 years were more than two times greater than in areas where septic systems had been used less than 20 years. Lower nitrate-N concentrations in the areas where septic systems were less than 20 years old probably result from temporary storage of nitrogen leaching from septic systems into the unsaturated zone. In areas where septic systems are abundant, nitrate-N concentrations were predicted to 2059 by using numerical models within the Ruhenstroth and Johnson Lane subdivisions in the Carson Valley. Model results indicated that nitrate-N concentrations will continue to increase and could exceed the maximum contaminant level over extended areas inside and outside the subdivisions. Two modeling scenarios were used to simulate future transport as a result of removal of septic systems (source of nitrate-N contamination) and the termination of domestic pumping of groundwater. The models showed the largest decrease in nitrate-N concentrations when septic systems were removed and wells continued to pump. Nitrate-N concentrations probably will continue to increase in areas that are dependent on septic systems for waste disposal either under current land-use conditions in the valley or with continued growth and change in land use in the valley.

A Performance Comparison on the Probability Plot Correlation Coefficient Test using Several Plotting Positions for GEV Distribution.

NASA Astrophysics Data System (ADS)

Ahn, Hyunjun; Jung, Younghun; Om, Ju-Seong; Heo, Jun-Haeng

2014-05-01

It is very important to select the probability distribution in Statistical hydrology. Goodness of fit test is a statistical method that selects an appropriate probability model for a given data. The probability plot correlation coefficient (PPCC) test as one of the goodness of fit tests was originally developed for normal distribution. Since then, this test has been widely applied to other probability models. The PPCC test is known as one of the best goodness of fit test because it shows higher rejection powers among them. In this study, we focus on the PPCC tests for the GEV distribution which is widely used in the world. For the GEV model, several plotting position formulas are suggested. However, the PPCC statistics are derived only for the plotting position formulas (Goel and De, In-na and Nguyen, and Kim et al.) in which the skewness coefficient (or shape parameter) are included. And then the regression equations are derived as a function of the shape parameter and sample size for a given significance level. In addition, the rejection powers of these formulas are compared using Monte-Carlo simulation. Keywords: Goodness-of-fit test, Probability plot correlation coefficient test, Plotting position, Monte-Carlo Simulation ACKNOWLEDGEMENTS This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-12-NH-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

Classic maximum entropy recovery of the average joint distribution of apparent FRET efficiency and fluorescence photons for single-molecule burst measurements.

PubMed

DeVore, Matthew S; Gull, Stephen F; Johnson, Carey K

2012-04-05

We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions.

Probabilistic Estimates of Climate Impacts of the Paris Agreement and Contributions from Different Countries.

NASA Astrophysics Data System (ADS)

Sokolov, A. P.; Paltsev, S.; Chen, Y. H. H.; Monier, E.; Libardoni, A. G.; Forest, C. E.

2017-12-01

In December of 2015 during COP21 meeting in Paris almost 200 countries signed an agreement pledging to reduce their anthropogenic greenhouse gas (GHG) emissions. Recently USA announced plans to withdraw from the agreement. In this study, we estimate an impact of this decision on future climate using the MIT Integrated Global System Model, which consists of the human activity model, Economic Projection and Policy Analysis (EPPA) model, and a climate model of intermediate complexity, the MIT Earth System Model (MESM). For comparison, we also estimated impacts of possible withdrawals of China, Europe or India. In addition to the "no climate policy" scenario, we consider five emissions scenarios: Paris, Paris_no_USA, Paris_no_EUR and so on. Climate simulations were carried out from 1861 to 2005 driven by prescribed changes in GHGs and natural forcings and them continued to 2100 driven by GHG emissions produced by EPPA model. Because Paris agreement only cover the period up to 2030, last five scenarios were created assuming that emissions or carbon intensity will continue to decrease after 2030 at the same rate as in the 2020-2030 period. To account for uncertainty in climate system response to external forcing, we carry out 400 member ensembles on climate simulations for each scenario. Probability distributions for climate parameters are obtained by comparing simulated climate for 1861 to 2010 with observations. Our analysis shows that, full implementation of Paris agreement (under above-descried assumptions) will increase probability of surface air temperature in the last decade of this century increasing by less than 3oC relative to pre-industrial form about 20% for "no climate policy" to about 86%. Withdrawal of USA, China, Europe or India will decrease this probability to about 63, 67, 75 and 82%, respectively.

Improved first-order uncertainty method for water-quality modeling

USGS Publications Warehouse

Melching, C.S.; Anmangandla, S.

1992-01-01

Uncertainties are unavoidable in water-quality modeling and subsequent management decisions. Monte Carlo simulation and first-order uncertainty analysis (involving linearization at central values of the uncertain variables) have been frequently used to estimate probability distributions for water-quality model output due to their simplicity. Each method has its drawbacks: Monte Carlo simulation's is mainly computational time; and first-order analysis are mainly questions of accuracy and representativeness, especially for nonlinear systems and extreme conditions. An improved (advanced) first-order method is presented, where the linearization point varies to match the output level whose exceedance probability is sought. The advanced first-order method is tested on the Streeter-Phelps equation to estimate the probability distribution of critical dissolved-oxygen deficit and critical dissolved oxygen using two hypothetical examples from the literature. The advanced first-order method provides a close approximation of the exceedance probability for the Streeter-Phelps model output estimated by Monte Carlo simulation using less computer time - by two orders of magnitude - regardless of the probability distributions assumed for the uncertain model parameters.

Measures for a multidimensional multiverse

NASA Astrophysics Data System (ADS)

Chung, Hyeyoun

2015-04-01

We explore the phenomenological implications of generalizing the causal patch and fat geodesic measures to a multidimensional multiverse, where the vacua can have differing numbers of large dimensions. We consider a simple model in which the vacua are nucleated from a D -dimensional parent spacetime through dynamical compactification of the extra dimensions, and compute the geometric contribution to the probability distribution of observations within the multiverse for each measure. We then study how the shape of this probability distribution depends on the time scales for the existence of observers, for vacuum domination, and for curvature domination (tobs,tΛ , and tc, respectively.) In this work we restrict ourselves to bubbles with positive cosmological constant, Λ . We find that in the case of the causal patch cutoff, when the bubble universes have p +1 large spatial dimensions with p ≥2 , the shape of the probability distribution is such that we obtain the coincidence of time scales tobs˜tΛ˜tc . Moreover, the size of the cosmological constant is related to the size of the landscape. However, the exact shape of the probability distribution is different in the case p =2 , compared to p ≥3 . In the case of the fat geodesic measure, the result is even more robust: the shape of the probability distribution is the same for all p ≥2 , and we once again obtain the coincidence tobs˜tΛ˜tc . These results require only very mild conditions on the prior probability of the distribution of vacua in the landscape. Our work shows that the observed double coincidence of time scales is a robust prediction even when the multiverse is generalized to be multidimensional; that this coincidence is not a consequence of our particular Universe being (3 +1 )-dimensional; and that this observable cannot be used to preferentially select one measure over another in a multidimensional multiverse.

Shape of growth-rate distribution determines the type of Non-Gibrat’s Property

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki

2011-11-01

In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and business growth trends. Here, profits denote net profits. First, detailed balance is observed not only in profits data but also in sales data. Furthermore, the growth-rate distribution of sales has wider tails than the linear growth-rate distribution of profits in log-log scale. On the one hand, in the mid-scale range of profits, the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases. This is called Non-Gibrat’s First Property. On the other hand, in the mid-scale range of sales, the probability of positive growth decreases as the initial value increases, while the probability of negative growth hardly changes. This is called Non-Gibrat’s Second Property. Under detailed balance, Non-Gibrat’s First and Second Properties are analytically derived from the linear and quadratic growth-rate distributions in log-log scale, respectively. In both cases, the log-normal distribution is inferred from Non-Gibrat’s Properties and detailed balance. These analytic results are verified by empirical data. Consequently, this clarifies the notion that the difference in shapes between growth-rate distributions of sales and profits is closely related to the difference between the two Non-Gibrat’s Properties in the mid-scale range.

Estimation of distribution overlap of urn models.

PubMed

Hampton, Jerrad; Lladser, Manuel E

2012-01-01

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a draw from one distribution not being observed in [Formula: see text] draws from another distribution. We show our estimator of dissimilarity to be a [Formula: see text]-statistic and a uniformly minimum variance unbiased estimator of dissimilarity over the largest appropriate range of [Formula: see text]. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over [Formula: see text], we show it converges uniformly in probability to the dissimilarity parameter, and we present criteria when it is approximately normally distributed and admits a consistent jackknife estimator of its variance. As proof of concept, we analyze V35 16S rRNA data to discern between various microbial environments. Other potential applications concern any situation where dissimilarity of two discrete distributions may be of interest. For instance, in SELEX experiments, each urn could represent a random RNA pool and each draw a possible solution to a particular binding site problem over that pool. The dissimilarity of these pools is then related to the probability of finding binding site solutions in one pool that are absent in the other.

Diffusion of active chiral particles

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.

2016-12-01

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v ̂ at time t , and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

A Search Model for Imperfectly Detected Targets

NASA Technical Reports Server (NTRS)

Ahumada, Albert

2012-01-01

Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.

Optimizing probability of detection point estimate demonstration

NASA Astrophysics Data System (ADS)

Koshti, Ajay M.

2017-04-01

The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using point estimate method. 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. 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. Traditionally largest flaw size in the set is considered to be a conservative estimate of the flaw size with minimum 90% probability and 95% confidence. The flaw size is denoted as α90/95PE. The paper investigates relationship between range of flaw sizes in relation to α90, i.e. 90% probability flaw size, to provide a desired PPD. The range of flaw sizes is expressed as a proportion of the standard deviation of the probability density distribution. Difference between median or average of the 29 flaws and α90 is also expressed as a proportion of standard deviation of the probability density distribution. In general, it is concluded that, if probability of detection increases with flaw size, average of 29 flaw sizes would always be larger than or equal to α90 and is an acceptable measure of α90/95PE. If NDE technique has sufficient sensitivity and signal-to-noise ratio, then the 29 flaw-set can be optimized to meet requirements of minimum required PPD, maximum allowable POF, requirements on flaw size tolerance about mean flaw size and flaw size detectability requirements. The paper provides procedure for optimizing flaw sizes in the point estimate demonstration flaw-set.

A Computational Model of Word Segmentation from Continuous Speech Using Transitional Probabilities of Atomic Acoustic Events

ERIC Educational Resources Information Center

Rasanen, Okko

2011-01-01

Word segmentation from continuous speech is a difficult task that is faced by human infants when they start to learn their native language. Several studies indicate that infants might use several different cues to solve this problem, including intonation, linguistic stress, and transitional probabilities between subsequent speech sounds. In this…

Completion of the Edward Air Force Base Statistical Guidance Wind Tool

NASA Technical Reports Server (NTRS)

Dreher, Joseph G.

2008-01-01

The goal of this task was to develop a GUI using EAFB wind tower data similar to the KSC SLF peak wind tool that is already in operations at SMG. In 2004, MSFC personnel began work to replicate the KSC SLF tool using several wind towers at EAFB. They completed the analysis and QC of the data, but due to higher priority work did not start development of the GUI. MSFC personnel calculated wind climatologies and probabilities of 10-minute peak wind occurrence based on the 2-minute average wind speed for several EAFB wind towers. Once the data were QC'ed and analyzed the climatologies were calculated following the methodology outlined in Lambert (2003). The climatologies were calculated for each tower and month, and then were stratified by hour, direction (10" sectors), and direction (45" sectors)/hour. For all climatologies, MSFC calculated the mean, standard deviation and observation counts of the Zminute average and 10-minute peak wind speeds. MSFC personnel also calculated empirical and modeled probabilities of meeting or exceeding specific 10- minute peak wind speeds using PDFs. The empirical PDFs were asymmetrical and bounded on the left by the 2- minute average wind speed. They calculated the parametric PDFs by fitting the GEV distribution to the empirical distributions. Parametric PDFs were calculated in order to smooth and interpolate over variations in the observed values due to possible under-sampling of certain peak winds and to estimate probabilities associated with average winds outside the observed range. MSFC calculated the individual probabilities of meeting or exceeding specific 10- minute peak wind speeds by integrating the area under each curve. The probabilities assist SMG forecasters in assessing the shuttle FR for various Zminute average wind speeds. The A M ' obtained the processed EAFB data from Dr. Lee Bums of MSFC and reformatted them for input to Excel PivotTables, which allow users to display different values with point-click-drag techniques. The GUI was created from the PivotTables using VBA code. It is run through a macro within Excel and allows forecasters to quickly display and interpret peak wind climatology and probabilities in a fast-paced operational environment. The GUI was designed to look and operate exactly the same as the KSC SLF tool since SMG forecasters were already familiar with that product. SMG feedback was continually incorporated into the GUI ensuring the end product met their needs. The final version of the GUI along with all climatologies, PDFs, and probabilities has been delivered to SMG and will be put into operational use.

Theoretical cratering rates on Ida, Mathilde, Eros and Gaspra

NASA Astrophysics Data System (ADS)

Jeffers, S. V.; Asher, D. J.; Bailey, M. E.

2002-11-01

We investigate the main influences on crater size distributions, by deriving results for the four example target objects, (951) Gaspra, (243) Ida, (253) Mathilde and (433) Eros. The dynamical history of each of these asteroids is modelled using the MERCURY (Chambers 1999) numerical integrator. The use of an efficient, Öpik-type, collision code enables the calculation of a velocity histogram and the probability of impact. This when combined with a crater scaling law and an impactor size distribution, through a Monte Carlo method, results in a crater size distribution. The resulting crater probability distributions are in good agreement with observed crater distributions on these asteroids.

Resistance of virus to extinction on bottleneck passages: study of a decaying and fluctuating pattern of fitness loss

NASA Technical Reports Server (NTRS)

Lazaro, Ester; Escarmis, Cristina; Perez-Mercader, Juan; Manrubia, Susanna C.; Domingo, Esteban

2003-01-01

RNA viruses display high mutation rates and their populations replicate as dynamic and complex mutant distributions, termed viral quasispecies. Repeated genetic bottlenecks, which experimentally are carried out through serial plaque-to-plaque transfers of the virus, lead to fitness decrease (measured here as diminished capacity to produce infectious progeny). Here we report an analysis of fitness evolution of several low fitness foot-and-mouth disease virus clones subjected to 50 plaque-to-plaque transfers. Unexpectedly, fitness decrease, rather than being continuous and monotonic, displayed a fluctuating pattern, which was influenced by both the virus and the state of the host cell as shown by effects of recent cell passage history. The amplitude of the fluctuations increased as fitness decreased, resulting in a remarkable resistance of virus to extinction. Whereas the frequency distribution of fitness in control (independent) experiments follows a log-normal distribution, the probability of fitness values in the evolving bottlenecked populations fitted a Weibull distribution. We suggest that multiple functions of viral genomic RNA and its encoded proteins, subjected to high mutational pressure, interact with cellular components to produce this nontrivial, fluctuating pattern.

Velocity distributions among colliding asteroids

NASA Technical Reports Server (NTRS)

Bottke, William F., Jr.; Nolan, Michael C.; Greenberg, Richard; Kolvoord, Robert A.

1994-01-01

The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.

The Probability Distribution for a Biased Spinner

ERIC Educational Resources Information Center

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.)

A probable probability distribution of a series nonequilibrium states in a simple system out of equilibrium

NASA Astrophysics Data System (ADS)

Gao, Haixia; Li, Ting; Xiao, Changming

2016-05-01

When a simple system is in its nonequilibrium state, it will shift to its equilibrium state. Obviously, in this process, there are a series of nonequilibrium states. With the assistance of Bayesian statistics and hyperensemble, a probable probability distribution of these nonequilibrium states can be determined by maximizing the hyperensemble entropy. It is known that the largest probability is the equilibrium state, and the far a nonequilibrium state is away from the equilibrium one, the smaller the probability will be, and the same conclusion can also be obtained in the multi-state space. Furthermore, if the probability stands for the relative time the corresponding nonequilibrium state can stay, then the velocity of a nonequilibrium state returning back to its equilibrium can also be determined through the reciprocal of the derivative of this probability. It tells us that the far away the state from the equilibrium is, the faster the returning velocity will be; if the system is near to its equilibrium state, the velocity will tend to be smaller and smaller, and finally tends to 0 when it gets the equilibrium state.

Study on probability distributions for evolution in modified extremal optimization

NASA Astrophysics Data System (ADS)

Zeng, Guo-Qiang; Lu, Yong-Zai; Mao, Wei-Jie; Chu, Jian

2010-05-01

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.

Rapidly assessing the probability of exceptionally high natural hazard losses

NASA Astrophysics Data System (ADS)

Gollini, Isabella; Rougier, Jonathan

2014-05-01

One of the objectives in catastrophe modeling is to assess the probability distribution of losses for a specified period, such as a year. From the point of view of an insurance company, the whole of the loss distribution is interesting, and valuable in determining insurance premiums. But the shape of the righthand tail is critical, because it impinges on the solvency of the company. A simple measure of the risk of insolvency is the probability that the annual loss will exceed the company's current operating capital. Imposing an upper limit on this probability is one of the objectives of the EU Solvency II directive. If a probabilistic model is supplied for the loss process, then this tail probability can be computed, either directly, or by simulation. This can be a lengthy calculation for complex losses. Given the inevitably subjective nature of quantifying loss distributions, computational resources might be better used in a sensitivity analysis. This requires either a quick approximation to the tail probability or an upper bound on the probability, ideally a tight one. We present several different bounds, all of which can be computed nearly instantly from a very general event loss table. We provide a numerical illustration, and discuss the conditions under which the bound is tight. Although we consider the perspective of insurance and reinsurance companies, exactly the same issues concern the risk manager, who is typically very sensitive to large losses.

Variation in the standard deviation of the lure rating distribution: Implications for estimates of recollection probability.

PubMed

Dopkins, Stephen; Varner, Kaitlin; Hoyer, Darin

2017-10-01

In word recognition semantic priming of test words increased the false-alarm rate and the mean of confidence ratings to lures. Such priming also increased the standard deviation of confidence ratings to lures and the slope of the z-ROC function, suggesting that the priming increased the standard deviation of the lure evidence distribution. The Unequal Variance Signal Detection (UVSD) model interpreted the priming as increasing the standard deviation of the lure evidence distribution. Without additional parameters the Dual Process Signal Detection (DPSD) model could only accommodate the results by fitting the data for related and unrelated primes separately, interpreting the priming, implausibly, as decreasing the probability of target recollection (DPSD). With an additional parameter, for the probability of false (lure) recollection the model could fit the data for related and unrelated primes together, interpreting the priming as increasing the probability of false recollection. These results suggest that DPSD estimates of target recollection probability will decrease with increases in the lure confidence/evidence standard deviation unless a parameter is included for false recollection. Unfortunately the size of a given lure confidence/evidence standard deviation relative to other possible lure confidence/evidence standard deviations is often unspecified by context. Hence the model often has no way of estimating false recollection probability and thereby correcting its estimates of target recollection probability.

Probability distributions for Markov chain based quantum walks

NASA Astrophysics Data System (ADS)

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.

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains

PubMed Central

Meyer, Denny; Forbes, Don; Clarke, Stephen R.

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key Points A comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition. The Markov assumption appears to be valid. However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play. Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes. PMID:24357946

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains.

PubMed

Meyer, Denny; Forbes, Don; Clarke, Stephen R

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key PointsA comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition.The Markov assumption appears to be valid.However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play.Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes.

Digital simulation of an arbitrary stationary stochastic process by spectral representation.

PubMed

Yura, Harold T; Hanson, Steen G

2011-04-01

In this paper we present a straightforward, efficient, and computationally fast method for creating a large number of discrete samples with an arbitrary given probability density function and a specified spectral content. 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 contrast to previous work, where the analyses were limited to auto regressive and or iterative techniques to obtain satisfactory results, we find that a single application of the inverse transform method yields satisfactory results for a wide class of arbitrary probability distributions. Although a single application of the inverse transform technique does not conserve the power spectra exactly, it yields highly accurate numerical results for a wide range of probability distributions and target power spectra that are sufficient for system simulation purposes and can thus be regarded as an accurate engineering approximation, which can be used for wide range of practical applications. A sufficiency condition is presented regarding the range of parameter values where a single application of the inverse transform method yields satisfactory agreement between the simulated and target power spectra, and a series of examples relevant for the optics community are presented and discussed. Outside this parameter range the agreement gracefully degrades but does not distort in shape. Although we demonstrate the method here focusing on stationary random processes, we see no reason why the method could not be extended to simulate non-stationary random processes. © 2011 Optical Society of America

Estimating alarm thresholds and the number of components in mixture distributions

NASA Astrophysics Data System (ADS)

Burr, Tom; Hamada, Michael S.

2012-09-01

Mixtures of probability distributions arise in many nuclear assay and forensic applications, including nuclear weapon detection, neutron multiplicity counting, and in solution monitoring (SM) for nuclear safeguards. SM data is increasingly used to enhance nuclear safeguards in aqueous reprocessing facilities having plutonium in solution form in many tanks. This paper provides background for mixture probability distributions and then focuses on mixtures arising in SM data. SM data can be analyzed by evaluating transfer-mode residuals defined as tank-to-tank transfer differences, and wait-mode residuals defined as changes during non-transfer modes. A previous paper investigated impacts on transfer-mode and wait-mode residuals of event marking errors which arise when the estimated start and/or stop times of tank events such as transfers are somewhat different from the true start and/or stop times. Event marking errors contribute to non-Gaussian behavior and larger variation than predicted on the basis of individual tank calibration studies. This paper illustrates evidence for mixture probability distributions arising from such event marking errors and from effects such as condensation or evaporation during non-transfer modes, and pump carryover during transfer modes. A quantitative assessment of the sample size required to adequately characterize a mixture probability distribution arising in any context is included.

Construction and identification of a D-Vine model applied to the probability distribution of modal parameters in structural dynamics

NASA Astrophysics Data System (ADS)

Dubreuil, S.; Salaün, M.; Rodriguez, E.; Petitjean, F.

2018-01-01

This study investigates the construction and identification of the probability distribution of random modal parameters (natural frequencies and effective parameters) in structural dynamics. As these parameters present various types of dependence structures, the retained approach is based on pair copula construction (PCC). A literature review leads us to choose a D-Vine model for the construction of modal parameters probability distributions. Identification of this model is based on likelihood maximization which makes it sensitive to the dimension of the distribution, namely the number of considered modes in our context. To this respect, a mode selection preprocessing step is proposed. It allows the selection of the relevant random modes for a given transfer function. The second point, addressed in this study, concerns the choice of the D-Vine model. Indeed, D-Vine model is not uniquely defined. Two strategies are proposed and compared. The first one is based on the context of the study whereas the second one is purely based on statistical considerations. Finally, the proposed approaches are numerically studied and compared with respect to their capabilities, first in the identification of the probability distribution of random modal parameters and second in the estimation of the 99 % quantiles of some transfer functions.

Probability distribution functions in turbulent convection

NASA Technical Reports Server (NTRS)

Balachandar, S.; Sirovich, L.

1991-01-01

Results of an extensive investigation of probability distribution functions (pdfs) for Rayleigh-Benard convection, in hard turbulence regime, are presented. It is shown that the pdfs exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to the universality is presented.

Power-law tail probabilities of drainage areas in river basins

USGS Publications Warehouse

Veitzer, S.A.; Troutman, B.M.; Gupta, V.K.

2003-01-01

The significance of power-law tail probabilities of drainage areas in river basins was discussed. The convergence to a power law was not observed for all underlying distributions, but for a large class of statistical distributions with specific limiting properties. The article also discussed about the scaling properties of topologic and geometric network properties in river basins.

KINETICS OF LOW SOURCE REACTOR STARTUPS. PART II

DOE Office of Scientific and Technical Information (OSTI.GOV)

hurwitz, H. Jr.; MacMillan, D.B.; Smith, J.H.

1962-06-01

A computational technique is described for computation of the probability distribution of power level for a low source reactor startup. The technique uses a mathematical model, for the time-dependent probability distribution of neutron and precursor concentration, having finite neutron lifetime, one group of delayed neutron precursors, and no spatial dependence. Results obtained by the technique are given. (auth)

Generating an Empirical Probability Distribution for the Andrews-Pregibon Statistic.

ERIC Educational Resources Information Center

Jarrell, Michele G.

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

Animating Statistics: A New Kind of Applet for Exploring Probability Distributions

ERIC Educational Resources Information Center

Kahle, David

2014-01-01

In this article, I introduce a novel applet ("module") for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive…

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

PubMed

Hansen, John P

2003-01-01

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

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

Multivariate probability distribution for sewer system vulnerability assessment under data-limited conditions.

PubMed

Del Giudice, G; Padulano, R; Siciliano, D

2016-01-01

The lack of geometrical and hydraulic information about sewer networks often excludes the adoption of in-deep modeling tools to obtain prioritization strategies for funds management. The present paper describes a novel statistical procedure for defining the prioritization scheme for preventive maintenance strategies based on a small sample of failure data collected by the Sewer Office of the Municipality of Naples (IT). Novelty issues involve, among others, considering sewer parameters as continuous statistical variables and accounting for their interdependences. After a statistical analysis of maintenance interventions, the most important available factors affecting the process are selected and their mutual correlations identified. Then, after a Box-Cox transformation of the original variables, a methodology is provided for the evaluation of a vulnerability map of the sewer network by adopting a joint multivariate normal distribution with different parameter sets. The goodness-of-fit is eventually tested for each distribution by means of a multivariate plotting position. The developed methodology is expected to assist municipal engineers in identifying critical sewers, prioritizing sewer inspections in order to fulfill rehabilitation requirements.

Neural correlates of the divergence of instrumental probability distributions.

PubMed

Liljeholm, Mimi; Wang, Shuo; Zhang, June; O'Doherty, John P

2013-07-24

Flexible action selection requires knowledge about how alternative actions impact the environment: a "cognitive map" of instrumental contingencies. Reinforcement learning theories formalize this map as a set of stochastic relationships between actions and states, such that for any given action considered in a current state, a probability distribution is specified over possible outcome states. Here, we show that activity in the human inferior parietal lobule correlates with the divergence of such outcome distributions-a measure that reflects whether discrimination between alternative actions increases the controllability of the future-and, further, that this effect is dissociable from those of other information theoretic and motivational variables, such as outcome entropy, action values, and outcome utilities. Our results suggest that, although ultimately combined with reward estimates to generate action values, outcome probability distributions associated with alternative actions may be contrasted independently of valence computations, to narrow the scope of the action selection problem.

Qualitative fusion technique based on information poor system and its application to factor analysis for vibration of rolling bearings

NASA Astrophysics Data System (ADS)

Xia, Xintao; Wang, Zhongyu

2008-10-01

For some methods of stability analysis of a system using statistics, it is difficult to resolve the problems of unknown probability distribution and small sample. Therefore, a novel method is proposed in this paper to resolve these problems. This method is independent of probability distribution, and is useful for small sample systems. After rearrangement of the original data series, the order difference and two polynomial membership functions are introduced to estimate the true value, the lower bound and the supper bound of the system using fuzzy-set theory. Then empirical distribution function is investigated to ensure confidence level above 95%, and the degree of similarity is presented to evaluate stability of the system. Cases of computer simulation investigate stable systems with various probability distribution, unstable systems with linear systematic errors and periodic systematic errors and some mixed systems. The method of analysis for systematic stability is approved.

A double hit model for the distribution of time to AIDS onset

NASA Astrophysics Data System (ADS)

Chillale, Nagaraja Rao

2013-09-01

Incubation time is a key epidemiologic descriptor of an infectious disease. In the case of HIV infection this is a random variable and is probably the longest one. The probability distribution of incubation time is the major determinant of the relation between the incidences of HIV infection and its manifestation to Aids. This is also one of the key factors used for accurate estimation of AIDS incidence in a region. The present article i) briefly reviews the work done, points out uncertainties in estimation of AIDS onset time and stresses the need for its precise estimation, ii) highlights some of the modelling features of onset distribution including immune failure mechanism, and iii) proposes a 'Double Hit' model for the distribution of time to AIDS onset in the cases of (a) independent and (b) dependent time variables of the two markers and examined the applicability of a few standard probability models.

Good Practices in Free-energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Jarzynski, Christopher; Chipot, Christopher

2013-01-01

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.

Evaluation of the reproducibility of lung motion probability distribution function (PDF) using dynamic MRI.

PubMed

Cai, Jing; Read, Paul W; Altes, Talissa A; Molloy, Janelle A; Brookeman, James R; Sheng, Ke

2007-01-21

Treatment planning based on probability distribution function (PDF) of patient geometries has been shown a potential off-line strategy to incorporate organ motion, but the application of such approach highly depends upon the reproducibility of the PDF. In this paper, we investigated the dependences of the PDF reproducibility on the imaging acquisition parameters, specifically the scan time and the frame rate. Three healthy subjects underwent a continuous 5 min magnetic resonance (MR) scan in the sagittal plane with a frame rate of approximately 10 f s-1, and the experiments were repeated with an interval of 2 to 3 weeks. A total of nine pulmonary vessels from different lung regions (upper, middle and lower) were tracked and the dependences of their displacement PDF reproducibility were evaluated as a function of scan time and frame rate. As results, the PDF reproducibility error decreased with prolonged scans and appeared to approach equilibrium state in subjects 2 and 3 within the 5 min scan. The PDF accuracy increased in the power function with the increase of frame rate; however, the PDF reproducibility showed less sensitivity to frame rate presumably due to the randomness of breathing which dominates the effects. As the key component of the PDF-based treatment planning, the reproducibility of the PDF affects the dosimetric accuracy substantially. This study provides a reference for acquiring MR-based PDF of structures in the lung.

ZERODUR - bending strength: review of achievements

NASA Astrophysics Data System (ADS)

Hartmann, Peter

2017-08-01

Increased demand for using the glass ceramic ZERODUR® with high mechanical loads called for strength data based on larger statistical samples. Design calculations for failure probability target value below 1: 100 000 cannot be made reliable with parameters derived from 20 specimen samples. The data now available for a variety of surface conditions, ground with different grain sizes and acid etched for full micro crack removal, allow stresses by factors four to ten times higher than before. The large sample revealed that breakage stresses of ground surfaces follow the three parameter Weibull distribution instead of the two parameter version. This is more reasonable considering that the micro cracks of such surfaces have a maximum depth which is reflected in the existence of a threshold breakage stress below which breakage probability is zero. This minimum strength allows calculating minimum lifetimes. Fatigue under load can be taken into account by using the stress corrosion coefficient for the actual environmental humidity. For fully etched surfaces Weibull statistics fails. The precondition of the Weibull distribution, the existence of one unique failure mechanism, is not given anymore. ZERODUR® with fully etched surfaces free from damages introduced after etching endures easily 100 MPa tensile stress. The possibility to use ZERODUR® for combined high precision and high stress application was confirmed by the successful launch and continuing operation of LISA Pathfinder the precursor experiment for the gravitational wave antenna satellite array eLISA.

Bimodality emerges from transport model calculations of heavy ion collisions at intermediate energy

NASA Astrophysics Data System (ADS)

Mallik, S.; Das Gupta, S.; Chaudhuri, G.

2016-04-01

This work is a continuation of our effort [S. Mallik, S. Das Gupta, and G. Chaudhuri, Phys. Rev. C 91, 034616 (2015)], 10.1103/PhysRevC.91.034616 to examine if signatures of a phase transition can be extracted from transport model calculations of heavy ion collisions at intermediate energy. A signature of first-order phase transition is the appearance of a bimodal distribution in Pm(k ) in finite systems. Here Pm(k ) is the probability that the maximum of the multiplicity distribution occurs at mass number k . Using a well-known model for event generation [Botzmann-Uehling-Uhlenbeck (BUU) plus fluctuation], we study two cases of central collision: mass 40 on mass 40 and mass 120 on mass 120. Bimodality is seen in both the cases. The results are quite similar to those obtained in statistical model calculations. An intriguing feature is seen. We observe that at the energy where bimodality occurs, other phase-transition-like signatures appear. There are breaks in certain first-order derivatives. We then examine if such breaks appear in standard BUU calculations without fluctuations. They do. The implication is interesting. If first-order phase transition occurs, it may be possible to recognize that from ordinary BUU calculations. Probably the reason this has not been seen already is because this aspect was not investigated before.

Computing Real-time Streamflow Using Emerging Technologies: Non-contact Radars and the Probability Concept

NASA Astrophysics Data System (ADS)

Fulton, J. W.; Bjerklie, D. M.; Jones, J. W.; Minear, J. T.

2015-12-01

Measuring streamflow, developing, and maintaining rating curves at new streamgaging stations is both time-consuming and problematic. Hydro 21 was an initiative by the U.S. Geological Survey to provide vision and leadership to identify and evaluate new technologies and methods that had the potential to change the way in which streamgaging is conducted. Since 2014, additional trials have been conducted to evaluate some of the methods promoted by the Hydro 21 Committee. Emerging technologies such as continuous-wave radars and computationally-efficient methods such as the Probability Concept require significantly less field time, promote real-time velocity and streamflow measurements, and apply to unsteady flow conditions such as looped ratings and unsteady-flood flows. Portable and fixed-mount radars have advanced beyond the development phase, are cost effective, and readily available in the marketplace. The Probability Concept is based on an alternative velocity-distribution equation developed by C.-L. Chiu, who pioneered the concept. By measuring the surface-water velocity and correcting for environmental influences such as wind drift, radars offer a reliable alternative for measuring and computing real-time streamflow for a variety of hydraulic conditions. If successful, these tools may allow us to establish ratings more efficiently, assess unsteady flow conditions, and report real-time streamflow at new streamgaging stations.

Learning Probabilities From Random Observables in High Dimensions: The Maximum Entropy Distribution and Others

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Cocco, Simona; Monasson, Rémi

2015-11-01

We consider the problem of learning a target probability distribution over a set of N binary variables from the knowledge of the expectation values (with this target distribution) of M observables, drawn uniformly at random. The space of all probability distributions compatible with these M expectation values within some fixed accuracy, called version space, is studied. We introduce a biased measure over the version space, which gives a boost increasing exponentially with the entropy of the distributions and with an arbitrary inverse `temperature' Γ . The choice of Γ allows us to interpolate smoothly between the unbiased measure over all distributions in the version space (Γ =0) and the pointwise measure concentrated at the maximum entropy distribution (Γ → ∞ ). Using the replica method we compute the volume of the version space and other quantities of interest, such as the distance R between the target distribution and the center-of-mass distribution over the version space, as functions of α =(log M)/N and Γ for large N. Phase transitions at critical values of α are found, corresponding to qualitative improvements in the learning of the target distribution and to the decrease of the distance R. However, for fixed α the distance R does not vary with Γ which means that the maximum entropy distribution is not closer to the target distribution than any other distribution compatible with the observable values. Our results are confirmed by Monte Carlo sampling of the version space for small system sizes (N≤ 10).

Statistical Characterization of the Mechanical Parameters of Intact Rock Under Triaxial Compression: An Experimental Proof of the Jinping Marble

NASA Astrophysics Data System (ADS)

Jiang, Quan; Zhong, Shan; Cui, Jie; Feng, Xia-Ting; Song, Leibo

2016-12-01

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress-strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble's probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young's elastic modulus and Poisson's ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering.

Modeling potential distribution of Oligoryzomys longicaudatus, the Andes virus (Genus: Hantavirus) reservoir, in Argentina.

PubMed

Andreo, Verónica; Glass, Gregory; Shields, Timothy; Provensal, Cecilia; Polop, Jaime

2011-09-01

We constructed a model to predict the potential distribution of Oligoryzomys longicaudatus, the reservoir of Andes virus (Genus: Hantavirus), in Argentina. We developed an extensive database of occurrence records from published studies and our own surveys and compared two methods to model the probability of O. longicaudatus presence; logistic regression and MaxEnt algorithm. The environmental variables used were tree, grass and bare soil cover from MODIS imagery and, altitude and 19 bioclimatic variables from WorldClim database. The models performances were evaluated and compared both by threshold dependent and independent measures. The best models included tree and grass cover, mean diurnal temperature range, and precipitation of the warmest and coldest seasons. The potential distribution maps for O. longicaudatus predicted the highest occurrence probabilities along the Andes range, from 32°S and narrowing southwards. They also predicted high probabilities for the south-central area of Argentina, reaching the Atlantic coast. The Hantavirus Pulmonary Syndrome cases coincided with mean occurrence probabilities of 95 and 77% for logistic and MaxEnt models, respectively. HPS transmission zones in Argentine Patagonia matched the areas with the highest probability of presence. Therefore, colilargos presence probability may provide an approximate risk of transmission and act as an early tool to guide control and prevention plans.

Computation of marginal distributions of peak-heights in electropherograms for analysing single source and mixture STR DNA samples.

PubMed

Cowell, Robert G

2018-05-04

Current models for single source and mixture samples, and probabilistic genotyping software based on them used for analysing STR electropherogram data, assume simple probability distributions, such as the gamma distribution, to model the allelic peak height variability given the initial amount of DNA prior to PCR amplification. Here we illustrate how amplicon number distributions, for a model of the process of sample DNA collection and PCR amplification, may be efficiently computed by evaluating probability generating functions using discrete Fourier transforms. Copyright © 2018 Elsevier B.V. All rights reserved.

An Integrated Framework for Model-Based Distributed Diagnosis and Prognosis

DTIC Science & Technology

2012-09-01

0 : t) denotes all measurements observed up to time t. The goal of prognosis is to determine the end of (use- ful) life ( EOL ) of a system, and/or its...remaining useful life (RUL). For a given fault, f , using the fault estimate, p(xf (t),θf (t)|y(0 : t)), a probability distribution of EOL , p(EOLf (tP...is stochas- tic, EOL /RUL are random variables and we represent them by probability distributions. The acceptable behavior of the system is expressed

Encounter risk analysis of rainfall and reference crop evapotranspiration in the irrigation district

NASA Astrophysics Data System (ADS)

Zhang, Jinping; Lin, Xiaomin; Zhao, Yong; Hong, Yang

2017-09-01

Rainfall and reference crop evapotranspiration are random but mutually affected variables in the irrigation district, and their encounter situation can determine water shortage risks under the contexts of natural water supply and demand. However, in reality, the rainfall and reference crop evapotranspiration may have different marginal distributions and their relations are nonlinear. In this study, based on the annual rainfall and reference crop evapotranspiration data series from 1970 to 2013 in the Luhun irrigation district of China, the joint probability distribution of rainfall and reference crop evapotranspiration are developed with the Frank copula function. Using the joint probability distribution, the synchronous-asynchronous encounter risk, conditional joint probability, and conditional return period of different combinations of rainfall and reference crop evapotranspiration are analyzed. The results show that the copula-based joint probability distributions of rainfall and reference crop evapotranspiration are reasonable. The asynchronous encounter probability of rainfall and reference crop evapotranspiration is greater than their synchronous encounter probability, and the water shortage risk associated with meteorological drought (i.e. rainfall variability) is more prone to appear. Compared with other states, there are higher conditional joint probability and lower conditional return period in either low rainfall or high reference crop evapotranspiration. For a specifically high reference crop evapotranspiration with a certain frequency, the encounter risk of low rainfall and high reference crop evapotranspiration is increased with the decrease in frequency. For a specifically low rainfall with a certain frequency, the encounter risk of low rainfall and high reference crop evapotranspiration is decreased with the decrease in frequency. When either the high reference crop evapotranspiration exceeds a certain frequency or low rainfall does not exceed a certain frequency, the higher conditional joint probability and lower conditional return period of various combinations likely cause a water shortage, but the water shortage is not severe.

Study on probability distribution of prices in electricity market: A case study of zhejiang province, china

NASA Astrophysics Data System (ADS)

Zhou, H.; Chen, B.; Han, Z. X.; Zhang, F. Q.

2009-05-01

The study on probability density function and distribution function of electricity prices contributes to the power suppliers and purchasers to estimate their own management accurately, and helps the regulator monitor the periods deviating from normal distribution. Based on the assumption of normal distribution load and non-linear characteristic of the aggregate supply curve, this paper has derived the distribution of electricity prices as the function of random variable of load. The conclusion has been validated with the electricity price data of Zhejiang market. The results show that electricity prices obey normal distribution approximately only when supply-demand relationship is loose, whereas the prices deviate from normal distribution and present strong right-skewness characteristic. Finally, the real electricity markets also display the narrow-peak characteristic when undersupply occurs.

Classic Maximum Entropy Recovery of the Average Joint Distribution of Apparent FRET Efficiency and Fluorescence Photons for Single-molecule Burst Measurements

PubMed Central

DeVore, Matthew S.; Gull, Stephen F.; Johnson, Carey K.

2012-01-01

We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions. PMID:22338694

The effect of microscopic friction and size distributions on conditional probability distributions in soft particle packings

NASA Astrophysics Data System (ADS)

Saitoh, Kuniyasu; Magnanimo, Vanessa; Luding, Stefan

2017-10-01

Employing two-dimensional molecular dynamics (MD) simulations of soft particles, we study their non-affine responses to quasi-static isotropic compression where the effects of microscopic friction between the particles in contact and particle size distributions are examined. To quantify complicated restructuring of force-chain networks under isotropic compression, we introduce the conditional probability distributions (CPDs) of particle overlaps such that a master equation for distribution of overlaps in the soft particle packings can be constructed. From our MD simulations, we observe that the CPDs are well described by q-Gaussian distributions, where we find that the correlation for the evolution of particle overlaps is suppressed by microscopic friction, while it significantly increases with the increase of poly-dispersity.

Ordinal probability effect measures for group comparisons in multinomial cumulative link models.

PubMed

Agresti, Alan; Kateri, Maria

2017-03-01

We consider simple ordinal model-based probability effect measures for comparing distributions of two groups, adjusted for explanatory variables. An "ordinal superiority" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model. The measure applies directly to normal linear models and to a normal latent variable model for ordinal response variables. It equals Φ(β/2) for the corresponding ordinal model that applies a probit link function to cumulative multinomial probabilities, for standard normal cdf Φ and effect β that is the coefficient of the group indicator variable. For the more general latent variable model for ordinal responses that corresponds to a linear model with other possible error distributions and corresponding link functions for cumulative multinomial probabilities, the ordinal superiority measure equals exp(β)/[1+exp(β)] with the log-log link and equals approximately exp(β/2)/[1+exp(β/2)] with the logit link, where β is the group effect. Another ordinal superiority measure generalizes the difference of proportions from binary to ordinal responses. We also present related measures directly for ordinal models for the observed response that need not assume corresponding latent response models. We present confidence intervals for the measures and illustrate with an example. © 2016, The International Biometric Society.

Sampling--how big a sample?

PubMed

Aitken, C G

1999-07-01

It is thought that, in a consignment of discrete units, a certain proportion of the units contain illegal material. A sample of the consignment is to be inspected. Various methods for the determination of the sample size are compared. The consignment will be considered as a random sample from some super-population of units, a certain proportion of which contain drugs. For large consignments, a probability distribution, known as the beta distribution, for the proportion of the consignment which contains illegal material is obtained. This distribution is based on prior beliefs about the proportion. Under certain specific conditions the beta distribution gives the same numerical results as an approach based on the binomial distribution. The binomial distribution provides a probability for the number of units in a sample which contain illegal material, conditional on knowing the proportion of the consignment which contains illegal material. This is in contrast to the beta distribution which provides probabilities for the proportion of a consignment which contains illegal material, conditional on knowing the number of units in the sample which contain illegal material. The interpretation when the beta distribution is used is much more intuitively satisfactory. It is also much more flexible in its ability to cater for prior beliefs which may vary given the different circumstances of different crimes. For small consignments, a distribution, known as the beta-binomial distribution, for the number of units in the consignment which are found to contain illegal material, is obtained, based on prior beliefs about the number of units in the consignment which are thought to contain illegal material. As with the beta and binomial distributions for large samples, it is shown that, in certain specific conditions, the beta-binomial and hypergeometric distributions give the same numerical results. However, the beta-binomial distribution, as with the beta distribution, has a more intuitively satisfactory interpretation and greater flexibility. The beta and the beta-binomial distributions provide methods for the determination of the minimum sample size to be taken from a consignment in order to satisfy a certain criterion. The criterion requires the specification of a proportion and a probability.

Distribution and habitat in Mexico of Dactylopius Costa (Hemiptera: Dactylopiidae) and their cacti hosts (Cactaceae: Opuntioideae).

PubMed

Chávez-Moreno, C K; Tecante, A; Casas, A; Claps, L E

2011-01-01

The distribution pattern of species of the genus Dactylopius Costa in Mexico was analyzed in relation to the distribution of their host plants (subfamily Opuntioideae) to evaluate the specificity of the insect-host association. The distribution of Dactylopius currently recognized is narrower than that of its hosts and probably is not representative. Therefore, a broader distribution of the Dactylopius species in correspondence with those of their hosts was hypothesized. Insects and their hosts were collected and georeferenced in 14 states of Mexico from 2005 to 2007. The distribution areas, maps, and habitat characteristics of Dactylopius, Opuntia sensu stricto, Nopalea and Cylindropuntia were determined on the basis of field collections and examination of museum collections. This information was complemented with information from the exhaustive examination of microscope slides from a local insect collection, plants from local herbaria, and literature reviews. The current distribution of the genus Dactylopius and its hosts included 22 and 25 states of Mexico, respectively, and Dactylopius had a continuous distribution according to its hosts, broader than recognized hitherto. The new georeferenced records of the five Mexican Dactylopius species are reported. Insects with morphological characteristics of D. confusus combined with those of D. salmianus were identified, as well as insects with characteristics of D. opuntiae combined with those of D. salmianus. These records suggest that the number of local Dactylopius species could be higher than previously thought or that possible new processes of hybridization between native and introduced species may be occurring.

A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

Bretthorst, G. Larry

2013-08-01

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.

Precipitation intensity probability distribution modelling for hydrological and construction design purposes

NASA Astrophysics Data System (ADS)

Koshinchanov, Georgy; Dimitrov, Dobri

2008-11-01

The characteristics of rainfall intensity are important for many purposes, including design of sewage and drainage systems, tuning flood warning procedures, etc. Those estimates are usually statistical estimates of the intensity of precipitation realized for certain period of time (e.g. 5, 10 min., etc) with different return period (e.g. 20, 100 years, etc). The traditional approach in evaluating the mentioned precipitation intensities is to process the pluviometer's records and fit probability distribution to samples of intensities valid for certain locations ore regions. Those estimates further become part of the state regulations to be used for various economic activities. Two problems occur using the mentioned approach: 1. Due to various factors the climate conditions are changed and the precipitation intensity estimates need regular update; 2. As far as the extremes of the probability distribution are of particular importance for the practice, the methodology of the distribution fitting needs specific attention to those parts of the distribution. The aim of this paper is to make review of the existing methodologies for processing the intensive rainfalls and to refresh some of the statistical estimates for the studied areas. The methodologies used in Bulgaria for analyzing the intensive rainfalls and produce relevant statistical estimates: The method of the maximum intensity, used in the National Institute of Meteorology and Hydrology to process and decode the pluviometer's records, followed by distribution fitting for each precipitation duration period; As the above, but with separate modeling of probability distribution for the middle and high probability quantiles. Method is similar to the first one, but with a threshold of 0,36 mm/min of intensity; Another method proposed by the Russian hydrologist G. A. Aleksiev for regionalization of estimates over some territory, improved and adapted by S. Gerasimov for Bulgaria; Next method is considering only the intensive rainfalls (if any) during the day with the maximal annual daily precipitation total for a given year; Conclusions are drown on the relevance and adequacy of the applied methods.

Streamflow distribution maps for the Cannon River drainage basin, southeast Minnesota, and the St. Louis River drainage basin, northeast Minnesota

USGS Publications Warehouse

Smith, Erik A.; Sanocki, Chris A.; Lorenz, David L.; Jacobsen, Katrin E.

2017-12-27

Streamflow distribution maps for the Cannon River and St. Louis River drainage basins were developed by the U.S. Geological Survey, in cooperation with the Legislative-Citizen Commission on Minnesota Resources, to illustrate relative and cumulative streamflow distributions. The Cannon River was selected to provide baseline data to assess the effects of potential surficial sand mining, and the St. Louis River was selected to determine the effects of ongoing Mesabi Iron Range mining. Each drainage basin (Cannon, St. Louis) was subdivided into nested drainage basins: the Cannon River was subdivided into 152 nested drainage basins, and the St. Louis River was subdivided into 353 nested drainage basins. For each smaller drainage basin, the estimated volumes of groundwater discharge (as base flow) and surface runoff flowing into all surface-water features were displayed under the following conditions: (1) extreme low-flow conditions, comparable to an exceedance-probability quantile of 0.95; (2) low-flow conditions, comparable to an exceedance-probability quantile of 0.90; (3) a median condition, comparable to an exceedance-probability quantile of 0.50; and (4) a high-flow condition, comparable to an exceedance-probability quantile of 0.02.Streamflow distribution maps were developed using flow-duration curve exceedance-probability quantiles in conjunction with Soil-Water-Balance model outputs; both the flow-duration curve and Soil-Water-Balance models were built upon previously published U.S. Geological Survey reports. The selected streamflow distribution maps provide a proactive water management tool for State cooperators by illustrating flow rates during a range of hydraulic conditions. Furthermore, after the nested drainage basins are highlighted in terms of surface-water flows, the streamflows can be evaluated in the context of meeting specific ecological flows under different flow regimes and potentially assist with decisions regarding groundwater and surface-water appropriations. Presented streamflow distribution maps are foundational work intended to support the development of additional streamflow distribution maps that include statistical constraints on the selected flow conditions.

Multiclass Posterior Probability Twin SVM for Motor Imagery EEG Classification.

PubMed

She, Qingshan; Ma, Yuliang; Meng, Ming; Luo, Zhizeng

2015-01-01

Motor imagery electroencephalography is widely used in the brain-computer interface systems. Due to inherent characteristics of electroencephalography signals, accurate and real-time multiclass classification is always challenging. In order to solve this problem, a multiclass posterior probability solution for twin SVM is proposed by the ranking continuous output and pairwise coupling in this paper. First, two-class posterior probability model is constructed to approximate the posterior probability by the ranking continuous output techniques and Platt's estimating method. Secondly, a solution of multiclass probabilistic outputs for twin SVM is provided by combining every pair of class probabilities according to the method of pairwise coupling. Finally, the proposed method is compared with multiclass SVM and twin SVM via voting, and multiclass posterior probability SVM using different coupling approaches. The efficacy on the classification accuracy and time complexity of the proposed method has been demonstrated by both the UCI benchmark datasets and real world EEG data from BCI Competition IV Dataset 2a, respectively.

A formula for the entropy of the convolution of Gibbs probabilities on the circle

NASA Astrophysics Data System (ADS)

Lopes, Artur O.

2018-07-01

Consider the transformation , such that (mod 1), and where S 1 is the unitary circle. Suppose is Hölder continuous and positive, and moreover that, for any , we have that We say that ρ is a Gibbs probability for the Hölder continuous potential , if where is the Ruelle operator for . We call J the Jacobian of ρ. Suppose is the convolution of two Gibbs probabilities and associated, respectively, to and . We show that ν is also Gibbs and its Jacobian is given by . In this case, the entropy is given by the expression For a fixed we consider differentiable variations , , of on the Banach manifold of Gibbs probabilities, where , and we estimate the derivative of the entropy at t  =  0. We also present an expression for the Jacobian of the convolution of a Gibbs probability ρ with the invariant probability with support on a periodic orbit of period two. This expression is based on the Jacobian of ρ and two Radon–Nidodym derivatives.

Four-dimensional symmetry from a broad viewpoint. II Invariant distribution of quantized field oscillators and questions on infinities

NASA Technical Reports Server (NTRS)

Hsu, J. P.

1983-01-01

The foundation of the quantum field theory is changed by introducing a new universal probability principle into field operators: one single inherent and invariant probability distribution P(/k/) is postulated for boson and fermion field oscillators. This can be accomplished only when one treats the four-dimensional symmetry from a broad viewpoint. Special relativity is too restrictive to allow such a universal probability principle. A radical length, R, appears in physics through the probability distribution P(/k/). The force between two point particles vanishes when their relative distance tends to zero. This appears to be a general property for all forces and resembles the property of asymptotic freedom. The usual infinities in vacuum fluctuations and in local interactions, however complicated they may be, are all removed from quantum field theories. In appendix A a simple finite and unitary theory of unified electroweak interactions is discussed without assuming Higgs scalar bosons.

Probabilistic sensitivity analysis for decision trees with multiple branches: use of the Dirichlet distribution in a Bayesian framework.

PubMed

Briggs, Andrew H; Ades, A E; Price, Martin J

2003-01-01

In structuring decision models of medical interventions, it is commonly recommended that only 2 branches be used for each chance node to avoid logical inconsistencies that can arise during sensitivity analyses if the branching probabilities do not sum to 1. However, information may be naturally available in an unconditional form, and structuring a tree in conditional form may complicate rather than simplify the sensitivity analysis of the unconditional probabilities. Current guidance emphasizes using probabilistic sensitivity analysis, and a method is required to provide probabilistic probabilities over multiple branches that appropriately represents uncertainty while satisfying the requirement that mutually exclusive event probabilities should sum to 1. The authors argue that the Dirichlet distribution, the multivariate equivalent of the beta distribution, is appropriate for this purpose and illustrate its use for generating a fully probabilistic transition matrix for a Markov model. Furthermore, they demonstrate that by adopting a Bayesian approach, the problem of observing zero counts for transitions of interest can be overcome.

Leads Detection Using Mixture Statistical Distribution Based CRF Algorithm from Sentinel-1 Dual Polarization SAR Imagery

NASA Astrophysics Data System (ADS)

Zhang, Yu; Li, Fei; Zhang, Shengkai; Zhu, Tingting

2017-04-01

Synthetic Aperture Radar (SAR) is significantly important for polar remote sensing since it can provide continuous observations in all days and all weather. SAR can be used for extracting the surface roughness information characterized by the variance of dielectric properties and different polarization channels, which make it possible to observe different ice types and surface structure for deformation analysis. In November, 2016, Chinese National Antarctic Research Expedition (CHINARE) 33rd cruise has set sails in sea ice zone in Antarctic. Accurate leads spatial distribution in sea ice zone for routine planning of ship navigation is essential. In this study, the semantic relationship between leads and sea ice categories has been described by the Conditional Random Fields (CRF) model, and leads characteristics have been modeled by statistical distributions in SAR imagery. In the proposed algorithm, a mixture statistical distribution based CRF is developed by considering the contexture information and the statistical characteristics of sea ice for improving leads detection in Sentinel-1A dual polarization SAR imagery. The unary potential and pairwise potential in CRF model is constructed by integrating the posteriori probability estimated from statistical distributions. For mixture statistical distribution parameter estimation, Method of Logarithmic Cumulants (MoLC) is exploited for single statistical distribution parameters estimation. The iteration based Expectation Maximal (EM) algorithm is investigated to calculate the parameters in mixture statistical distribution based CRF model. In the posteriori probability inference, graph-cut energy minimization method is adopted in the initial leads detection. The post-processing procedures including aspect ratio constrain and spatial smoothing approaches are utilized to improve the visual result. The proposed method is validated on Sentinel-1A SAR C-band Extra Wide Swath (EW) Ground Range Detected (GRD) imagery with a pixel spacing of 40 meters near Prydz Bay area, East Antarctica. Main work is listed as follows: 1) A mixture statistical distribution based CRF algorithm has been developed for leads detection from Sentinel-1A dual polarization images. 2) The assessment of the proposed mixture statistical distribution based CRF method and single distribution based CRF algorithm has been presented. 3) The preferable parameters sets including statistical distributions, the aspect ratio threshold and spatial smoothing window size have been provided. In the future, the proposed algorithm will be developed for the operational Sentinel series data sets processing due to its less time consuming cost and high accuracy in leads detection.

Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling

Treesearch

Jeffrey H. Gove

2003-01-01

Many of the most popular sampling schemes used in forestry are probability proportional to size methods. These methods are also referred to as size biased because sampling is actually from a weighted form of the underlying population distribution. Length- and area-biased sampling are special cases of size-biased sampling where the probability weighting comes from a...

Surface Impact Simulations of Helium Nanodroplets

DTIC Science & Technology

2015-06-30

mechanical delocalization of the individual helium atoms in the droplet and the quan- tum statistical effects that accompany the interchange of identical...incorporates the effects of atomic delocaliza- tion by treating individual atoms as smeared-out probability distributions that move along classical...probability density distributions to give effec- tive interatomic potential energy curves that have zero-point averaging effects built into them [25

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

ERIC Educational Resources Information Center

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

2006-01-01

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

Misinterpretation of statistical distance in security of quantum key distribution shown by simulation

NASA Astrophysics Data System (ADS)

Iwakoshi, Takehisa; Hirota, Osamu

2014-10-01

This study will test an interpretation in quantum key distribution (QKD) that trace distance between the distributed quantum state and the ideal mixed state is a maximum failure probability of the protocol. Around 2004, this interpretation was proposed and standardized to satisfy both of the key uniformity in the context of universal composability and operational meaning of the failure probability of the key extraction. However, this proposal has not been verified concretely yet for many years while H. P. Yuen and O. Hirota have thrown doubt on this interpretation since 2009. To ascertain this interpretation, a physical random number generator was employed to evaluate key uniformity in QKD. In this way, we calculated statistical distance which correspond to trace distance in quantum theory after a quantum measurement is done, then we compared it with the failure probability whether universal composability was obtained. As a result, the degree of statistical distance of the probability distribution of the physical random numbers and the ideal uniformity was very large. It is also explained why trace distance is not suitable to guarantee the security in QKD from the view point of quantum binary decision theory.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

Option volatility and the acceleration Lagrangian

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Cao, Yang

2014-01-01

This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent Lagrangian. The acceleration Lagrangian is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the Lagrangian is fixed. The call option price is obtained using the conditional probability and the path integral method.

A statistical model for interpreting computerized dynamic posturography data

NASA Technical Reports Server (NTRS)

Feiveson, Alan H.; Metter, E. Jeffrey; Paloski, William H.

2002-01-01

Computerized dynamic posturography (CDP) is widely used for assessment of altered balance control. CDP trials are quantified using the equilibrium score (ES), which ranges from zero to 100, as a decreasing function of peak sway angle. The problem of how best to model and analyze ESs from a controlled study is considered. The ES often exhibits a skewed distribution in repeated trials, which can lead to incorrect inference when applying standard regression or analysis of variance models. Furthermore, CDP trials are terminated when a patient loses balance. In these situations, the ES is not observable, but is assigned the lowest possible score--zero. As a result, the response variable has a mixed discrete-continuous distribution, further compromising inference obtained by standard statistical methods. Here, we develop alternative methodology for analyzing ESs under a stochastic model extending the ES to a continuous latent random variable that always exists, but is unobserved in the event of a fall. Loss of balance occurs conditionally, with probability depending on the realized latent ES. After fitting the model by a form of quasi-maximum-likelihood, one may perform statistical inference to assess the effects of explanatory variables. An example is provided, using data from the NIH/NIA Baltimore Longitudinal Study on Aging.

Distribution of glucosinolates and sulphur-rich cells in roots of field-grown canola (Brassica napus).

PubMed

McCully, Margaret E; Miller, Celia; Sprague, Susan J; Huang, Cheng X; Kirkegaard, John A

2008-01-01

To investigate the role played by the distribution pattern of glucosinolates (GSLs) in root systems in the release of biocides to the rhizosphere, GSLs have been localized, for the first time, to specific regions and cells in field-grown roots. GSL concentrations in separated tissues of canola (Brassica napus) were determined by chemical analysis, and cell-specific concentrations by extrapolation from sulphur concentrations obtained by quantitative cryo-analytical scanning electron microscopy (SEM). In roots with secondary growth, GSL concentrations in the outer secondary tissues were up to 5x those of the inner core. The highest GSL concentrations (from sulphur measurements) were in two cell layers just under the outermost periderm layer, with up to 100x published concentrations for whole roots. Primary tissues had negligible GSL. Release and renewal of the peripheral GSLs is probably a normal developmental process as secondary thickening continues and surface cells senesce, accounting for published observations that intact roots release GSLs and their biocide hydrolosates to the rhizosphere. Absence of myrosin idioblasts close to the root surface suggests that GSLs released developmentally are hydrolysed by myrosinase in the rhizosphere, ensuring a continuous localized source of biotoxic hydrolysates which can deter soil-borne pests, and influence microbial populations associated with long-lived components of the root system.

On the Structure of a Best Possible Crossover Selection Strategy in Genetic Algorithms

NASA Astrophysics Data System (ADS)

Lässig, Jörg; Hoffmann, Karl Heinz

The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover to find a solution with high fitness for a given optimization problem. Many different schemes have been described in the literature as possible strategies for this task but so far comparisons have been predominantly empirical. It is shown that if one wishes to maximize any linear function of the final state probabilities, e.g. the fitness of the best individual in the final population of the algorithm, then a best probability distribution for selecting an individual in each generation is a rectangular distribution over the individuals sorted in descending sequence by their fitness values. This means uniform probabilities have to be assigned to a group of the best individuals of the population but probabilities equal to zero to individuals with lower fitness, assuming that the probability distribution to choose individuals from the current population can be chosen independently for each iteration and each individual. This result is then generalized also to typical practically applied performance measures, such as maximizing the expected fitness value of the best individual seen in any generation.

Low-flow characteristics of Virginia streams

USGS Publications Warehouse

Austin, Samuel H.; Krstolic, Jennifer L.; Wiegand, Ute

2011-01-01

Low-flow annual non-exceedance probabilities (ANEP), called probability-percent chance (P-percent chance) flow estimates, regional regression equations, and transfer methods are provided describing the low-flow characteristics of Virginia streams. Statistical methods are used to evaluate streamflow data. Analysis of Virginia streamflow data collected from 1895 through 2007 is summarized. Methods are provided for estimating low-flow characteristics of gaged and ungaged streams. The 1-, 4-, 7-, and 30-day average streamgaging station low-flow characteristics for 290 long-term, continuous-record, streamgaging stations are determined, adjusted for instances of zero flow using a conditional probability adjustment method, and presented for non-exceedance probabilities of 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05, 0.02, 0.01, and 0.005. Stream basin characteristics computed using spatial data and a geographic information system are used as explanatory variables in regional regression equations to estimate annual non-exceedance probabilities at gaged and ungaged sites and are summarized for 290 long-term, continuous-record streamgaging stations, 136 short-term, continuous-record streamgaging stations, and 613 partial-record streamgaging stations. Regional regression equations for six physiographic regions use basin characteristics to estimate 1-, 4-, 7-, and 30-day average low-flow annual non-exceedance probabilities at gaged and ungaged sites. Weighted low-flow values that combine computed streamgaging station low-flow characteristics and annual non-exceedance probabilities from regional regression equations provide improved low-flow estimates. Regression equations developed using the Maintenance of Variance with Extension (MOVE.1) method describe the line of organic correlation (LOC) with an appropriate index site for low-flow characteristics at 136 short-term, continuous-record streamgaging stations and 613 partial-record streamgaging stations. Monthly streamflow statistics computed on the individual daily mean streamflows of selected continuous-record streamgaging stations and curves describing flow-duration are presented. Text, figures, and lists are provided summarizing low-flow estimates, selected low-flow sites, delineated physiographic regions, basin characteristics, regression equations, error estimates, definitions, and data sources. This study supersedes previous studies of low flows in Virginia.

Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory

NASA Astrophysics Data System (ADS)

Alvarez, Diego A.; Uribe, Felipe; Hurtado, Jorge E.

2018-02-01

Random set theory is a general framework which comprises uncertainty in the form of probability boxes, possibility distributions, cumulative distribution functions, Dempster-Shafer structures or intervals; in addition, the dependence between the input variables can be expressed using copulas. In this paper, the lower and upper bounds on the probability of failure are calculated by means of random set theory. In order to accelerate the calculation, a well-known and efficient probability-based reliability method known as subset simulation is employed. This method is especially useful for finding small failure probabilities in both low- and high-dimensional spaces, disjoint failure domains and nonlinear limit state functions. The proposed methodology represents a drastic reduction of the computational labor implied by plain Monte Carlo simulation for problems defined with a mixture of representations for the input variables, while delivering similar results. Numerical examples illustrate the efficiency of the proposed approach.

Properties of the probability density function of the non-central chi-squared distribution

NASA Astrophysics Data System (ADS)

András, Szilárd; Baricz, Árpád

2008-10-01

In this paper we consider the probability density function (pdf) of a non-central [chi]2 distribution with arbitrary number of degrees of freedom. For this function we prove that can be represented as a finite sum and we deduce a partial derivative formula. Moreover, we show that the pdf is log-concave when the degrees of freedom is greater or equal than 2. At the end of this paper we present some Turán-type inequalities for this function and an elegant application of the monotone form of l'Hospital's rule in probability theory is given.

An efficient distribution method for nonlinear transport problems in highly heterogeneous stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi

2016-04-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction in the prior knowledge of input distributions. We provide various examples and comparisons with MC simulations to illustrate the performance of the method.

Temperature Inversions and Permafrost Distribution in a Mountain Valley: Preliminary Results From Wolf Creek, Yukon Territory, Canada

NASA Astrophysics Data System (ADS)

Lewkowicz, A. G.; Smith, K. M.

2004-12-01

The BTS (Basal Temperature of Snow) method to predict permafrost probability in mountain basins uses elevation as an easily available and spatially distributed independent variable. The elevation coefficient in the BTS regression model is, in effect, a substitute for ground temperature lapse rates. Previous work in Wolf Creek (60° 8'N 135° W), a mountain basin near Whitehorse, has shown that the model breaks down in a mid-elevation valley (1250 m asl) where actual permafrost probability is roughly twice that predicted by the model (60% vs. 20-30%). The existence of a double tree-line at the site suggested that air temperature inversions might be the cause of this inaccuracy (Lewkowicz and Ednie, 2004). This paper reports on a first year (08/2003-08/2004) of hourly air and ground temperature data collected along an altitudinal transect within the valley in upper Wolf Creek. Measurements were made at sites located 4, 8, 22, 82 and 162 m above the valley floor. Air temperature inversions between the lowest and highest measurement points occurred 42% of the time and in all months, but were most frequent and intense in winter (>60% of December and January) and least frequent in September (<25% of time). They generally developed after sunset and reached a maximum amplitude before sunrise. Only 11 inversions that lasted through more than one day occurred during the year, and only from October to February. The longest continuous duration was 145 h while the greatest inversion magnitude measured over the 160 m transect was 19° C. Ground surface temperatures are more difficult to interpret because of differences in soils and vegetation cover along the transect and the effects of seasonal snow cover. In many cases, however, air temperature inversions are not duplicated in the ground temperature record. Nevertheless, the annual altitudinal ground temperature gradient is much lower than would be expected from a standard atmospheric lapse rate, suggesting that the inversions do have an important impact on permafrost distribution at this site. More generally, therefore, it appears probable that any reduction in inversion frequency resulting from a more vigorous atmospheric circulation in the context of future climate change, would have a significant effect on permafrost distribution in mountain basins.

Distribution of rain height over subtropical region: Durban, South Africa for satellite communication systems

NASA Astrophysics Data System (ADS)

Olurotimi, E. O.; Sokoya, O.; Ojo, J. S.; Owolawi, P. A.

2018-03-01

Rain height is one of the significant parameters for prediction of rain attenuation for Earth-space telecommunication links, especially those operating at frequencies above 10 GHz. This study examines Three-parameter Dagum distribution of the rain height over Durban, South Africa. 5-year data were used to study the monthly, seasonal, and annual variations using the parameters estimated by the maximum likelihood of the distribution. The performance estimation of the distribution was determined using the statistical goodness of fit. Three-parameter Dagum distribution shows an appropriate distribution for the modeling of rain height over Durban with the Root Mean Square Error of 0.26. Also, the shape and scale parameters for the distribution show a wide variation. The probability exceedance of time for 0.01% indicates the high probability of rain attenuation at higher frequencies.

Radial particle distributions in PARMILA simulation beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boicourt, G.P.

1984-03-01

The estimation of beam spill in particle accelerators is becoming of greater importance as higher current designs are being funded. To the present, no numerical method for predicting beam-spill has been available. In this paper, we present an approach to the loss-estimation problem that uses probability distributions fitted to particle-simulation beams. The properties of the PARMILA code's radial particle distribution are discussed, and a broad class of probability distributions are examined to check their ability to fit it. The possibility that the PARMILA distribution is a mixture is discussed, and a fitting distribution consisting of a mixture of two generalizedmore » gamma distributions is found. An efficient algorithm to accomplish the fit is presented. Examples of the relative prediction of beam spill are given. 26 references, 18 figures, 1 table.« less

Geodesic Monte Carlo on Embedded Manifolds

PubMed Central

Byrne, Simon; Girolami, Mark

2013-01-01

Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

Reconstructing the equilibrium Boltzmann distribution from well-tempered metadynamics.

PubMed

Bonomi, M; Barducci, A; Parrinello, M

2009-08-01

Metadynamics is a widely used and successful method for reconstructing the free-energy surface of complex systems as a function of a small number of suitably chosen collective variables. This is achieved by biasing the dynamics of the system. The bias acting on the collective variables distorts the probability distribution of the other variables. Here we present a simple reweighting algorithm for recovering the unbiased probability distribution of any variable from a well-tempered metadynamics simulation. We show the efficiency of the reweighting procedure by reconstructing the distribution of the four backbone dihedral angles of alanine dipeptide from two and even one dimensional metadynamics simulation. 2009 Wiley Periodicals, Inc.

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: II. Fatigue crack growth, lifetime and scaling

NASA Astrophysics Data System (ADS)

Le, Jia-Liang; Bažant, Zdeněk P.

2011-07-01

This paper extends the theoretical framework presented in the preceding Part I to the lifetime distribution of quasibrittle structures failing at the fracture of one representative volume element under constant amplitude fatigue. The probability distribution of the critical stress amplitude is derived for a given number of cycles and a given minimum-to-maximum stress ratio. The physical mechanism underlying the Paris law for fatigue crack growth is explained under certain plausible assumptions about the damage accumulation in the cyclic fracture process zone at the tip of subcritical crack. This law is then used to relate the probability distribution of critical stress amplitude to the probability distribution of fatigue lifetime. The theory naturally yields a power-law relation for the stress-life curve (S-N curve), which agrees with Basquin's law. Furthermore, the theory indicates that, for quasibrittle structures, the S-N curve must be size dependent. Finally, physical explanation is provided to the experimentally observed systematic deviations of lifetime histograms of various ceramics and bones from the Weibull distribution, and their close fits by the present theory are demonstrated.

Voronoi cell patterns: Theoretical model and applications

NASA Astrophysics Data System (ADS)

González, Diego Luis; Einstein, T. L.

2011-11-01

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car-parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris Métro stations.

Voronoi Cell Patterns: theoretical model and application to submonolayer growth

NASA Astrophysics Data System (ADS)

González, Diego Luis; Einstein, T. L.

2012-02-01

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We apply our model to describe the Voronoi cell patterns of island nucleation for critical island sizes i=0,1,2,3. Experimental results for the Voronoi cells of InAs/GaAs quantum dots are also described by our model.

The probability distribution model of air pollution index and its dominants in Kuala Lumpur

NASA Astrophysics Data System (ADS)

AL-Dhurafi, Nasr Ahmed; Razali, Ahmad Mahir; Masseran, Nurulkamal; Zamzuri, Zamira Hasanah

2016-11-01

This paper focuses on the statistical modeling for the distributions of air pollution index (API) and its sub-indexes data observed at Kuala Lumpur in Malaysia. Five pollutants or sub-indexes are measured including, carbon monoxide (CO); sulphur dioxide (SO2); nitrogen dioxide (NO2), and; particulate matter (PM10). Four probability distributions are considered, namely log-normal, exponential, Gamma and Weibull in search for the best fit distribution to the Malaysian air pollutants data. In order to determine the best distribution for describing the air pollutants data, five goodness-of-fit criteria's are applied. This will help in minimizing the uncertainty in pollution resource estimates and improving the assessment phase of planning. The conflict in criterion results for selecting the best distribution was overcome by using the weight of ranks method. We found that the Gamma distribution is the best distribution for the majority of air pollutants data in Kuala Lumpur.

Probability distribution of extreme share returns in Malaysia

NASA Astrophysics Data System (ADS)

Zin, Wan Zawiah Wan; Safari, Muhammad Aslam Mohd; Jaaman, Saiful Hafizah; Yie, Wendy Ling Shin

2014-09-01

The objective of this study is to investigate the suitable probability distribution to model the extreme share returns in Malaysia. To achieve this, weekly and monthly maximum daily share returns are derived from share prices data obtained from Bursa Malaysia over the period of 2000 to 2012. The study starts with summary statistics of the data which will provide a clue on the likely candidates for the best fitting distribution. Next, the suitability of six extreme value distributions, namely the Gumbel, Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA), the Lognormal (GNO) and the Pearson (PE3) distributions are evaluated. The method of L-moments is used in parameter estimation. Based on several goodness of fit tests and L-moment diagram test, the Generalized Pareto distribution and the Pearson distribution are found to be the best fitted distribution to represent the weekly and monthly maximum share returns in Malaysia stock market during the studied period, respectively.

Discrete Sparse Coding.

PubMed

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

Performance assessment of a Bayesian Forecasting System (BFS) for real-time flood forecasting

NASA Astrophysics Data System (ADS)

Biondi, D.; De Luca, D. L.

2013-02-01

SummaryThe paper evaluates, for a number of flood events, the performance of a Bayesian Forecasting System (BFS), with the aim of evaluating total uncertainty in real-time flood forecasting. The predictive uncertainty of future streamflow is estimated through the Bayesian integration of two separate processors. The former evaluates the propagation of input uncertainty on simulated river discharge, the latter computes the hydrological uncertainty of actual river discharge associated with all other possible sources of error. A stochastic model and a distributed rainfall-runoff model were assumed, respectively, for rainfall and hydrological response simulations. A case study was carried out for a small basin in the Calabria region (southern Italy). The performance assessment of the BFS was performed with adequate verification tools suited for probabilistic forecasts of continuous variables such as streamflow. Graphical tools and scalar metrics were used to evaluate several attributes of the forecast quality of the entire time-varying predictive distributions: calibration, sharpness, accuracy, and continuous ranked probability score (CRPS). Besides the overall system, which incorporates both sources of uncertainty, other hypotheses resulting from the BFS properties were examined, corresponding to (i) a perfect hydrological model; (ii) a non-informative rainfall forecast for predicting streamflow; and (iii) a perfect input forecast. The results emphasize the importance of using different diagnostic approaches to perform comprehensive analyses of predictive distributions, to arrive at a multifaceted view of the attributes of the prediction. For the case study, the selected criteria revealed the interaction of the different sources of error, in particular the crucial role of the hydrological uncertainty processor when compensating, at the cost of wider forecast intervals, for the unreliable and biased predictive distribution resulting from the Precipitation Uncertainty Processor.

Frequency domain analysis of errors in cross-correlations of ambient seismic noise

NASA Astrophysics Data System (ADS)

Liu, Xin; Ben-Zion, Yehuda; Zigone, Dimitri

2016-12-01

We analyse random errors (variances) in cross-correlations of ambient seismic noise in the frequency domain, which differ from previous time domain methods. Extending previous theoretical results on ensemble averaged cross-spectrum, we estimate confidence interval of stacked cross-spectrum of finite amount of data at each frequency using non-overlapping windows with fixed length. The extended theory also connects amplitude and phase variances with the variance of each complex spectrum value. Analysis of synthetic stationary ambient noise is used to estimate the confidence interval of stacked cross-spectrum obtained with different length of noise data corresponding to different number of evenly spaced windows of the same duration. This method allows estimating Signal/Noise Ratio (SNR) of noise cross-correlation in the frequency domain, without specifying filter bandwidth or signal/noise windows that are needed for time domain SNR estimations. Based on synthetic ambient noise data, we also compare the probability distributions, causal part amplitude and SNR of stacked cross-spectrum function using one-bit normalization or pre-whitening with those obtained without these pre-processing steps. Natural continuous noise records contain both ambient noise and small earthquakes that are inseparable from the noise with the existing pre-processing steps. Using probability distributions of random cross-spectrum values based on the theoretical results provides an effective way to exclude such small earthquakes, and additional data segments (outliers) contaminated by signals of different statistics (e.g. rain, cultural noise), from continuous noise waveforms. This technique is applied to constrain values and uncertainties of amplitude and phase velocity of stacked noise cross-spectrum at different frequencies, using data from southern California at both regional scale (˜35 km) and dense linear array (˜20 m) across the plate-boundary faults. A block bootstrap resampling method is used to account for temporal correlation of noise cross-spectrum at low frequencies (0.05-0.2 Hz) near the ocean microseismic peaks.

The role of lower-hybrid-wave collapse in the auroral ionosphere.

PubMed

Schuck, P W; Ganguli, G I; Kintner, P M

2002-08-05

In regions where lower-hybrid solitary structures (LHSS) are observed, the character of auroral lower-hybrid turbulence (LHT) (0-20 kHz) is investigated using the amplitude probability distribution of the electric field. The observed probability distributions are accurately described by a Rayleigh distribution with two degrees of freedom. The statistics of the LHT exhibit no evidence of the global modulational instability or self-similar wave collapse. We conclude that nucleation and resonant scattering in preexisting density depletions are the processes responsible for LHSS in auroral LHT.

Bivariate Rainfall and Runoff Analysis Using Shannon Entropy Theory

NASA Astrophysics Data System (ADS)

Rahimi, A.; Zhang, L.

2012-12-01

Rainfall-Runoff analysis is the key component for many hydrological and hydraulic designs in which the dependence of rainfall and runoff needs to be studied. It is known that the convenient bivariate distribution are often unable to model the rainfall-runoff variables due to that they either have constraints on the range of the dependence or fixed form for the marginal distributions. Thus, this paper presents an approach to derive the entropy-based joint rainfall-runoff distribution using Shannon entropy theory. The distribution derived can model the full range of dependence and allow different specified marginals. The modeling and estimation can be proceeded as: (i) univariate analysis of marginal distributions which includes two steps, (a) using the nonparametric statistics approach to detect modes and underlying probability density, and (b) fitting the appropriate parametric probability density functions; (ii) define the constraints based on the univariate analysis and the dependence structure; (iii) derive and validate the entropy-based joint distribution. As to validate the method, the rainfall-runoff data are collected from the small agricultural experimental watersheds located in semi-arid region near Riesel (Waco), Texas, maintained by the USDA. The results of unviariate analysis show that the rainfall variables follow the gamma distribution, whereas the runoff variables have mixed structure and follow the mixed-gamma distribution. With this information, the entropy-based joint distribution is derived using the first moments, the first moments of logarithm transformed rainfall and runoff, and the covariance between rainfall and runoff. The results of entropy-based joint distribution indicate: (1) the joint distribution derived successfully preserves the dependence between rainfall and runoff, and (2) the K-S goodness of fit statistical tests confirm the marginal distributions re-derived reveal the underlying univariate probability densities which further assure that the entropy-based joint rainfall-runoff distribution are satisfactorily derived. Overall, the study shows the Shannon entropy theory can be satisfactorily applied to model the dependence between rainfall and runoff. The study also shows that the entropy-based joint distribution is an appropriate approach to capture the dependence structure that cannot be captured by the convenient bivariate joint distributions. Joint Rainfall-Runoff Entropy Based PDF, and Corresponding Marginal PDF and Histogram for W12 Watershed The K-S Test Result and RMSE on Univariate Distributions Derived from the Maximum Entropy Based Joint Probability Distribution;