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.

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

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.

Delineating Hydrofacies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics

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

Song, Xuehang; Chen, Xingyuan; Ye, Ming

2015-07-01

This study develops a new framework of facies-based data assimilation for characterizing spatial distribution of hydrofacies and estimating their associated hydraulic properties. This framework couples ensemble data assimilation with transition probability-based geostatistical model via a parameterization based on a level set function. The nature of ensemble data assimilation makes the framework efficient and flexible to be integrated with various types of observation data. The transition probability-based geostatistical model keeps the updated hydrofacies distributions under geological constrains. The framework is illustrated by using a two-dimensional synthetic study that estimates hydrofacies spatial distribution and permeability in each hydrofacies from transient head data.more » Our results show that the proposed framework can characterize hydrofacies distribution and associated permeability with adequate accuracy even with limited direct measurements of hydrofacies. Our study provides a promising starting point for hydrofacies delineation in complex real problems.« less

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

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.

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.

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.

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.

Constructing inverse probability weights for continuous exposures: a comparison of methods.

PubMed

Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S

2014-03-01

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.

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.

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.

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

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.

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.

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.

Derivation of low flow frequency distributions under human activities and its implications

NASA Astrophysics Data System (ADS)

Gao, Shida; Liu, Pan; Pan, Zhengke; Ming, Bo; Guo, Shenglian; Xiong, Lihua

2017-06-01

Low flow, refers to a minimum streamflow in dry seasons, is crucial to water supply, agricultural irrigation and navigation. Human activities, such as groundwater pumping, influence low flow severely. In order to derive the low flow frequency distribution functions under human activities, this study incorporates groundwater pumping and return flow as variables in the recession process. Steps are as follows: (1) the original low flow without human activities is assumed to follow a Pearson type three distribution, (2) the probability distribution of climatic dry spell periods is derived based on a base flow recession model, (3) the base flow recession model is updated under human activities, and (4) the low flow distribution under human activities is obtained based on the derived probability distribution of dry spell periods and the updated base flow recession model. Linear and nonlinear reservoir models are used to describe the base flow recession, respectively. The Wudinghe basin is chosen for the case study, with daily streamflow observations during 1958-2000. Results show that human activities change the location parameter of the low flow frequency curve for the linear reservoir model, while alter the frequency distribution function for the nonlinear one. It is indicated that alter the parameters of the low flow frequency distribution is not always feasible to tackle the changing environment.

Computing exact bundle compliance control charts via probability generating functions.

PubMed

Chen, Binchao; Matis, Timothy; Benneyan, James

2016-06-01

Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.

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.

Open quantum random walk in terms of quantum Bernoulli noise

NASA Astrophysics Data System (ADS)

Wang, Caishi; Wang, Ce; Ren, Suling; Tang, Yuling

2018-03-01

In this paper, we introduce an open quantum random walk, which we call the QBN-based open walk, by means of quantum Bernoulli noise, and study its properties from a random walk point of view. We prove that, with the localized ground state as its initial state, the QBN-based open walk has the same limit probability distribution as the classical random walk. We also show that the probability distributions of the QBN-based open walk include those of the unitary quantum walk recently introduced by Wang and Ye (Quantum Inf Process 15:1897-1908, 2016) as a special case.

Cluster-based control of a separating flow over a smoothly contoured ramp

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Noack, Bernd R.; Spohn, Andreas; Cattafesta, Louis N.; Morzyński, Marek

2017-12-01

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin-Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

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

Beating the odds: The poisson distribution of all input cells during limiting dilution grossly underestimates whether a cell line is clonally-derived or not.

PubMed

Zhou, Yizhou; Shaw, David; Lam, Cynthia; Tsukuda, Joni; Yim, Mandy; Tang, Danming; Louie, Salina; Laird, Michael W; Snedecor, Brad; Misaghi, Shahram

2017-09-23

Establishing that a cell line was derived from a single cell progenitor and defined as clonally-derived for the production of clinical and commercial therapeutic protein drugs has been the subject of increased emphasis in cell line development (CLD). Several regulatory agencies have expressed that the prospective probability of clonality for CHO cell lines is assumed to follow the Poisson distribution based on the input cell count. The probability of obtaining monoclonal progenitors based on the Poisson distribution of all cells suggests that one round of limiting dilution may not be sufficient to assure the resulting cell lines are clonally-derived. We experimentally analyzed clonal derivatives originating from single cell cloning (SCC) via one round of limiting dilution, following our standard legacy cell line development practice. Two cell populations with stably integrated DNA spacers were mixed and subjected to SCC via limiting dilution. Cells were cultured in the presence of selection agent, screened, and ranked based on product titer. Post-SCC, the growing cell lines were screened by PCR analysis for the presence of identifying spacers. We observed that the percentage of nonclonal populations was below 9%, which is considerably lower than the determined probability based on the Poisson distribution of all cells. These results were further confirmed using fluorescence imaging of clonal derivatives originating from SCC via limiting dilution of mixed cell populations expressing GFP or RFP. Our results demonstrate that in the presence of selection agent, the Poisson distribution of all cells clearly underestimates the probability of obtaining clonally-derived cell lines. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 2017. © 2017 American Institute of Chemical Engineers.

Predictions of malaria vector distribution in Belize based on multispectral satellite data.

PubMed

Roberts, D R; Paris, J F; Manguin, S; Harbach, R E; Woodruff, R; Rejmankova, E; Polanco, J; Wullschleger, B; Legters, L J

1996-03-01

Use of multispectral satellite data to predict arthropod-borne disease trouble spots is dependent on clear understandings of environmental factors that determine the presence of disease vectors. A blind test of remote sensing-based predictions for the spatial distribution of a malaria vector, Anopheles pseudopunctipennis, was conducted as a follow-up to two years of studies on vector-environmental relationships in Belize. Four of eight sites that were predicted to be high probability locations for presence of An. pseudopunctipennis were positive and all low probability sites (0 of 12) were negative. The absence of An. pseudopunctipennis at four high probability locations probably reflects the low densities that seem to characterize field populations of this species, i.e., the population densities were below the threshold of our sampling effort. Another important malaria vector, An. darlingi, was also present at all high probability sites and absent at all low probability sites. Anopheles darlingi, like An. pseudopunctipennis, is a riverine species. Prior to these collections at ecologically defined locations, this species was last detected in Belize in 1946.

Predictions of malaria vector distribution in Belize based on multispectral satellite data

NASA Technical Reports Server (NTRS)

Roberts, D. R.; Paris, J. F.; Manguin, S.; Harbach, R. E.; Woodruff, R.; Rejmankova, E.; Polanco, J.; Wullschleger, B.; Legters, L. J.

1996-01-01

Use of multispectral satellite data to predict arthropod-borne disease trouble spots is dependent on clear understandings of environmental factors that determine the presence of disease vectors. A blind test of remote sensing-based predictions for the spatial distribution of a malaria vector, Anopheles pseudopunctipennis, was conducted as a follow-up to two years of studies on vector-environmental relationships in Belize. Four of eight sites that were predicted to be high probability locations for presence of An. pseudopunctipennis were positive and all low probability sites (0 of 12) were negative. The absence of An. pseudopunctipennis at four high probability locations probably reflects the low densities that seem to characterize field populations of this species, i.e., the population densities were below the threshold of our sampling effort. Another important malaria vector, An. darlingi, was also present at all high probability sites and absent at all low probability sites. Anopheles darlingi, like An. pseudopunctipennis, is a riverine species. Prior to these collections at ecologically defined locations, this species was last detected in Belize in 1946.

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.

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)

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

Chen, Hang, E-mail: hangchen@mit.edu; Thill, Peter; Cao, Jianshu

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes withmore » the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.« less

A hydroclimatological approach to predicting regional landslide probability using Landlab

NASA Astrophysics Data System (ADS)

Strauch, Ronda; Istanbulluoglu, Erkan; Nudurupati, Sai Siddhartha; Bandaragoda, Christina; Gasparini, Nicole M.; Tucker, Gregory E.

2018-02-01

We develop a hydroclimatological approach to the modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation based on Monte Carlo simulations. The physically based model couples the infinite-slope stability model with a steady-state subsurface flow representation and operates in a digital elevation model. Spatially distributed gridded data for soil properties and vegetation classification are used for parameter estimation of probability distributions that characterize model input uncertainty. Hydrologic forcing to the model is through annual maximum daily recharge to subsurface flow obtained from a macroscale hydrologic model. We demonstrate the model in a steep mountainous region in northern Washington, USA, over 2700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting the uncertainty of soil depth and its potential long-term variability. We found elevation-dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests at low elevations, an increased landslide probability with forest decline at mid-elevations (1400 to 2400 m), and soil limitation and steep topographic controls at high alpine elevations and in post-glacial landscapes. These dominant controls manifest themselves in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similarly moderate model confidence for the three hazard maps, suggesting suitable use as relative hazard products. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.

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.

In favor of general probability distributions: lateral prefrontal and insular cortices respond to stimulus inherent, but irrelevant differences.

PubMed

Mestres-Missé, Anna; Trampel, Robert; Turner, Robert; Kotz, Sonja A

2016-04-01

A key aspect of optimal behavior is the ability to predict what will come next. To achieve this, we must have a fairly good idea of the probability of occurrence of possible outcomes. This is based both on prior knowledge about a particular or similar situation and on immediately relevant new information. One question that arises is: when considering converging prior probability and external evidence, is the most probable outcome selected or does the brain represent degrees of uncertainty, even highly improbable ones? Using functional magnetic resonance imaging, the current study explored these possibilities by contrasting words that differ in their probability of occurrence, namely, unbalanced ambiguous words and unambiguous words. Unbalanced ambiguous words have a strong frequency-based bias towards one meaning, while unambiguous words have only one meaning. The current results reveal larger activation in lateral prefrontal and insular cortices in response to dominant ambiguous compared to unambiguous words even when prior and contextual information biases one interpretation only. These results suggest a probability distribution, whereby all outcomes and their associated probabilities of occurrence--even if very low--are represented and maintained.

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.

Correlation between discrete probability and reaction front propagation rate in heterogeneous mixtures

NASA Astrophysics Data System (ADS)

Naine, Tarun Bharath; Gundawar, Manoj Kumar

2017-09-01

We demonstrate a very powerful correlation between the discrete probability of distances of neighboring cells and thermal wave propagation rate, for a system of cells spread on a one-dimensional chain. A gamma distribution is employed to model the distances of neighboring cells. In the absence of an analytical solution and the differences in ignition times of adjacent reaction cells following non-Markovian statistics, invariably the solution for thermal wave propagation rate for a one-dimensional system with randomly distributed cells is obtained by numerical simulations. However, such simulations which are based on Monte-Carlo methods require several iterations of calculations for different realizations of distribution of adjacent cells. For several one-dimensional systems, differing in the value of shaping parameter of the gamma distribution, we show that the average reaction front propagation rates obtained by a discrete probability between two limits, shows excellent agreement with those obtained numerically. With the upper limit at 1.3, the lower limit depends on the non-dimensional ignition temperature. Additionally, this approach also facilitates the prediction of burning limits of heterogeneous thermal mixtures. The proposed method completely eliminates the need for laborious, time intensive numerical calculations where the thermal wave propagation rates can now be calculated based only on macroscopic entity of discrete probability.

Quantile Functions, Convergence in Quantile, and Extreme Value Distribution Theory.

DTIC Science & Technology

1980-11-01

Gnanadesikan (1968). Quantile functions are advocated by Parzen (1979) as providing an approach to probability-based data analysis. Quantile functions are... Gnanadesikan , R. (1968). Probability Plotting Methods for the Analysis of Data, Biomtrika, 55, 1-17.

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.

Quantum probabilistic logic programming

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan

2015-05-01

We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.

A fast elitism Gaussian estimation of distribution algorithm and application for PID optimization.

PubMed

Xu, Qingyang; Zhang, Chengjin; Zhang, Li

2014-01-01

Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA.

A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization

PubMed Central

Xu, Qingyang; Zhang, Chengjin; Zhang, Li

2014-01-01

Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA. PMID:24892059

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.

On fitting the Pareto Levy distribution to stock market index data: Selecting a suitable cutoff value

NASA Astrophysics Data System (ADS)

Coronel-Brizio, H. F.; Hernández-Montoya, A. R.

2005-08-01

The so-called Pareto-Levy or power-law distribution has been successfully used as a model to describe probabilities associated to extreme variations of stock markets indexes worldwide. The selection of the threshold parameter from empirical data and consequently, the determination of the exponent of the distribution, is often done using a simple graphical method based on a log-log scale, where a power-law probability plot shows a straight line with slope equal to the exponent of the power-law distribution. This procedure can be considered subjective, particularly with regard to the choice of the threshold or cutoff parameter. In this work, a more objective procedure based on a statistical measure of discrepancy between the empirical and the Pareto-Levy distribution is presented. The technique is illustrated for data sets from the New York Stock Exchange (DJIA) and the Mexican Stock Market (IPC).

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.

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.

Quantum decision-maker theory and simulation

NASA Astrophysics Data System (ADS)

Zak, Michail; Meyers, Ronald E.; Deacon, Keith S.

2000-07-01

A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics. The autonomy of the decision making process is achieved by a feedback from the mental to motor dynamics which changes the stochastic matrix based upon the probability distribution. This feedback replaces unavailable external information by an internal knowledge- base stored in the mental model in the form of probability distributions. As a result, the coupled motor-mental dynamics is described by a nonlinear version of Markov chains which can decrease entropy without an external source of information. Applications to common sense based decisions as well as to evolutionary games are discussed. An example exhibiting self-organization is computed using quantum computer simulation. Force on force and mutual aircraft engagements using the quantum decision maker dynamics are considered.

Probabilistic Cloning of Three Real States with Optimal Success Probabilities

NASA Astrophysics Data System (ADS)

Rui, Pin-shu

2017-06-01

We investigate the probabilistic quantum cloning (PQC) of three real states with average probability distribution. To get the analytic forms of the optimal success probabilities we assume that the three states have only two pairwise inner products. Based on the optimal success probabilities, we derive the explicit form of 1 →2 PQC for cloning three real states. The unitary operation needed in the PQC process is worked out too. The optimal success probabilities are also generalized to the M→ N PQC case.

Entropy-based goodness-of-fit test: Application to the Pareto distribution

NASA Astrophysics Data System (ADS)

Lequesne, Justine

2013-08-01

Goodness-of-fit tests based on entropy have been introduced in [13] for testing normality. The maximum entropy distribution in a class of probability distributions defined by linear constraints induces a Pythagorean equality between the Kullback-Leibler information and an entropy difference. This allows one to propose a goodness-of-fit test for maximum entropy parametric distributions which is based on the Kullback-Leibler information. We will focus on the application of the method to the Pareto distribution. The power of the proposed test is computed through Monte Carlo simulation.

Meaner king uses biased bases

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

Reimpell, Michael; Werner, Reinhard F.

2007-06-15

The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases aremore » mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell's original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.« less

Meaner king uses biased bases

NASA Astrophysics Data System (ADS)

Reimpell, Michael; Werner, Reinhard F.

2007-06-01

The mean king problem is a quantum mechanical retrodiction problem, in which Alice has to name the outcome of an ideal measurement made in one of several different orthonormal bases. Alice is allowed to prepare the state of the system and to do a final measurement, possibly including an entangled copy. However, Alice gains knowledge about which basis was measured only after she no longer has access to the quantum system or its copy. We give a necessary and sufficient condition on the bases, for Alice to have a strategy to solve this problem, without assuming that the bases are mutually unbiased. The condition requires the existence of an overall joint probability distribution for random variables, whose marginal pair distributions are fixed as the transition probability matrices of the given bases. In particular, in the qubit case the problem is decided by Bell’s original three variable inequality. In the standard setting of mutually unbiased bases, when they do exist, Alice can always succeed. However, for randomly chosen bases her success probability rapidly goes to zero with increasing dimension.

Dynamical complexity changes during two forms of meditation

NASA Astrophysics Data System (ADS)

Li, Jin; Hu, Jing; Zhang, Yinhong; Zhang, Xiaofeng

2011-06-01

Detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meaning. We use the base-scale entropy method to analyze dynamical complexity changes for heart rate variability (HRV) series during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. The results show that dynamical complexity decreases in meditation states for two forms of meditation. Meanwhile, we detected changes in probability distribution of m-words during meditation and explained this changes using probability distribution of sine function. The base-scale entropy method may be used on a wider range of physiologic signals.

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

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.

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.

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

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.

Weighing Clinical Evidence Using Patient Preferences: An Application of Probabilistic Multi-Criteria Decision Analysis.

PubMed

Broekhuizen, Henk; IJzerman, Maarten J; Hauber, A Brett; Groothuis-Oudshoorn, Catharina G M

2017-03-01

The need for patient engagement has been recognized by regulatory agencies, but there is no consensus about how to operationalize this. One approach is the formal elicitation and use of patient preferences for weighing clinical outcomes. The aim of this study was to demonstrate how patient preferences can be used to weigh clinical outcomes when both preferences and clinical outcomes are uncertain by applying a probabilistic value-based multi-criteria decision analysis (MCDA) method. Probability distributions were used to model random variation and parameter uncertainty in preferences, and parameter uncertainty in clinical outcomes. The posterior value distributions and rank probabilities for each treatment were obtained using Monte-Carlo simulations. The probability of achieving the first rank is the probability that a treatment represents the highest value to patients. We illustrated our methodology for a simplified case on six HIV treatments. Preferences were modeled with normal distributions and clinical outcomes were modeled with beta distributions. The treatment value distributions showed the rank order of treatments according to patients and illustrate the remaining decision uncertainty. This study demonstrated how patient preference data can be used to weigh clinical evidence using MCDA. The model takes into account uncertainty in preferences and clinical outcomes. The model can support decision makers during the aggregation step of the MCDA process and provides a first step toward preference-based personalized medicine, yet requires further testing regarding its appropriate use in real-world settings.

Normal probability plots with confidence.

PubMed

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

2015-01-01

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

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 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.

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.

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

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.

Tornado damage risk assessment

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

Reinhold, T.A.; Ellingwood, B.

1982-09-01

Several proposed models were evaluated for predicting tornado wind speed probabilities at nuclear plant sites as part of a program to develop statistical data on tornadoes needed for probability-based load combination analysis. A unified model was developed which synthesized the desired aspects of tornado occurrence and damage potential. The sensitivity of wind speed probability estimates to various tornado modeling assumptions are examined, and the probability distributions of tornado wind speed that are needed for load combination studies are presented.

Probability distributions of bed load particle velocities, accelerations, hop distances, and travel times informed by Jaynes's principle of maximum entropy

USGS Publications Warehouse

Furbish, David; Schmeeckle, Mark; Schumer, Rina; Fathel, Siobhan

2016-01-01

We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high-resolution measurements obtained from high-speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight.

Stochastic optimal operation of reservoirs based on copula functions

NASA Astrophysics Data System (ADS)

Lei, Xiao-hui; Tan, Qiao-feng; Wang, Xu; Wang, Hao; Wen, Xin; Wang, Chao; Zhang, Jing-wen

2018-02-01

Stochastic dynamic programming (SDP) has been widely used to derive operating policies for reservoirs considering streamflow uncertainties. In SDP, there is a need to calculate the transition probability matrix more accurately and efficiently in order to improve the economic benefit of reservoir operation. In this study, we proposed a stochastic optimization model for hydropower generation reservoirs, in which 1) the transition probability matrix was calculated based on copula functions; and 2) the value function of the last period was calculated by stepwise iteration. Firstly, the marginal distribution of stochastic inflow in each period was built and the joint distributions of adjacent periods were obtained using the three members of the Archimedean copulas, based on which the conditional probability formula was derived. Then, the value in the last period was calculated by a simple recursive equation with the proposed stepwise iteration method and the value function was fitted with a linear regression model. These improvements were incorporated into the classic SDP and applied to the case study in Ertan reservoir, China. The results show that the transition probability matrix can be more easily and accurately obtained by the proposed copula function based method than conventional methods based on the observed or synthetic streamflow series, and the reservoir operation benefit can also be increased.

Distributed Immune Systems for Wireless Network Information Assurance

DTIC Science & Technology

2010-04-26

ratio test (SPRT), where the goal is to optimize a hypothesis testing problem given a trade-off between the probability of errors and the...using cumulative sum (CUSUM) and Girshik-Rubin-Shiryaev (GRSh) statistics. In sequential versions of the problem the sequential probability ratio ...the more complicated problems, in particular those where no clear mean can be established. We developed algorithms based on the sequential probability

SU-F-T-450: The Investigation of Radiotherapy Quality Assurance and Automatic Treatment Planning Based On the Kernel Density Estimation Method

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

Fan, J; Fan, J; Hu, W

Purpose: To develop a fast automatic algorithm based on the two dimensional kernel density estimation (2D KDE) to predict the dose-volume histogram (DVH) which can be employed for the investigation of radiotherapy quality assurance and automatic treatment planning. Methods: We propose a machine learning method that uses previous treatment plans to predict the DVH. The key to the approach is the framing of DVH in a probabilistic setting. The training consists of estimating, from the patients in the training set, the joint probability distribution of the dose and the predictive features. The joint distribution provides an estimation of the conditionalmore » probability of the dose given the values of the predictive features. For the new patient, the prediction consists of estimating the distribution of the predictive features and marginalizing the conditional probability from the training over this. Integrating the resulting probability distribution for the dose yields an estimation of the DVH. The 2D KDE is implemented to predict the joint probability distribution of the training set and the distribution of the predictive features for the new patient. Two variables, including the signed minimal distance from each OAR (organs at risk) voxel to the target boundary and its opening angle with respect to the origin of voxel coordinate, are considered as the predictive features to represent the OAR-target spatial relationship. The feasibility of our method has been demonstrated with the rectum, breast and head-and-neck cancer cases by comparing the predicted DVHs with the planned ones. Results: The consistent result has been found between these two DVHs for each cancer and the average of relative point-wise differences is about 5% within the clinical acceptable extent. Conclusion: According to the result of this study, our method can be used to predict the clinical acceptable DVH and has ability to evaluate the quality and consistency of the treatment planning.« less

A risk-based multi-objective model for optimal placement of sensors in water distribution system

NASA Astrophysics Data System (ADS)

Naserizade, Sareh S.; Nikoo, Mohammad Reza; Montaseri, Hossein

2018-02-01

In this study, a new stochastic model based on Conditional Value at Risk (CVaR) and multi-objective optimization methods is developed for optimal placement of sensors in water distribution system (WDS). This model determines minimization of risk which is caused by simultaneous multi-point contamination injection in WDS using CVaR approach. The CVaR considers uncertainties of contamination injection in the form of probability distribution function and calculates low-probability extreme events. In this approach, extreme losses occur at tail of the losses distribution function. Four-objective optimization model based on NSGA-II algorithm is developed to minimize losses of contamination injection (through CVaR of affected population and detection time) and also minimize the two other main criteria of optimal placement of sensors including probability of undetected events and cost. Finally, to determine the best solution, Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE), as a subgroup of Multi Criteria Decision Making (MCDM) approach, is utilized to rank the alternatives on the trade-off curve among objective functions. Also, sensitivity analysis is done to investigate the importance of each criterion on PROMETHEE results considering three relative weighting scenarios. The effectiveness of the proposed methodology is examined through applying it to Lamerd WDS in the southwestern part of Iran. The PROMETHEE suggests 6 sensors with suitable distribution that approximately cover all regions of WDS. Optimal values related to CVaR of affected population and detection time as well as probability of undetected events for the best optimal solution are equal to 17,055 persons, 31 mins and 0.045%, respectively. The obtained results of the proposed methodology in Lamerd WDS show applicability of CVaR-based multi-objective simulation-optimization model for incorporating the main uncertainties of contamination injection in order to evaluate extreme value of losses in WDS.

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.

Distribution of Base Pair Alternations in a Periodic DNA Chain: Application of Pólya Counting to a Physical System

NASA Astrophysics Data System (ADS)

Hillebrand, Malcolm; Paterson-Jones, Guy; Kalosakas, George; Skokos, Charalampos

2018-03-01

In modeling DNA chains, the number of alternations between Adenine-Thymine (AT) and Guanine-Cytosine (GC) base pairs can be considered as a measure of the heterogeneity of the chain, which in turn could affect its dynamics. A probability distribution function of the number of these alternations is derived for circular or periodic DNA. Since there are several symmetries to account for in the periodic chain, necklace counting methods are used. In particular, Polya's Enumeration Theorem is extended for the case of a group action that preserves partitioned necklaces. This, along with the treatment of generating functions as formal power series, allows for the direct calculation of the number of possible necklaces with a given number of AT base pairs, GC base pairs and alternations. The theoretically obtained probability distribution functions of the number of alternations are accurately reproduced by Monte Carlo simulations and fitted by Gaussians. The effect of the number of base pairs on the characteristics of these distributions is also discussed, as well as the effect of the ratios of the numbers of AT and GC base pairs.

Effect of Individual Component Life Distribution on Engine Life Prediction

NASA Technical Reports Server (NTRS)

Zaretsky, Erwin V.; Hendricks, Robert C.; Soditus, Sherry M.

2003-01-01

The effect of individual engine component life distributions on engine life prediction was determined. A Weibull-based life and reliability analysis of the NASA Energy Efficient Engine was conducted. The engine s life at a 95 and 99.9 percent probability of survival was determined based upon the engine manufacturer s original life calculations and assumed values of each of the component s cumulative life distributions as represented by a Weibull slope. The lives of the high-pressure turbine (HPT) disks and blades were also evaluated individually and as a system in a similar manner. Knowing the statistical cumulative distribution of each engine component with reasonable engineering certainty is a condition precedent to predicting the life and reliability of an entire engine. The life of a system at a given reliability will be less than the lowest-lived component in the system at the same reliability (probability of survival). Where Weibull slopes of all the engine components are equal, the Weibull slope had a minimal effect on engine L(sub 0.1) life prediction. However, at a probability of survival of 95 percent (L(sub 5) life), life decreased with increasing Weibull slope.

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.

VizieR Online Data Catalog: Proper motions of PM2000 open clusters (Krone-Martins+, 2010)

NASA Astrophysics Data System (ADS)

Krone-Martins, A.; Soubiran, C.; Ducourant, C.; Teixeira, R.; Le Campion, J. F.

2010-04-01

We present lists of proper-motions and kinematic membership probabilities in the region of 49 open clusters or possible open clusters. The stellar proper motions were taken from the Bordeaux PM2000 catalogue. The segregation between cluster and field stars and the assignment of membership probabilities was accomplished by applying a fully automated method based on parametrisations for the probability distribution functions and genetic algorithm optimisation heuristics associated with a derivative-based hill climbing algorithm for the likelihood optimization. (3 data files).

Technology Development Risk Assessment for Space Transportation Systems

NASA Technical Reports Server (NTRS)

Mathias, Donovan L.; Godsell, Aga M.; Go, Susie

2006-01-01

A new approach for assessing development risk associated with technology development projects is presented. The method represents technology evolution in terms of sector-specific discrete development stages. A Monte Carlo simulation is used to generate development probability distributions based on statistical models of the discrete transitions. Development risk is derived from the resulting probability distributions and specific program requirements. Two sample cases are discussed to illustrate the approach, a single rocket engine development and a three-technology space transportation portfolio.

A probabilistic approach to photovoltaic generator performance prediction

NASA Astrophysics Data System (ADS)

Khallat, M. A.; Rahman, S.

1986-09-01

A method for predicting the performance of a photovoltaic (PV) generator based on long term climatological data and expected cell performance is described. The equations for cell model formulation are provided. Use of the statistical model for characterizing the insolation level is discussed. The insolation data is fitted to appropriate probability distribution functions (Weibull, beta, normal). The probability distribution functions are utilized to evaluate the capacity factors of PV panels or arrays. An example is presented revealing the applicability of the procedure.

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.

A Simple Method for Estimating Informative Node Age Priors for the Fossil Calibration of Molecular Divergence Time Analyses

PubMed Central

Nowak, Michael D.; Smith, Andrew B.; Simpson, Carl; Zwickl, Derrick J.

2013-01-01

Molecular divergence time analyses often rely on the age of fossil lineages to calibrate node age estimates. Most divergence time analyses are now performed in a Bayesian framework, where fossil calibrations are incorporated as parametric prior probabilities on node ages. It is widely accepted that an ideal parameterization of such node age prior probabilities should be based on a comprehensive analysis of the fossil record of the clade of interest, but there is currently no generally applicable approach for calculating such informative priors. We provide here a simple and easily implemented method that employs fossil data to estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade, which can be used to fit an informative parametric prior probability distribution on a node age. Specifically, our method uses the extant diversity and the stratigraphic distribution of fossil lineages confidently assigned to a clade to fit a branching model of lineage diversification. Conditioning this on a simple model of fossil preservation, we estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade. The likelihood surface of missing history can then be translated into a parametric prior probability distribution on the age of the clade of interest. We show that the method performs well with simulated fossil distribution data, but that the likelihood surface of missing history can at times be too complex for the distribution-fitting algorithm employed by our software tool. An empirical example of the application of our method is performed to estimate echinoid node ages. A simulation-based sensitivity analysis using the echinoid data set shows that node age prior distributions estimated under poor preservation rates are significantly less informative than those estimated under high preservation rates. PMID:23755303

Modeling stream fish distributions using interval-censored detection times.

PubMed

Ferreira, Mário; Filipe, Ana Filipa; Bardos, David C; Magalhães, Maria Filomena; Beja, Pedro

2016-08-01

Controlling for imperfect detection is important for developing species distribution models (SDMs). Occupancy-detection models based on the time needed to detect a species can be used to address this problem, but this is hindered when times to detection are not known precisely. Here, we extend the time-to-detection model to deal with detections recorded in time intervals and illustrate the method using a case study on stream fish distribution modeling. We collected electrofishing samples of six fish species across a Mediterranean watershed in Northeast Portugal. Based on a Bayesian hierarchical framework, we modeled the probability of water presence in stream channels, and the probability of species occupancy conditional on water presence, in relation to environmental and spatial variables. We also modeled time-to-first detection conditional on occupancy in relation to local factors, using modified interval-censored exponential survival models. Posterior distributions of occupancy probabilities derived from the models were used to produce species distribution maps. Simulations indicated that the modified time-to-detection model provided unbiased parameter estimates despite interval-censoring. There was a tendency for spatial variation in detection rates to be primarily influenced by depth and, to a lesser extent, stream width. Species occupancies were consistently affected by stream order, elevation, and annual precipitation. Bayesian P-values and AUCs indicated that all models had adequate fit and high discrimination ability, respectively. Mapping of predicted occupancy probabilities showed widespread distribution by most species, but uncertainty was generally higher in tributaries and upper reaches. The interval-censored time-to-detection model provides a practical solution to model occupancy-detection when detections are recorded in time intervals. This modeling framework is useful for developing SDMs while controlling for variation in detection rates, as it uses simple data that can be readily collected by field ecologists.

Distribution of apparent activation energy counterparts during thermo - And thermo-oxidative degradation of Aronia melanocarpa (black chokeberry).

PubMed

Janković, Bojan; Marinović-Cincović, Milena; Janković, Marija

2017-09-01

Kinetics of degradation for Aronia melanocarpa fresh fruits in argon and air atmospheres were investigated. The investigation was based on probability distributions of apparent activation energy of counterparts (ε a ). Isoconversional analysis results indicated that the degradation process in an inert atmosphere was governed by decomposition reactions of esterified compounds. Also, based on same kinetics approach, it was assumed that in an air atmosphere, the primary compound in degradation pathways could be anthocyanins, which undergo rapid chemical reactions. A new model of reactivity demonstrated that, under inert atmospheres, expectation values for ε a occured at levels of statistical probability. These values corresponded to decomposition processes in which polyphenolic compounds might be involved. ε a values obeyed laws of binomial distribution. It was established that, for thermo-oxidative degradation, Poisson distribution represented a very successful approximation for ε a values where there was additional mechanistic complexity and the binomial distribution was no longer valid. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Proposal of a method for evaluating tsunami risk using response-surface methodology

NASA Astrophysics Data System (ADS)

Fukutani, Y.

2017-12-01

Information on probabilistic tsunami inundation hazards is needed to define and evaluate tsunami risk. Several methods for calculating these hazards have been proposed (e.g. Løvholt et al. (2012), Thio (2012), Fukutani et al. (2014), Goda et al. (2015)). However, these methods are inefficient, and their calculation cost is high, since they require multiple tsunami numerical simulations, therefore lacking versatility. In this study, we proposed a simpler method for tsunami risk evaluation using response-surface methodology. Kotani et al. (2016) proposed an evaluation method for the probabilistic distribution of tsunami wave-height using a response-surface methodology. We expanded their study and developed a probabilistic distribution of tsunami inundation depth. We set the depth (x1) and the slip (x2) of an earthquake fault as explanatory variables and tsunami inundation depth (y) as an object variable. Subsequently, tsunami risk could be evaluated by conducting a Monte Carlo simulation, assuming that the generation probability of an earthquake follows a Poisson distribution, the probability distribution of tsunami inundation depth follows the distribution derived from a response-surface, and the damage probability of a target follows a log normal distribution. We applied the proposed method to a wood building located on the coast of Tokyo Bay. We implemented a regression analysis based on the results of 25 tsunami numerical calculations and developed a response-surface, which was defined as y=ax1+bx2+c (a:0.2615, b:3.1763, c=-1.1802). We assumed proper probabilistic distribution for earthquake generation, inundation height, and vulnerability. Based on these probabilistic distributions, we conducted Monte Carlo simulations of 1,000,000 years. We clarified that the expected damage probability of the studied wood building is 22.5%, assuming that an earthquake occurs. The proposed method is therefore a useful and simple way to evaluate tsunami risk using a response-surface and Monte Carlo simulation without conducting multiple tsunami numerical simulations.

A non-stationary cost-benefit based bivariate extreme flood estimation approach

NASA Astrophysics Data System (ADS)

Qi, Wei; Liu, Junguo

2018-02-01

Cost-benefit analysis and flood frequency analysis have been integrated into a comprehensive framework to estimate cost effective design values. However, previous cost-benefit based extreme flood estimation is based on stationary assumptions and analyze dependent flood variables separately. A Non-Stationary Cost-Benefit based bivariate design flood estimation (NSCOBE) approach is developed in this study to investigate influence of non-stationarities in both the dependence of flood variables and the marginal distributions on extreme flood estimation. The dependence is modeled utilizing copula functions. Previous design flood selection criteria are not suitable for NSCOBE since they ignore time changing dependence of flood variables. Therefore, a risk calculation approach is proposed based on non-stationarities in both marginal probability distributions and copula functions. A case study with 54-year observed data is utilized to illustrate the application of NSCOBE. Results show NSCOBE can effectively integrate non-stationarities in both copula functions and marginal distributions into cost-benefit based design flood estimation. It is also found that there is a trade-off between maximum probability of exceedance calculated from copula functions and marginal distributions. This study for the first time provides a new approach towards a better understanding of influence of non-stationarities in both copula functions and marginal distributions on extreme flood estimation, and could be beneficial to cost-benefit based non-stationary bivariate design flood estimation across the world.

Power Allocation and Outage Probability Analysis for SDN-based Radio Access Networks

NASA Astrophysics Data System (ADS)

Zhao, Yongxu; Chen, Yueyun; Mai, Zhiyuan

2018-01-01

In this paper, performance of Access network Architecture based SDN (Software Defined Network) is analyzed with respect to the power allocation issue. A power allocation scheme PSO-PA (Particle Swarm Optimization-power allocation) algorithm is proposed, the proposed scheme is subjected to constant total power with the objective of minimizing system outage probability. The entire access network resource configuration is controlled by the SDN controller, then it sends the optimized power distribution factor to the base station source node (SN) and the relay node (RN). Simulation results show that the proposed scheme reduces the system outage probability at a low complexity.

Dynamic probability control limits for risk-adjusted CUSUM charts based on multiresponses.

PubMed

Zhang, Xiang; Loda, Justin B; Woodall, William H

2017-07-20

For a patient who has survived a surgery, there could be several levels of recovery. Thus, it is reasonable to consider more than two outcomes when monitoring surgical outcome quality. The risk-adjusted cumulative sum (CUSUM) chart based on multiresponses has been developed for monitoring a surgical process with three or more outcomes. However, there is a significant effect of varying risk distributions on the in-control performance of the chart when constant control limits are applied. To overcome this disadvantage, we apply the dynamic probability control limits to the risk-adjusted CUSUM charts for multiresponses. The simulation results demonstrate that the in-control performance of the charts with dynamic probability control limits can be controlled for different patient populations because these limits are determined for each specific sequence of patients. Thus, the use of dynamic probability control limits for risk-adjusted CUSUM charts based on multiresponses allows each chart to be designed for the corresponding patient sequence of a surgeon or a hospital and therefore does not require estimating or monitoring the patients' risk distribution. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Redundancy and reduction: Speakers manage syntactic information density

PubMed Central

Florian Jaeger, T.

2010-01-01

A principle of efficient language production based on information theoretic considerations is proposed: Uniform Information Density predicts that language production is affected by a preference to distribute information uniformly across the linguistic signal. This prediction is tested against data from syntactic reduction. A single multilevel logit model analysis of naturally distributed data from a corpus of spontaneous speech is used to assess the effect of information density on complementizer that-mentioning, while simultaneously evaluating the predictions of several influential alternative accounts: availability, ambiguity avoidance, and dependency processing accounts. Information density emerges as an important predictor of speakers’ preferences during production. As information is defined in terms of probabilities, it follows that production is probability-sensitive, in that speakers’ preferences are affected by the contextual probability of syntactic structures. The merits of a corpus-based approach to the study of language production are discussed as well. PMID:20434141

A dynamic programming approach to estimate the capacity value of energy storage

DOE PAGES

Sioshansi, Ramteen; Madaeni, Seyed Hossein; Denholm, Paul

2013-09-17

Here, we present a method to estimate the capacity value of storage. Our method uses a dynamic program to model the effect of power system outages on the operation and state of charge of storage in subsequent periods. We combine the optimized dispatch from the dynamic program with estimated system loss of load probabilities to compute a probability distribution for the state of charge of storage in each period. This probability distribution can be used as a forced outage rate for storage in standard reliability-based capacity value estimation methods. Our proposed method has the advantage over existing approximations that itmore » explicitly captures the effect of system shortage events on the state of charge of storage in subsequent periods. We also use a numerical case study, based on five utility systems in the U.S., to demonstrate our technique and compare it to existing approximation methods.« less

Estimation and applications of size-based distributions in forestry

Treesearch

Jeffrey H. Gove

2003-01-01

Size-based distributions arise in several contexts in forestry and ecology. Simple power relationships (e.g., basal area and diameter at breast height) between variables are one such area of interest arising from a modeling perspective. Another, probability proportional to size sampline (PPS), is found in the most widely used methods for sampling standing or dead and...

Analysis of HIV-1 intersubtype recombination breakpoints suggests region with high pairing probability may be a more fundamental factor than sequence similarity affecting HIV-1 recombination.

PubMed

Jia, Lei; Li, Lin; Gui, Tao; Liu, Siyang; Li, Hanping; Han, Jingwan; Guo, Wei; Liu, Yongjian; Li, Jingyun

2016-09-21

With increasing data on HIV-1, a more relevant molecular model describing mechanism details of HIV-1 genetic recombination usually requires upgrades. Currently an incomplete structural understanding of the copy choice mechanism along with several other issues in the field that lack elucidation led us to perform an analysis of the correlation between breakpoint distributions and (1) the probability of base pairing, and (2) intersubtype genetic similarity to further explore structural mechanisms. Near full length sequences of URFs from Asia, Europe, and Africa (one sequence/patient), and representative sequences of worldwide CRFs were retrieved from the Los Alamos HIV database. Their recombination patterns were analyzed by jpHMM in detail. Then the relationships between breakpoint distributions and (1) the probability of base pairing, and (2) intersubtype genetic similarities were investigated. Pearson correlation test showed that all URF groups and the CRF group exhibit the same breakpoint distribution pattern. Additionally, the Wilcoxon two-sample test indicated a significant and inexplicable limitation of recombination in regions with high pairing probability. These regions have been found to be strongly conserved across distinct biological states (i.e., strong intersubtype similarity), and genetic similarity has been determined to be a very important factor promoting recombination. Thus, the results revealed an unexpected disagreement between intersubtype similarity and breakpoint distribution, which were further confirmed by genetic similarity analysis. Our analysis reveals a critical conflict between results from natural HIV-1 isolates and those from HIV-1-based assay vectors in which genetic similarity has been shown to be a very critical factor promoting recombination. These results indicate the region with high-pairing probabilities may be a more fundamental factor affecting HIV-1 recombination than sequence similarity in natural HIV-1 infections. Our findings will be relevant in furthering the understanding of HIV-1 recombination mechanisms.

In-beam Fission Study at JAEA

NASA Astrophysics Data System (ADS)

Nishio, Katsuhisa

2013-12-01

Fission fragment mass distributions were measured in heavy-ion induced fissions using 238U target nucleus. The measured mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and quasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model in the reactions of 30Si + 238U and 34S + 238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections for seaborgium and hassium isotopes.

In-beam fission study for Heavy Element Synthesis

NASA Astrophysics Data System (ADS)

Nishio, Katsuhisa

2013-12-01

Fission fragment mass distributions were measured in heavy-ion induced fissions using 238U target nucleus. The measured mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and qasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model in the reactions of 30Si + 238U and 34S + 238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections for seaborgium and hassium isotopes.

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.

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.

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.

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.

Bayesian Cherry Picking Revisited

NASA Astrophysics Data System (ADS)

Garrett, Anthony J. M.; Prozesky, Victor M.; Padayachee, J.

2004-04-01

Tins are marketed as containing nine cherries. To fill the tins, cherries are fed into a drum containing twelve holes through which air is sucked; either zero, one or two cherries stick in each hole. Dielectric measurements are then made on each hole. Three outcomes are distinguished: empty hole (which is reliable); one cherry (which indicates one cherry with high probability, or two cherries with a complementary low probability known from calibration); or an uncertain number (which also indicates one cherry or two, with known probabilities that are quite similar). A choice can be made from which holes simultaneously to discharge contents into the tin. The sum and product rules of probability are applied in a Bayesian manner to find the distribution for the number of cherries in the tin. Based on this distribution, ways are discussed to optimise the number to nine cherries.

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.

Statistical description of non-Gaussian samples in the F2 layer of the ionosphere during heliogeophysical disturbances

NASA Astrophysics Data System (ADS)

Sergeenko, N. P.

2017-11-01

An adequate statistical method should be developed in order to predict probabilistically the range of ionospheric parameters. This problem is solved in this paper. The time series of the critical frequency of the layer F2- foF2( t) were subjected to statistical processing. For the obtained samples {δ foF2}, statistical distributions and invariants up to the fourth order are calculated. The analysis shows that the distributions differ from the Gaussian law during the disturbances. At levels of sufficiently small probability distributions, there are arbitrarily large deviations from the model of the normal process. Therefore, it is attempted to describe statistical samples {δ foF2} based on the Poisson model. For the studied samples, the exponential characteristic function is selected under the assumption that time series are a superposition of some deterministic and random processes. Using the Fourier transform, the characteristic function is transformed into a nonholomorphic excessive-asymmetric probability-density function. The statistical distributions of the samples {δ foF2} calculated for the disturbed periods are compared with the obtained model distribution function. According to the Kolmogorov's criterion, the probabilities of the coincidence of a posteriori distributions with the theoretical ones are P 0.7-0.9. The conducted analysis makes it possible to draw a conclusion about the applicability of a model based on the Poisson random process for the statistical description and probabilistic variation estimates during heliogeophysical disturbances of the variations {δ foF2}.

TU-AB-BRB-03: Coverage-Based Treatment Planning to Accommodate Organ Deformable Motions and Contouring Uncertainties for Prostate Treatment

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

Xu, H.

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. Themore » treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.« less

An innovative method for offshore wind farm site selection based on the interval number with probability distribution

NASA Astrophysics Data System (ADS)

Wu, Yunna; Chen, Kaifeng; Xu, Hu; Xu, Chuanbo; Zhang, Haobo; Yang, Meng

2017-12-01

There is insufficient research relating to offshore wind farm site selection in China. The current methods for site selection have some defects. First, information loss is caused by two aspects: the implicit assumption that the probability distribution on the interval number is uniform; and ignoring the value of decision makers' (DMs') common opinion on the criteria information evaluation. Secondly, the difference in DMs' utility function has failed to receive attention. An innovative method is proposed in this article to solve these drawbacks. First, a new form of interval number and its weighted operator are proposed to reflect the uncertainty and reduce information loss. Secondly, a new stochastic dominance degree is proposed to quantify the interval number with a probability distribution. Thirdly, a two-stage method integrating the weighted operator with stochastic dominance degree is proposed to evaluate the alternatives. Finally, a case from China proves the effectiveness of this method.

Estimation of transition probabilities of credit ratings

NASA Astrophysics Data System (ADS)

Peng, Gan Chew; Hin, Pooi Ah

2015-12-01

The present research is based on the quarterly credit ratings of ten companies over 15 years taken from the database of the Taiwan Economic Journal. The components in the vector mi (mi1, mi2,⋯, mi10) may first be used to denote the credit ratings of the ten companies in the i-th quarter. The vector mi+1 in the next quarter is modelled to be dependent on the vector mi via a conditional distribution which is derived from a 20-dimensional power-normal mixture distribution. The transition probability Pkl (i ,j ) for getting mi+1,j = l given that mi, j = k is then computed from the conditional distribution. It is found that the variation of the transition probability Pkl (i ,j ) as i varies is able to give indication for the possible transition of the credit rating of the j-th company in the near future.

Method and device for landing aircraft dependent on runway occupancy time

NASA Technical Reports Server (NTRS)

Ghalebsaz Jeddi, Babak (Inventor)

2012-01-01

A technique for landing aircraft using an aircraft landing accident avoidance device is disclosed. The technique includes determining at least two probability distribution functions; determining a safe lower limit on a separation between a lead aircraft and a trail aircraft on a glide slope to the runway; determining a maximum sustainable safe attempt-to-land rate on the runway based on the safe lower limit and the probability distribution functions; directing the trail aircraft to enter the glide slope with a target separation from the lead aircraft corresponding to the maximum sustainable safe attempt-to-land rate; while the trail aircraft is in the glide slope, determining an actual separation between the lead aircraft and the trail aircraft; and directing the trail aircraft to execute a go-around maneuver if the actual separation approaches the safe lower limit. Probability distribution functions include runway occupancy time, and landing time interval and/or inter-arrival distance.

Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

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

Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com; Grana, Dario; Santos, Marcio

We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well datamore » multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.« less

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.

A Dasymetric-Based Monte Carlo Simulation Approach to the Probabilistic Analysis of Spatial Variables

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

Morton, April M; Piburn, Jesse O; McManamay, Ryan A

2017-01-01

Monte Carlo simulation is a popular numerical experimentation technique used in a range of scientific fields to obtain the statistics of unknown random output variables. Despite its widespread applicability, it can be difficult to infer required input probability distributions when they are related to population counts unknown at desired spatial resolutions. To overcome this challenge, we propose a framework that uses a dasymetric model to infer the probability distributions needed for a specific class of Monte Carlo simulations which depend on population counts.

On the issues of probability distribution of GPS carrier phase observations

NASA Astrophysics Data System (ADS)

Luo, X.; Mayer, M.; Heck, B.

2009-04-01

In common practice the observables related to Global Positioning System (GPS) are assumed to follow a Gauss-Laplace normal distribution. Actually, full knowledge of the observables' distribution is not required for parameter estimation by means of the least-squares algorithm based on the functional relation between observations and unknown parameters as well as the associated variance-covariance matrix. However, the probability distribution of GPS observations plays a key role in procedures for quality control (e.g. outlier and cycle slips detection, ambiguity resolution) and in reliability-related assessments of the estimation results. Under non-ideal observation conditions with respect to the factors impacting GPS data quality, for example multipath effects and atmospheric delays, the validity of the normal distribution postulate of GPS observations is in doubt. This paper presents a detailed analysis of the distribution properties of GPS carrier phase observations using double difference residuals. For this purpose 1-Hz observation data from the permanent SAPOS

Newsvendor problem under complete uncertainty: a case of innovative products.

PubMed

Gaspars-Wieloch, Helena

2017-01-01

The paper presents a new scenario-based decision rule for the classical version of the newsvendor problem (NP) under complete uncertainty (i.e. uncertainty with unknown probabilities). So far, NP has been analyzed under uncertainty with known probabilities or under uncertainty with partial information (probabilities known incompletely). The novel approach is designed for the sale of new, innovative products, where it is quite complicated to define probabilities or even probability-like quantities, because there are no data available for forecasting the upcoming demand via statistical analysis. The new procedure described in the contribution is based on a hybrid of Hurwicz and Bayes decision rules. It takes into account the decision maker's attitude towards risk (measured by coefficients of optimism and pessimism) and the dispersion (asymmetry, range, frequency of extremes values) of payoffs connected with particular order quantities. It does not require any information about the probability distribution.

Diversification and biogeography of Juniperus (Cupressaceae): variable diversification rates and multiple intercontinental dispersals.

PubMed

Mao, Kangshan; Hao, Gang; Liu, Jianquan; Adams, Robert P; Milne, Richard I

2010-10-01

• A central aim of biogeography is to understand when and how modern patterns of species diversity and distribution developed. Many plant groups have disjunct distributions within the Northern Hemisphere, but among these very few have been studied that prefer warm semi-arid habitats. • Here we examine the biogeography and diversification history of Juniperus, which occurs in semi-arid habitats through much of the Northern Hemisphere. A phylogeny was generated based on > 10,000 bp of cpDNA for 51 Juniperus species plus many outgroups. Phylogenies based on fewer species were also constructed based on nuclear internal transcribed spacer (nrITS) and combined nrITS/cpDNA data sets to check for congruence. Divergence time-scales and ancestral distributions were further inferred. • Both long dispersal and migration across land bridges probably contributed to the modern range of Juniperus, while long-term climatic changes and the uplift of the Qinghai-Tibetan plateau probably drove its diversification. Diversification apparently slowed down during climate-stable period of the Oligocene, and then speeded up from the Miocene onwards. • Juniperus probably originated in Eurasia, and was a part of the south Eurasian Tethyan vegetation of the Eocene to Oligocene. It reached America once at this time, once in the Miocene and once more recently.

Calibration of micromechanical parameters for DEM simulations by using the particle filter

NASA Astrophysics Data System (ADS)

Cheng, Hongyang; Shuku, Takayuki; Thoeni, Klaus; Yamamoto, Haruyuki

2017-06-01

The calibration of DEM models is typically accomplished by trail and error. However, the procedure lacks of objectivity and has several uncertainties. To deal with these issues, the particle filter is employed as a novel approach to calibrate DEM models of granular soils. The posterior probability distribution of the microparameters that give numerical results in good agreement with the experimental response of a Toyoura sand specimen is approximated by independent model trajectories, referred as `particles', based on Monte Carlo sampling. The soil specimen is modeled by polydisperse packings with different numbers of spherical grains. Prepared in `stress-free' states, the packings are subjected to triaxial quasistatic loading. Given the experimental data, the posterior probability distribution is incrementally updated, until convergence is reached. The resulting `particles' with higher weights are identified as the calibration results. The evolutions of the weighted averages and posterior probability distribution of the micro-parameters are plotted to show the advantage of using a particle filter, i.e., multiple solutions are identified for each parameter with known probabilities of reproducing the experimental response.

Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

NASA Technical Reports Server (NTRS)

Nemeth, Noel

2013-01-01

Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

Launch Vehicle Debris Models and Crew Vehicle Ascent Abort Risk

NASA Technical Reports Server (NTRS)

Gee, Ken; Lawrence, Scott

2013-01-01

For manned space launch systems, a reliable abort system is required to reduce the risks associated with a launch vehicle failure during ascent. Understanding the risks associated with failure environments can be achieved through the use of physics-based models of these environments. Debris fields due to destruction of the launch vehicle is one such environment. To better analyze the risk posed by debris, a physics-based model for generating launch vehicle debris catalogs has been developed. The model predicts the mass distribution of the debris field based on formulae developed from analysis of explosions. Imparted velocity distributions are computed using a shock-physics code to model the explosions within the launch vehicle. A comparison of the debris catalog with an existing catalog for the Shuttle external tank show good comparison in the debris characteristics and the predicted debris strike probability. The model is used to analyze the effects of number of debris pieces and velocity distributions on the strike probability and risk.

A novel method for correcting scanline-observational bias of discontinuity orientation

PubMed Central

Huang, Lei; Tang, Huiming; Tan, Qinwen; Wang, Dingjian; Wang, Liangqing; Ez Eldin, Mutasim A. M.; Li, Changdong; Wu, Qiong

2016-01-01

Scanline observation is known to introduce an angular bias into the probability distribution of orientation in three-dimensional space. In this paper, numerical solutions expressing the functional relationship between the scanline-observational distribution (in one-dimensional space) and the inherent distribution (in three-dimensional space) are derived using probability theory and calculus under the independence hypothesis of dip direction and dip angle. Based on these solutions, a novel method for obtaining the inherent distribution (also for correcting the bias) is proposed, an approach which includes two procedures: 1) Correcting the cumulative probabilities of orientation according to the solutions, and 2) Determining the distribution of the corrected orientations using approximation methods such as the one-sample Kolmogorov-Smirnov test. The inherent distribution corrected by the proposed method can be used for discrete fracture network (DFN) modelling, which is applied to such areas as rockmass stability evaluation, rockmass permeability analysis, rockmass quality calculation and other related fields. To maximize the correction capacity of the proposed method, the observed sample size is suggested through effectiveness tests for different distribution types, dispersions and sample sizes. The performance of the proposed method and the comparison of its correction capacity with existing methods are illustrated with two case studies. PMID:26961249

ERMiT: Estimating Post-Fire Erosion in Probabilistic Terms

NASA Astrophysics Data System (ADS)

Pierson, F. B.; Robichaud, P. R.; Elliot, W. J.; Hall, D. E.; Moffet, C. A.

2006-12-01

Mitigating the impact of post-wildfire runoff and erosion on life, property, and natural resources have cost the United States government tens of millions of dollars over the past decade. The decision of where, when, and how to apply the most effective mitigation treatments requires land managers to assess the risk of damaging runoff and erosion events occurring after a fire. The Erosion Risk Management Tool (ERMiT) is a web-based application that estimates erosion in probabilistic terms on burned and recovering forest, range, and chaparral lands. Unlike most erosion prediction models, ERMiT does not provide `average annual erosion rates;' rather, it provides a distribution of erosion rates with the likelihood of their occurrence. ERMiT combines rain event variability with spatial and temporal variabilities of hillslope burn severity, soil properties, and ground cover to estimate Water Erosion Prediction Project (WEPP) model input parameter values. Based on 20 to 40 individual WEPP runs, ERMiT produces a distribution of rain event erosion rates with a probability of occurrence for each of five post-fire years. Over the 5 years of modeled recovery, the occurrence probability of the less erodible soil parameters is increased and the occurrence probability of the more erodible soil parameters is decreased. In addition, the occurrence probabilities and the four spatial arrangements of burn severity (arrangements of overland flow elements (OFE's)), are shifted toward lower burn severity with each year of recovery. These yearly adjustments are based on field measurements made through post-fire recovery periods. ERMiT also provides rain event erosion rate distributions for hillslopes that have been treated with seeding, straw mulch, straw wattles and contour-felled log erosion barriers. Such output can help managers make erosion mitigation treatment decisions based on the probability of high sediment yields occurring, the value of resources at risk for damage, cost, and other management considerations.

Failure probability analysis of optical grid

NASA Astrophysics Data System (ADS)

Zhong, Yaoquan; Guo, Wei; Sun, Weiqiang; Jin, Yaohui; Hu, Weisheng

2008-11-01

Optical grid, the integrated computing environment based on optical network, is expected to be an efficient infrastructure to support advanced data-intensive grid applications. In optical grid, the faults of both computational and network resources are inevitable due to the large scale and high complexity of the system. With the optical network based distributed computing systems extensive applied in the processing of data, the requirement of the application failure probability have been an important indicator of the quality of application and an important aspect the operators consider. This paper will present a task-based analysis method of the application failure probability in optical grid. Then the failure probability of the entire application can be quantified, and the performance of reducing application failure probability in different backup strategies can be compared, so that the different requirements of different clients can be satisfied according to the application failure probability respectively. In optical grid, when the application based DAG (directed acyclic graph) is executed in different backup strategies, the application failure probability and the application complete time is different. This paper will propose new multi-objective differentiated services algorithm (MDSA). New application scheduling algorithm can guarantee the requirement of the failure probability and improve the network resource utilization, realize a compromise between the network operator and the application submission. Then differentiated services can be achieved in optical grid.

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

Cuevas, F.A.; Curilef, S., E-mail: scurilef@ucn.cl; Plastino, A.R., E-mail: arplastino@ugr.es

The spread of a wave-packet (or its deformation) is a very important topic in quantum mechanics. Understanding this phenomenon is relevant in connection with the study of diverse physical systems. In this paper we apply various 'spreading measures' to characterize the evolution of an initially localized wave-packet in a tight-binding lattice, with special emphasis on information-theoretical measures. We investigate the behavior of both the probability distribution associated with the wave packet and the concomitant probability current. Complexity measures based upon Renyi entropies appear to be particularly good descriptors of the details of the delocalization process. - Highlights: > Spread ofmore » highly localized wave-packet in the tight-binding lattice. > Entropic and information-theoretical characterization is used to understand the delocalization. > The behavior of both the probability distribution and the concomitant probability current is investigated. > Renyi entropies appear to be good descriptors of the details of the delocalization process.« less

Rockfall travel distances theoretical distributions

NASA Astrophysics Data System (ADS)

Jaboyedoff, Michel; Derron, Marc-Henri; Pedrazzini, Andrea

2017-04-01

The probability of propagation of rockfalls is a key part of hazard assessment, because it permits to extrapolate the probability of propagation of rockfall either based on partial data or simply theoretically. The propagation can be assumed frictional which permits to describe on average the propagation by a line of kinetic energy which corresponds to the loss of energy along the path. But loss of energy can also be assumed as a multiplicative process or a purely random process. The distributions of the rockfall block stop points can be deduced from such simple models, they lead to Gaussian, Inverse-Gaussian, Log-normal or exponential negative distributions. The theoretical background is presented, and the comparisons of some of these models with existing data indicate that these assumptions are relevant. The results are either based on theoretical considerations or by fitting results. They are potentially very useful for rockfall hazard zoning and risk assessment. This approach will need further investigations.

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

Sampling considerations for disease surveillance in wildlife populations

USGS Publications Warehouse

Nusser, S.M.; Clark, W.R.; Otis, D.L.; Huang, L.

2008-01-01

Disease surveillance in wildlife populations involves detecting the presence of a disease, characterizing its prevalence and spread, and subsequent monitoring. A probability sample of animals selected from the population and corresponding estimators of disease prevalence and detection provide estimates with quantifiable statistical properties, but this approach is rarely used. Although wildlife scientists often assume probability sampling and random disease distributions to calculate sample sizes, convenience samples (i.e., samples of readily available animals) are typically used, and disease distributions are rarely random. We demonstrate how landscape-based simulation can be used to explore properties of estimators from convenience samples in relation to probability samples. We used simulation methods to model what is known about the habitat preferences of the wildlife population, the disease distribution, and the potential biases of the convenience-sample approach. Using chronic wasting disease in free-ranging deer (Odocoileus virginianus) as a simple illustration, we show that using probability sample designs with appropriate estimators provides unbiased surveillance parameter estimates but that the selection bias and coverage errors associated with convenience samples can lead to biased and misleading results. We also suggest practical alternatives to convenience samples that mix probability and convenience sampling. For example, a sample of land areas can be selected using a probability design that oversamples areas with larger animal populations, followed by harvesting of individual animals within sampled areas using a convenience sampling method.

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.

Optimized lower leg injury probability curves from postmortem human subject tests under axial impacts.

PubMed

Yoganandan, Narayan; Arun, Mike W J; Pintar, Frank A; Szabo, Aniko

2014-01-01

Derive optimum injury probability curves to describe human tolerance of the lower leg using parametric survival analysis. The study reexamined lower leg postmortem human subjects (PMHS) data from a large group of specimens. Briefly, axial loading experiments were conducted by impacting the plantar surface of the foot. Both injury and noninjury tests were included in the testing process. They were identified by pre- and posttest radiographic images and detailed dissection following the impact test. Fractures included injuries to the calcaneus and distal tibia-fibula complex (including pylon), representing severities at the Abbreviated Injury Score (AIS) level 2+. For the statistical analysis, peak force was chosen as the main explanatory variable and the age was chosen as the covariable. Censoring statuses depended on experimental outcomes. Parameters from the parametric survival analysis were estimated using the maximum likelihood approach and the dfbetas statistic was used to identify overly influential samples. The best fit from the Weibull, log-normal, and log-logistic distributions was based on the Akaike information criterion. Plus and minus 95% confidence intervals were obtained for the optimum injury probability distribution. The relative sizes of the interval were determined at predetermined risk levels. Quality indices were described at each of the selected probability levels. The mean age, stature, and weight were 58.2±15.1 years, 1.74±0.08 m, and 74.9±13.8 kg, respectively. Excluding all overly influential tests resulted in the tightest confidence intervals. The Weibull distribution was the most optimum function compared to the other 2 distributions. A majority of quality indices were in the good category for this optimum distribution when results were extracted for 25-, 45- and 65-year-olds at 5, 25, and 50% risk levels age groups for lower leg fracture. For 25, 45, and 65 years, peak forces were 8.1, 6.5, and 5.1 kN at 5% risk; 9.6, 7.7, and 6.1 kN at 25% risk; and 10.4, 8.3, and 6.6 kN at 50% risk, respectively. This study derived axial loading-induced injury risk curves based on survival analysis using peak force and specimen age; adopting different censoring schemes; considering overly influential samples in the analysis; and assessing the quality of the distribution at discrete probability levels. Because procedures used in the present survival analysis are accepted by international automotive communities, current optimum human injury probability distributions can be used at all risk levels with more confidence in future crashworthiness applications for automotive and other disciplines.

On the use of the energy probability distribution zeros in the study of phase transitions

NASA Astrophysics Data System (ADS)

Mól, L. A. S.; Rodrigues, R. G. M.; Stancioli, R. A.; Rocha, J. C. S.; Costa, B. V.

2018-04-01

This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition function zeros and has been shown to be extremely efficient to precisely locate phase transition temperatures. It is based on an iterative method in such a way that the transition temperature can be approached at will. The iterative method will be detailed and some convergence issues that has been observed in its application to the 2D Ising model and to an artificial spin ice model will be shown, together with ways to circumvent them.

Non-Gaussian statistics of soliton timing jitter induced by amplifier noise.

PubMed

Ho, Keang-Po

2003-11-15

Based on first-order perturbation theory of the soliton, the Gordon-Haus timing jitter induced by amplifier noise is found to be non-Gaussian distributed. Both frequency and timing jitter have larger tail probabilities than Gaussian distribution given by the linearized perturbation theory. The timing jitter has a larger discrepancy from Gaussian distribution than does the frequency jitter.

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.

Explosion probability of unexploded ordnance: expert beliefs.

PubMed

MacDonald, Jacqueline Anne; Small, Mitchell J; Morgan, M G

2008-08-01

This article reports on a study to quantify expert beliefs about the explosion probability of unexploded ordnance (UXO). Some 1,976 sites at closed military bases in the United States are contaminated with UXO and are slated for cleanup, at an estimated cost of $15-140 billion. Because no available technology can guarantee 100% removal of UXO, information about explosion probability is needed to assess the residual risks of civilian reuse of closed military bases and to make decisions about how much to invest in cleanup. This study elicited probability distributions for the chance of UXO explosion from 25 experts in explosive ordnance disposal, all of whom have had field experience in UXO identification and deactivation. The study considered six different scenarios: three different types of UXO handled in two different ways (one involving children and the other involving construction workers). We also asked the experts to rank by sensitivity to explosion 20 different kinds of UXO found at a case study site at Fort Ord, California. We found that the experts do not agree about the probability of UXO explosion, with significant differences among experts in their mean estimates of explosion probabilities and in the amount of uncertainty that they express in their estimates. In three of the six scenarios, the divergence was so great that the average of all the expert probability distributions was statistically indistinguishable from a uniform (0, 1) distribution-suggesting that the sum of expert opinion provides no information at all about the explosion risk. The experts' opinions on the relative sensitivity to explosion of the 20 UXO items also diverged. The average correlation between rankings of any pair of experts was 0.41, which, statistically, is barely significant (p= 0.049) at the 95% confidence level. Thus, one expert's rankings provide little predictive information about another's rankings. The lack of consensus among experts suggests that empirical studies are needed to better understand the explosion risks of UXO.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

NASA Astrophysics Data System (ADS)

Li, Dong; Svensson, J.; Thomsen, H.; Medina, F.; Werner, A.; Wolf, R.

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

Bayesian soft X-ray tomography using non-stationary Gaussian Processes.

PubMed

Li, Dong; Svensson, J; Thomsen, H; Medina, F; Werner, A; Wolf, R

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

The genomic structure: proof of the role of non-coding DNA.

PubMed

Bouaynaya, Nidhal; Schonfeld, Dan

2006-01-01

We prove that the introns play the role of a decoy in absorbing mutations in the same way hollow uninhabited structures are used by the military to protect important installations. Our approach is based on a probability of error analysis, where errors are mutations which occur in the exon sequences. We derive the optimal exon length distribution, which minimizes the probability of error in the genome. Furthermore, to understand how can Nature generate the optimal distribution, we propose a diffusive random walk model for exon generation throughout evolution. This model results in an alpha stable exon length distribution, which is asymptotically equivalent to the optimal distribution. Experimental results show that both distributions accurately fit the real data. Given that introns also drive biological evolution by increasing the rate of unequal crossover between genes, we conclude that the role of introns is to maintain a genius balance between stability and adaptability in eukaryotic genomes.

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

2017-03-01

We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

Multivariate η-μ fading distribution with arbitrary correlation model

NASA Astrophysics Data System (ADS)

Ghareeb, Ibrahim; Atiani, Amani

2018-03-01

An extensive analysis for the multivariate ? distribution with arbitrary correlation is presented, where novel analytical expressions for the multivariate probability density function, cumulative distribution function and moment generating function (MGF) of arbitrarily correlated and not necessarily identically distributed ? power random variables are derived. Also, this paper provides exact-form expression for the MGF of the instantaneous signal-to-noise ratio at the combiner output in a diversity reception system with maximal-ratio combining and post-detection equal-gain combining operating in slow frequency nonselective arbitrarily correlated not necessarily identically distributed ?-fading channels. The average bit error probability of differentially detected quadrature phase shift keying signals with post-detection diversity reception system over arbitrarily correlated and not necessarily identical fading parameters ?-fading channels is determined by using the MGF-based approach. The effect of fading correlation between diversity branches, fading severity parameters and diversity level is studied.

Intra-Urban Human Mobility and Activity Transition: Evidence from Social Media Check-In Data

PubMed Central

Wu, Lun; Zhi, Ye; Sui, Zhengwei; Liu, Yu

2014-01-01

Most existing human mobility literature focuses on exterior characteristics of movements but neglects activities, the driving force that underlies human movements. In this research, we combine activity-based analysis with a movement-based approach to model the intra-urban human mobility observed from about 15 million check-in records during a yearlong period in Shanghai, China. The proposed model is activity-based and includes two parts: the transition of travel demands during a specific time period and the movement between locations. For the first part, we find the transition probability between activities varies over time, and then we construct a temporal transition probability matrix to represent the transition probability of travel demands during a time interval. For the second part, we suggest that the travel demands can be divided into two classes, locationally mandatory activity (LMA) and locationally stochastic activity (LSA), according to whether the demand is associated with fixed location or not. By judging the combination of predecessor activity type and successor activity type we determine three trip patterns, each associated with a different decay parameter. To validate the model, we adopt the mechanism of an agent-based model and compare the simulated results with the observed pattern from the displacement distance distribution, the spatio-temporal distribution of activities, and the temporal distribution of travel demand transitions. The results show that the simulated patterns fit the observed data well, indicating that these findings open new directions for combining activity-based analysis with a movement-based approach using social media check-in data. PMID:24824892

Risk-based decision making to manage water quality failures caused by combined sewer overflows

NASA Astrophysics Data System (ADS)

Sriwastava, A. K.; Torres-Matallana, J. A.; Tait, S.; Schellart, A.

2017-12-01

Regulatory authorities set certain environmental permit for water utilities such that the combined sewer overflows (CSO) managed by these companies conform to the regulations. These utility companies face the risk of paying penalty or negative publicity in case they breach the environmental permit. These risks can be addressed by designing appropriate solutions such as investing in additional infrastructure which improve the system capacity and reduce the impact of CSO spills. The performance of these solutions is often estimated using urban drainage models. Hence, any uncertainty in these models can have a significant effect on the decision making process. This study outlines a risk-based decision making approach to address water quality failure caused by CSO spills. A calibrated lumped urban drainage model is used to simulate CSO spill quality in Haute-Sûre catchment in Luxembourg. Uncertainty in rainfall and model parameters is propagated through Monte Carlo simulations to quantify uncertainty in the concentration of ammonia in the CSO spill. A combination of decision alternatives such as the construction of a storage tank at the CSO and the reduction in the flow contribution of catchment surfaces are selected as planning measures to avoid the water quality failure. Failure is defined as exceedance of a concentration-duration based threshold based on Austrian emission standards for ammonia (De Toffol, 2006) with a certain frequency. For each decision alternative, uncertainty quantification results into a probability distribution of the number of annual CSO spill events which exceed the threshold. For each alternative, a buffered failure probability as defined in Rockafellar & Royset (2010), is estimated. Buffered failure probability (pbf) is a conservative estimate of failure probability (pf), however, unlike failure probability, it includes information about the upper tail of the distribution. A pareto-optimal set of solutions is obtained by performing mean- pbf optimization. The effectiveness of using buffered failure probability compared to the failure probability is tested by comparing the solutions obtained by using mean-pbf and mean-pf optimizations.

Coalescence computations for large samples drawn from populations of time-varying sizes

PubMed Central

Polanski, Andrzej; Szczesna, Agnieszka; Garbulowski, Mateusz; Kimmel, Marek

2017-01-01

We present new results concerning probability distributions of times in the coalescence tree and expected allele frequencies for coalescent with large sample size. The obtained results are based on computational methodologies, which involve combining coalescence time scale changes with techniques of integral transformations and using analytical formulae for infinite products. We show applications of the proposed methodologies for computing probability distributions of times in the coalescence tree and their limits, for evaluation of accuracy of approximate expressions for times in the coalescence tree and expected allele frequencies, and for analysis of large human mitochondrial DNA dataset. PMID:28170404

Methods for Combining Payload Parameter Variations with Input Environment

NASA Technical Reports Server (NTRS)

Merchant, D. H.; Straayer, J. W.

1975-01-01

Methods are presented for calculating design limit loads compatible with probabilistic structural design criteria. The approach is based on the concept that the desired limit load, defined as the largest load occuring in a mission, is a random variable having a specific probability distribution which may be determined from extreme-value theory. The design limit load, defined as a particular value of this random limit load, is the value conventionally used in structural design. Methods are presented for determining the limit load probability distributions from both time-domain and frequency-domain dynamic load simulations. Numerical demonstrations of the methods are also presented.

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

Chang, Shih-Jung

Dynamic strength of the High Flux Isotope Reactor (HFIR) vessel to resist hypothetical accidents is analyzed by using the method of fracture mechanics. Vessel critical stresses are estimated by applying dynamic pressure pulses of a range of magnitudes and pulse-durations. The pulses versus time functions are assumed to be step functions. The probability of vessel fracture is then calculated by assuming a distribution of possible surface cracks of different crack depths. The probability distribution function for the crack depths is based on the form that is recommended by the Marshall report. The toughness of the vessel steel used in themore » analysis is based on the projected and embrittled value after 10 effective full power years from 1986. From the study made by Cheverton, Merkle and Nanstad, the weakest point on the vessel for fracture evaluation is known to be located within the region surrounding the tangential beam tube HB3. The increase in the probability of fracture is obtained as an extension of the result from that report for the regular operating condition to include conditions of higher dynamic pressures due to accident loadings. The increase in the probability of vessel fracture is plotted for a range of hoop stresses to indicate the vessel strength against hypothetical accident conditions.« less

Determination of a Limited Scope Network's Lightning Detection Efficiency

NASA Technical Reports Server (NTRS)

Rompala, John T.; Blakeslee, R.

2008-01-01

This paper outlines a modeling technique to map lightning detection efficiency variations over a region surveyed by a sparse array of ground based detectors. A reliable flash peak current distribution (PCD) for the region serves as the technique's base. This distribution is recast as an event probability distribution function. The technique then uses the PCD together with information regarding: site signal detection thresholds, type of solution algorithm used, and range attenuation; to formulate the probability that a flash at a specified location will yield a solution. Applying this technique to the full region produces detection efficiency contour maps specific to the parameters employed. These contours facilitate a comparative analysis of each parameter's effect on the network's detection efficiency. In an alternate application, this modeling technique gives an estimate of the number, strength, and distribution of events going undetected. This approach leads to a variety of event density contour maps. This application is also illustrated. The technique's base PCD can be empirical or analytical. A process for formulating an empirical PCD specific to the region and network being studied is presented. A new method for producing an analytical representation of the empirical PCD is also introduced.

TU-AB-BRB-01: Coverage Evaluation and Probabilistic Treatment Planning as a Margin Alternative

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

Siebers, J.

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. Themore » treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.« less

TU-AB-BRB-02: Stochastic Programming Methods for Handling Uncertainty and Motion in IMRT Planning

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

Unkelbach, J.

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. Themore » treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.« less

TU-AB-BRB-00: New Methods to Ensure Target Coverage

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

NONE

2015-06-15

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. Themore » treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.« less

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.

Performance of mixed RF/FSO systems in exponentiated Weibull distributed channels

NASA Astrophysics Data System (ADS)

Zhao, Jing; Zhao, Shang-Hong; Zhao, Wei-Hu; Liu, Yun; Li, Xuan

2017-12-01

This paper presented the performances of asymmetric mixed radio frequency (RF)/free-space optical (FSO) system with the amplify-and-forward relaying scheme. The RF channel undergoes Nakagami- m channel, and the Exponentiated Weibull distribution is adopted for the FSO component. The mathematical formulas for cumulative distribution function (CDF), probability density function (PDF) and moment generating function (MGF) of equivalent signal-to-noise ratio (SNR) are achieved. According to the end-to-end statistical characteristics, the new analytical expressions of outage probability are obtained. Under various modulation techniques, we derive the average bit-error-rate (BER) based on the Meijer's G function. The evaluation and simulation are provided for the system performance, and the aperture average effect is discussed as well.

Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems.

PubMed

Namikawa, Jun

2005-08-01

Chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line and a Markov chain with a transition probability matrix. The stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins. It is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of (truncated) power-law distributions if the basin of attraction for each attractor ruin has a zero measure. This result is confirmed by simulation of models exhibiting chaotic itinerancy. Chaotic itinerancy is also shown to be absent in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.

Heavy Metal Pollution Delineation Based on Uncertainty in a Coastal Industrial City in the Yangtze River Delta, China

PubMed Central

Zhao, Ruiying; Chen, Songchao; Zhou, Yue; Jin, Bin; Li, Yan

2018-01-01

Assessing heavy metal pollution and delineating pollution are the bases for evaluating pollution and determining a cost-effective remediation plan. Most existing studies are based on the spatial distribution of pollutants but ignore related uncertainty. In this study, eight heavy-metal concentrations (Cr, Pb, Cd, Hg, Zn, Cu, Ni, and Zn) were collected at 1040 sampling sites in a coastal industrial city in the Yangtze River Delta, China. The single pollution index (PI) and Nemerow integrated pollution index (NIPI) were calculated for every surface sample (0–20 cm) to assess the degree of heavy metal pollution. Ordinary kriging (OK) was used to map the spatial distribution of heavy metals content and NIPI. Then, we delineated composite heavy metal contamination based on the uncertainty produced by indicator kriging (IK). The results showed that mean values of all PIs and NIPIs were at safe levels. Heavy metals were most accumulated in the central portion of the study area. Based on IK, the spatial probability of composite heavy metal pollution was computed. The probability of composite contamination in the central core urban area was highest. A probability of 0.6 was found as the optimum probability threshold to delineate polluted areas from unpolluted areas for integrative heavy metal contamination. Results of pollution delineation based on uncertainty showed the proportion of false negative error areas was 6.34%, while the proportion of false positive error areas was 0.86%. The accuracy of the classification was 92.80%. This indicated the method we developed is a valuable tool for delineating heavy metal pollution. PMID:29642623

Heavy Metal Pollution Delineation Based on Uncertainty in a Coastal Industrial City in the Yangtze River Delta, China.

PubMed

Hu, Bifeng; Zhao, Ruiying; Chen, Songchao; Zhou, Yue; Jin, Bin; Li, Yan; Shi, Zhou

2018-04-10

Assessing heavy metal pollution and delineating pollution are the bases for evaluating pollution and determining a cost-effective remediation plan. Most existing studies are based on the spatial distribution of pollutants but ignore related uncertainty. In this study, eight heavy-metal concentrations (Cr, Pb, Cd, Hg, Zn, Cu, Ni, and Zn) were collected at 1040 sampling sites in a coastal industrial city in the Yangtze River Delta, China. The single pollution index (PI) and Nemerow integrated pollution index (NIPI) were calculated for every surface sample (0-20 cm) to assess the degree of heavy metal pollution. Ordinary kriging (OK) was used to map the spatial distribution of heavy metals content and NIPI. Then, we delineated composite heavy metal contamination based on the uncertainty produced by indicator kriging (IK). The results showed that mean values of all PIs and NIPIs were at safe levels. Heavy metals were most accumulated in the central portion of the study area. Based on IK, the spatial probability of composite heavy metal pollution was computed. The probability of composite contamination in the central core urban area was highest. A probability of 0.6 was found as the optimum probability threshold to delineate polluted areas from unpolluted areas for integrative heavy metal contamination. Results of pollution delineation based on uncertainty showed the proportion of false negative error areas was 6.34%, while the proportion of false positive error areas was 0.86%. The accuracy of the classification was 92.80%. This indicated the method we developed is a valuable tool for delineating heavy metal pollution.

Species Distribution Models and Ecological Suitability Analysis for Potential Tick Vectors of Lyme Disease in Mexico

PubMed Central

Illoldi-Rangel, Patricia; Rivaldi, Chissa-Louise; Sissel, Blake; Trout Fryxell, Rebecca; Gordillo-Pérez, Guadalupe; Rodríguez-Moreno, Angel; Williamson, Phillip; Montiel-Parra, Griselda; Sánchez-Cordero, Víctor; Sarkar, Sahotra

2012-01-01

Species distribution models were constructed for ten Ixodes species and Amblyomma cajennense for a region including Mexico and Texas. The model was based on a maximum entropy algorithm that used environmental layers to predict the relative probability of presence for each taxon. For Mexico, species geographic ranges were predicted by restricting the models to cells which have a higher probability than the lowest probability of the cells in which a presence record was located. There was spatial nonconcordance between the distributions of Amblyomma cajennense and the Ixodes group with the former restricted to lowlands and mainly the eastern coast of Mexico and the latter to montane regions with lower temperature. The risk of Lyme disease is, therefore, mainly present in the highlands where some Ixodes species are known vectors; if Amblyomma cajennense turns out to be a competent vector, the area of risk also extends to the lowlands and the east coast. PMID:22518171

Species distribution models and ecological suitability analysis for potential tick vectors of lyme disease in Mexico.

PubMed

Illoldi-Rangel, Patricia; Rivaldi, Chissa-Louise; Sissel, Blake; Trout Fryxell, Rebecca; Gordillo-Pérez, Guadalupe; Rodríguez-Moreno, Angel; Williamson, Phillip; Montiel-Parra, Griselda; Sánchez-Cordero, Víctor; Sarkar, Sahotra

2012-01-01

Species distribution models were constructed for ten Ixodes species and Amblyomma cajennense for a region including Mexico and Texas. The model was based on a maximum entropy algorithm that used environmental layers to predict the relative probability of presence for each taxon. For Mexico, species geographic ranges were predicted by restricting the models to cells which have a higher probability than the lowest probability of the cells in which a presence record was located. There was spatial nonconcordance between the distributions of Amblyomma cajennense and the Ixodes group with the former restricted to lowlands and mainly the eastern coast of Mexico and the latter to montane regions with lower temperature. The risk of Lyme disease is, therefore, mainly present in the highlands where some Ixodes species are known vectors; if Amblyomma cajennense turns out to be a competent vector, the area of risk also extends to the lowlands and the east coast.

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 microcomputer program for energy assessment and aggregation using the triangular probability distribution

USGS Publications Warehouse

Crovelli, R.A.; Balay, R.H.

1991-01-01

A general risk-analysis method was developed for petroleum-resource assessment and other applications. The triangular probability distribution is used as a model with an analytic aggregation methodology based on probability theory rather than Monte-Carlo simulation. Among the advantages of the analytic method are its computational speed and flexibility, and the saving of time and cost on a microcomputer. The input into the model consists of a set of components (e.g. geologic provinces) and, for each component, three potential resource estimates: minimum, most likely (mode), and maximum. Assuming a triangular probability distribution, the mean, standard deviation, and seven fractiles (F100, F95, F75, F50, F25, F5, and F0) are computed for each component, where for example, the probability of more than F95 is equal to 0.95. The components are aggregated by combining the means, standard deviations, and respective fractiles under three possible siutations (1) perfect positive correlation, (2) complete independence, and (3) any degree of dependence between these two polar situations. A package of computer programs named the TRIAGG system was written in the Turbo Pascal 4.0 language for performing the analytic probabilistic methodology. The system consists of a program for processing triangular probability distribution assessments and aggregations, and a separate aggregation routine for aggregating aggregations. The user's documentation and program diskette of the TRIAGG system are available from USGS Open File Services. TRIAGG requires an IBM-PC/XT/AT compatible microcomputer with 256kbyte of main memory, MS-DOS 3.1 or later, either two diskette drives or a fixed disk, and a 132 column printer. A graphics adapter and color display are optional. ?? 1991.

Ensemble Kalman filtering in presence of inequality constraints

NASA Astrophysics Data System (ADS)

van Leeuwen, P. J.

2009-04-01

Kalman filtering is presence of constraints is an active area of research. Based on the Gaussian assumption for the probability-density functions, it looks hard to bring in extra constraints in the formalism. On the other hand, in geophysical systems we often encounter constraints related to e.g. the underlying physics or chemistry, which are violated by the Gaussian assumption. For instance, concentrations are always non-negative, model layers have non-negative thickness, and sea-ice concentration is between 0 and 1. Several methods to bring inequality constraints into the Kalman-filter formalism have been proposed. One of them is probability density function (pdf) truncation, in which the Gaussian mass from the non-allowed part of the variables is just equally distributed over the pdf where the variables are alolwed, as proposed by Shimada et al. 1998. However, a problem with this method is that the probability that e.g. the sea-ice concentration is zero, is zero! The new method proposed here does not have this drawback. It assumes that the probability-density function is a truncated Gaussian, but the truncated mass is not distributed equally over all allowed values of the variables, but put into a delta distribution at the truncation point. This delta distribution can easily be handled with in Bayes theorem, leading to posterior probability density functions that are also truncated Gaussians with delta distributions at the truncation location. In this way a much better representation of the system is obtained, while still keeping most of the benefits of the Kalman-filter formalism. In the full Kalman filter the formalism is prohibitively expensive in large-scale systems, but efficient implementation is possible in ensemble variants of the kalman filter. Applications to low-dimensional systems and large-scale systems will be discussed.

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

A functional model of sensemaking in a neurocognitive architecture.

PubMed

Lebiere, Christian; Pirolli, Peter; Thomson, Robert; Paik, Jaehyon; Rutledge-Taylor, Matthew; Staszewski, James; Anderson, John R

2013-01-01

Sensemaking is the active process of constructing a meaningful representation (i.e., making sense) of some complex aspect of the world. In relation to intelligence analysis, sensemaking is the act of finding and interpreting relevant facts amongst the sea of incoming reports, images, and intelligence. We present a cognitive model of core information-foraging and hypothesis-updating sensemaking processes applied to complex spatial probability estimation and decision-making tasks. While the model was developed in a hybrid symbolic-statistical cognitive architecture, its correspondence to neural frameworks in terms of both structure and mechanisms provided a direct bridge between rational and neural levels of description. Compared against data from two participant groups, the model correctly predicted both the presence and degree of four biases: confirmation, anchoring and adjustment, representativeness, and probability matching. It also favorably predicted human performance in generating probability distributions across categories, assigning resources based on these distributions, and selecting relevant features given a prior probability distribution. This model provides a constrained theoretical framework describing cognitive biases as arising from three interacting factors: the structure of the task environment, the mechanisms and limitations of the cognitive architecture, and the use of strategies to adapt to the dual constraints of cognition and the environment.

Goodness of fit of probability distributions for sightings as species approach extinction.

PubMed

Vogel, Richard M; Hosking, Jonathan R M; Elphick, Chris S; Roberts, David L; Reed, J Michael

2009-04-01

Estimating the probability that a species is extinct and the timing of extinctions is useful in biological fields ranging from paleoecology to conservation biology. Various statistical methods have been introduced to infer the time of extinction and extinction probability from a series of individual sightings. There is little evidence, however, as to which of these models provide adequate fit to actual sighting records. We use L-moment diagrams and probability plot correlation coefficient (PPCC) hypothesis tests to evaluate the goodness of fit of various probabilistic models to sighting data collected for a set of North American and Hawaiian bird populations that have either gone extinct, or are suspected of having gone extinct, during the past 150 years. For our data, the uniform, truncated exponential, and generalized Pareto models performed moderately well, but the Weibull model performed poorly. Of the acceptable models, the uniform distribution performed best based on PPCC goodness of fit comparisons and sequential Bonferroni-type tests. Further analyses using field significance tests suggest that although the uniform distribution is the best of those considered, additional work remains to evaluate the truncated exponential model more fully. The methods we present here provide a framework for evaluating subsequent models.

A Functional Model of Sensemaking in a Neurocognitive Architecture

PubMed Central

Lebiere, Christian; Paik, Jaehyon; Rutledge-Taylor, Matthew; Staszewski, James; Anderson, John R.

2013-01-01

Sensemaking is the active process of constructing a meaningful representation (i.e., making sense) of some complex aspect of the world. In relation to intelligence analysis, sensemaking is the act of finding and interpreting relevant facts amongst the sea of incoming reports, images, and intelligence. We present a cognitive model of core information-foraging and hypothesis-updating sensemaking processes applied to complex spatial probability estimation and decision-making tasks. While the model was developed in a hybrid symbolic-statistical cognitive architecture, its correspondence to neural frameworks in terms of both structure and mechanisms provided a direct bridge between rational and neural levels of description. Compared against data from two participant groups, the model correctly predicted both the presence and degree of four biases: confirmation, anchoring and adjustment, representativeness, and probability matching. It also favorably predicted human performance in generating probability distributions across categories, assigning resources based on these distributions, and selecting relevant features given a prior probability distribution. This model provides a constrained theoretical framework describing cognitive biases as arising from three interacting factors: the structure of the task environment, the mechanisms and limitations of the cognitive architecture, and the use of strategies to adapt to the dual constraints of cognition and the environment. PMID:24302930

Noise deconvolution based on the L1-metric and decomposition of discrete distributions of postsynaptic responses.

PubMed

Astrelin, A V; Sokolov, M V; Behnisch, T; Reymann, K G; Voronin, L L

1997-04-25

A statistical approach to analysis of amplitude fluctuations of postsynaptic responses is described. This includes (1) using a L1-metric in the space of distribution functions for minimisation with application of linear programming methods to decompose amplitude distributions into a convolution of Gaussian and discrete distributions; (2) deconvolution of the resulting discrete distribution with determination of the release probabilities and the quantal amplitude for cases with a small number (< 5) of discrete components. The methods were tested against simulated data over a range of sample sizes and signal-to-noise ratios which mimicked those observed in physiological experiments. In computer simulation experiments, comparisons were made with other methods of 'unconstrained' (generalized) and constrained reconstruction of discrete components from convolutions. The simulation results provided additional criteria for improving the solutions to overcome 'over-fitting phenomena' and to constrain the number of components with small probabilities. Application of the programme to recordings from hippocampal neurones demonstrated its usefulness for the analysis of amplitude distributions of postsynaptic responses.

A brief introduction to probability.

PubMed

Di Paola, Gioacchino; Bertani, Alessandro; De Monte, Lavinia; Tuzzolino, Fabio

2018-02-01

The theory of probability has been debated for centuries: back in 1600, French mathematics used the rules of probability to place and win bets. Subsequently, the knowledge of probability has significantly evolved and is now an essential tool for statistics. In this paper, the basic theoretical principles of probability will be reviewed, with the aim of facilitating the comprehension of statistical inference. After a brief general introduction on probability, we will review the concept of the "probability distribution" that is a function providing the probabilities of occurrence of different possible outcomes of a categorical or continuous variable. Specific attention will be focused on normal distribution that is the most relevant distribution applied to statistical analysis.

Advances in modeling trait-based plant community assembly.

PubMed

Laughlin, Daniel C; Laughlin, David E

2013-10-01

In this review, we examine two new trait-based models of community assembly that predict the relative abundance of species from a regional species pool. The models use fundamentally different mathematical approaches and the predictions can differ considerably. Maxent obtains the most even probability distribution subject to community-weighted mean trait constraints. Traitspace predicts low probabilities for any species whose trait distribution does not pass through the environmental filter. Neither model maximizes functional diversity because of the emphasis on environmental filtering over limiting similarity. Traitspace can test for the effects of limiting similarity by explicitly incorporating intraspecific trait variation. The range of solutions in both models could be used to define the range of natural variability of community composition in restoration projects. Copyright © 2013 Elsevier Ltd. All rights reserved.

Inverse Gaussian gamma distribution model for turbulence-induced fading in free-space optical communication.

PubMed

Cheng, Mingjian; Guo, Ya; Li, Jiangting; Zheng, Xiaotong; Guo, Lixin

2018-04-20

We introduce an alternative distribution to the gamma-gamma (GG) distribution, called inverse Gaussian gamma (IGG) distribution, which can efficiently describe moderate-to-strong irradiance fluctuations. The proposed stochastic model is based on a modulation process between small- and large-scale irradiance fluctuations, which are modeled by gamma and inverse Gaussian distributions, respectively. The model parameters of the IGG distribution are directly related to atmospheric parameters. The accuracy of the fit among the IGG, log-normal, and GG distributions with the experimental probability density functions in moderate-to-strong turbulence are compared, and results indicate that the newly proposed IGG model provides an excellent fit to the experimental data. As the receiving diameter is comparable with the atmospheric coherence radius, the proposed IGG model can reproduce the shape of the experimental data, whereas the GG and LN models fail to match the experimental data. The fundamental channel statistics of a free-space optical communication system are also investigated in an IGG-distributed turbulent atmosphere, and a closed-form expression for the outage probability of the system is derived with Meijer's G-function.

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.

A global logrank test for adaptive treatment strategies based on observational studies.

PubMed

Li, Zhiguo; Valenstein, Marcia; Pfeiffer, Paul; Ganoczy, Dara

2014-02-28

In studying adaptive treatment strategies, a natural question that is of paramount interest is whether there is any significant difference among all possible treatment strategies. When the outcome variable of interest is time-to-event, we propose an inverse probability weighted logrank test for testing the equivalence of a fixed set of pre-specified adaptive treatment strategies based on data from an observational study. The weights take into account both the possible selection bias in an observational study and the fact that the same subject may be consistent with more than one treatment strategy. The asymptotic distribution of the weighted logrank statistic under the null hypothesis is obtained. We show that, in an observational study where the treatment selection probabilities need to be estimated, the estimation of these probabilities does not have an effect on the asymptotic distribution of the weighted logrank statistic, as long as the estimation of the parameters in the models for these probabilities is n-consistent. Finite sample performance of the test is assessed via a simulation study. We also show in the simulation that the test can be pretty robust to misspecification of the models for the probabilities of treatment selection. The method is applied to analyze data on antidepressant adherence time from an observational database maintained at the Department of Veterans Affairs' Serious Mental Illness Treatment Research and Evaluation Center. Copyright © 2013 John Wiley & Sons, Ltd.

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.

How might Model-based Probabilities Extracted from Imperfect Models Guide Rational Decisions: The Case for non-probabilistic odds

NASA Astrophysics Data System (ADS)

Smith, Leonard A.

2010-05-01

This contribution concerns "deep" or "second-order" uncertainty, such as the uncertainty in our probability forecasts themselves. It asks the question: "Is it rational to take (or offer) bets using model-based probabilities as if they were objective probabilities?" If not, what alternative approaches for determining odds, perhaps non-probabilistic odds, might prove useful in practice, given the fact we know our models are imperfect? We consider the case where the aim is to provide sustainable odds: not to produce a profit but merely to rationally expect to break even in the long run. In other words, to run a quantified risk of ruin that is relatively small. Thus the cooperative insurance schemes of coastal villages provide a more appropriate parallel than a casino. A "better" probability forecast would lead to lower premiums charged and less volatile fluctuations in the cash reserves of the village. Note that the Bayesian paradigm does not constrain one to interpret model distributions as subjective probabilities, unless one believes the model to be empirically adequate for the task at hand. In geophysics, this is rarely the case. When a probability forecast is interpreted as the objective probability of an event, the odds on that event can be easily computed as one divided by the probability of the event, and one need not favour taking either side of the wager. (Here we are using "odds-for" not "odds-to", the difference being whether of not the stake is returned; odds of one to one are equivalent to odds of two for one.) The critical question is how to compute sustainable odds based on information from imperfect models. We suggest that this breaks the symmetry between the odds-on an event and the odds-against it. While a probability distribution can always be translated into odds, interpreting the odds on a set of events might result in "implied-probabilities" that sum to more than one. And/or the set of odds may be incomplete, not covering all events. We ask whether or not probabilities based on imperfect models can be expected to yield probabilistic odds which are sustainable. Evidence is provided that suggest this is not the case. Even with very good models (good in an Root-Mean-Square sense), the risk of ruin of probabilistic odds is significantly higher than might be expected. Methods for constructing model-based non-probabilistic odds which are sustainable are discussed. The aim here is to be relevant to real world decision support, and so unrealistic assumptions of equal knowledge, equal compute power, or equal access to information are to be avoided. Finally, the use of non-probabilistic odds as a method for communicating deep uncertainty (uncertainty in a probability forecast itself) is discussed in the context of other methods, such as stating one's subjective probability that the models will prove inadequate in each particular instance (that is, the Probability of a "Big Surprise").

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-03-01

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.

MapReduce Based Parallel Bayesian Network for Manufacturing Quality Control

NASA Astrophysics Data System (ADS)

Zheng, Mao-Kuan; Ming, Xin-Guo; Zhang, Xian-Yu; Li, Guo-Ming

2017-09-01

Increasing complexity of industrial products and manufacturing processes have challenged conventional statistics based quality management approaches in the circumstances of dynamic production. A Bayesian network and big data analytics integrated approach for manufacturing process quality analysis and control is proposed. Based on Hadoop distributed architecture and MapReduce parallel computing model, big volume and variety quality related data generated during the manufacturing process could be dealt with. Artificial intelligent algorithms, including Bayesian network learning, classification and reasoning, are embedded into the Reduce process. Relying on the ability of the Bayesian network in dealing with dynamic and uncertain problem and the parallel computing power of MapReduce, Bayesian network of impact factors on quality are built based on prior probability distribution and modified with posterior probability distribution. A case study on hull segment manufacturing precision management for ship and offshore platform building shows that computing speed accelerates almost directly proportionally to the increase of computing nodes. It is also proved that the proposed model is feasible for locating and reasoning of root causes, forecasting of manufacturing outcome, and intelligent decision for precision problem solving. The integration of bigdata analytics and BN method offers a whole new perspective in manufacturing quality control.

Optimized lower leg injury probability curves from post-mortem human subject tests under axial impacts

PubMed Central

Yoganandan, Narayan; Arun, Mike W.J.; Pintar, Frank A.; Szabo, Aniko

2015-01-01

Objective Derive optimum injury probability curves to describe human tolerance of the lower leg using parametric survival analysis. Methods The study re-examined lower leg PMHS data from a large group of specimens. Briefly, axial loading experiments were conducted by impacting the plantar surface of the foot. Both injury and non-injury tests were included in the testing process. They were identified by pre- and posttest radiographic images and detailed dissection following the impact test. Fractures included injuries to the calcaneus and distal tibia-fibula complex (including pylon), representing severities at the Abbreviated Injury Score (AIS) level 2+. For the statistical analysis, peak force was chosen as the main explanatory variable and the age was chosen as the co-variable. Censoring statuses depended on experimental outcomes. Parameters from the parametric survival analysis were estimated using the maximum likelihood approach and the dfbetas statistic was used to identify overly influential samples. The best fit from the Weibull, log-normal and log-logistic distributions was based on the Akaike Information Criterion. Plus and minus 95% confidence intervals were obtained for the optimum injury probability distribution. The relative sizes of the interval were determined at predetermined risk levels. Quality indices were described at each of the selected probability levels. Results The mean age, stature and weight: 58.2 ± 15.1 years, 1.74 ± 0.08 m and 74.9 ± 13.8 kg. Excluding all overly influential tests resulted in the tightest confidence intervals. The Weibull distribution was the most optimum function compared to the other two distributions. A majority of quality indices were in the good category for this optimum distribution when results were extracted for 25-, 45- and 65-year-old at five, 25 and 50% risk levels age groups for lower leg fracture. For 25, 45 and 65 years, peak forces were 8.1, 6.5, and 5.1 kN at 5% risk; 9.6, 7.7, and 6.1 kN at 25% risk; and 10.4, 8.3, and 6.6 kN at 50% risk, respectively. Conclusions This study derived axial loading-induced injury risk curves based on survival analysis using peak force and specimen age; adopting different censoring schemes; considering overly influential samples in the analysis; and assessing the quality of the distribution at discrete probability levels. Because procedures used in the present survival analysis are accepted by international automotive communities, current optimum human injury probability distributions can be used at all risk levels with more confidence in future crashworthiness applications for automotive and other disciplines. PMID:25307381

On the emergence of a generalised Gamma distribution. Application to traded volume in financial markets

NASA Astrophysics Data System (ADS)

Duarte Queirós, S. M.

2005-08-01

This letter reports on a stochastic dynamical scenario whose associated stationary probability density function is exactly a generalised form, with a power law instead of exponencial decay, of the ubiquitous Gamma distribution. This generalisation, also known as F-distribution, was empirically proposed for the first time to adjust for high-frequency stock traded volume distributions in financial markets and verified in experiments with granular material. The dynamical assumption presented herein is based on local temporal fluctuations of the average value of the observable under study. This proposal is related to superstatistics and thus to the current nonextensive statistical mechanics framework. For the specific case of stock traded volume, we connect the local fluctuations in the mean stock traded volume with the typical herding behaviour presented by financial traders. Last of all, NASDAQ 1 and 2 minute stock traded volume sequences and probability density functions are numerically reproduced.

Representation of complex probabilities and complex Gibbs sampling

NASA Astrophysics Data System (ADS)

Salcedo, Lorenzo Luis

2018-03-01

Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the wellknown sign problem. The complex Langevin approach amounts to effectively construct a positive distribution on the complexified manifold reproducing the expectation values of the observables through their analytical extension. Here we discuss the direct construction of such positive distributions paying attention to their localization on the complexified manifold. Explicit localized representations are obtained for complex probabilities defined on Abelian and non Abelian groups. The viability and performance of a complex version of the heat bath method, based on such representations, is analyzed.

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2011-07-01

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density pnXY(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for pnXY(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

One-dimensional soil temperature assimilation experiment based on unscented particle filter and Common Land Model

NASA Astrophysics Data System (ADS)

Fu, Xiao Lei; Jin, Bao Ming; Jiang, Xiao Lei; Chen, Cheng

2018-06-01

Data assimilation is an efficient way to improve the simulation/prediction accuracy in many fields of geosciences especially in meteorological and hydrological applications. This study takes unscented particle filter (UPF) as an example to test its performance at different two probability distribution, Gaussian and Uniform distributions with two different assimilation frequencies experiments (1) assimilating hourly in situ soil surface temperature, (2) assimilating the original Moderate Resolution Imaging Spectroradiometer (MODIS) Land Surface Temperature (LST) once per day. The numerical experiment results show that the filter performs better when increasing the assimilation frequency. In addition, UPF is efficient for improving the soil variables (e.g., soil temperature) simulation/prediction accuracy, though it is not sensitive to the probability distribution for observation error in soil temperature assimilation.

The Statistical Value of Raw Fluorescence Signal in Luminex xMAP Based Multiplex Immunoassays

PubMed Central

Breen, Edmond J.; Tan, Woei; Khan, Alamgir

2016-01-01

Tissue samples (plasma, saliva, serum or urine) from 169 patients classified as either normal or having one of seven possible diseases are analysed across three 96-well plates for the presences of 37 analytes using cytokine inflammation multiplexed immunoassay panels. Censoring for concentration data caused problems for analysis of the low abundant analytes. Using fluorescence analysis over concentration based analysis allowed analysis of these low abundant analytes. Mixed-effects analysis on the resulting fluorescence and concentration responses reveals a combination of censoring and mapping the fluorescence responses to concentration values, through a 5PL curve, changed observed analyte concentrations. Simulation verifies this, by showing a dependence on the mean florescence response and its distribution on the observed analyte concentration levels. Differences from normality, in the fluorescence responses, can lead to differences in concentration estimates and unreliable probabilities for treatment effects. It is seen that when fluorescence responses are normally distributed, probabilities of treatment effects for fluorescence based t-tests has greater statistical power than the same probabilities from concentration based t-tests. We add evidence that the fluorescence response, unlike concentration values, doesn’t require censoring and we show with respect to differential analysis on the fluorescence responses that background correction is not required. PMID:27243383

Optimum space shuttle launch times relative to natural environment

NASA Technical Reports Server (NTRS)

King, R. L.

1977-01-01

The probabilities of favorable and unfavorable weather conditions for launch and landing of the STS under different criteria were computed for every three hours on a yearly basis using 14 years of weather data. These temporal probability distributions were considered for three sets of weather criteria encompassing benign, moderate and severe weather conditions for both Kennedy Space Center and for Edwards Air Force Base. In addition, the conditional probabilities were computed for unfavorable weather conditions occurring after a delay which may or may not be due to weather conditions. Also for KSC, the probabilities of favorable landing conditions at various times after favorable launch conditions have prevailed. The probabilities were computed to indicate the significance of each weather element to the overall result.

The Shape of Things to Come: The Computational Pictograph as a Bridge from Combinatorial Space to Outcome Distribution

ERIC Educational Resources Information Center

Abrahamson, Dor

2006-01-01

This snapshot introduces a computer-based representation and activity that enables students to simultaneously "see" the combinatorial space of a stochastic device (e.g., dice, spinner, coins) and its outcome distribution. The author argues that the "ambiguous" representation fosters student insight into probability. [Snapshots are subject to peer…

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.

Stimulated luminescence emission from localized recombination in randomly distributed defects.

PubMed

Jain, Mayank; Guralnik, Benny; Andersen, Martin Thalbitzer

2012-09-26

We present a new kinetic model describing localized electronic recombination through the excited state of the donor (d) to an acceptor (a) centre in luminescent materials. In contrast to the existing models based on the localized transition model (LTM) of Halperin and Braner (1960 Phys. Rev. 117 408-15) which assumes a fixed d → a tunnelling probability for the entire crystal, our model is based on nearest-neighbour recombination within randomly distributed centres. Such a random distribution can occur through the entire volume or within the defect complexes of the dosimeter, and implies that the tunnelling probability varies with the donor-acceptor (d-a) separation distance. We first develop an 'exact kinetic model' that incorporates this variation in tunnelling probabilities, and evolves both in spatial as well as temporal domains. We then develop a simplified one-dimensional, semi-analytical model that evolves only in the temporal domain. An excellent agreement is observed between thermally and optically stimulated luminescence (TL and OSL) results produced from the two models. In comparison to the first-order kinetic behaviour of the LTM of Halperin and Braner (1960 Phys. Rev. 117 408-15), our model results in a highly asymmetric TL peak; this peak can be understood to derive from a continuum of several first-order TL peaks. Our model also shows an extended power law behaviour for OSL (or prompt luminescence), which is expected from localized recombination mechanisms in materials with random distribution of centres.

Testing option pricing with the Edgeworth expansion

NASA Astrophysics Data System (ADS)

Balieiro Filho, Ruy Gabriel; Rosenfeld, Rogerio

2004-12-01

There is a well-developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments.

Assessing risk based on uncertain avalanche activity patterns

NASA Astrophysics Data System (ADS)

Zeidler, Antonia; Fromm, Reinhard

2015-04-01

Avalanches may affect critical infrastructure and may cause great economic losses. The planning horizon of infrastructures, e.g. hydropower generation facilities, reaches well into the future. Based on the results of previous studies on the effect of changing meteorological parameters (precipitation, temperature) and the effect on avalanche activity we assume that there will be a change of the risk pattern in future. The decision makers need to understand what the future might bring to best formulate their mitigation strategies. Therefore, we explore a commercial risk software to calculate risk for the coming years that might help in decision processes. The software @risk, is known to many larger companies, and therefore we explore its capabilities to include avalanche risk simulations in order to guarantee a comparability of different risks. In a first step, we develop a model for a hydropower generation facility that reflects the problem of changing avalanche activity patterns in future by selecting relevant input parameters and assigning likely probability distributions. The uncertain input variables include the probability of avalanches affecting an object, the vulnerability of an object, the expected costs for repairing the object and the expected cost due to interruption. The crux is to find the distribution that best represents the input variables under changing meteorological conditions. Our focus is on including the uncertain probability of avalanches based on the analysis of past avalanche data and expert knowledge. In order to explore different likely outcomes we base the analysis on three different climate scenarios (likely, worst case, baseline). For some variables, it is possible to fit a distribution to historical data, whereas in cases where the past dataset is insufficient or not available the software allows to select from over 30 different distribution types. The Monte Carlo simulation uses the probability distribution of uncertain variables using all valid combinations of the values of input variables to simulate all possible outcomes. In our case the output is the expected risk (Euro/year) for each object (e.g. water intake) considered and the entire hydropower generation system. The output is again a distribution that is interpreted by the decision makers as the final strategy depends on the needs and requirements of the end-user, which may be driven by personal preferences. In this presentation, we will show a way on how we used the uncertain information on avalanche activity in future to subsequently use it in a commercial risk software and therefore bringing the knowledge of natural hazard experts to decision makers.

Collective odor source estimation and search in time-variant airflow environments using mobile robots.

PubMed

Meng, Qing-Hao; Yang, Wei-Xing; Wang, Yang; Zeng, Ming

2011-01-01

This paper addresses the collective odor source localization (OSL) problem in a time-varying airflow environment using mobile robots. A novel OSL methodology which combines odor-source probability estimation and multiple robots' search is proposed. The estimation phase consists of two steps: firstly, the separate probability-distribution map of odor source is estimated via Bayesian rules and fuzzy inference based on a single robot's detection events; secondly, the separate maps estimated by different robots at different times are fused into a combined map by way of distance based superposition. The multi-robot search behaviors are coordinated via a particle swarm optimization algorithm, where the estimated odor-source probability distribution is used to express the fitness functions. In the process of OSL, the estimation phase provides the prior knowledge for the searching while the searching verifies the estimation results, and both phases are implemented iteratively. The results of simulations for large-scale advection-diffusion plume environments and experiments using real robots in an indoor airflow environment validate the feasibility and robustness of the proposed OSL method.

Collective Odor Source Estimation and Search in Time-Variant Airflow Environments Using Mobile Robots

PubMed Central

Meng, Qing-Hao; Yang, Wei-Xing; Wang, Yang; Zeng, Ming

2011-01-01

This paper addresses the collective odor source localization (OSL) problem in a time-varying airflow environment using mobile robots. A novel OSL methodology which combines odor-source probability estimation and multiple robots’ search is proposed. The estimation phase consists of two steps: firstly, the separate probability-distribution map of odor source is estimated via Bayesian rules and fuzzy inference based on a single robot’s detection events; secondly, the separate maps estimated by different robots at different times are fused into a combined map by way of distance based superposition. The multi-robot search behaviors are coordinated via a particle swarm optimization algorithm, where the estimated odor-source probability distribution is used to express the fitness functions. In the process of OSL, the estimation phase provides the prior knowledge for the searching while the searching verifies the estimation results, and both phases are implemented iteratively. The results of simulations for large-scale advection–diffusion plume environments and experiments using real robots in an indoor airflow environment validate the feasibility and robustness of the proposed OSL method. PMID:22346650

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

Probability versus representativeness in infancy: can infants use naïve physics to adjust population base rates in probabilistic inference?

PubMed

Denison, Stephanie; Trikutam, Pallavi; Xu, Fei

2014-08-01

A rich tradition in developmental psychology explores physical reasoning in infancy. However, no research to date has investigated whether infants can reason about physical objects that behave probabilistically, rather than deterministically. Physical events are often quite variable, in that similar-looking objects can be placed in similar contexts with different outcomes. Can infants rapidly acquire probabilistic physical knowledge, such as some leaves fall and some glasses break by simply observing the statistical regularity with which objects behave and apply that knowledge in subsequent reasoning? We taught 11-month-old infants physical constraints on objects and asked them to reason about the probability of different outcomes when objects were drawn from a large distribution. Infants could have reasoned either by using the perceptual similarity between the samples and larger distributions or by applying physical rules to adjust base rates and estimate the probabilities. Infants learned the physical constraints quickly and used them to estimate probabilities, rather than relying on similarity, a version of the representativeness heuristic. These results indicate that infants can rapidly and flexibly acquire physical knowledge about objects following very brief exposure and apply it in subsequent reasoning. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina

2016-01-01

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

Wireless cellular networks with Pareto-distributed call holding times

NASA Astrophysics Data System (ADS)

Rodriguez-Dagnino, Ramon M.; Takagi, Hideaki

2001-07-01

Nowadays, there is a growing interest in providing internet to mobile users. For instance, NTT DoCoMo in Japan deploys an important mobile phone network with that offers the Internet service, named 'i-mode', to more than 17 million subscribers. Internet traffic measurements show that the session duration of Call Holding Time (CHT) has probability distributions with heavy-tails, which tells us that they depart significantly from the traffic statistics of traditional voice services. In this environment, it is particularly important to know the number of handovers during a call for a network designer to make an appropriate dimensioning of virtual circuits for a wireless cell. The handover traffic has a direct impact on the Quality of Service (QoS); e.g. the service disruption due to the handover failure may significantly degrade the specified QoS of time-constrained services. In this paper, we first study the random behavior of the number of handovers during a call, where we assume that the CHT are Pareto distributed (heavy-tail distribution), and the Cell Residence Times (CRT) are exponentially distributed. Our approach is based on renewal theory arguments. We present closed-form formulae for the probability mass function (pmf) of the number of handovers during a Pareto distributed CHT, and obtain the probability of call completion as well as handover rates. Most of the formulae are expressed in terms of the Whittaker's function. We compare the Pareto case with cases of $k(subscript Erlang and hyperexponential distributions for the CHT.

Risk-based maintenance of ethylene oxide production facilities.

PubMed

Khan, Faisal I; Haddara, Mahmoud R

2004-05-20

This paper discusses a methodology for the design of an optimum inspection and maintenance program. The methodology, called risk-based maintenance (RBM) is based on integrating a reliability approach and a risk assessment strategy to obtain an optimum maintenance schedule. First, the likely equipment failure scenarios are formulated. Out of many likely failure scenarios, the ones, which are most probable, are subjected to a detailed study. Detailed consequence analysis is done for the selected scenarios. Subsequently, these failure scenarios are subjected to a fault tree analysis to determine their probabilities. Finally, risk is computed by combining the results of the consequence and the probability analyses. The calculated risk is compared against known acceptable criteria. The frequencies of the maintenance tasks are obtained by minimizing the estimated risk. A case study involving an ethylene oxide production facility is presented. Out of the five most hazardous units considered, the pipeline used for the transportation of the ethylene is found to have the highest risk. Using available failure data and a lognormal reliability distribution function human health risk factors are calculated. Both societal risk factors and individual risk factors exceeded the acceptable risk criteria. To determine an optimal maintenance interval, a reverse fault tree analysis was used. The maintenance interval was determined such that the original high risk is brought down to an acceptable level. A sensitivity analysis is also undertaken to study the impact of changing the distribution of the reliability model as well as the error in the distribution parameters on the maintenance interval.

Maximum Entropy Principle for Transportation

NASA Astrophysics Data System (ADS)

Bilich, F.; DaSilva, R.

2008-11-01

In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utility concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.

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.

A quantile-based Time at Risk: A new approach for assessing risk in financial markets

NASA Astrophysics Data System (ADS)

Bolgorian, Meysam; Raei, Reza

2013-11-01

In this paper, we provide a new measure for evaluation of risk in financial markets. This measure is based on the return interval of critical events in financial markets or other investment situations. Our main goal was to devise a model like Value at Risk (VaR). As VaR, for a given financial asset, probability level and time horizon, gives a critical value such that the likelihood of loss on the asset over the time horizon exceeds this value is equal to the given probability level, our concept of Time at Risk (TaR), using a probability distribution function of return intervals, provides a critical time such that the probability that the return interval of a critical event exceeds this time equals the given probability level. As an empirical application, we applied our model to data from the Tehran Stock Exchange Price Index (TEPIX) as a financial asset (market portfolio) and reported the results.

Moving on From Representativeness: Testing the Utility of the Global Drug Survey.

PubMed

Barratt, Monica J; Ferris, Jason A; Zahnow, Renee; Palamar, Joseph J; Maier, Larissa J; Winstock, Adam R

2017-01-01

A decline in response rates in traditional household surveys, combined with increased internet coverage and decreased research budgets, has resulted in increased attractiveness of web survey research designs based on purposive and voluntary opt-in sampling strategies. In the study of hidden or stigmatised behaviours, such as cannabis use, web survey methods are increasingly common. However, opt-in web surveys are often heavily criticised due to their lack of sampling frame and unknown representativeness. In this article, we outline the current state of the debate about the relevance of pursuing representativeness, the state of probability sampling methods, and the utility of non-probability, web survey methods especially for accessing hidden or minority populations. Our article has two aims: (1) to present a comprehensive description of the methodology we use at Global Drug Survey (GDS), an annual cross-sectional web survey and (2) to compare the age and sex distributions of cannabis users who voluntarily completed (a) a household survey or (b) a large web-based purposive survey (GDS), across three countries: Australia, the United States, and Switzerland. We find that within each set of country comparisons, the demographic distributions among recent cannabis users are broadly similar, demonstrating that the age and sex distributions of those who volunteer to be surveyed are not vastly different between these non-probability and probability methods. We conclude that opt-in web surveys of hard-to-reach populations are an efficient way of gaining in-depth understanding of stigmatised behaviours and are appropriate, as long as they are not used to estimate drug use prevalence of the general population.

Moving on From Representativeness: Testing the Utility of the Global Drug Survey

PubMed Central

Barratt, Monica J; Ferris, Jason A; Zahnow, Renee; Palamar, Joseph J; Maier, Larissa J; Winstock, Adam R

2017-01-01

A decline in response rates in traditional household surveys, combined with increased internet coverage and decreased research budgets, has resulted in increased attractiveness of web survey research designs based on purposive and voluntary opt-in sampling strategies. In the study of hidden or stigmatised behaviours, such as cannabis use, web survey methods are increasingly common. However, opt-in web surveys are often heavily criticised due to their lack of sampling frame and unknown representativeness. In this article, we outline the current state of the debate about the relevance of pursuing representativeness, the state of probability sampling methods, and the utility of non-probability, web survey methods especially for accessing hidden or minority populations. Our article has two aims: (1) to present a comprehensive description of the methodology we use at Global Drug Survey (GDS), an annual cross-sectional web survey and (2) to compare the age and sex distributions of cannabis users who voluntarily completed (a) a household survey or (b) a large web-based purposive survey (GDS), across three countries: Australia, the United States, and Switzerland. We find that within each set of country comparisons, the demographic distributions among recent cannabis users are broadly similar, demonstrating that the age and sex distributions of those who volunteer to be surveyed are not vastly different between these non-probability and probability methods. We conclude that opt-in web surveys of hard-to-reach populations are an efficient way of gaining in-depth understanding of stigmatised behaviours and are appropriate, as long as they are not used to estimate drug use prevalence of the general population. PMID:28924351

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.

Neural Mechanisms for Integrating Prior Knowledge and Likelihood in Value-Based Probabilistic Inference

PubMed Central

Ting, Chih-Chung; Yu, Chia-Chen; Maloney, Laurence T.

2015-01-01

In Bayesian decision theory, knowledge about the probabilities of possible outcomes is captured by a prior distribution and a likelihood function. The prior reflects past knowledge and the likelihood summarizes current sensory information. The two combined (integrated) form a posterior distribution that allows estimation of the probability of different possible outcomes. In this study, we investigated the neural mechanisms underlying Bayesian integration using a novel lottery decision task in which both prior knowledge and likelihood information about reward probability were systematically manipulated on a trial-by-trial basis. Consistent with Bayesian integration, as sample size increased, subjects tended to weigh likelihood information more compared with prior information. Using fMRI in humans, we found that the medial prefrontal cortex (mPFC) correlated with the mean of the posterior distribution, a statistic that reflects the integration of prior knowledge and likelihood of reward probability. Subsequent analysis revealed that both prior and likelihood information were represented in mPFC and that the neural representations of prior and likelihood in mPFC reflected changes in the behaviorally estimated weights assigned to these different sources of information in response to changes in the environment. Together, these results establish the role of mPFC in prior-likelihood integration and highlight its involvement in representing and integrating these distinct sources of information. PMID:25632152

Estimating the Probability of Traditional Copying, Conditional on Answer-Copying Statistics.

PubMed

Allen, Jeff; Ghattas, Andrew

2016-06-01

Statistics for detecting copying on multiple-choice tests produce p values measuring the probability of a value at least as large as that observed, under the null hypothesis of no copying. The posterior probability of copying is arguably more relevant than the p value, but cannot be derived from Bayes' theorem unless the population probability of copying and probability distribution of the answer-copying statistic under copying are known. In this article, the authors develop an estimator for the posterior probability of copying that is based on estimable quantities and can be used with any answer-copying statistic. The performance of the estimator is evaluated via simulation, and the authors demonstrate how to apply the formula using actual data. Potential uses, generalizability to other types of cheating, and limitations of the approach are discussed.

GIS-based probability assessment of natural hazards in forested landscapes of Central and South-Eastern Europe.

PubMed

Lorz, C; Fürst, C; Galic, Z; Matijasic, D; Podrazky, V; Potocic, N; Simoncic, P; Strauch, M; Vacik, H; Makeschin, F

2010-12-01

We assessed the probability of three major natural hazards--windthrow, drought, and forest fire--for Central and South-Eastern European forests which are major threats for the provision of forest goods and ecosystem services. In addition, we analyzed spatial distribution and implications for a future oriented management of forested landscapes. For estimating the probability of windthrow, we used rooting depth and average wind speed. Probabilities of drought and fire were calculated from climatic and total water balance during growing season. As an approximation to climate change scenarios, we used a simplified approach with a general increase of pET by 20%. Monitoring data from the pan-European forests crown condition program and observed burnt areas and hot spots from the European Forest Fire Information System were used to test the plausibility of probability maps. Regions with high probabilities of natural hazard are identified and management strategies to minimize probability of natural hazards are discussed. We suggest future research should focus on (i) estimating probabilities using process based models (including sensitivity analysis), (ii) defining probability in terms of economic loss, (iii) including biotic hazards, (iv) using more detailed data sets on natural hazards, forest inventories and climate change scenarios, and (v) developing a framework of adaptive risk management.

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

Modeling marine oily wastewater treatment by a probabilistic agent-based approach.

PubMed

Jing, Liang; Chen, Bing; Zhang, Baiyu; Ye, Xudong

2018-02-01

This study developed a novel probabilistic agent-based approach for modeling of marine oily wastewater treatment processes. It begins first by constructing a probability-based agent simulation model, followed by a global sensitivity analysis and a genetic algorithm-based calibration. The proposed modeling approach was tested through a case study of the removal of naphthalene from marine oily wastewater using UV irradiation. The removal of naphthalene was described by an agent-based simulation model using 8 types of agents and 11 reactions. Each reaction was governed by a probability parameter to determine its occurrence. The modeling results showed that the root mean square errors between modeled and observed removal rates were 8.73 and 11.03% for calibration and validation runs, respectively. Reaction competition was analyzed by comparing agent-based reaction probabilities, while agents' heterogeneity was visualized by plotting their real-time spatial distribution, showing a strong potential for reactor design and process optimization. Copyright © 2017 Elsevier Ltd. All rights reserved.

Distribution of Hydrocarbon-Utilizing Microorganisms and Hydrocarbon Biodegradation Potentials in Alaskan Continental Shelf Areas

PubMed Central

Roubal, George; Atlas, Ronald M.

1978-01-01

Hydrocarbon-utilizing microorganisms were enumerated from Alaskan continental shelf areas by using plate counts and a new most-probable-number procedure based on mineralization of 14C-labeled hydrocarbons. Hydrocarbon utilizers were ubiquitously distributed, with no significant overall concentration differences between sampling regions or between surface water and sediment samples. There were, however, significant seasonal differences in numbers of hydrocarbon utilizers. Distribution of hydrocarbon utilizers within Cook Inlet was positively correlated with occurrence of hydrocarbons in the environment. Hydrocarbon biodegradation potentials were measured by using 14C-radiolabeled hydrocarbon-spiked crude oil. There was no significant correlation between numbers of hydrocarbon utilizers and hydrocarbon biodegradation potentials. The biodegradation potentials showed large seasonal variations in the Beaufort Sea, probably due to seasonal depletion of available nutrients. Non-nutrient-limited biodegradation potentials followed the order hexadecane > naphthalene ≫ pristane > benzanthracene. In Cook Inlet, biodegradation potentials for hexadecane and naphthalene were dependent on availability of inorganic nutrients. Biodegradation potentials for pristane and benzanthracene were restricted, probably by resistance to attack by available enzymes in the indigenous population. PMID:655706

Dynamic probability control limits for risk-adjusted Bernoulli CUSUM charts.

PubMed

Zhang, Xiang; Woodall, William H

2015-11-10

The risk-adjusted Bernoulli cumulative sum (CUSUM) chart developed by Steiner et al. (2000) is an increasingly popular tool for monitoring clinical and surgical performance. In practice, however, the use of a fixed control limit for the chart leads to a quite variable in-control average run length performance for patient populations with different risk score distributions. To overcome this problem, we determine simulation-based dynamic probability control limits (DPCLs) patient-by-patient for the risk-adjusted Bernoulli CUSUM charts. By maintaining the probability of a false alarm at a constant level conditional on no false alarm for previous observations, our risk-adjusted CUSUM charts with DPCLs have consistent in-control performance at the desired level with approximately geometrically distributed run lengths. Our simulation results demonstrate that our method does not rely on any information or assumptions about the patients' risk distributions. The use of DPCLs for risk-adjusted Bernoulli CUSUM charts allows each chart to be designed for the corresponding particular sequence of patients for a surgeon or hospital. Copyright © 2015 John Wiley & Sons, Ltd.

Reinforcement Learning for Constrained Energy Trading Games With Incomplete Information.

PubMed

Wang, Huiwei; Huang, Tingwen; Liao, Xiaofeng; Abu-Rub, Haitham; Chen, Guo

2017-10-01

This paper considers the problem of designing adaptive learning algorithms to seek the Nash equilibrium (NE) of the constrained energy trading game among individually strategic players with incomplete information. In this game, each player uses the learning automaton scheme to generate the action probability distribution based on his/her private information for maximizing his own averaged utility. It is shown that if one of admissible mixed-strategies converges to the NE with probability one, then the averaged utility and trading quantity almost surely converge to their expected ones, respectively. For the given discontinuous pricing function, the utility function has already been proved to be upper semicontinuous and payoff secure which guarantee the existence of the mixed-strategy NE. By the strict diagonal concavity of the regularized Lagrange function, the uniqueness of NE is also guaranteed. Finally, an adaptive learning algorithm is provided to generate the strategy probability distribution for seeking the mixed-strategy NE.

The estimated lifetime probability of acquiring human papillomavirus in the United States.

PubMed

Chesson, Harrell W; Dunne, Eileen F; Hariri, Susan; Markowitz, Lauri E

2014-11-01

Estimates of the lifetime probability of acquiring human papillomavirus (HPV) can help to quantify HPV incidence, illustrate how common HPV infection is, and highlight the importance of HPV vaccination. We developed a simple model, based primarily on the distribution of lifetime numbers of sex partners across the population and the per-partnership probability of acquiring HPV, to estimate the lifetime probability of acquiring HPV in the United States in the time frame before HPV vaccine availability. We estimated the average lifetime probability of acquiring HPV among those with at least 1 opposite sex partner to be 84.6% (range, 53.6%-95.0%) for women and 91.3% (range, 69.5%-97.7%) for men. Under base case assumptions, more than 80% of women and men acquire HPV by age 45 years. Our results are consistent with estimates in the existing literature suggesting a high lifetime probability of HPV acquisition and are supported by cohort studies showing high cumulative HPV incidence over a relatively short period, such as 3 to 5 years.

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.

Electron number probability distributions for correlated wave functions.

PubMed

Francisco, E; Martín Pendás, A; Blanco, M A

2007-03-07

Efficient formulas for computing the probability of finding exactly an integer number of electrons in an arbitrarily chosen volume are only known for single-determinant wave functions [E. Cances et al., Theor. Chem. Acc. 111, 373 (2004)]. In this article, an algebraic method is presented that extends these formulas to the case of multideterminant wave functions and any number of disjoint volumes. The derived expressions are applied to compute the probabilities within the atomic domains derived from the space partitioning based on the quantum theory of atoms in molecules. Results for a series of test molecules are presented, paying particular attention to the effects of electron correlation and of some numerical approximations on the computed probabilities.

Estimation of distributional parameters for censored trace level water quality data: 1. Estimation techniques

USGS Publications Warehouse

Gilliom, Robert J.; Helsel, Dennis R.

1986-01-01

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations, for determining the best performing parameter estimation method for any particular data set. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.

Estimation of distributional parameters for censored trace level water quality data. 1. Estimation Techniques

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

Gilliom, R.J.; Helsel, D.R.

1986-02-01

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensoredmore » observations, for determining the best performing parameter estimation method for any particular data det. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.« less

Estimation of distributional parameters for censored trace-level water-quality data

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

Gilliom, R.J.; Helsel, D.R.

1984-01-01

A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water-sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations,more » for determining the best-performing parameter estimation method for any particular data set. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least-squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification. 6 figs., 6 tabs.« less

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.

(abstract) Infrared Cirrus and Future Space Based Astronomy

NASA Technical Reports Server (NTRS)

Gautier, T. N.

1993-01-01

A review of the known properties of the distribution of infrared cirrus is followed by a discussion of the implications of cirrus on observations from space. Probable limitations on space observations due to IR cirrus.

A probabilistic Sperner's theorem, with applications to the problem of retrieving information from a data base

NASA Technical Reports Server (NTRS)

Baumert, L. D.; Mceliece, R. J.; Rodemich, E. R.; Rumsey, H., Jr.

1978-01-01

The design of an optimal merged keycode data base information retrieval system is detailed. A probability distribution of n-bit binary words that minimized false drops was developed for the case where the set of desired records was a subset of tagged records.

Robust optimization based upon statistical theory.

PubMed

Sobotta, B; Söhn, M; Alber, M

2010-08-01

Organ movement is still the biggest challenge in cancer treatment despite advances in online imaging. Due to the resulting geometric uncertainties, the delivered dose cannot be predicted precisely at treatment planning time. Consequently, all associated dose metrics (e.g., EUD and maxDose) are random variables with a patient-specific probability distribution. The method that the authors propose makes these distributions the basis of the optimization and evaluation process. The authors start from a model of motion derived from patient-specific imaging. On a multitude of geometry instances sampled from this model, a dose metric is evaluated. The resulting pdf of this dose metric is termed outcome distribution. The approach optimizes the shape of the outcome distribution based on its mean and variance. This is in contrast to the conventional optimization of a nominal value (e.g., PTV EUD) computed on a single geometry instance. The mean and variance allow for an estimate of the expected treatment outcome along with the residual uncertainty. Besides being applicable to the target, the proposed method also seamlessly includes the organs at risk (OARs). The likelihood that a given value of a metric is reached in the treatment is predicted quantitatively. This information reveals potential hazards that may occur during the course of the treatment, thus helping the expert to find the right balance between the risk of insufficient normal tissue sparing and the risk of insufficient tumor control. By feeding this information to the optimizer, outcome distributions can be obtained where the probability of exceeding a given OAR maximum and that of falling short of a given target goal can be minimized simultaneously. The method is applicable to any source of residual motion uncertainty in treatment delivery. Any model that quantifies organ movement and deformation in terms of probability distributions can be used as basis for the algorithm. Thus, it can generate dose distributions that are robust against interfraction and intrafraction motion alike, effectively removing the need for indiscriminate safety margins.

Efficient Iris Recognition Based on Optimal Subfeature Selection and Weighted Subregion Fusion

PubMed Central

Deng, Ning

2014-01-01

In this paper, we propose three discriminative feature selection strategies and weighted subregion matching method to improve the performance of iris recognition system. Firstly, we introduce the process of feature extraction and representation based on scale invariant feature transformation (SIFT) in detail. Secondly, three strategies are described, which are orientation probability distribution function (OPDF) based strategy to delete some redundant feature keypoints, magnitude probability distribution function (MPDF) based strategy to reduce dimensionality of feature element, and compounded strategy combined OPDF and MPDF to further select optimal subfeature. Thirdly, to make matching more effective, this paper proposes a novel matching method based on weighted sub-region matching fusion. Particle swarm optimization is utilized to accelerate achieve different sub-region's weights and then weighted different subregions' matching scores to generate the final decision. The experimental results, on three public and renowned iris databases (CASIA-V3 Interval, Lamp, andMMU-V1), demonstrate that our proposed methods outperform some of the existing methods in terms of correct recognition rate, equal error rate, and computation complexity. PMID:24683317

Efficient iris recognition based on optimal subfeature selection and weighted subregion fusion.

PubMed

Chen, Ying; Liu, Yuanning; Zhu, Xiaodong; He, Fei; Wang, Hongye; Deng, Ning

2014-01-01

In this paper, we propose three discriminative feature selection strategies and weighted subregion matching method to improve the performance of iris recognition system. Firstly, we introduce the process of feature extraction and representation based on scale invariant feature transformation (SIFT) in detail. Secondly, three strategies are described, which are orientation probability distribution function (OPDF) based strategy to delete some redundant feature keypoints, magnitude probability distribution function (MPDF) based strategy to reduce dimensionality of feature element, and compounded strategy combined OPDF and MPDF to further select optimal subfeature. Thirdly, to make matching more effective, this paper proposes a novel matching method based on weighted sub-region matching fusion. Particle swarm optimization is utilized to accelerate achieve different sub-region's weights and then weighted different subregions' matching scores to generate the final decision. The experimental results, on three public and renowned iris databases (CASIA-V3 Interval, Lamp, and MMU-V1), demonstrate that our proposed methods outperform some of the existing methods in terms of correct recognition rate, equal error rate, and computation complexity.

Evolution of the microstructure during the process of consolidation and bonding in soft granular solids.

PubMed

Yohannes, B; Gonzalez, M; Abebe, A; Sprockel, O; Nikfar, F; Kiang, S; Cuitiño, A M

2016-04-30

The evolution of microstructure during powder compaction process was investigated using a discrete particle modeling, which accounts for particle size distribution and material properties, such as plasticity, elasticity, and inter-particle bonding. The material properties were calibrated based on powder compaction experiments and validated based on tensile strength test experiments for lactose monohydrate and microcrystalline cellulose, which are commonly used excipient in pharmaceutical industry. The probability distribution function and the orientation of contact forces were used to study the evolution of the microstructure during the application of compaction pressure, unloading, and ejection of the compact from the die. The probability distribution function reveals that the compression contact forces increase as the compaction force increases (or the relative density increases), while the maximum value of the tensile contact forces remains the same. During unloading of the compaction pressure, the distribution approaches a normal distribution with a mean value of zero. As the contact forces evolve, the anisotropy of the powder bed also changes. Particularly, during loading, the compression contact forces are aligned along the direction of the compaction pressure, whereas the tensile contact forces are oriented perpendicular to direction of the compaction pressure. After ejection, the contact forces become isotropic. Copyright © 2016 Elsevier B.V. All rights reserved.

Site-to-Source Finite Fault Distance Probability Distribution in Probabilistic Seismic Hazard and the Relationship Between Minimum Distances

NASA Astrophysics Data System (ADS)

Ortega, R.; Gutierrez, E.; Carciumaru, D. D.; Huesca-Perez, E.

2017-12-01

We present a method to compute the conditional and no-conditional probability density function (PDF) of the finite fault distance distribution (FFDD). Two cases are described: lines and areas. The case of lines has a simple analytical solution while, in the case of areas, the geometrical probability of a fault based on the strike, dip, and fault segment vertices is obtained using the projection of spheres in a piecewise rectangular surface. The cumulative distribution is computed by measuring the projection of a sphere of radius r in an effective area using an algorithm that estimates the area of a circle within a rectangle. In addition, we introduce the finite fault distance metrics. This distance is the distance where the maximum stress release occurs within the fault plane and generates a peak ground motion. Later, we can apply the appropriate ground motion prediction equations (GMPE) for PSHA. The conditional probability of distance given magnitude is also presented using different scaling laws. A simple model of constant distribution of the centroid at the geometrical mean is discussed, in this model hazard is reduced at the edges because the effective size is reduced. Nowadays there is a trend of using extended source distances in PSHA, however it is not possible to separate the fault geometry from the GMPE. With this new approach, it is possible to add fault rupture models separating geometrical and propagation effects.

Second look at the spread of epidemics on networks

NASA Astrophysics Data System (ADS)

Kenah, Eben; Robins, James M.

2007-09-01

In an important paper, Newman [Phys. Rev. E66, 016128 (2002)] claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In the Appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.

Study of Heavy-ion Induced Fission for Heavy Element Synthesis

NASA Astrophysics Data System (ADS)

Nishio, K.; Ikezoe, H.; Hofmann, S.; Ackermann, D.; Aritomo, Y.; Comas, V. F.; Düllmann, Ch. E.; Heinz, S.; Heredia, J. A.; Heßberger, F. P.; Hirose, K.; Khuyagbaatar, J.; Kindler, B.; Kojouharov, I.; Lommel, B.; Makii, M.; Mann, R.; Mitsuoka, S.; Nishinaka, I.; Ohtsuki, T.; Saro, S.; Schädel, M.; Popeko, A. G.; Türler, A.; Wakabayashi, Y.; Watanabe, Y.; Yakushev, A.; Yeremin, A.

2014-05-01

Fission fragment mass distributions were measured in heavy-ion induced fission of 238U. The mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and quasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model for the reactions of 30Si+238U and 34S+238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections of 263,264Sg and 267,268Hs, produced by 30Si+238U and 34S+238U, respectively. It is also suggested that sub-barrier energies can be used for heavy element synthesis.

Probabilistic properties of wavelets in kinetic surface roughening

NASA Astrophysics Data System (ADS)

Bershadskii, A.

2001-08-01

Using the data of a recent numerical simulation [M. Ahr and M. Biehl, Phys. Rev. E 62, 1773 (2000)] of homoepitaxial growth it is shown that the observed probability distribution of a wavelet based measure of the growing surface roughness is consistent with a stretched log-normal distribution and the corresponding branching dimension depends on the level of particle desorption.

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

PubMed Central

Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass. PMID:24278198

Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation W = a(D2H)b was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.

On the Empirical Importance of the Conditional Skewness Assumption in Modelling the Relationship between Risk and Return

NASA Astrophysics Data System (ADS)

Pipień, M.

2008-09-01

We present the results of an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal Capital Asset Pricing Model, proposed by Merton we built a general sampling distribution suitable in analysing this relationship. The most important feature of our assumptions is that the skewness of the conditional distribution of returns is used as an alternative source of relation between risk and return. This general specification relates to Skewed Generalized Autoregressive Conditionally Heteroscedastic-in-Mean model. In order to make conditional distribution of financial returns skewed we considered the unified approach based on the inverse probability integral transformation. In particular, we applied hidden truncation mechanism, inverse scale factors, order statistics concept, Beta and Bernstein distribution transformations and also a constructive method. Based on the daily excess returns on the Warsaw Stock Exchange Index we checked the empirical importance of the conditional skewness assumption on the relation between risk and return on the Warsaw Stock Market. We present posterior probabilities of all competing specifications as well as the posterior analysis of the positive sign of the tested relationship.

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.

Exploiting vibrational resonance in weak-signal detection

NASA Astrophysics Data System (ADS)

Ren, Yuhao; Pan, Yan; Duan, Fabing; Chapeau-Blondeau, François; Abbott, Derek

2017-08-01

In this paper, we investigate the first exploitation of the vibrational resonance (VR) effect to detect weak signals in the presence of strong background noise. By injecting a series of sinusoidal interference signals of the same amplitude but with different frequencies into a generalized correlation detector, we show that the detection probability can be maximized at an appropriate interference amplitude. Based on a dual-Dirac probability density model, we compare the VR method with the stochastic resonance approach via adding dichotomous noise. The compared results indicate that the VR method can achieve a higher detection probability for a wider variety of noise distributions.

Exploiting vibrational resonance in weak-signal detection.

PubMed

Ren, Yuhao; Pan, Yan; Duan, Fabing; Chapeau-Blondeau, François; Abbott, Derek

2017-08-01

In this paper, we investigate the first exploitation of the vibrational resonance (VR) effect to detect weak signals in the presence of strong background noise. By injecting a series of sinusoidal interference signals of the same amplitude but with different frequencies into a generalized correlation detector, we show that the detection probability can be maximized at an appropriate interference amplitude. Based on a dual-Dirac probability density model, we compare the VR method with the stochastic resonance approach via adding dichotomous noise. The compared results indicate that the VR method can achieve a higher detection probability for a wider variety of noise distributions.

A Method for Evaluating Tuning Functions of Single Neurons based on Mutual Information Maximization

NASA Astrophysics Data System (ADS)

Brostek, Lukas; Eggert, Thomas; Ono, Seiji; Mustari, Michael J.; Büttner, Ulrich; Glasauer, Stefan

2011-03-01

We introduce a novel approach for evaluation of neuronal tuning functions, which can be expressed by the conditional probability of observing a spike given any combination of independent variables. This probability can be estimated out of experimentally available data. By maximizing the mutual information between the probability distribution of the spike occurrence and that of the variables, the dependence of the spike on the input variables is maximized as well. We used this method to analyze the dependence of neuronal activity in cortical area MSTd on signals related to movement of the eye and retinal image movement.

Bounding the Failure Probability Range of Polynomial Systems Subject to P-box Uncertainties

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2012-01-01

This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.

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

Friar, James Lewis; Goldman, Terrance J.; Pérez-Mercader, J.

In this paper, we apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdf's), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdf's results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. Finally, we separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropymore » for size-class distributions with uniform bin sizes.« less

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.

Statistical computation of tolerance limits

NASA Technical Reports Server (NTRS)

Wheeler, J. T.

1993-01-01

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Methods for combining payload parameter variations with input environment. [calculating design limit loads compatible with probabilistic structural design criteria

NASA Technical Reports Server (NTRS)

Merchant, D. H.

1976-01-01

Methods are presented for calculating design limit loads compatible with probabilistic structural design criteria. The approach is based on the concept that the desired limit load, defined as the largest load occurring in a mission, is a random variable having a specific probability distribution which may be determined from extreme-value theory. The design limit load, defined as a particular of this random limit load, is the value conventionally used in structural design. Methods are presented for determining the limit load probability distributions from both time-domain and frequency-domain dynamic load simulations. Numerical demonstrations of the method are also presented.

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.

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

NASA Astrophysics Data System (ADS)

Le, Jia-Liang; Bažant, Zdeněk P.; Bazant, Martin Z.

2011-07-01

Engineering structures must be designed for an extremely low failure probability such as 10 -6, which is beyond the means of direct verification by histogram testing. This is not a problem for brittle or ductile materials because the type of probability distribution of structural strength is fixed and known, making it possible to predict the tail probabilities from the mean and variance. It is a problem, though, for quasibrittle materials for which the type of strength distribution transitions from Gaussian to Weibullian as the structure size increases. These are heterogeneous materials with brittle constituents, characterized by material inhomogeneities that are not negligible compared to the structure size. Examples include concrete, fiber composites, coarse-grained or toughened ceramics, rocks, sea ice, rigid foams and bone, as well as many materials used in nano- and microscale devices. This study presents a unified theory of strength and lifetime for such materials, based on activation energy controlled random jumps of the nano-crack front, and on the nano-macro multiscale transition of tail probabilities. Part I of this study deals with the case of monotonic and sustained (or creep) loading, and Part II with fatigue (or cyclic) loading. On the scale of the representative volume element of material, the probability distribution of strength has a Gaussian core onto which a remote Weibull tail is grafted at failure probability of the order of 10 -3. With increasing structure size, the Weibull tail penetrates into the Gaussian core. The probability distribution of static (creep) lifetime is related to the strength distribution by the power law for the static crack growth rate, for which a physical justification is given. The present theory yields a simple relation between the exponent of this law and the Weibull moduli for strength and lifetime. The benefit is that the lifetime distribution can be predicted from short-time tests of the mean size effect on strength and tests of the power law for the crack growth rate. The theory is shown to match closely numerous test data on strength and static lifetime of ceramics and concrete, and explains why their histograms deviate systematically from the straight line in Weibull scale. Although the present unified theory is built on several previous advances, new contributions are here made to address: (i) a crack in a disordered nano-structure (such as that of hydrated Portland cement), (ii) tail probability of a fiber bundle (or parallel coupling) model with softening elements, (iii) convergence of this model to the Gaussian distribution, (iv) the stress-life curve under constant load, and (v) a detailed random walk analysis of crack front jumps in an atomic lattice. The nonlocal behavior is captured in the present theory through the finiteness of the number of links in the weakest-link model, which explains why the mean size effect coincides with that of the previously formulated nonlocal Weibull theory. Brittle structures correspond to the large-size limit of the present theory. An important practical conclusion is that the safety factors for strength and tolerable minimum lifetime for large quasibrittle structures (e.g., concrete structures and composite airframes or ship hulls, as well as various micro-devices) should be calculated as a function of structure size and geometry.

Probability estimates of seismic event occurrence compared to health hazards - Forecasting Taipei's Earthquakes

NASA Astrophysics Data System (ADS)

Fung, D. C. N.; Wang, J. P.; Chang, S. H.; Chang, S. C.

2014-12-01

Using a revised statistical model built on past seismic probability models, the probability of different magnitude earthquakes occurring within variable timespans can be estimated. The revised model is based on Poisson distribution and includes the use of best-estimate values of the probability distribution of different magnitude earthquakes recurring from a fault from literature sources. Our study aims to apply this model to the Taipei metropolitan area with a population of 7 million, which lies in the Taipei Basin and is bounded by two normal faults: the Sanchaio and Taipei faults. The Sanchaio fault is suggested to be responsible for previous large magnitude earthquakes, such as the 1694 magnitude 7 earthquake in northwestern Taipei (Cheng et. al., 2010). Based on a magnitude 7 earthquake return period of 543 years, the model predicts the occurrence of a magnitude 7 earthquake within 20 years at 1.81%, within 79 years at 6.77% and within 300 years at 21.22%. These estimates increase significantly when considering a magnitude 6 earthquake; the chance of one occurring within the next 20 years is estimated to be 3.61%, 79 years at 13.54% and 300 years at 42.45%. The 79 year period represents the average lifespan of the Taiwan population. In contrast, based on data from 2013, the probability of Taiwan residents experiencing heart disease or malignant neoplasm is 11.5% and 29%. The inference of this study is that the calculated risk that the Taipei population is at from a potentially damaging magnitude 6 or greater earthquake occurring within their lifetime is just as great as of suffering from a heart attack or other health ailments.

Benford's law and the FSD distribution of economic behavioral micro data

NASA Astrophysics Data System (ADS)

Villas-Boas, Sofia B.; Fu, Qiuzi; Judge, George

2017-11-01

In this paper, we focus on the first significant digit (FSD) distribution of European micro income data and use information theoretic-entropy based methods to investigate the degree to which Benford's FSD law is consistent with the nature of these economic behavioral systems. We demonstrate that Benford's law is not an empirical phenomenon that occurs only in important distributions in physical statistics, but that it also arises in self-organizing dynamic economic behavioral systems. The empirical likelihood member of the minimum divergence-entropy family, is used to recover country based income FSD probability density functions and to demonstrate the implications of using a Benford prior reference distribution in economic behavioral system information recovery.

Ubiquity of Benford's law and emergence of the reciprocal distribution

DOE PAGES

Friar, James Lewis; Goldman, Terrance J.; Pérez-Mercader, J.

2016-04-07

In this paper, we apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdf's), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdf's results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. Finally, we separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropymore » for size-class distributions with uniform bin sizes.« less

UQ for Decision Making: How (at least five) Kinds of Probability Might Come Into Play

NASA Astrophysics Data System (ADS)

Smith, L. A.

2013-12-01

In 1959 IJ Good published the discussion "Kinds of Probability" in Science. Good identified (at least) five kinds. The need for (at least) a sixth kind of probability when quantifying uncertainty in the context of climate science is discussed. This discussion brings out the differences in weather-like forecasting tasks and climate-links tasks, with a focus on the effective use both of science and of modelling in support of decision making. Good also introduced the idea of a "Dynamic probability" a probability one expects to change without any additional empirical evidence; the probabilities assigned by a chess playing program when it is only half thorough its analysis being an example. This case is contrasted with the case of "Mature probabilities" where a forecast algorithm (or model) has converged on its asymptotic probabilities and the question hinges in whether or not those probabilities are expected to change significantly before the event in question occurs, even in the absence of new empirical evidence. If so, then how might one report and deploy such immature probabilities in scientific-support of decision-making rationally? Mature Probability is suggested as a useful sixth kind, although Good would doubtlessly argue that we can get by with just one, effective communication with decision makers may be enhanced by speaking as if the others existed. This again highlights the distinction between weather-like contexts and climate-like contexts. In the former context one has access to a relevant climatology (a relevant, arguably informative distribution prior to any model simulations), in the latter context that information is not available although one can fall back on the scientific basis upon which the model itself rests, and estimate the probability that the model output is in fact misinformative. This subjective "probability of a big surprise" is one way to communicate the probability of model-based information holding in practice, the probability that the information the model-based probability is conditioned on holds. It is argued that no model-based climate-like probability forecast is complete without a quantitative estimate of its own irrelevance, and that the clear identification of model-based probability forecasts as mature or immature, are critical elements for maintaining the credibility of science-based decision support, and can shape uncertainty quantification more widely.

Discrepancy-based error estimates for Quasi-Monte Carlo III. Error distributions and central limits

NASA Astrophysics Data System (ADS)

Hoogland, Jiri; Kleiss, Ronald

1997-04-01

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-random point sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit Theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.

Zero-truncated negative binomial - Erlang distribution

NASA Astrophysics Data System (ADS)

Bodhisuwan, Winai; Pudprommarat, Chookait; Bodhisuwan, Rujira; Saothayanun, Luckhana

2017-11-01

The zero-truncated negative binomial-Erlang distribution is introduced. It is developed from negative binomial-Erlang distribution. In this work, the probability mass function is derived and some properties are included. The parameters of the zero-truncated negative binomial-Erlang distribution are estimated by using the maximum likelihood estimation. Finally, the proposed distribution is applied to real data, the number of methamphetamine in the Bangkok, Thailand. Based on the results, it shows that the zero-truncated negative binomial-Erlang distribution provided a better fit than the zero-truncated Poisson, zero-truncated negative binomial, zero-truncated generalized negative-binomial and zero-truncated Poisson-Lindley distributions for this data.

On the use of Bayesian Monte-Carlo in evaluation of nuclear data

NASA Astrophysics Data System (ADS)

De Saint Jean, Cyrille; Archier, Pascal; Privas, Edwin; Noguere, Gilles

2017-09-01

As model parameters, necessary ingredients of theoretical models, are not always predicted by theory, a formal mathematical framework associated to the evaluation work is needed to obtain the best set of parameters (resonance parameters, optical models, fission barrier, average width, multigroup cross sections) with Bayesian statistical inference by comparing theory to experiment. The formal rule related to this methodology is to estimate the posterior density probability function of a set of parameters by solving an equation of the following type: pdf(posterior) ˜ pdf(prior) × a likelihood function. A fitting procedure can be seen as an estimation of the posterior density probability of a set of parameters (referred as x→?) knowing a prior information on these parameters and a likelihood which gives the probability density function of observing a data set knowing x→?. To solve this problem, two major paths could be taken: add approximations and hypothesis and obtain an equation to be solved numerically (minimum of a cost function or Generalized least Square method, referred as GLS) or use Monte-Carlo sampling of all prior distributions and estimate the final posterior distribution. Monte Carlo methods are natural solution for Bayesian inference problems. They avoid approximations (existing in traditional adjustment procedure based on chi-square minimization) and propose alternative in the choice of probability density distribution for priors and likelihoods. This paper will propose the use of what we are calling Bayesian Monte Carlo (referred as BMC in the rest of the manuscript) in the whole energy range from thermal, resonance and continuum range for all nuclear reaction models at these energies. Algorithms will be presented based on Monte-Carlo sampling and Markov chain. The objectives of BMC are to propose a reference calculation for validating the GLS calculations and approximations, to test probability density distributions effects and to provide the framework of finding global minimum if several local minimums exist. Application to resolved resonance, unresolved resonance and continuum evaluation as well as multigroup cross section data assimilation will be presented.

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.

Statistical analysis of PM₁₀ concentrations at different locations in Malaysia.

PubMed

Sansuddin, Nurulilyana; Ramli, Nor Azam; Yahaya, Ahmad Shukri; Yusof, Noor Faizah Fitri Md; Ghazali, Nurul Adyani; Madhoun, Wesam Ahmed Al

2011-09-01

Malaysia has experienced several haze events since the 1980s as a consequence of the transboundary movement of air pollutants emitted from forest fires and open burning activities. Hazy episodes can result from local activities and be categorized as "localized haze". General probability distributions (i.e., gamma and log-normal) were chosen to analyze the PM(10) concentrations data at two different types of locations in Malaysia: industrial (Johor Bahru and Nilai) and residential (Kota Kinabalu and Kuantan). These areas were chosen based on their frequently high PM(10) concentration readings. The best models representing the areas were chosen based on their performance indicator values. The best distributions provided the probability of exceedances and the return period between the actual and predicted concentrations based on the threshold limit given by the Malaysian Ambient Air Quality Guidelines (24-h average of 150 μg/m(3)) for PM(10) concentrations. The short-term prediction for PM(10) exceedances in 14 days was obtained using the autoregressive model.

Comparing the ISO-recommended and the cumulative data-reduction algorithms in S-on-1 laser damage test by a reverse approach method

NASA Astrophysics Data System (ADS)

Zorila, Alexandru; Stratan, Aurel; Nemes, George

2018-01-01

We compare the ISO-recommended (the standard) data-reduction algorithm used to determine the surface laser-induced damage threshold of optical materials by the S-on-1 test with two newly suggested algorithms, both named "cumulative" algorithms/methods, a regular one and a limit-case one, intended to perform in some respects better than the standard one. To avoid additional errors due to real experiments, a simulated test is performed, named the reverse approach. This approach simulates the real damage experiments, by generating artificial test-data of damaged and non-damaged sites, based on an assumed, known damage threshold fluence of the target and on a given probability distribution function to induce the damage. In this work, a database of 12 sets of test-data containing both damaged and non-damaged sites was generated by using four different reverse techniques and by assuming three specific damage probability distribution functions. The same value for the threshold fluence was assumed, and a Gaussian fluence distribution on each irradiated site was considered, as usual for the S-on-1 test. Each of the test-data was independently processed by the standard and by the two cumulative data-reduction algorithms, the resulting fitted probability distributions were compared with the initially assumed probability distribution functions, and the quantities used to compare these algorithms were determined. These quantities characterize the accuracy and the precision in determining the damage threshold and the goodness of fit of the damage probability curves. The results indicate that the accuracy in determining the absolute damage threshold is best for the ISO-recommended method, the precision is best for the limit-case of the cumulative method, and the goodness of fit estimator (adjusted R-squared) is almost the same for all three algorithms.

Optimum space shuttle launch times relative to natural environment

NASA Technical Reports Server (NTRS)

King, R. L.

1977-01-01

Three sets of meteorological criteria were analyzed to determine the probabilities of favorable launch and landing conditions. Probabilities were computed for every 3 hours on a yearly basis using 14 years of weather data. These temporal probability distributions, applicable to the three sets of weather criteria encompassing benign, moderate and severe weather conditions, were computed for both Kennedy Space Center (KSC) and Edwards Air Force Base. In addition, conditional probabilities were computed for unfavorable weather conditions occurring after a delay which may or may not be due to weather conditions. Also, for KSC, the probabilities of favorable landing conditions at various times after favorable launch conditions have prevailed have been computed so that mission probabilities may be more accurately computed for those time periods when persistence strongly correlates weather conditions. Moreover, the probabilities and conditional probabilities of the occurrence of both favorable and unfavorable events for each individual criterion were computed to indicate the significance of each weather element to the overall result.

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.

Gesture Recognition Based on the Probability Distribution of Arm Trajectories

NASA Astrophysics Data System (ADS)

Wan, Khairunizam; Sawada, Hideyuki

The use of human motions for the interaction between humans and computers is becoming an attractive alternative to verbal media, especially through the visual interpretation of the human body motion. In particular, hand gestures are used as non-verbal media for the humans to communicate with machines that pertain to the use of the human gestures to interact with them. This paper introduces a 3D motion measurement of the human upper body for the purpose of the gesture recognition, which is based on the probability distribution of arm trajectories. In this study, by examining the characteristics of the arm trajectories given by a signer, motion features are selected and classified by using a fuzzy technique. Experimental results show that the use of the features extracted from arm trajectories effectively works on the recognition of dynamic gestures of a human, and gives a good performance to classify various gesture patterns.

An information measure for class discrimination. [in remote sensing of crop observation

NASA Technical Reports Server (NTRS)

Shen, S. S.; Badhwar, G. D.

1986-01-01

This article describes a separability measure for class discrimination. This measure is based on the Fisher information measure for estimating the mixing proportion of two classes. The Fisher information measure not only provides a means to assess quantitatively the information content in the features for separating classes, but also gives the lower bound for the variance of any unbiased estimate of the mixing proportion based on observations of the features. Unlike most commonly used separability measures, this measure is not dependent on the form of the probability distribution of the features and does not imply a specific estimation procedure. This is important because the probability distribution function that describes the data for a given class does not have simple analytic forms, such as a Gaussian. Results of applying this measure to compare the information content provided by three Landsat-derived feature vectors for the purpose of separating small grains from other crops are presented.

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling.

PubMed

Richard, David; Speck, Thomas

2018-03-28

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersaturations and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large effective interfacial tension.

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling

NASA Astrophysics Data System (ADS)

Richard, David; Speck, Thomas

2018-03-01

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersaturations and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large effective interfacial tension.

[Establishment of the mathematic model of total quantum statistical moment standard similarity for application to medical theoretical research].

PubMed

He, Fu-yuan; Deng, Kai-wen; Huang, Sheng; Liu, Wen-long; Shi, Ji-lian

2013-09-01

The paper aims to elucidate and establish a new mathematic model: the total quantum statistical moment standard similarity (TQSMSS) on the base of the original total quantum statistical moment model and to illustrate the application of the model to medical theoretical research. The model was established combined with the statistical moment principle and the normal distribution probability density function properties, then validated and illustrated by the pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical method for them, and by analysis of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving the Buyanghanwu-decoction extract. The established model consists of four mainly parameters: (1) total quantum statistical moment similarity as ST, an overlapped area by two normal distribution probability density curves in conversion of the two TQSM parameters; (2) total variability as DT, a confidence limit of standard normal accumulation probability which is equal to the absolute difference value between the two normal accumulation probabilities within integration of their curve nodical; (3) total variable probability as 1-Ss, standard normal distribution probability within interval of D(T); (4) total variable probability (1-beta)alpha and (5) stable confident probability beta(1-alpha): the correct probability to make positive and negative conclusions under confident coefficient alpha. With the model, we had analyzed the TQSMS similarities of pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical methods for them were at range of 0.3852-0.9875 that illuminated different pharmacokinetic behaviors of each other; and the TQSMS similarities (ST) of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving Buyanghuanwu-decoction-extract were at range of 0.6842-0.999 2 that showed different constituents with various solvent extracts. The TQSMSS can characterize the sample similarity, by which we can quantitate the correct probability with the test of power under to make positive and negative conclusions no matter the samples come from same population under confident coefficient a or not, by which we can realize an analysis at both macroscopic and microcosmic levels, as an important similar analytical method for medical theoretical research.

Climate sensitivity estimated from temperature reconstructions of the Last Glacial Maximum

NASA Astrophysics Data System (ADS)

Schmittner, A.; Urban, N.; Shakun, J. D.; Mahowald, N. M.; Clark, P. U.; Bartlein, P. J.; Mix, A. C.; Rosell-Melé, A.

2011-12-01

In 1959 IJ Good published the discussion "Kinds of Probability" in Science. Good identified (at least) five kinds. The need for (at least) a sixth kind of probability when quantifying uncertainty in the context of climate science is discussed. This discussion brings out the differences in weather-like forecasting tasks and climate-links tasks, with a focus on the effective use both of science and of modelling in support of decision making. Good also introduced the idea of a "Dynamic probability" a probability one expects to change without any additional empirical evidence; the probabilities assigned by a chess playing program when it is only half thorough its analysis being an example. This case is contrasted with the case of "Mature probabilities" where a forecast algorithm (or model) has converged on its asymptotic probabilities and the question hinges in whether or not those probabilities are expected to change significantly before the event in question occurs, even in the absence of new empirical evidence. If so, then how might one report and deploy such immature probabilities in scientific-support of decision-making rationally? Mature Probability is suggested as a useful sixth kind, although Good would doubtlessly argue that we can get by with just one, effective communication with decision makers may be enhanced by speaking as if the others existed. This again highlights the distinction between weather-like contexts and climate-like contexts. In the former context one has access to a relevant climatology (a relevant, arguably informative distribution prior to any model simulations), in the latter context that information is not available although one can fall back on the scientific basis upon which the model itself rests, and estimate the probability that the model output is in fact misinformative. This subjective "probability of a big surprise" is one way to communicate the probability of model-based information holding in practice, the probability that the information the model-based probability is conditioned on holds. It is argued that no model-based climate-like probability forecast is complete without a quantitative estimate of its own irrelevance, and that the clear identification of model-based probability forecasts as mature or immature, are critical elements for maintaining the credibility of science-based decision support, and can shape uncertainty quantification more widely.

Combined risk assessment of nonstationary monthly water quality based on Markov chain and time-varying copula.

PubMed

Shi, Wei; Xia, Jun

2017-02-01

Water quality risk management is a global hot research linkage with the sustainable water resource development. Ammonium nitrogen (NH 3 -N) and permanganate index (COD Mn ) as the focus indicators in Huai River Basin, are selected to reveal their joint transition laws based on Markov theory. The time-varying moments model with either time or land cover index as explanatory variables is applied to build the time-varying marginal distributions of water quality time series. Time-varying copula model, which takes the non-stationarity in the marginal distribution and/or the time variation in dependence structure between water quality series into consideration, is constructed to describe a bivariate frequency analysis for NH 3 -N and COD Mn series at the same monitoring gauge. The larger first-order Markov joint transition probability indicates water quality state Class V w , Class IV and Class III will occur easily in the water body of Bengbu Sluice. Both marginal distribution and copula models are nonstationary, and the explanatory variable time yields better performance than land cover index in describing the non-stationarities in the marginal distributions. In modelling the dependence structure changes, time-varying copula has a better fitting performance than the copula with the constant or the time-trend dependence parameter. The largest synchronous encounter risk probability of NH 3 -N and COD Mn simultaneously reaching Class V is 50.61%, while the asynchronous encounter risk probability is largest when NH 3 -N and COD Mn is inferior to class V and class IV water quality standards, respectively.

A methodology for the transfer of probabilities between accident severity categories

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

Whitlow, J. D.; Neuhauser, K. S.

A methodology has been developed which allows the accident probabilities associated with one accident-severity category scheme to be transferred to another severity category scheme. The methodology requires that the schemes use a common set of parameters to define the categories. The transfer of accident probabilities is based on the relationships between probability of occurrence and each of the parameters used to define the categories. Because of the lack of historical data describing accident environments in engineering terms, these relationships may be difficult to obtain directly for some parameters. Numerical models or experienced judgement are often needed to obtain the relationships.more » These relationships, even if they are not exact, allow the accident probability associated with any severity category to be distributed within that category in a manner consistent with accident experience, which in turn will allow the accident probability to be appropriately transferred to a different category scheme.« less

Application of Archimedean copulas to the impact assessment of hydro-climatic variables in semi-arid aquifers of western India

NASA Astrophysics Data System (ADS)

Wable, Pawan S.; Jha, Madan K.

2018-02-01

The effects of rainfall and the El Niño Southern Oscillation (ENSO) on groundwater in a semi-arid basin of India were analyzed using Archimedean copulas considering 17 years of data for monsoon rainfall, post-monsoon groundwater level (PMGL) and ENSO Index. The evaluated dependence among these hydro-climatic variables revealed that PMGL-Rainfall and PMGL-ENSO Index pairs have significant dependence. Hence, these pairs were used for modeling dependence by employing four types of Archimedean copulas: Ali-Mikhail-Haq, Clayton, Gumbel-Hougaard, and Frank. For the copula modeling, the results of probability distributions fitting to these hydro-climatic variables indicated that the PMGL and rainfall time series are best represented by Weibull and lognormal distributions, respectively, while the non-parametric kernel-based normal distribution is the most suitable for the ENSO Index. Further, the PMGL-Rainfall pair is best modeled by the Clayton copula, and the PMGL-ENSO Index pair is best modeled by the Frank copula. The Clayton copula-based conditional probability of PMGL being less than or equal to its average value at a given mean rainfall is above 70% for 33% of the study area. In contrast, the spatial variation of the Frank copula-based probability of PMGL being less than or equal to its average value is 35-40% in 23% of the study area during El Niño phase, while it is below 15% in 35% of the area during the La Niña phase. This copula-based methodology can be applied under data-scarce conditions for exploring the impacts of rainfall and ENSO on groundwater at basin scales.

A Dirichlet-Multinomial Bayes Classifier for Disease Diagnosis with Microbial Compositions.

PubMed

Gao, Xiang; Lin, Huaiying; Dong, Qunfeng

2017-01-01

Dysbiosis of microbial communities is associated with various human diseases, raising the possibility of using microbial compositions as biomarkers for disease diagnosis. We have developed a Bayes classifier by modeling microbial compositions with Dirichlet-multinomial distributions, which are widely used to model multicategorical count data with extra variation. The parameters of the Dirichlet-multinomial distributions are estimated from training microbiome data sets based on maximum likelihood. The posterior probability of a microbiome sample belonging to a disease or healthy category is calculated based on Bayes' theorem, using the likelihood values computed from the estimated Dirichlet-multinomial distribution, as well as a prior probability estimated from the training microbiome data set or previously published information on disease prevalence. When tested on real-world microbiome data sets, our method, called DMBC (for Dirichlet-multinomial Bayes classifier), shows better classification accuracy than the only existing Bayesian microbiome classifier based on a Dirichlet-multinomial mixture model and the popular random forest method. The advantage of DMBC is its built-in automatic feature selection, capable of identifying a subset of microbial taxa with the best classification accuracy between different classes of samples based on cross-validation. This unique ability enables DMBC to maintain and even improve its accuracy at modeling species-level taxa. The R package for DMBC is freely available at https://github.com/qunfengdong/DMBC. IMPORTANCE By incorporating prior information on disease prevalence, Bayes classifiers have the potential to estimate disease probability better than other common machine-learning methods. Thus, it is important to develop Bayes classifiers specifically tailored for microbiome data. Our method shows higher classification accuracy than the only existing Bayesian classifier and the popular random forest method, and thus provides an alternative option for using microbial compositions for disease diagnosis.

A new probability distribution model of turbulent irradiance based on Born perturbation theory

NASA Astrophysics Data System (ADS)

Wang, Hongxing; Liu, Min; Hu, Hao; Wang, Qian; Liu, Xiguo

2010-10-01

The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled. Theory reliably describes the behavior in the weak turbulence regime, but theoretical description in the strong and whole turbulence regimes are still controversial. Based on Born perturbation theory, the physical manifestations and correlations of three typical PDF models (Rice-Nakagami, exponential-Bessel and negative-exponential distribution) were theoretically analyzed. It is shown that these models can be derived by separately making circular-Gaussian, strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory, which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications. In addition, a common shortcoming of the three models is that they are all approximations. A new model, called the Maclaurin-spread distribution, is proposed without any approximation except for assuming the correlation coefficient to be zero. So, it is considered that the new model can exactly reflect the Born perturbation theory. Simulated results prove the accuracy of this new model.

Financial derivative pricing under probability operator via Esscher transfomation

NASA Astrophysics Data System (ADS)

Achi, Godswill U.

2014-10-01

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing9 where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula using the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φx(u) of Xt we recuperate the Black-Scholes formula for financial derivative prices.

The discrete Laplace exponential family and estimation of Y-STR haplotype frequencies.

PubMed

Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels

2013-07-21

Estimating haplotype frequencies is important in e.g. forensic genetics, where the frequencies are needed to calculate the likelihood ratio for the evidential weight of a DNA profile found at a crime scene. Estimation is naturally based on a population model, motivating the investigation of the Fisher-Wright model of evolution for haploid lineage DNA markers. An exponential family (a class of probability distributions that is well understood in probability theory such that inference is easily made by using existing software) called the 'discrete Laplace distribution' is described. We illustrate how well the discrete Laplace distribution approximates a more complicated distribution that arises by investigating the well-known population genetic Fisher-Wright model of evolution by a single-step mutation process. It was shown how the discrete Laplace distribution can be used to estimate haplotype frequencies for haploid lineage DNA markers (such as Y-chromosomal short tandem repeats), which in turn can be used to assess the evidential weight of a DNA profile found at a crime scene. This was done by making inference in a mixture of multivariate, marginally independent, discrete Laplace distributions using the EM algorithm to estimate the probabilities of membership of a set of unobserved subpopulations. The discrete Laplace distribution can be used to estimate haplotype frequencies with lower prediction error than other existing estimators. Furthermore, the calculations could be performed on a normal computer. This method was implemented in the freely available open source software R that is supported on Linux, MacOS and MS Windows. Copyright © 2013 Elsevier Ltd. All rights reserved.

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

NASA Technical Reports Server (NTRS)

Cerniglia, M. C.; Douglass, A. R.; Rood, R. B.; Sparling, L. C..; Nielsen, J. E.

1999-01-01

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of understanding the relative contribution to the observations of air of either distinctly tropospheric or stratospheric origin. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High [low] potential vorticity at 300 hPa suggests that the tropopause is low [high], and the identification of the two groups helps to account for dynamic variability. Conditional probability distribution functions are used to define the statistics of the mix from both observations and model simulations. Two data sources are chosen. First, several years of ozonesonde observations are used to exploit the high vertical resolution. Second, observations made by the Halogen Occultation Experiment [HALOE] on the Upper Atmosphere Research Satellite [UARS] are used to understand the impact on the results of the spatial limitations of the ozonesonde network. The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause [about 380K]. Despite the differences in spatial and temporal sampling, the probability distribution functions are similar for the two data sources. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. By using the model, possible mechanisms for the maintenance of mix of air in the lowermost stratosphere are revealed. The relevance of the results to the assessment of the environmental impact of aircraft effluence is discussed.

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

NASA Technical Reports Server (NTRS)

Cerniglia, M. C.; Douglass, A. R.; Rood, R. B.; Sparling, L. C.; Nielsen, J. E.

1999-01-01

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of understanding the relative contribution to the observations of air of either distinctly tropospheric or stratospheric origin. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High [low] potential vorticity at 300 hPa suggests that the tropopause is low [high], and the identification of the two groups helps to account for dynamic variability. Conditional probability distribution functions are used to define the statistics of the mix from both observations and model simulations. Two data sources are chosen. First, several years of ozonesonde observations are used to exploit the high vertical resolution. Second, observations made by the Halogen Occultation Experiment [HALOE) on the Upper Atmosphere Research Satellite [UARS] are used to understand the impact on the results of the spatial limitations of the ozonesonde network. The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause [approximately 380K]. Despite the differences in spatial and temporal sampling, the probability distribution functions are similar for the two data sources. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. By using the model, possible mechanisms for the maintenance of mix of air in the lowermost stratosphere are revealed. The relevance of the results to the assessment of the environmental impact of aircraft effluence is discussed.

Analysis of mean seismic ground motion and its uncertainty based on the UCERF3 geologic slip rate model with uncertainty for California

USGS Publications Warehouse

Zeng, Yuehua

2018-01-01

The Uniform California Earthquake Rupture Forecast v.3 (UCERF3) model (Field et al., 2014) considers epistemic uncertainty in fault‐slip rate via the inclusion of multiple rate models based on geologic and/or geodetic data. However, these slip rates are commonly clustered about their mean value and do not reflect the broader distribution of possible rates and associated probabilities. Here, we consider both a double‐truncated 2σ Gaussian and a boxcar distribution of slip rates and use a Monte Carlo simulation to sample the entire range of the distribution for California fault‐slip rates. We compute the seismic hazard following the methodology and logic‐tree branch weights applied to the 2014 national seismic hazard model (NSHM) for the western U.S. region (Petersen et al., 2014, 2015). By applying a new approach developed in this study to the probabilistic seismic hazard analysis (PSHA) using precomputed rates of exceedance from each fault as a Green’s function, we reduce the computer time by about 10^5‐fold and apply it to the mean PSHA estimates with 1000 Monte Carlo samples of fault‐slip rates to compare with results calculated using only the mean or preferred slip rates. The difference in the mean probabilistic peak ground motion corresponding to a 2% in 50‐yr probability of exceedance is less than 1% on average over all of California for both the Gaussian and boxcar probability distributions for slip‐rate uncertainty but reaches about 18% in areas near faults compared with that calculated using the mean or preferred slip rates. The average uncertainties in 1σ peak ground‐motion level are 5.5% and 7.3% of the mean with the relative maximum uncertainties of 53% and 63% for the Gaussian and boxcar probability density function (PDF), respectively.

Drought forecasting in Luanhe River basin involving climatic indices

NASA Astrophysics Data System (ADS)

Ren, Weinan; Wang, Yixuan; Li, Jianzhu; Feng, Ping; Smith, Ronald J.

2017-11-01

Drought is regarded as one of the most severe natural disasters globally. This is especially the case in Tianjin City, Northern China, where drought can affect economic development and people's livelihoods. Drought forecasting, the basis of drought management, is an important mitigation strategy. In this paper, we evolve a probabilistic forecasting model, which forecasts transition probabilities from a current Standardized Precipitation Index (SPI) value to a future SPI class, based on conditional distribution of multivariate normal distribution to involve two large-scale climatic indices at the same time, and apply the forecasting model to 26 rain gauges in the Luanhe River basin in North China. The establishment of the model and the derivation of the SPI are based on the hypothesis of aggregated monthly precipitation that is normally distributed. Pearson correlation and Shapiro-Wilk normality tests are used to select appropriate SPI time scale and large-scale climatic indices. Findings indicated that longer-term aggregated monthly precipitation, in general, was more likely to be considered normally distributed and forecasting models should be applied to each gauge, respectively, rather than to the whole basin. Taking Liying Gauge as an example, we illustrate the impact of the SPI time scale and lead time on transition probabilities. Then, the controlled climatic indices of every gauge are selected by Pearson correlation test and the multivariate normality of SPI, corresponding climatic indices for current month and SPI 1, 2, and 3 months later are demonstrated using Shapiro-Wilk normality test. Subsequently, we illustrate the impact of large-scale oceanic-atmospheric circulation patterns on transition probabilities. Finally, we use a score method to evaluate and compare the performance of the three forecasting models and compare them with two traditional models which forecast transition probabilities from a current to a future SPI class. The results show that the three proposed models outperform the two traditional models and involving large-scale climatic indices can improve the forecasting accuracy.

Spatial Distribution and Conservation of Speckled Hind and Warsaw Grouper in the Atlantic Ocean off the Southeastern U.S.

PubMed Central

Farmer, Nicholas A.; Karnauskas, Mandy

2013-01-01

There is broad interest in the development of efficient marine protected areas (MPAs) to reduce bycatch and end overfishing of speckled hind (Epinephelus drummondhayi) and warsaw grouper (Hyporthodus nigritus) in the Atlantic Ocean off the southeastern U.S. We assimilated decades of data from many fishery-dependent, fishery-independent, and anecdotal sources to describe the spatial distribution of these data limited stocks. A spatial classification model was developed to categorize depth-grids based on the distribution of speckled hind and warsaw grouper point observations and identified benthic habitats. Logistic regression analysis was used to develop a quantitative model to predict the spatial distribution of speckled hind and warsaw grouper as a function of depth, latitude, and habitat. Models, controlling for sampling gear effects, were selected based on AIC and 10-fold cross validation. The best-fitting model for warsaw grouper included latitude and depth to explain 10.8% of the variability in probability of detection, with a false prediction rate of 28–33%. The best-fitting model for speckled hind, per cross-validation, included latitude and depth to explain 36.8% of the variability in probability of detection, with a false prediction rate of 25–27%. The best-fitting speckled hind model, per AIC, also included habitat, but had false prediction rates up to 36%. Speckled hind and warsaw grouper habitats followed a shelf-edge hardbottom ridge from North Carolina to southeast Florida, with speckled hind more common to the north and warsaw grouper more common to the south. The proportion of habitat classifications and model-estimated stock contained within established and proposed MPAs was computed. Existing MPAs covered 10% of probable shelf-edge habitats for speckled hind and warsaw grouper, protecting 3–8% of speckled hind and 8% of warsaw grouper stocks. Proposed MPAs could add 24% more probable shelf-edge habitat, and protect an additional 14–29% of speckled hind and 20% of warsaw grouper stocks. PMID:24260126

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.

A probability distribution model of tooth pits for evaluating time-varying mesh stiffness of pitting gears

NASA Astrophysics Data System (ADS)

Lei, Yaguo; Liu, Zongyao; Wang, Delong; Yang, Xiao; Liu, Huan; Lin, Jing

2018-06-01

Tooth damage often causes a reduction in gear mesh stiffness. Thus time-varying mesh stiffness (TVMS) can be treated as an indication of gear health conditions. This study is devoted to investigating the mesh stiffness variations of a pair of external spur gears with tooth pitting, and proposes a new model for describing tooth pitting based on probability distribution. In the model, considering the appearance and development process of tooth pitting, we model the pitting on the surface of spur gear teeth as a series of pits with a uniform distribution in the direction of tooth width and a normal distribution in the direction of tooth height, respectively. In addition, four pitting degrees, from no pitting to severe pitting, are modeled. Finally, influences of tooth pitting on TVMS are analyzed in details and the proposed model is validated by comparing with a finite element model. The comparison results show that the proposed model is effective for the TVMS evaluations of pitting gears.

On the properties of stochastic intermittency in rainfall processes.

PubMed

Molini, A; La, Barbera P; Lanza, L G

2002-01-01

In this work we propose a mixed approach to deal with the modelling of rainfall events, based on the analysis of geometrical and statistical properties of rain intermittency in time, combined with the predictability power derived from the analysis of no-rain periods distribution and from the binary decomposition of the rain signal. Some recent hypotheses on the nature of rain intermittency are reviewed too. In particular, the internal intermittent structure of a high resolution pluviometric time series covering one decade and recorded at the tipping bucket station of the University of Genova is analysed, by separating the internal intermittency of rainfall events from the inter-arrival process through a simple geometrical filtering procedure. In this way it is possible to associate no-rain intervals with a probability distribution both in virtue of their position within the event and their percentage. From this analysis, an invariant probability distribution for the no-rain periods within the events is obtained at different aggregation levels and its satisfactory agreement with a typical extreme value distribution is shown.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Estimation of the radiation-induced DNA double-strand breaks number by considering cell cycle and absorbed dose per cell nucleus

PubMed Central

Mori, Ryosuke; Matsuya, Yusuke; Yoshii, Yuji; Date, Hiroyuki

2018-01-01

Abstract DNA double-strand breaks (DSBs) are thought to be the main cause of cell death after irradiation. In this study, we estimated the probability distribution of the number of DSBs per cell nucleus by considering the DNA amount in a cell nucleus (which depends on the cell cycle) and the statistical variation in the energy imparted to the cell nucleus by X-ray irradiation. The probability estimation of DSB induction was made following these procedures: (i) making use of the Chinese Hamster Ovary (CHO)-K1 cell line as the target example, the amounts of DNA per nucleus in the logarithmic and the plateau phases of the growth curve were measured by flow cytometry with propidium iodide (PI) dyeing; (ii) the probability distribution of the DSB number per cell nucleus for each phase after irradiation with 1.0 Gy of 200 kVp X-rays was measured by means of γ-H2AX immunofluorescent staining; (iii) the distribution of the cell-specific energy deposition via secondary electrons produced by the incident X-rays was calculated by WLTrack (in-house Monte Carlo code); (iv) according to a mathematical model for estimating the DSB number per nucleus, we deduced the induction probability density of DSBs based on the measured DNA amount (depending on the cell cycle) and the calculated dose per nucleus. The model exhibited DSB induction probabilities in good agreement with the experimental results for the two phases, suggesting that the DNA amount (depending on the cell cycle) and the statistical variation in the local energy deposition are essential for estimating the DSB induction probability after X-ray exposure. PMID:29800455

Estimation of the radiation-induced DNA double-strand breaks number by considering cell cycle and absorbed dose per cell nucleus.

PubMed

Mori, Ryosuke; Matsuya, Yusuke; Yoshii, Yuji; Date, Hiroyuki

2018-05-01

DNA double-strand breaks (DSBs) are thought to be the main cause of cell death after irradiation. In this study, we estimated the probability distribution of the number of DSBs per cell nucleus by considering the DNA amount in a cell nucleus (which depends on the cell cycle) and the statistical variation in the energy imparted to the cell nucleus by X-ray irradiation. The probability estimation of DSB induction was made following these procedures: (i) making use of the Chinese Hamster Ovary (CHO)-K1 cell line as the target example, the amounts of DNA per nucleus in the logarithmic and the plateau phases of the growth curve were measured by flow cytometry with propidium iodide (PI) dyeing; (ii) the probability distribution of the DSB number per cell nucleus for each phase after irradiation with 1.0 Gy of 200 kVp X-rays was measured by means of γ-H2AX immunofluorescent staining; (iii) the distribution of the cell-specific energy deposition via secondary electrons produced by the incident X-rays was calculated by WLTrack (in-house Monte Carlo code); (iv) according to a mathematical model for estimating the DSB number per nucleus, we deduced the induction probability density of DSBs based on the measured DNA amount (depending on the cell cycle) and the calculated dose per nucleus. The model exhibited DSB induction probabilities in good agreement with the experimental results for the two phases, suggesting that the DNA amount (depending on the cell cycle) and the statistical variation in the local energy deposition are essential for estimating the DSB induction probability after X-ray exposure.

Maximum entropy principal for transportation

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

Bilich, F.; Da Silva, R.

In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utilitymore » concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.« less

Assignment of functional activations to probabilistic cytoarchitectonic areas revisited.

PubMed

Eickhoff, Simon B; Paus, Tomas; Caspers, Svenja; Grosbras, Marie-Helene; Evans, Alan C; Zilles, Karl; Amunts, Katrin

2007-07-01

Probabilistic cytoarchitectonic maps in standard reference space provide a powerful tool for the analysis of structure-function relationships in the human brain. While these microstructurally defined maps have already been successfully used in the analysis of somatosensory, motor or language functions, several conceptual issues in the analysis of structure-function relationships still demand further clarification. In this paper, we demonstrate the principle approaches for anatomical localisation of functional activations based on probabilistic cytoarchitectonic maps by exemplary analysis of an anterior parietal activation evoked by visual presentation of hand gestures. After consideration of the conceptual basis and implementation of volume or local maxima labelling, we comment on some potential interpretational difficulties, limitations and caveats that could be encountered. Extending and supplementing these methods, we then propose a supplementary approach for quantification of structure-function correspondences based on distribution analysis. This approach relates the cytoarchitectonic probabilities observed at a particular functionally defined location to the areal specific null distribution of probabilities across the whole brain (i.e., the full probability map). Importantly, this method avoids the need for a unique classification of voxels to a single cortical area and may increase the comparability between results obtained for different areas. Moreover, as distribution-based labelling quantifies the "central tendency" of an activation with respect to anatomical areas, it will, in combination with the established methods, allow an advanced characterisation of the anatomical substrates of functional activations. Finally, the advantages and disadvantages of the various methods are discussed, focussing on the question of which approach is most appropriate for a particular situation.

Greenhouse-gas emission targets for limiting global warming to 2 degrees C.

PubMed

Meinshausen, Malte; Meinshausen, Nicolai; Hare, William; Raper, Sarah C B; Frieler, Katja; Knutti, Reto; Frame, David J; Allen, Myles R

2009-04-30

More than 100 countries have adopted a global warming limit of 2 degrees C or below (relative to pre-industrial levels) as a guiding principle for mitigation efforts to reduce climate change risks, impacts and damages. However, the greenhouse gas (GHG) emissions corresponding to a specified maximum warming are poorly known owing to uncertainties in the carbon cycle and the climate response. Here we provide a comprehensive probabilistic analysis aimed at quantifying GHG emission budgets for the 2000-50 period that would limit warming throughout the twenty-first century to below 2 degrees C, based on a combination of published distributions of climate system properties and observational constraints. We show that, for the chosen class of emission scenarios, both cumulative emissions up to 2050 and emission levels in 2050 are robust indicators of the probability that twenty-first century warming will not exceed 2 degrees C relative to pre-industrial temperatures. Limiting cumulative CO(2) emissions over 2000-50 to 1,000 Gt CO(2) yields a 25% probability of warming exceeding 2 degrees C-and a limit of 1,440 Gt CO(2) yields a 50% probability-given a representative estimate of the distribution of climate system properties. As known 2000-06 CO(2) emissions were approximately 234 Gt CO(2), less than half the proven economically recoverable oil, gas and coal reserves can still be emitted up to 2050 to achieve such a goal. Recent G8 Communiqués envisage halved global GHG emissions by 2050, for which we estimate a 12-45% probability of exceeding 2 degrees C-assuming 1990 as emission base year and a range of published climate sensitivity distributions. Emissions levels in 2020 are a less robust indicator, but for the scenarios considered, the probability of exceeding 2 degrees C rises to 53-87% if global GHG emissions are still more than 25% above 2000 levels in 2020.

Migration of Dust Particles and Their Collisions with the Terrestrial Planets

NASA Technical Reports Server (NTRS)

Ipatov, S. I.; Mather, J. C.

2004-01-01

Our review of previously published papers on dust migration can be found in [1], where we also present different distributions of migrating dust particles. We considered a different set of initial orbits for the dust particles than those in the previous papers. Below we pay the main attention to the collisional probabilities of migrating dust particles with the planets based on a set of orbital elements during their evolution. Such probabilities were not calculated earlier.

A fully traits-based approach to modeling global vegetation distribution.

PubMed

van Bodegom, Peter M; Douma, Jacob C; Verheijen, Lieneke M

2014-09-23

Dynamic Global Vegetation Models (DGVMs) are indispensable for our understanding of climate change impacts. The application of traits in DGVMs is increasingly refined. However, a comprehensive analysis of the direct impacts of trait variation on global vegetation distribution does not yet exist. Here, we present such analysis as proof of principle. We run regressions of trait observations for leaf mass per area, stem-specific density, and seed mass from a global database against multiple environmental drivers, making use of findings of global trait convergence. This analysis explained up to 52% of the global variation of traits. Global trait maps, generated by coupling the regression equations to gridded soil and climate maps, showed up to orders of magnitude variation in trait values. Subsequently, nine vegetation types were characterized by the trait combinations that they possess using Gaussian mixture density functions. The trait maps were input to these functions to determine global occurrence probabilities for each vegetation type. We prepared vegetation maps, assuming that the most probable (and thus, most suited) vegetation type at each location will be realized. This fully traits-based vegetation map predicted 42% of the observed vegetation distribution correctly. Our results indicate that a major proportion of the predictive ability of DGVMs with respect to vegetation distribution can be attained by three traits alone if traits like stem-specific density and seed mass are included. We envision that our traits-based approach, our observation-driven trait maps, and our vegetation maps may inspire a new generation of powerful traits-based DGVMs.

PROCOS: computational analysis of protein-protein complexes.

PubMed

Fink, Florian; Hochrein, Jochen; Wolowski, Vincent; Merkl, Rainer; Gronwald, Wolfram

2011-09-01

One of the main challenges in protein-protein docking is a meaningful evaluation of the many putative solutions. Here we present a program (PROCOS) that calculates a probability-like measure to be native for a given complex. In contrast to scores often used for analyzing complex structures, the calculated probabilities offer the advantage of providing a fixed range of expected values. This will allow, in principle, the comparison of models corresponding to different targets that were solved with the same algorithm. Judgments are based on distributions of properties derived from a large database of native and false complexes. For complex analysis PROCOS uses these property distributions of native and false complexes together with a support vector machine (SVM). PROCOS was compared to the established scoring schemes of ZRANK and DFIRE. Employing a set of experimentally solved native complexes, high probability values above 50% were obtained for 90% of these structures. Next, the performance of PROCOS was tested on the 40 binary targets of the Dockground decoy set, on 14 targets of the RosettaDock decoy set and on 9 targets that participated in the CAPRI scoring evaluation. Again the advantage of using a probability-based scoring system becomes apparent and a reasonable number of near native complexes was found within the top ranked complexes. In conclusion, a novel fully automated method is presented that allows the reliable evaluation of protein-protein complexes. Copyright © 2011 Wiley Periodicals, Inc.

Study of heavy-ion induced fission for heavy-element synthesis

NASA Astrophysics Data System (ADS)

Nishio, K.; Ikezoe, H.; Hofmann, S.; Heßberger, F. P.; Ackermann, D.; Antalic, S.; Aritomo, Y.; Comas, V. F.; Düllman, Ch. E.; Gorshkov, A.; Graeger, R.; Heinz, S.; Heredia, J. A.; Hirose, K.; Khuyagbaatar, J.; Kindler, B.; Kojouharov, I.; Lommel, B.; Makii, H.; Mann, R.; Mitsuoka, S.; Nagame, Y.; Nishinaka, I.; Ohtsuki, T.; Popeko, A. G.; Saro, S.; Schädel, M.; Türler, A.; Wakabayashi, Y.; Watanabe, Y.; Yakushev, A.; Yeremin, A. V.

2014-03-01

Fission fragment mass distributions were measured in heavy-ion induced fissions using 238U target nucleus. The measured mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and qasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis, and the values were consistent with those determined from the evaporation residue cross sections.

Supervised variational model with statistical inference and its application in medical image segmentation.

PubMed

Li, Changyang; Wang, Xiuying; Eberl, Stefan; Fulham, Michael; Yin, Yong; Dagan Feng, David

2015-01-01

Automated and general medical image segmentation can be challenging because the foreground and the background may have complicated and overlapping density distributions in medical imaging. Conventional region-based level set algorithms often assume piecewise constant or piecewise smooth for segments, which are implausible for general medical image segmentation. Furthermore, low contrast and noise make identification of the boundaries between foreground and background difficult for edge-based level set algorithms. Thus, to address these problems, we suggest a supervised variational level set segmentation model to harness the statistical region energy functional with a weighted probability approximation. Our approach models the region density distributions by using the mixture-of-mixtures Gaussian model to better approximate real intensity distributions and distinguish statistical intensity differences between foreground and background. The region-based statistical model in our algorithm can intuitively provide better performance on noisy images. We constructed a weighted probability map on graphs to incorporate spatial indications from user input with a contextual constraint based on the minimization of contextual graphs energy functional. We measured the performance of our approach on ten noisy synthetic images and 58 medical datasets with heterogeneous intensities and ill-defined boundaries and compared our technique to the Chan-Vese region-based level set model, the geodesic active contour model with distance regularization, and the random walker model. Our method consistently achieved the highest Dice similarity coefficient when compared to the other methods.

Effects of ignition location models on the burn patterns of simulated wildfires

USGS Publications Warehouse

Bar-Massada, A.; Syphard, A.D.; Hawbaker, T.J.; Stewart, S.I.; Radeloff, V.C.

2011-01-01

Fire simulation studies that use models such as FARSITE often assume that ignition locations are distributed randomly, because spatially explicit information about actual ignition locations are difficult to obtain. However, many studies show that the spatial distribution of ignition locations, whether human-caused or natural, is non-random. Thus, predictions from fire simulations based on random ignitions may be unrealistic. However, the extent to which the assumption of ignition location affects the predictions of fire simulation models has never been systematically explored. Our goal was to assess the difference in fire simulations that are based on random versus non-random ignition location patterns. We conducted four sets of 6000 FARSITE simulations for the Santa Monica Mountains in California to quantify the influence of random and non-random ignition locations and normal and extreme weather conditions on fire size distributions and spatial patterns of burn probability. Under extreme weather conditions, fires were significantly larger for non-random ignitions compared to random ignitions (mean area of 344.5 ha and 230.1 ha, respectively), but burn probability maps were highly correlated (r = 0.83). Under normal weather, random ignitions produced significantly larger fires than non-random ignitions (17.5 ha and 13.3 ha, respectively), and the spatial correlations between burn probability maps were not high (r = 0.54), though the difference in the average burn probability was small. The results of the study suggest that the location of ignitions used in fire simulation models may substantially influence the spatial predictions of fire spread patterns. However, the spatial bias introduced by using a random ignition location model may be minimized if the fire simulations are conducted under extreme weather conditions when fire spread is greatest. ?? 2010 Elsevier Ltd.

Comparison of Deterministic and Probabilistic Radial Distribution Systems Load Flow

NASA Astrophysics Data System (ADS)

Gupta, Atma Ram; Kumar, Ashwani

2017-12-01

Distribution system network today is facing the challenge of meeting increased load demands from the industrial, commercial and residential sectors. The pattern of load is highly dependent on consumer behavior and temporal factors such as season of the year, day of the week or time of the day. For deterministic radial distribution load flow studies load is taken as constant. But, load varies continually with a high degree of uncertainty. So, there is a need to model probable realistic load. Monte-Carlo Simulation is used to model the probable realistic load by generating random values of active and reactive power load from the mean and standard deviation of the load and for solving a Deterministic Radial Load Flow with these values. The probabilistic solution is reconstructed from deterministic data obtained for each simulation. The main contribution of the work is: Finding impact of probable realistic ZIP load modeling on balanced radial distribution load flow. Finding impact of probable realistic ZIP load modeling on unbalanced radial distribution load flow. Compare the voltage profile and losses with probable realistic ZIP load modeling for balanced and unbalanced radial distribution load flow.

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.

Estimating true human and animal host source contribution in quantitative microbial source tracking using the Monte Carlo method.

PubMed

Wang, Dan; Silkie, Sarah S; Nelson, Kara L; Wuertz, Stefan

2010-09-01

Cultivation- and library-independent, quantitative PCR-based methods have become the method of choice in microbial source tracking. However, these qPCR assays are not 100% specific and sensitive for the target sequence in their respective hosts' genome. The factors that can lead to false positive and false negative information in qPCR results are well defined. It is highly desirable to have a way of removing such false information to estimate the true concentration of host-specific genetic markers and help guide the interpretation of environmental monitoring studies. Here we propose a statistical model based on the Law of Total Probability to predict the true concentration of these markers. The distributions of the probabilities of obtaining false information are estimated from representative fecal samples of known origin. Measurement error is derived from the sample precision error of replicated qPCR reactions. Then, the Monte Carlo method is applied to sample from these distributions of probabilities and measurement error. The set of equations given by the Law of Total Probability allows one to calculate the distribution of true concentrations, from which their expected value, confidence interval and other statistical characteristics can be easily evaluated. The output distributions of predicted true concentrations can then be used as input to watershed-wide total maximum daily load determinations, quantitative microbial risk assessment and other environmental models. This model was validated by both statistical simulations and real world samples. It was able to correct the intrinsic false information associated with qPCR assays and output the distribution of true concentrations of Bacteroidales for each animal host group. Model performance was strongly affected by the precision error. It could perform reliably and precisely when the standard deviation of the precision error was small (≤ 0.1). Further improvement on the precision of sample processing and qPCR reaction would greatly improve the performance of the model. This methodology, built upon Bacteroidales assays, is readily transferable to any other microbial source indicator where a universal assay for fecal sources of that indicator exists. Copyright © 2010 Elsevier Ltd. All rights reserved.

Data Base for a National Mineral-Resource Assessment of Undiscovered Deposits of Gold, Silver, Copper, Lead, and Zinc in the Conterminous United States

USGS Publications Warehouse

Ludington, S.D.; Cox, D.P.; McCammon, R.B.

1996-01-01

For this assessment, the conterminous United States was divided into 12 regions Adirondack Mountains, Central and Southern Rocky Mountains, Colorado Plateau, East Central, Great Basin, Great Plains, Lake Superior, Northern Appalachians, Northern Rocky Mountains, Pacific Coast, Southern Appalachians, and Southern Basin and Range. The assessment, which was conducted by regional assessment teams of scientists from the USGS, was based on the concepts of permissive tracts and deposit models. Permissive tracts are discrete areas of the United States for which estimates of numbers of undiscovered deposits of a particular deposit type were made. A permissive tract is defined by its geographic boundaries such that the probability of deposits of the type delineated occurring outside the boundary is neglible. Deposit models, which are based on a compilation of worldwide literature and on observation, are sets of data in a convenient form that describe a group of deposits which have similar characteristics and that contain information on the common geologic attributes of the deposits and the environments in which they are found. Within each region, the assessment teams delineated permissive tracts for those deposit models that were judged to be appropriate and, when the amount of information warranted, estimated the number of undiscovered deposits. A total of 46 deposit models were used to assess 236 separate permissive tracts. Estimates of undiscovered deposits were limited to a depth of 1 km beneath the surface of the Earth. The estimates of the number of undiscovered deposits of gold, silver, copper, lead, and zinc were expressed in the form of a probability distribution. Commonly, the number of undiscovered deposits was estimated at the 90th, 50th, and 10th percentiles. A Monte Carlo simulation computer program was used to combine the probability distribution of the number of undiscovered deposits with the grade and tonnage data sets associated with each deposit model to obtain the probability distribution for undiscovered metal.

Probability density function characterization for aggregated large-scale wind power based on Weibull mixtures

DOE PAGES

Gomez-Lazaro, Emilio; Bueso, Maria C.; Kessler, Mathieu; ...

2016-02-02

Here, the Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF) for aggregated wind power generation. PDFs of wind power datamore » are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.« less

Protein single-model quality assessment by feature-based probability density functions.

PubMed

Cao, Renzhi; Cheng, Jianlin

2016-04-04

Protein quality assessment (QA) has played an important role in protein structure prediction. We developed a novel single-model quality assessment method-Qprob. Qprob calculates the absolute error for each protein feature value against the true quality scores (i.e. GDT-TS scores) of protein structural models, and uses them to estimate its probability density distribution for quality assessment. Qprob has been blindly tested on the 11th Critical Assessment of Techniques for Protein Structure Prediction (CASP11) as MULTICOM-NOVEL server. The official CASP result shows that Qprob ranks as one of the top single-model QA methods. In addition, Qprob makes contributions to our protein tertiary structure predictor MULTICOM, which is officially ranked 3rd out of 143 predictors. The good performance shows that Qprob is good at assessing the quality of models of hard targets. These results demonstrate that this new probability density distribution based method is effective for protein single-model quality assessment and is useful for protein structure prediction. The webserver of Qprob is available at: http://calla.rnet.missouri.edu/qprob/. The software is now freely available in the web server of Qprob.

Fault and event tree analyses for process systems risk analysis: uncertainty handling formulations.

PubMed

Ferdous, Refaul; Khan, Faisal; Sadiq, Rehan; Amyotte, Paul; Veitch, Brian

2011-01-01

Quantitative risk analysis (QRA) is a systematic approach for evaluating likelihood, consequences, and risk of adverse events. QRA based on event (ETA) and fault tree analyses (FTA) employs two basic assumptions. The first assumption is related to likelihood values of input events, and the second assumption is regarding interdependence among the events (for ETA) or basic events (for FTA). Traditionally, FTA and ETA both use crisp probabilities; however, to deal with uncertainties, the probability distributions of input event likelihoods are assumed. These probability distributions are often hard to come by and even if available, they are subject to incompleteness (partial ignorance) and imprecision. Furthermore, both FTA and ETA assume that events (or basic events) are independent. In practice, these two assumptions are often unrealistic. This article focuses on handling uncertainty in a QRA framework of a process system. Fuzzy set theory and evidence theory are used to describe the uncertainties in the input event likelihoods. A method based on a dependency coefficient is used to express interdependencies of events (or basic events) in ETA and FTA. To demonstrate the approach, two case studies are discussed. © 2010 Society for Risk Analysis.

How to Assess the Existence of Competing Strategies in Cognitive Tasks: A Primer on the Fixed-Point Property

PubMed Central

van Maanen, Leendert; de Jong, Ritske; van Rijn, Hedderik

2014-01-01

When multiple strategies can be used to solve a type of problem, the observed response time distributions are often mixtures of multiple underlying base distributions each representing one of these strategies. For the case of two possible strategies, the observed response time distributions obey the fixed-point property. That is, there exists one reaction time that has the same probability of being observed irrespective of the actual mixture proportion of each strategy. In this paper we discuss how to compute this fixed-point, and how to statistically assess the probability that indeed the observed response times are generated by two competing strategies. Accompanying this paper is a free R package that can be used to compute and test the presence or absence of the fixed-point property in response time data, allowing for easy to use tests of strategic behavior. PMID:25170893

Wormholes and the cosmological constant problem.

NASA Astrophysics Data System (ADS)

Klebanov, I.

The author reviews the cosmological constant problem and the recently proposed wormhole mechanism for its solution. Summation over wormholes in the Euclidean path integral for gravity turns all the coupling parameters into dynamical variables, sampled from a probability distribution. A formal saddle point analysis results in a distribution with a sharp peak at the cosmological constant equal to zero, which appears to solve the cosmological constant problem. He discusses the instabilities of the gravitational Euclidean path integral and the difficulties with its interpretation. He presents an alternate formalism for baby universes, based on the "third quantization" of the Wheeler-De Witt equation. This approach is analyzed in a minisuperspace model for quantum gravity, where it reduces to simple quantum mechanics. Once again, the coupling parameters become dynamical. Unfortunately, the a priori probability distribution for the cosmological constant and other parameters is typically a smooth function, with no sharp peaks.

In-beam fissio study at JAEA for heavy element synthesis

NASA Astrophysics Data System (ADS)

Nishio, K.; Ikezoe, H.; Hofmann, S.; Ackermann, D.; Aritomo, Y.; Comas, V. F.; Düllmann, Ch. E.; Heinz, S.; Heredia, J. A.; Heßberger, F. P.; Hirose, K.; Khuyagbaatar, J.; Kindler, B.; Kojouharov, I.; Lommel, B.; Makii, M.; Mann, R.; Mitsuoka, S.; Nishinaka, I.; Ohtsuki, T.; Saro, S.; Schädel, M.; Popeko, A. G.; Türler, A.; Wakabayashi, Y.; Watanabe, Y.; Yakushev, A.; Yeremin, A.

2013-04-01

Fission fragment mass distributions were measured in the heavy-ion induced fission using 238U target nucleus. The mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and qasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model in the reactions of 30Si+238U and 34S+238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections of 263,264Sg and 267,268Hs, produced by 30Si+238U and 34S+238U, respectively. It is also suggested that the sub-barrier energies can be used for heavy element synthesis.

The bingo model of survivorship: 1. probabilistic aspects.

PubMed

Murphy, E A; Trojak, J E; Hou, W; Rohde, C A

1981-01-01

A "bingo" model is one in which the pattern of survival of a system is determined by whichever of several components, each with its own particular distribution for survival, fails first. The model is motivated by the study of lifespan in animals. A number of properties of such systems are discussed in general. They include the use of a special criterion of skewness that probably corresponds more closely than traditional measures to what the eye observes in casually inspecting data. This criterion is the ratio, r(h), of the probability density at a point an arbitrary distance, h, above the mode to that an equal distance below the mode. If this ratio is positive for all positive arguments, the distribution is considered positively asymmetrical and conversely. Details of the bingo model are worked out for several types of base distributions: the rectangular, the triangular, the logistic, and by numerical methods, the normal, lognormal, and gamma.

Analysis on flood generation processes by means of a continuous simulation model

NASA Astrophysics Data System (ADS)

Fiorentino, M.; Gioia, A.; Iacobellis, V.; Manfreda, S.

2006-03-01

In the present research, we exploited a continuous hydrological simulation to investigate on key variables responsible of flood peak formation. With this purpose, a distributed hydrological model (DREAM) is used in cascade with a rainfall generator (IRP-Iterated Random Pulse) to simulate a large number of extreme events providing insight into the main controls of flood generation mechanisms. Investigated variables are those used in theoretically derived probability distribution of floods based on the concept of partial contributing area (e.g. Iacobellis and Fiorentino, 2000). The continuous simulation model is used to investigate on the hydrological losses occurring during extreme events, the variability of the source area contributing to the flood peak and its lag-time. Results suggest interesting simplification for the theoretical probability distribution of floods according to the different climatic and geomorfologic environments. The study is applied to two basins located in Southern Italy with different climatic characteristics.

Modeling late rectal toxicities based on a parameterized representation of the 3D dose distribution

NASA Astrophysics Data System (ADS)

Buettner, Florian; Gulliford, Sarah L.; Webb, Steve; Partridge, Mike

2011-04-01

Many models exist for predicting toxicities based on dose-volume histograms (DVHs) or dose-surface histograms (DSHs). This approach has several drawbacks as firstly the reduction of the dose distribution to a histogram results in the loss of spatial information and secondly the bins of the histograms are highly correlated with each other. Furthermore, some of the complex nonlinear models proposed in the past lack a direct physical interpretation and the ability to predict probabilities rather than binary outcomes. We propose a parameterized representation of the 3D distribution of the dose to the rectal wall which explicitly includes geometrical information in the form of the eccentricity of the dose distribution as well as its lateral and longitudinal extent. We use a nonlinear kernel-based probabilistic model to predict late rectal toxicity based on the parameterized dose distribution and assessed its predictive power using data from the MRC RT01 trial (ISCTRN 47772397). The endpoints under consideration were rectal bleeding, loose stools, and a global toxicity score. We extract simple rules identifying 3D dose patterns related to a specifically low risk of complication. Normal tissue complication probability (NTCP) models based on parameterized representations of geometrical and volumetric measures resulted in areas under the curve (AUCs) of 0.66, 0.63 and 0.67 for predicting rectal bleeding, loose stools and global toxicity, respectively. In comparison, NTCP models based on standard DVHs performed worse and resulted in AUCs of 0.59 for all three endpoints. In conclusion, we have presented low-dimensional, interpretable and nonlinear NTCP models based on the parameterized representation of the dose to the rectal wall. These models had a higher predictive power than models based on standard DVHs and their low dimensionality allowed for the identification of 3D dose patterns related to a low risk of complication.

Spatial analysis of land use and shallow groundwater vulnerability in the watershed adjacent to Assateague Island National Seashore, Maryland and Virginia, USA

USGS Publications Warehouse

LaMotte, A.E.; Greene, E.A.

2007-01-01

Spatial relations between land use and groundwater quality in the watershed adjacent to Assateague Island National Seashore, Maryland and Virginia, USA were analyzed by the use of two spatial models. One model used a logit analysis and the other was based on geostatistics. The models were developed and compared on the basis of existing concentrations of nitrate as nitrogen in samples from 529 domestic wells. The models were applied to produce spatial probability maps that show areas in the watershed where concentrations of nitrate in groundwater are likely to exceed a predetermined management threshold value. Maps of the watershed generated by logistic regression and probability kriging analysis showing where the probability of nitrate concentrations would exceed 3 mg/L (>0.50) compared favorably. Logistic regression was less dependent on the spatial distribution of sampled wells, and identified an additional high probability area within the watershed that was missed by probability kriging. The spatial probability maps could be used to determine the natural or anthropogenic factors that best explain the occurrence and distribution of elevated concentrations of nitrate (or other constituents) in shallow groundwater. This information can be used by local land-use planners, ecologists, and managers to protect water supplies and identify land-use planning solutions and monitoring programs in vulnerable areas. ?? 2006 Springer-Verlag.

Characterizing the distribution of an endangered salmonid using environmental DNA analysis

USGS Publications Warehouse

Laramie, Matthew B.; Pilliod, David S.; Goldberg, Caren S.

2015-01-01

Determining species distributions accurately is crucial to developing conservation and management strategies for imperiled species, but a challenging task for small populations. We evaluated the efficacy of environmental DNA (eDNA) analysis for improving detection and thus potentially refining the known distribution of Chinook salmon (Oncorhynchus tshawytscha) in the Methow and Okanogan Subbasins of the Upper Columbia River, which span the border between Washington, USA and British Columbia, Canada. We developed an assay to target a 90 base pair sequence of Chinook DNA and used quantitative polymerase chain reaction (qPCR) to quantify the amount of Chinook eDNA in triplicate 1-L water samples collected at 48 stream locations in June and again in August 2012. The overall probability of detecting Chinook with our eDNA method in areas within the known distribution was 0.77 (±0.05 SE). Detection probability was lower in June (0.62, ±0.08 SE) during high flows and at the beginning of spring Chinook migration than during base flows in August (0.93, ±0.04 SE). In the Methow subbasin, mean eDNA concentration was higher in August compared to June, especially in smaller tributaries, probably resulting from the arrival of spring Chinook adults, reduced discharge, or both. Chinook eDNA concentrations did not appear to change in the Okanogan subbasin from June to August. Contrary to our expectations about downstream eDNA accumulation, Chinook eDNA did not decrease in concentration in upstream reaches (0–120 km). Further examination of factors influencing spatial distribution of eDNA in lotic systems may allow for greater inference of local population densities along stream networks or watersheds. These results demonstrate the potential effectiveness of eDNA detection methods for determining landscape-level distribution of anadromous salmonids in large river systems.

Distributed Denial of Service Attack Source Detection Using Efficient Traceback Technique (ETT) in Cloud-Assisted Healthcare Environment.

PubMed

Latif, Rabia; Abbas, Haider; Latif, Seemab; Masood, Ashraf

2016-07-01

Security and privacy are the first and foremost concerns that should be given special attention when dealing with Wireless Body Area Networks (WBANs). As WBAN sensors operate in an unattended environment and carry critical patient health information, Distributed Denial of Service (DDoS) attack is one of the major attacks in WBAN environment that not only exhausts the available resources but also influence the reliability of information being transmitted. This research work is an extension of our previous work in which a machine learning based attack detection algorithm is proposed to detect DDoS attack in WBAN environment. However, in order to avoid complexity, no consideration was given to the traceback mechanism. During traceback, the challenge lies in reconstructing the attack path leading to identify the attack source. Among existing traceback techniques, Probabilistic Packet Marking (PPM) approach is the most commonly used technique in conventional IP- based networks. However, since marking probability assignment has significant effect on both the convergence time and performance of a scheme, it is not directly applicable in WBAN environment due to high convergence time and overhead on intermediate nodes. Therefore, in this paper we have proposed a new scheme called Efficient Traceback Technique (ETT) based on Dynamic Probability Packet Marking (DPPM) approach and uses MAC header in place of IP header. Instead of using fixed marking probability, the proposed scheme uses variable marking probability based on the number of hops travelled by a packet to reach the target node. Finally, path reconstruction algorithms are proposed to traceback an attacker. Evaluation and simulation results indicate that the proposed solution outperforms fixed PPM in terms of convergence time and computational overhead on nodes.

Modeling the distribution of colonial species to improve estimation of plankton concentration in ballast water

NASA Astrophysics Data System (ADS)

Rajakaruna, Harshana; VandenByllaardt, Julie; Kydd, Jocelyn; Bailey, Sarah

2018-03-01

The International Maritime Organization (IMO) has set limits on allowable plankton concentrations in ballast water discharge to minimize aquatic invasions globally. Previous guidance on ballast water sampling and compliance decision thresholds was based on the assumption that probability distributions of plankton are Poisson when spatially homogenous, or negative binomial when heterogeneous. We propose a hierarchical probability model, which incorporates distributions at the level of particles (i.e., discrete individuals plus colonies per unit volume) and also within particles (i.e., individuals per particle) to estimate the average plankton concentration in ballast water. We examined the performance of the models using data for plankton in the size class ≥ 10 μm and < 50 μm, collected from five different depths of a ballast tank of a commercial ship in three independent surveys. We show that the data fit to the negative binomial and the hierarchical probability models equally well, with both models performing better than the Poisson model at the scale of our sampling. The hierarchical probability model, which accounts for both the individuals and the colonies in a sample, reduces the uncertainty associated with the concentration estimation, and improves the power of rejecting the decision on ship's compliance when a ship does not truly comply with the standard. We show examples of how to test ballast water compliance using the above models.

A Gaussian Model-Based Probabilistic Approach for Pulse Transit Time Estimation.

PubMed

Jang, Dae-Geun; Park, Seung-Hun; Hahn, Minsoo

2016-01-01

In this paper, we propose a new probabilistic approach to pulse transit time (PTT) estimation using a Gaussian distribution model. It is motivated basically by the hypothesis that PTTs normalized by RR intervals follow the Gaussian distribution. To verify the hypothesis, we demonstrate the effects of arterial compliance on the normalized PTTs using the Moens-Korteweg equation. Furthermore, we observe a Gaussian distribution of the normalized PTTs on real data. In order to estimate the PTT using the hypothesis, we first assumed that R-waves in the electrocardiogram (ECG) can be correctly identified. The R-waves limit searching ranges to detect pulse peaks in the photoplethysmogram (PPG) and to synchronize the results with cardiac beats--i.e., the peaks of the PPG are extracted within the corresponding RR interval of the ECG as pulse peak candidates. Their probabilities of being the actual pulse peak are then calculated using a Gaussian probability function. The parameters of the Gaussian function are automatically updated when a new pulse peak is identified. This update makes the probability function adaptive to variations of cardiac cycles. Finally, the pulse peak is identified as the candidate with the highest probability. The proposed approach is tested on a database where ECG and PPG waveforms are collected simultaneously during the submaximal bicycle ergometer exercise test. The results are promising, suggesting that the method provides a simple but more accurate PTT estimation in real applications.

Biomechanical Tolerance of Calcaneal Fractures

PubMed Central

Yoganandan, Narayan; Pintar, Frank A.; Gennarelli, Thomas A.; Seipel, Robert; Marks, Richard

1999-01-01

Biomechanical studies have been conducted in the past to understand the mechanisms of injury to the foot-ankle complex. However, statistically based tolerance criteria for calcaneal complex injuries are lacking. Consequently, this research was designed to derive a probability distribution that represents human calcaneal tolerance under impact loading such as those encountered in vehicular collisions. Information for deriving the distribution was obtained by experiments on unembalmed human cadaver lower extremities. Briefly, the protocol included the following. The knee joint was disarticulated such that the entire lower extremity distal to the knee joint remained intact. The proximal tibia was fixed in polymethylmethacrylate. The specimens were aligned and impact loading was applied using mini-sled pendulum equipment. The pendulum impactor dynamically loaded the plantar aspect of the foot once. Following the test, specimens were palpated and radiographs in multiple planes were obtained. Injuries were classified into no fracture, and extra-and intra-articular fractures of the calcaneus. There were 14 cases of no injury and 12 cases of calcaneal fracture. The fracture forces (mean: 7802 N) were significantly different (p<0.01) from the forces in the no injury (mean: 4144 N) group. The probability of calcaneal fracture determined using logistic regression indicated that a force of 6.2 kN corresponds to 50 percent probability of calcaneal fracture. The derived probability distribution is useful in the design of dummies and vehicular surfaces.

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

Mean Excess Function as a method of identifying sub-exponential tails: Application to extreme daily rainfall

NASA Astrophysics Data System (ADS)

Nerantzaki, Sofia; Papalexiou, Simon Michael

2017-04-01

Identifying precisely the distribution tail of a geophysical variable is tough, or, even impossible. First, the tail is the part of the distribution for which we have the less empirical information available; second, a universally accepted definition of tail does not and cannot exist; and third, a tail may change over time due to long-term changes. Unfortunately, the tail is the most important part of the distribution as it dictates the estimates of exceedance probabilities or return periods. Fortunately, based on their tail behavior, probability distributions can be generally categorized into two major families, i.e., sub-exponentials (heavy-tailed) and hyper-exponentials (light-tailed). This study aims to update the Mean Excess Function (MEF), providing a useful tool in order to asses which type of tail better describes empirical data. The MEF is based on the mean value of a variable over a threshold and results in a zero slope regression line when applied for the Exponential distribution. Here, we construct slope confidence intervals for the Exponential distribution as functions of sample size. The validation of the method using Monte Carlo techniques on four theoretical distributions covering major tail cases (Pareto type II, Log-normal, Weibull and Gamma) revealed that it performs well especially for large samples. Finally, the method is used to investigate the behavior of daily rainfall extremes; thousands of rainfall records were examined, from all over the world and with sample size over 100 years, revealing that heavy-tailed distributions can describe more accurately rainfall extremes.

Study of sea-surface slope distribution and its effect on radar backscatter based on Global Precipitation Measurement Ku-band precipitation radar measurements

NASA Astrophysics Data System (ADS)

Yan, Qiushuang; Zhang, Jie; Fan, Chenqing; Wang, Jing; Meng, Junmin

2018-01-01

The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram-Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram-Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram-Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.

Time analysis of volcanic activity on Io by means of plasma observations

NASA Technical Reports Server (NTRS)

Mekler, Y.; Eviatar, A.

1980-01-01

A model of Io volcanism in which the probability of activity obeys a binomial distribution is presented. Observed values of the electron density obtained over a 3-year period by ground-based spectroscopy are fitted to such a distribution. The best fit is found for a total number of 15 volcanoes with a probability of individual activity at any time of 0.143. The Pioneer 10 ultraviolet observations are reinterpreted as emissions of sulfur and oxygen ions and are found to be consistent with a plasma much less dense than that observed by the Voyager spacecraft. Late 1978 and the first half of 1979 are shown to be periods of anomalous volcanicity. Rapid variations in electron density are related to enhanced radial diffusion.

Applications of the first digit law to measure correlations.

PubMed

Gramm, R; Yost, J; Su, Q; Grobe, R

2017-04-01

The quasiempirical Benford law predicts that the distribution of the first significant digit of random numbers obtained from mixed probability distributions is surprisingly meaningful and reveals some universal behavior. We generalize this finding to examine the joint first-digit probability of a pair of two random numbers and show that undetectable correlations by means of the usual covariance-based measure can be identified in the statistics of the corresponding first digits. We illustrate this new measure by analyzing the correlations and anticorrelations of the positions of two interacting particles in their quantum mechanical ground state. This suggests that by using this measure, the presence or absence of correlations can be determined even if only the first digit of noisy experimental data can be measured accurately.

Author Credit for Transdisciplinary Collaboration

PubMed Central

Xu, Jian; Ding, Ying; Malic, Vincent

2015-01-01

Transdisciplinary collaboration is the key for innovation. An evaluation mechanism is necessary to ensure that academic credit for this costly process can be allocated fairly among coauthors. This paper proposes a set of quantitative measures (e.g., t_credit and t_index) to reflect authors’ transdisciplinary contributions to publications. These measures are based on paper-topic probability distributions and author-topic probability distributions. We conduct an empirical analysis of the information retrieval domain which demonstrates that these measures effectively improve the results of harmonic_credit and h_index measures by taking into account the transdisciplinary contributions of authors. The definitions of t_credit and t_index provide a fair and effective way for research organizations to assign credit to authors of transdisciplinary publications. PMID:26375678

A classification scheme for edge-localized modes based on their probability distributions

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

Shabbir, A., E-mail: aqsa.shabbir@ugent.be; Max Planck Institute for Plasma Physics, D-85748 Garching; Hornung, G.

We present here an automated classification scheme which is particularly well suited to scenarios where the parameters have significant uncertainties or are stochastic quantities. To this end, the parameters are modeled with probability distributions in a metric space and classification is conducted using the notion of nearest neighbors. The presented framework is then applied to the classification of type I and type III edge-localized modes (ELMs) from a set of carbon-wall plasmas at JET. This provides a fast, standardized classification of ELM types which is expected to significantly reduce the effort of ELM experts in identifying ELM types. Further, themore » classification scheme is general and can be applied to various other plasma phenomena as well.« less

Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain

DOE PAGES

Palmer, Jeremy A.; Paez, Thomas L.

2011-01-01

Modern electro-optical instruments are typically designed with assemblies of optomechanical members that support optics such that alignment is maintained in service environments that include random vibration loads. This paper presents a nonlinear numerical analysis that calculates statistics for the peak lateral response of optics in an optomechanical sub-assembly subject to random excitation of the housing. The work is unique in that the prior art does not address peak response probability distribution for stationary random vibration in the time domain for a common lens-retainer-housing system with Coulomb damping. Analytical results are validated by using displacement response data from random vibration testingmore » of representative prototype sub-assemblies. A comparison of predictions to experimental results yields reasonable agreement. The Type I Asymptotic form provides the cumulative distribution function for peak response probabilities. Probabilities are calculated for actual lens centration tolerances. The probability that peak response will not exceed the centration tolerance is greater than 80% for prototype configurations where the tolerance is high (on the order of 30 micrometers). Conversely, the probability is low for those where the tolerance is less than 20 micrometers. The analysis suggests a design paradigm based on the influence of lateral stiffness on the magnitude of the response.« less

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.

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.

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.

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.

Modelling road accident blackspots data with the discrete generalized Pareto distribution.

PubMed

Prieto, Faustino; Gómez-Déniz, Emilio; Sarabia, José María

2014-10-01

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed. Copyright © 2014 Elsevier Ltd. All rights reserved.

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.

Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B

DOE PAGES

Santra, Kalyan; Smith, Emily A.; Petrich, Jacob W.; ...

2016-12-12

It is often convenient to know the minimum amount of data needed in order to obtain a result of desired accuracy and precision. It is a necessity in the case of subdiffraction-limited microscopies, such as stimulated emission depletion (STED) microscopy, owing to the limited sample volumes and the extreme sensitivity of the samples to photobleaching and photodamage. We present a detailed comparison of probability-based techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimization-based techniques for retrieving the fluorescence decay parameters for various two-fluorophore mixtures, as a function of the total numbermore » of photon counts, in time-correlated, single-photon counting experiments. The probability-based techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 2-3 significant figures. This is to be expected, as we demonstrate that the three methods are fundamentally related. Furthermore, methods based on the Poisson and binomial distributions have the desirable feature of providing a bin-by-bin analysis of a single fluorescence decay trace, which thus permits statistics to be acquired using only the one trace for not only the mean and median values of the fluorescence decay parameters but also for the associated standard deviations. Lastly, these probability-based methods lend themselves well to the analysis of the sparse data sets that are encountered in subdiffraction-limited microscopies.« less

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

NASA Technical Reports Server (NTRS)

Rood, Richard B.; Douglass, Anne R.; Cerniglia, Mark C.; Sparling, Lynn C.; Nielsen, J. Eric

1999-01-01

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of characterizing the observed variability. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High (low) potential vorticity at 300 hPa indicates that the tropopause is low (high), and the identification of these two groups is made to account for the dynamic variability. Conditional probability distribution functions are used to define the statistics of the ozone distribution from both observations and a three-dimensional model simulation using winds from the Goddard Earth Observing System Data Assimilation System for transport. Ozone data sets include ozonesonde observations from northern midlatitude stations (1991-96) and midlatitude observations made by the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS) (1994- 1998). The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause (approximately 380K). The probability distribution functions are similar for the two data sources, despite differences in horizontal and vertical resolution and spatial and temporal sampling. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. Results show that during summer, much of the observed variability is explained by the height of the tropopause. During the winter and spring, when the tropopause fluctuations are larger, less of the variability is explained by tropopause height. This suggests that more mixing occurs during these seasons. During all seasons, there is a transition zone near the tropopause that contains air characteristic of both the troposphere and the stratosphere. The relevance of the results to the assessment of the environmental impact of aircraft effluence is also discussed.

Deviation from Power Law Behavior in Landslide Phenomenon

NASA Astrophysics Data System (ADS)

Li, L.; Lan, H.; Wu, Y.

2013-12-01

Power law distribution of magnitude is widely observed in many natural hazards (e.g., earthquake, floods, tornadoes, and forest fires). Landslide is unique as the size distribution of landslide is characterized by a power law decrease with a rollover in the small size end. Yet, the emergence of the rollover, i.e., the deviation from power law behavior for small size landslides, remains a mystery. In this contribution, we grouped the forces applied on landslide bodies into two categories: 1) the forces proportional to the volume of failure mass (gravity and friction), and 2) the forces proportional to the area of failure surface (cohesion). Failure occurs when the forces proportional to volume exceed the forces proportional to surface area. As such, given a certain mechanical configuration, the failure volume to failure surface area ratio must exceed a corresponding threshold to guarantee a failure. Assuming all landslides share a uniform shape, which means the volume to surface area ratio of landslide regularly increase with the landslide volume, a cutoff of landslide volume distribution in the small size end can be defined. However, in realistic landslide phenomena, where heterogeneities of landslide shape and mechanical configuration are existent, a simple cutoff of landslide volume distribution does not exist. The stochasticity of landslide shape introduce a probability distribution of the volume to surface area ratio with regard to landslide volume, with which the probability that the volume to surface ratio exceed the threshold can be estimated regarding values of landslide volume. An experiment based on empirical data showed that this probability can induce the power law distribution of landslide volume roll down in the small size end. We therefore proposed that the constraints on the failure volume to failure surface area ratio together with the heterogeneity of landslide geometry and mechanical configuration attribute for the deviation from power law behavior in landslide phenomenon. Figure shows that a rollover of landslide size distribution in the small size end is produced as the probability for V/S (the failure volume to failure surface ratio of landslide) exceeding the mechanical threshold applied to the power law distribution of landslide volume.

Software Supportability Risk Assessment in OT&E (Operational Test and Evaluation): Literature Review, Current Research Review, and Data Base Assemblage.

DTIC Science & Technology

1984-09-28

variables before simula- tion of model - Search for reality checks a, - Express uncertainty as a probability density distribution. a. H2 a, H-22 TWIF... probability that the software con- tains errors. This prior is updated as test failure data are accumulated. Only a p of 1 (software known to contain...discusssed; both parametric and nonparametric versions are presented. It is shown by the author that the bootstrap underlies the jackknife method and

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…

Application of Weakest Link Probabilistic Framework for Fatigue Notch Factor to Aero Engine Materials

DTIC Science & Technology

2014-08-25

11 distributed cyclic microplasticity . Recent approaches have been developed to incorporate these finite process zone effects at notches [25, 26...the distribution of microvoids [50] or microplasticity [51]. According to the hypotheses on which the weakest link theory is based, given a structure...high cycle fatigue regime, where scatter of heterogeneous microplasticity in the fatigue specimen is a common occurrence. The probability of success

Frequency-Locked Detector Threshold Setting Criteria Based on Mean-Time-To-Lose-Lock (MTLL) for GPS Receivers

PubMed Central

Zhao, Na; Qin, Honglei; Sun, Kewen; Ji, Yuanfa

2017-01-01

Frequency-locked detector (FLD) has been widely utilized in tracking loops of Global Positioning System (GPS) receivers to indicate their locking status. The relation between FLD and lock status has been seldom discussed. The traditional PLL experience is not suitable for FLL. In this paper, the threshold setting criteria for frequency-locked detector in the GPS receiver has been proposed by analyzing statistical characteristic of FLD output. The approximate probability distribution of frequency-locked detector is theoretically derived by using a statistical approach, which reveals the relationship between probabilities of frequency-locked detector and the carrier-to-noise ratio (C/N0) of the received GPS signal. The relationship among mean-time-to-lose-lock (MTLL), detection threshold and lock probability related to C/N0 can be further discovered by utilizing this probability. Therefore, a theoretical basis for threshold setting criteria in frequency locked loops for GPS receivers is provided based on mean-time-to-lose-lock analysis. PMID:29207546

Frequency-Locked Detector Threshold Setting Criteria Based on Mean-Time-To-Lose-Lock (MTLL) for GPS Receivers.

PubMed

Jin, Tian; Yuan, Heliang; Zhao, Na; Qin, Honglei; Sun, Kewen; Ji, Yuanfa

2017-12-04

Frequency-locked detector (FLD) has been widely utilized in tracking loops of Global Positioning System (GPS) receivers to indicate their locking status. The relation between FLD and lock status has been seldom discussed. The traditional PLL experience is not suitable for FLL. In this paper, the threshold setting criteria for frequency-locked detector in the GPS receiver has been proposed by analyzing statistical characteristic of FLD output. The approximate probability distribution of frequency-locked detector is theoretically derived by using a statistical approach, which reveals the relationship between probabilities of frequency-locked detector and the carrier-to-noise ratio ( C / N ₀) of the received GPS signal. The relationship among mean-time-to-lose-lock (MTLL), detection threshold and lock probability related to C / N ₀ can be further discovered by utilizing this probability. Therefore, a theoretical basis for threshold setting criteria in frequency locked loops for GPS receivers is provided based on mean-time-to-lose-lock analysis.

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.

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

Multi-Agent Cooperative Target Search

PubMed Central

Hu, Jinwen; Xie, Lihua; Xu, Jun; Xu, Zhao

2014-01-01

This paper addresses a vision-based cooperative search for multiple mobile ground targets by a group of unmanned aerial vehicles (UAVs) with limited sensing and communication capabilities. The airborne camera on each UAV has a limited field of view and its target discriminability varies as a function of altitude. First, by dividing the whole surveillance region into cells, a probability map can be formed for each UAV indicating the probability of target existence within each cell. Then, we propose a distributed probability map updating model which includes the fusion of measurement information, information sharing among neighboring agents, information decay and transmission due to environmental changes such as the target movement. Furthermore, we formulate the target search problem as a multi-agent cooperative coverage control problem by optimizing the collective coverage area and the detection performance. The proposed map updating model and the cooperative control scheme are distributed, i.e., assuming that each agent only communicates with its neighbors within its communication range. Finally, the effectiveness of the proposed algorithms is illustrated by simulation. PMID:24865884

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.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

Aerosol-type retrieval and uncertainty quantification from OMI data

NASA Astrophysics Data System (ADS)

Kauppi, Anu; Kolmonen, Pekka; Laine, Marko; Tamminen, Johanna

2017-11-01

We discuss uncertainty quantification for aerosol-type selection in satellite-based atmospheric aerosol retrieval. The retrieval procedure uses precalculated aerosol microphysical models stored in look-up tables (LUTs) and top-of-atmosphere (TOA) spectral reflectance measurements to solve the aerosol characteristics. The forward model approximations cause systematic differences between the modelled and observed reflectance. Acknowledging this model discrepancy as a source of uncertainty allows us to produce more realistic uncertainty estimates and assists the selection of the most appropriate LUTs for each individual retrieval.This paper focuses on the aerosol microphysical model selection and characterisation of uncertainty in the retrieved aerosol type and aerosol optical depth (AOD). The concept of model evidence is used as a tool for model comparison. The method is based on Bayesian inference approach, in which all uncertainties are described as a posterior probability distribution. When there is no single best-matching aerosol microphysical model, we use a statistical technique based on Bayesian model averaging to combine AOD posterior probability densities of the best-fitting models to obtain an averaged AOD estimate. We also determine the shared evidence of the best-matching models of a certain main aerosol type in order to quantify how plausible it is that it represents the underlying atmospheric aerosol conditions.The developed method is applied to Ozone Monitoring Instrument (OMI) measurements using a multiwavelength approach for retrieving the aerosol type and AOD estimate with uncertainty quantification for cloud-free over-land pixels. Several larger pixel set areas were studied in order to investigate the robustness of the developed method. We evaluated the retrieved AOD by comparison with ground-based measurements at example sites. We found that the uncertainty of AOD expressed by posterior probability distribution reflects the difficulty in model selection. The posterior probability distribution can provide a comprehensive characterisation of the uncertainty in this kind of problem for aerosol-type selection. As a result, the proposed method can account for the model error and also include the model selection uncertainty in the total uncertainty budget.

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

NASA Technical Reports Server (NTRS)

Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell

2012-01-01

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

A testable model of earthquake probability based on changes in mean event size

NASA Astrophysics Data System (ADS)

Imoto, Masajiro

2003-02-01

We studied changes in mean event size using data on microearthquakes obtained from a local network in Kanto, central Japan, from a viewpoint that a mean event size tends to increase as the critical point is approached. A parameter describing changes was defined using a simple weighting average procedure. In order to obtain the distribution of the parameter in the background, we surveyed values of the parameter from 1982 to 1999 in a 160 × 160 × 80 km volume. The 16 events of M5.5 or larger in this volume were selected as target events. The conditional distribution of the parameter was estimated from the 16 values, each of which referred to the value immediately prior to each target event. The distribution of the background becomes a function of symmetry, the center of which corresponds to no change in b value. In contrast, the conditional distribution exhibits an asymmetric feature, which tends to decrease the b value. The difference in the distributions between the two groups was significant and provided us a hazard function for estimating earthquake probabilities. Comparing the hazard function with a Poisson process, we obtained an Akaike Information Criterion (AIC) reduction of 24. This reduction agreed closely with the probability gains of a retrospective study in a range of 2-4. A successful example of the proposed model can be seen in the earthquake of 3 June 2000, which is the only event during the period of prospective testing.

Integrated drought risk assessment of multi-hazard-affected bodies based on copulas in the Taoerhe Basin, China

NASA Astrophysics Data System (ADS)

Wang, Rui; Zhang, Jiquan; Guo, Enliang; Alu, Si; Li, Danjun; Ha, Si; Dong, Zhenhua

2018-02-01

Along with global warming, drought disasters are occurring more frequently and are seriously affecting normal life and food security in China. Drought risk assessments are necessary to provide support for local governments. This study aimed to establish an integrated drought risk model based on the relation curve of drought joint probabilities and drought losses of multi-hazard-affected bodies. First, drought characteristics, including duration and severity, were classified using the 1953-2010 precipitation anomaly in the Taoerhe Basin based on run theory, and their marginal distributions were identified by exponential and Gamma distributions, respectively. Then, drought duration and severity were related to construct a joint probability distribution based on the copula function. We used the EPIC (Environmental Policy Integrated Climate) model to simulate maize yield and historical data to calculate the loss rates of agriculture, industry, and animal husbandry in the study area. Next, we constructed vulnerability curves. Finally, the spatial distributions of drought risk for 10-, 20-, and 50-year return periods were expressed using inverse distance weighting. Our results indicate that the spatial distributions of the three return periods are consistent. The highest drought risk is in Ulanhot, and the duration and severity there were both highest. This means that higher drought risk corresponds to longer drought duration and larger drought severity, thus providing useful information for drought and water resource management. For 10-, 20-, and 50-year return periods, the drought risk values ranged from 0.41 to 0.53, 0.45 to 0.59, and 0.50 to 0.67, respectively. Therefore, when the return period increases, the drought risk increases.

Evaluation of carotid plaque echogenicity based on the integral of the cumulative probability distribution using gray-scale ultrasound images.

PubMed

Huang, Xiaowei; Zhang, Yanling; Meng, Long; Abbott, Derek; Qian, Ming; Wong, Kelvin K L; Zheng, Rongqing; Zheng, Hairong; Niu, Lili

2017-01-01

Carotid plaque echogenicity is associated with the risk of cardiovascular events. Gray-scale median (GSM) of the ultrasound image of carotid plaques has been widely used as an objective method for evaluation of plaque echogenicity in patients with atherosclerosis. We proposed a computer-aided method to evaluate plaque echogenicity and compared its efficiency with GSM. One hundred and twenty-five carotid plaques (43 echo-rich, 35 intermediate, 47 echolucent) were collected from 72 patients in this study. The cumulative probability distribution curves were obtained based on statistics of the pixels in the gray-level images of plaques. The area under the cumulative probability distribution curve (AUCPDC) was calculated as its integral value to evaluate plaque echogenicity. The classification accuracy for three types of plaques is 78.4% (kappa value, κ = 0.673), when the AUCPDC is used for classifier training, whereas GSM is 64.8% (κ = 0.460). The receiver operating characteristic curves were produced to test the effectiveness of AUCPDC and GSM for the identification of echolucent plaques. The area under the curve (AUC) was 0.817 when AUCPDC was used for training the classifier, which is higher than that achieved using GSM (AUC = 0.746). Compared with GSM, the AUCPDC showed a borderline association with coronary heart disease (Spearman r = 0.234, p = 0.050). Our experimental results suggest that AUCPDC analysis is a promising method for evaluation of plaque echogenicity and predicting cardiovascular events in patients with plaques.

Power-law tails in the distribution of order imbalance

NASA Astrophysics Data System (ADS)

Zhang, Ting; Gu, Gao-Feng; Xu, Hai-Chuan; Xiong, Xiong; Chen, Wei; Zhou, Wei-Xing

2017-10-01

We investigate the probability distribution of order imbalance calculated from the order flow data of 43 Chinese stocks traded on the Shenzhen Stock Exchange. Two definitions of order imbalance are considered based on the order number and the order size. We find that the order imbalance distributions of individual stocks have power-law tails. However, the tail index fluctuates remarkably from stock to stock. We also investigate the distributions of aggregated order imbalance of all stocks at different timescales Δt. We find no clear trend in the tail index with respect Δt. All the analyses suggest that the distributions of order imbalance are asymmetric.

Probability hazard map for future vent opening at Etna volcano (Sicily, Italy).

NASA Astrophysics Data System (ADS)

Brancato, Alfonso; Tusa, Giuseppina; Coltelli, Mauro; Proietti, Cristina

2014-05-01

Mount Etna is a composite stratovolcano located along the Ionian coast of eastern Sicily. The frequent flank eruptions occurrence (at an interval of years, mostly concentrated along the NE, S and W rift zones) lead to a high volcanic hazard that, linked with intense urbanization, poses a high volcanic risk. A long-term volcanic hazard assessment, mainly based on the past behaviour of the Etna volcano, is the basic tool for the evaluation of this risk. Then, a reliable forecast where the next eruption will occur is needed. A computer-assisted analysis and probabilistic evaluations will provide the relative map, thus allowing identification of the areas prone to the highest hazard. Based on these grounds, the use of a code such BET_EF (Bayesian Event Tree_Eruption Forecasting) showed that a suitable analysis can be explored (Selva et al., 2012). Following an analysis we are performing, a total of 6886 point-vents referring to the last 4.0 ka of Etna flank activity, and spread over an area of 744 km2 (divided into N=2976 squared cell, with side of 500 m), allowed us to estimate a pdf by applying a Gaussian kernel. The probability values represent a complete set of outcomes mutually exclusive and the relative sum is normalized to one over the investigated area; then, the basic assumptions of a Dirichlet distribution (the prior distribution set in the BET_EF code (Marzocchi et al., 2004, 2008)) still hold. One fundamental parameter is the the equivalent number of data, that depicts our confidence on the best guess probability. The BET_EF code also works with a likelihood function. This is modelled by a Multinomial distribution, with parameters representing the number of vents in each cell and the total number of past data (i.e. the 6886 point-vents). Given the grid of N cells, the final posterior distribution will be evaluated by multiplying the a priori Dirichlet probability distribution with the past data in each cell through the likelihood. The probability hazard map shows a tendency to concentrate along the NE and S rifts, as well as Valle del Bove, increasing the difference in probability between these areas and the rest of the volcano edifice. It is worthy notice that a higher significance is still evident along the W rift, even if not comparable with the ones of the above mentioned areas. References Marzocchi W., Sandri L., Gasparini P., Newhall C. and Boschi E.; 2004: Quantifying probabilities of volcanic events: The example of volcanic hazard at Mount Vesuvius, J. Geophys. Res., 109, B11201, doi:10.1029/2004JB00315U. Marzocchi W., Sandri, L. and Selva, J.; 2008: BET_EF: a probabilistic tool for long- and short-term eruption forecasting, Bull. Volcanol., 70, 623 - 632, doi: 10.1007/s00445-007-0157-y. Selva J., Orsi G., Di Vito M.A., Marzocchi W. And Sandri L.; 2012: Probability hazard mapfor future vent opening atthe Campi Flegrei caldera, Italy, Bull. Volcanol., 74, 497 - 510, doi: 10.1007/s00445-011-0528-2.

Probabilistic Analysis of a Composite Crew Module

NASA Technical Reports Server (NTRS)

Mason, Brian H.; Krishnamurthy, Thiagarajan

2011-01-01

An approach for conducting reliability-based analysis (RBA) of a Composite Crew Module (CCM) is presented. The goal is to identify and quantify the benefits of probabilistic design methods for the CCM and future space vehicles. The coarse finite element model from a previous NASA Engineering and Safety Center (NESC) project is used as the baseline deterministic analysis model to evaluate the performance of the CCM using a strength-based failure index. The first step in the probabilistic analysis process is the determination of the uncertainty distributions for key parameters in the model. Analytical data from water landing simulations are used to develop an uncertainty distribution, but such data were unavailable for other load cases. The uncertainty distributions for the other load scale factors and the strength allowables are generated based on assumed coefficients of variation. Probability of first-ply failure is estimated using three methods: the first order reliability method (FORM), Monte Carlo simulation, and conditional sampling. Results for the three methods were consistent. The reliability is shown to be driven by first ply failure in one region of the CCM at the high altitude abort load set. The final predicted probability of failure is on the order of 10-11 due to the conservative nature of the factors of safety on the deterministic loads.

Artificial Intelligence-Based Student Learning Evaluation: A Concept Map-Based Approach for Analyzing a Student's Understanding of a Topic

ERIC Educational Resources Information Center

Jain, G. Panka; Gurupur, Varadraj P.; Schroeder, Jennifer L.; Faulkenberry, Eileen D.

2014-01-01

In this paper, we describe a tool coined as artificial intelligence-based student learning evaluation tool (AISLE). The main purpose of this tool is to improve the use of artificial intelligence techniques in evaluating a student's understanding of a particular topic of study using concept maps. Here, we calculate the probability distribution of…

Derived distribution of floods based on the concept of partial area coverage with a climatic appeal

NASA Astrophysics Data System (ADS)

Iacobellis, Vito; Fiorentino, Mauro

2000-02-01

A new rationale for deriving the probability distribution of floods and help in understanding the physical processes underlying the distribution itself is presented. On the basis of this a model that presents a number of new assumptions is developed. The basic ideas are as follows: (1) The peak direct streamflow Q can always be expressed as the product of two random variates, namely, the average runoff per unit area ua and the peak contributing area a; (2) the distribution of ua conditional on a can be related to that of the rainfall depth occurring in a duration equal to a characteristic response time тa of the contributing part of the basin; and (3) тa is assumed to vary with a according to a power law. Consequently, the probability density function of Q can be found as the integral, over the total basin area A of that of a times the density function of ua given a. It is suggested that ua can be expressed as a fraction of the excess rainfall and that the annual flood distribution can be related to that of Q by the hypothesis that the flood occurrence process is Poissonian. In the proposed model it is assumed, as an exploratory attempt, that a and ua are gamma and Weibull distributed, respectively. The model was applied to the annual flood series of eight gauged basins in Basilicata (southern Italy) with catchment areas ranging from 40 to 1600 km2. The results showed strong physical consistence as the parameters tended to assume values in good agreement with well-consolidated geomorphologic knowledge and suggested a new key to understanding the climatic control of the probability distribution of floods.

Stylized facts in internal rates of return on stock index and its derivative transactions

NASA Astrophysics Data System (ADS)

Pichl, Lukáš; Kaizoji, Taisei; Yamano, Takuya

2007-08-01

Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in normalized log returns, the probability distributions for such single asset encounters incorporate the time factor by means of the internal rate of return, defined as the continuous compound interest. Resulting stylized facts are shown in the probability distributions derived from the daily series of TOPIX, S & P 500 and FTSE 100 index close values. The application of the above analysis to minute-tick data of NIKKEI 225 and its futures market, respectively, reveals an interesting difference in the behavior of the two probability distributions, in case a threshold on the minimal duration of the long position is imposed. It is therefore suggested that the probability distributions of the internal rates of return could be used for causality mining between the underlying and derivative stock markets. The highly specific discrete spectrum, which results from noise trader strategies as opposed to the smooth distributions observed for fundamentalist strategies in single encounter transactions may be useful in deducing the type of investment strategy from trading revenues of small portfolio investors.

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.

A stochastic Markov chain model to describe lung cancer growth and metastasis.

PubMed

Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter

2012-01-01

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.

A Physically-Based and Distributed Tool for Modeling the Hydrological and Mechanical Processes of Shallow Landslides

NASA Astrophysics Data System (ADS)

Arnone, E.; Noto, L. V.; Dialynas, Y. G.; Caracciolo, D.; Bras, R. L.

2015-12-01

This work presents the capabilities of a model, i.e. the tRIBS-VEGGIE-Landslide, in two different versions, i.e. developed within a probabilistic framework and coupled with a root cohesion module. The probabilistic model treats geotechnical and soil retention curve parameters as random variables across the basin and estimates theoretical probability distributions of slope stability and the associated "factor of safety" commonly used to describe the occurrence of shallow landslides. The derived distributions are used to obtain the spatio-temporal dynamics of probability of failure, conditioned on soil moisture dynamics at each watershed location. The framework has been tested in the Luquillo Experimental Forest (Puerto Rico) where shallow landslides are common. In particular, the methodology was used to evaluate how the spatial and temporal patterns of precipitation, whose variability is significant over the basin, affect the distribution of probability of failure. Another version of the model accounts for the additional cohesion exerted by vegetation roots. The approach is to use the Fiber Bundle Model (FBM) framework that allows for the evaluation of the root strength as a function of the stress-strain relationships of bundles of fibers. The model requires the knowledge of the root architecture to evaluate the additional reinforcement from each root diameter class. The root architecture is represented with a branching topology model based on Leonardo's rule. The methodology has been tested on a simple case study to explore the role of both hydrological and mechanical root effects. Results demonstrate that the effects of root water uptake can at times be more significant than the mechanical reinforcement; and that the additional resistance provided by roots depends heavily on the vegetation root structure and length.

A Bayesian Method for Identifying Contaminated Detectors in Low-Level Alpha Spectrometers

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

Maclellan, Jay A.; Strom, Daniel J.; Joyce, Kevin E.

2011-11-02

Analyses used for radiobioassay and other radiochemical tests are normally designed to meet specified quality objectives, such relative bias, precision, and minimum detectable activity (MDA). In the case of radiobioassay analyses for alpha emitting radionuclides, a major determiner of the process MDA is the instrument background. Alpha spectrometry detectors are often restricted to only a few counts over multi-day periods in order to meet required MDAs for nuclides such as plutonium-239 and americium-241. A detector background criterion is often set empirically based on experience, or frequentist or classical statistics are applied to the calculated background count necessary to meet amore » required MDA. An acceptance criterion for the detector background is set at the multiple of the estimated background standard deviation above the assumed mean that provides an acceptably small probability of observation if the mean and standard deviation estimate are correct. The major problem with this method is that the observed background counts used to estimate the mean, and thereby the standard deviation when a Poisson distribution is assumed, are often in the range of zero to three counts. At those expected count levels it is impossible to obtain a good estimate of the true mean from a single measurement. As an alternative, Bayesian statistical methods allow calculation of the expected detector background count distribution based on historical counts from new, uncontaminated detectors. This distribution can then be used to identify detectors showing an increased probability of contamination. The effect of varying the assumed range of background counts (i.e., the prior probability distribution) from new, uncontaminated detectors will be is discussed.« less

Simultaneous population pharmacokinetic modelling of plasma and intracellular PBMC miltefosine concentrations in New World cutaneous leishmaniasis and exploration of exposure-response relationships.

PubMed

Kip, Anke E; Castro, María Del Mar; Gomez, Maria Adelaida; Cossio, Alexandra; Schellens, Jan H M; Beijnen, Jos H; Saravia, Nancy Gore; Dorlo, Thomas P C

2018-05-10

Leishmania parasites reside within macrophages and the direct target of antileishmanial drugs is therefore intracellular. We aimed to characterize the intracellular PBMC miltefosine kinetics by developing a population pharmacokinetic (PK) model simultaneously describing plasma and intracellular PBMC pharmacokinetics. Furthermore, we explored exposure-response relationships and simulated alternative dosing regimens. A population PK model was developed with NONMEM, based on 339 plasma and 194 PBMC miltefosine concentrations from Colombian cutaneous leishmaniasis patients [29 children (2-12 years old) and 22 adults] receiving 1.8-2.5 mg/kg/day miltefosine for 28 days. A three-compartment model with miltefosine distribution into an intracellular PBMC effect compartment best fitted the data. Intracellular PBMC distribution was described with an intracellular-to-plasma concentration ratio of 2.17 [relative standard error (RSE) 4.9%] and intracellular distribution rate constant of 1.23 day-1 (RSE 14%). In exploring exposure-response relationships, both plasma and intracellular model-based exposure estimates significantly influenced probability of cure. A proposed PK target for the area under the plasma concentration-time curve (day 0-28) of >535 mg·day/L corresponded to >95% probability of cure. In linear dosing simulations, 18.3% of children compared with 2.8% of adults failed to reach 535 mg·day/L. In children, this decreased to 1.8% after allometric dosing simulation. The developed population PK model described the rate and extent of miltefosine distribution from plasma into PBMCs. Miltefosine exposure was significantly related to probability of cure in this cutaneous leishmaniasis patient population. We propose an exploratory PK target, which should be validated in a larger cohort study.

Can we expect to predict climate if we cannot shadow weather?

NASA Astrophysics Data System (ADS)

Smith, Leonard

2010-05-01

What limits our ability to predict (or project) useful statistics of future climate? And how might we quantify those limits? In the early 1960s, Ed Lorenz illustrated one constraint on point forecasts of the weather (chaos) while noting another (model imperfections). In the mid-sixties he went on to discuss climate prediction, noting that chaos, per se, need not limit accurate forecasts of averages and the distributions that define climate. In short, chaos might place draconian limits on what we can say about a particular summer day in 2010 (or 2040), but it need not limit our ability to make accurate and informative statements about the weather over this summer as a whole, or climate distributions of the 2040's. If not chaos, what limits our ability to produce decision relevant probability distribution functions (PDFs)? Is this just a question of technology (raw computer power) and uncertain boundary conditions (emission scenarios)? Arguably, current model simulations of the Earth's climate are limited by model inadequacy: not that the initial or boundary conditions are unknown but that state-of-the-art models would not yield decision-relevant probability distributions even if they were known. Or to place this statement in an empirically falsifiable format: that in 2100 when the boundary conditions are known and computer power is (hopefully) sufficient to allow exhaustive exploration of today's state-of-the-art models: we will find today's models do not admit a trajectory consistent with our knowledge of the state of the earth in 2009 which would prove of decision support relevance for, say, 25 km, hourly resolution. In short: today's models cannot shadow the weather of this century even after the fact. Restating this conjecture in a more positive frame: a 2100 historian of science will be able to determine the highest space and time scales on which 2009 models could have (i) produced trajectories plausibly consistent with the (by then) observed twenty-first century and (ii) produced probability distributions useful as such for decision support. As it will be some time until such conjectures can be refuted, how might we best advise decision makers of the detail (specifically, space and time resolution of a quantity of interest as a function of lead-time) that it is rational to interpret model-based PDFs as decision-relevant probability distributions? Given the nonlinearities already incorporated in our models, how far into the future can one expect a simulation to get the temperature "right" given the simulation has precipitation badly "wrong"? When can biases in local temperature which melt model-ice no longer be dismissed, and neglected by presenting model-anomalies? At what lead times will feedbacks due to model inadequacies cause the 2007 model simulations to drift away from what today's basic science (and 2100 computer power) would suggest? How might one justify quantitative claims regarding "extreme events" (or NUMB weather)? Models are unlikely to forecast things they cannot shadow, or at least track. There is no constraint on rational scientists to take model distributions as their subjective probabilities, unless they believe the model is empirically adequate. How then are we to use today's simulations to inform today's decisions? Two approaches are considered. The first augments the model-based PDF with an explicit subjective-probability of a "Big Surprise". The second is to look not for a PDF but, following Solvency II, consider the risk from any event that cannot be ruled out at, say, the one in 200 level. The fact that neither approach provides the simplicity and apparent confidence of interpreting model-based PDFs as if they were objective probabilities does not contradict the claim that either might lead to better decision-making.

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.

Binomial probability distribution model-based protein identification algorithm for tandem mass spectrometry utilizing peak intensity information.

PubMed

Xiao, Chuan-Le; Chen, Xiao-Zhou; Du, Yang-Li; Sun, Xuesong; Zhang, Gong; He, Qing-Yu

2013-01-04

Mass spectrometry has become one of the most important technologies in proteomic analysis. Tandem mass spectrometry (LC-MS/MS) is a major tool for the analysis of peptide mixtures from protein samples. The key step of MS data processing is the identification of peptides from experimental spectra by searching public sequence databases. Although a number of algorithms to identify peptides from MS/MS data have been already proposed, e.g. Sequest, OMSSA, X!Tandem, Mascot, etc., they are mainly based on statistical models considering only peak-matches between experimental and theoretical spectra, but not peak intensity information. Moreover, different algorithms gave different results from the same MS data, implying their probable incompleteness and questionable reproducibility. We developed a novel peptide identification algorithm, ProVerB, based on a binomial probability distribution model of protein tandem mass spectrometry combined with a new scoring function, making full use of peak intensity information and, thus, enhancing the ability of identification. Compared with Mascot, Sequest, and SQID, ProVerB identified significantly more peptides from LC-MS/MS data sets than the current algorithms at 1% False Discovery Rate (FDR) and provided more confident peptide identifications. ProVerB is also compatible with various platforms and experimental data sets, showing its robustness and versatility. The open-source program ProVerB is available at http://bioinformatics.jnu.edu.cn/software/proverb/ .

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.

Time difference of arrival estimation of microseismic signals based on alpha-stable distribution

NASA Astrophysics Data System (ADS)

Jia, Rui-Sheng; Gong, Yue; Peng, Yan-Jun; Sun, Hong-Mei; Zhang, Xing-Li; Lu, Xin-Ming

2018-05-01

Microseismic signals are generally considered to follow the Gauss distribution. A comparison of the dynamic characteristics of sample variance and the symmetry of microseismic signals with the signals which follow α-stable distribution reveals that the microseismic signals have obvious pulse characteristics and that the probability density curve of the microseismic signal is approximately symmetric. Thus, the hypothesis that microseismic signals follow the symmetric α-stable distribution is proposed. On the premise of this hypothesis, the characteristic exponent α of the microseismic signals is obtained by utilizing the fractional low-order statistics, and then a new method of time difference of arrival (TDOA) estimation of microseismic signals based on fractional low-order covariance (FLOC) is proposed. Upon applying this method to the TDOA estimation of Ricker wavelet simulation signals and real microseismic signals, experimental results show that the FLOC method, which is based on the assumption of the symmetric α-stable distribution, leads to enhanced spatial resolution of the TDOA estimation relative to the generalized cross correlation (GCC) method, which is based on the assumption of the Gaussian distribution.

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.

Glyph-based analysis of multimodal directional distributions in vector field ensembles

NASA Astrophysics Data System (ADS)

Jarema, Mihaela; Demir, Ismail; Kehrer, Johannes; Westermann, Rüdiger

2015-04-01

Ensemble simulations are increasingly often performed in the geosciences in order to study the uncertainty and variability of model predictions. Describing ensemble data by mean and standard deviation can be misleading in case of multimodal distributions. We present first results of a glyph-based visualization of multimodal directional distributions in 2D and 3D vector ensemble data. Directional information on the circle/sphere is modeled using mixtures of probability density functions (pdfs), which enables us to characterize the distributions with relatively few parameters. The resulting mixture models are represented by 2D and 3D lobular glyphs showing direction, spread and strength of each principal mode of the distributions. A 3D extension of our approach is realized by means of an efficient GPU rendering technique. We demonstrate our method in the context of ensemble weather simulations.

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.

Exploration of Use of Copulas in Analysing the Relationship between Precipitation and Meteorological Drought in Beijing, China

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

Fan, Linlin; Wang, Hongrui; Wang, Cheng

Drought risk analysis is essential for regional water resource management. In this study, the probabilistic relationship between precipitation and meteorological drought in Beijing, China, was calculated under three different precipitation conditions (precipitation equal to, greater than, or less than a threshold) based on copulas. The Standardized Precipitation Evapotranspiration Index (SPEI) was calculated based on monthly total precipitation and monthly mean temperature data. The trends and variations in the SPEI were analysed using Hilbert-Huang Transform (HHT) and Mann-Kendall (MK) trend tests with a running approach. The results of the HHT and MK test indicated a significant decreasing trend in the SPEI.more » The copula-based conditional probability indicated that the probability of meteorological drought decreased as monthly precipitation increased and that 10 mm can be regarded as the threshold for triggering extreme drought. From a quantitative perspective, when R ≤ mm, the probabilities of moderate drought, severe drought, and extreme drought were 22.1%, 18%, and 13.6%, respectively. This conditional probability distribution not only revealed the occurrence of meteorological drought in Beijing but also provided a quantitative way to analyse the probability of drought under different precipitation conditions. Furthermore, the results provide a useful reference for future drought prediction.« less

Exploration of Use of Copulas in Analysing the Relationship between Precipitation and Meteorological Drought in Beijing, China

DOE PAGES

Fan, Linlin; Wang, Hongrui; Wang, Cheng; ...

2017-05-16

Drought risk analysis is essential for regional water resource management. In this study, the probabilistic relationship between precipitation and meteorological drought in Beijing, China, was calculated under three different precipitation conditions (precipitation equal to, greater than, or less than a threshold) based on copulas. The Standardized Precipitation Evapotranspiration Index (SPEI) was calculated based on monthly total precipitation and monthly mean temperature data. The trends and variations in the SPEI were analysed using Hilbert-Huang Transform (HHT) and Mann-Kendall (MK) trend tests with a running approach. The results of the HHT and MK test indicated a significant decreasing trend in the SPEI.more » The copula-based conditional probability indicated that the probability of meteorological drought decreased as monthly precipitation increased and that 10 mm can be regarded as the threshold for triggering extreme drought. From a quantitative perspective, when R ≤ mm, the probabilities of moderate drought, severe drought, and extreme drought were 22.1%, 18%, and 13.6%, respectively. This conditional probability distribution not only revealed the occurrence of meteorological drought in Beijing but also provided a quantitative way to analyse the probability of drought under different precipitation conditions. Furthermore, the results provide a useful reference for future drought prediction.« less

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

Probabilistic Tsunami Hazard Assessment along Nankai Trough (1) An assessment based on the information of the forthcoming earthquake that Earthquake Research Committee(2013) evaluated

NASA Astrophysics Data System (ADS)

Hirata, K.; Fujiwara, H.; Nakamura, H.; Osada, M.; Morikawa, N.; Kawai, S.; Ohsumi, T.; Aoi, S.; Yamamoto, N.; Matsuyama, H.; Toyama, N.; Kito, T.; Murashima, Y.; Murata, Y.; Inoue, T.; Saito, R.; Takayama, J.; Akiyama, S.; Korenaga, M.; Abe, Y.; Hashimoto, N.

2015-12-01

The Earthquake Research Committee(ERC)/HERP, Government of Japan (2013) revised their long-term evaluation of the forthcoming large earthquake along the Nankai Trough; the next earthquake is estimated M8 to 9 class, and the probability (P30) that the next earthquake will occur within the next 30 years (from Jan. 1, 2013) is 60% to 70%. In this study, we assess tsunami hazards (maximum coastal tsunami heights) in the near future, in terms of a probabilistic approach, from the next earthquake along Nankai Trough, on the basis of ERC(2013)'s report. The probabilistic tsunami hazard assessment that we applied is as follows; (1) Characterized earthquake fault models (CEFMs) are constructed on each of the 15 hypothetical source areas (HSA) that ERC(2013) showed. The characterization rule follows Toyama et al.(2015, JpGU). As results, we obtained total of 1441 CEFMs. (2) We calculate tsunamis due to CEFMs by solving nonlinear, finite-amplitude, long-wave equations with advection and bottom friction terms by finite-difference method. Run-up computation on land is included. (3) A time predictable model predicts the recurrent interval of the present seismic cycle is T=88.2 years (ERC,2013). We fix P30 = 67% by applying the renewal process based on BPT distribution with T and alpha=0.24 as its aperiodicity. (4) We divide the probability P30 into P30(i) for i-th subgroup consisting of the earthquakes occurring in each of 15 HSA by following a probability re-distribution concept (ERC,2014). Then each earthquake (CEFM) in i-th subgroup is assigned a probability P30(i)/N where N is the number of CEFMs in each sub-group. Note that such re-distribution concept of the probability is nothing but tentative because the present seismology cannot give deep knowledge enough to do it. Epistemic logic-tree approach may be required in future. (5) We synthesize a number of tsunami hazard curves at every evaluation points on coasts by integrating the information about 30 years occurrence probabilities P30(i) for all earthquakes (CEFMs) and calculated maximum coastal tsunami heights. In the synthesis, aleatory uncertainties relating to incompleteness of governing equations, CEFM modeling, bathymetry and topography data, etc, are modeled assuming a log-normal probabilistic distribution. Examples of tsunami hazard curves will be presented.

Regional analysis and derivation of copula-based drought Severity-Area-Frequency curve in Lake Urmia basin, Iran.

PubMed

Amirataee, Babak; Montaseri, Majid; Rezaie, Hossein

2018-01-15

Droughts are extreme events characterized by temporal duration and spatial large-scale effects. In general, regional droughts are affected by general circulation of the atmosphere (at large-scale) and regional natural factors, including the topography, natural lakes, the position relative to the center and the path of the ocean currents (at small-scale), and they don't cover the exact same effects in a wide area. Therefore, drought Severity-Area-Frequency (S-A-F) curve investigation is an essential task to develop decision making rule for regional drought management. This study developed the copula-based joint probability distribution of drought severity and percent of area under drought across the Lake Urmia basin, Iran. To do this end, one-month Standardized Precipitation Index (SPI) values during the 1971-2013 were applied across 24 rainfall stations in the study area. Then, seven copula functions of various families, including Clayton, Gumbel, Frank, Joe, Galambos, Plackett and Normal copulas, were used to model the joint probability distribution of drought severity and drought area. Using AIC, BIC and RMSE criteria, the Frank copula was selected as the most appropriate copula in order to develop the joint probability distribution of severity-percent of area under drought across the study area. Based on the Frank copula, the drought S-A-F curve for the study area was derived. The results indicated that severe/extreme drought and non-drought (wet) behaviors have affected the majority of study areas (Lake Urmia basin). However, the area covered by the specific semi-drought effects is limited and has been subject to significant variations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Why Are Product Prices in Online Markets Not Converging?

PubMed Central

Mizuno, Takayuki; Watanabe, Tsutomu

2013-01-01

Why are product prices in online markets dispersed in spite of very small search costs? To address this question, we construct a unique dataset from a Japanese price comparison site, which records price quotes offered by e-retailers as well as customers’ clicks on products, which occur when they proceed to purchase the product. The novelty of our approach is that we seek to extract useful information on the source of price dispersion from the shape of price distributions rather than focusing merely on the standard deviation or the coefficient of variation of prices, as previous studies have done. We find that the distribution of prices retailers quote for a particular product at a particular point in time (divided by the lowest price) follows an exponential distribution, showing the presence of substantial price dispersion. For example, 20 percent of all retailers quote prices that are more than 50 percent higher than the lowest price. Next, comparing the probability that customers click on a retailer with a particular rank and the probability that retailers post prices at a particular rank, we show that both decline exponentially with price rank and that the exponents associated with the probabilities are quite close. This suggests that the reason why some retailers set prices at a level substantially higher than the lowest price is that they know that some customers will choose them even at that high price. Based on these findings, we hypothesize that price dispersion in online markets stems from heterogeneity in customers’ preferences over retailers; that is, customers choose a set of candidate retailers based on their preferences, which are heterogeneous across customers, and then pick a particular retailer among the candidates based on the price ranking. PMID:24015219

Why are product prices in online markets not converging?

PubMed

Mizuno, Takayuki; Watanabe, Tsutomu

2013-01-01

Why are product prices in online markets dispersed in spite of very small search costs? To address this question, we construct a unique dataset from a Japanese price comparison site, which records price quotes offered by e-retailers as well as customers' clicks on products, which occur when they proceed to purchase the product. The novelty of our approach is that we seek to extract useful information on the source of price dispersion from the shape of price distributions rather than focusing merely on the standard deviation or the coefficient of variation of prices, as previous studies have done. We find that the distribution of prices retailers quote for a particular product at a particular point in time (divided by the lowest price) follows an exponential distribution, showing the presence of substantial price dispersion. For example, 20 percent of all retailers quote prices that are more than 50 percent higher than the lowest price. Next, comparing the probability that customers click on a retailer with a particular rank and the probability that retailers post prices at a particular rank, we show that both decline exponentially with price rank and that the exponents associated with the probabilities are quite close. This suggests that the reason why some retailers set prices at a level substantially higher than the lowest price is that they know that some customers will choose them even at that high price. Based on these findings, we hypothesize that price dispersion in online markets stems from heterogeneity in customers' preferences over retailers; that is, customers choose a set of candidate retailers based on their preferences, which are heterogeneous across customers, and then pick a particular retailer among the candidates based on the price ranking.

Predictive modelling of habitat selection by marine predators with respect to the abundance and depth distribution of pelagic prey.

PubMed

Boyd, Charlotte; Castillo, Ramiro; Hunt, George L; Punt, André E; VanBlaricom, Glenn R; Weimerskirch, Henri; Bertrand, Sophie

2015-11-01

Understanding the ecological processes that underpin species distribution patterns is a fundamental goal in spatial ecology. However, developing predictive models of habitat use is challenging for species that forage in marine environments, as both predators and prey are often highly mobile and difficult to monitor. Consequently, few studies have developed resource selection functions for marine predators based directly on the abundance and distribution of their prey. We analysed contemporaneous data on the diving locations of two seabird species, the shallow-diving Peruvian Booby (Sula variegata) and deeper diving Guanay Cormorant (Phalacrocorax bougainvilliorum), and the abundance and depth distribution of their main prey, Peruvian anchoveta (Engraulis ringens). Based on this unique data set, we developed resource selection functions to test the hypothesis that the probability of seabird diving behaviour at a given location is a function of the relative abundance of prey in the upper water column. For both species, we show that the probability of diving behaviour is mostly explained by the distribution of prey at shallow depths. While the probability of diving behaviour increases sharply with prey abundance at relatively low levels of abundance, support for including abundance in addition to the depth distribution of prey is weak, suggesting that prey abundance was not a major factor determining the location of diving behaviour during the study period. The study thus highlights the importance of the depth distribution of prey for two species of seabird with different diving capabilities. The results complement previous research that points towards the importance of oceanographic processes that enhance the accessibility of prey to seabirds. The implications are that locations where prey is predictably found at accessible depths may be more important for surface foragers, such as seabirds, than locations where prey is predictably abundant. Analysis of the relative importance of abundance and accessibility is essential for the design and evaluation of effective management responses to reduced prey availability for seabirds and other top predators in marine systems. © 2015 The Authors. Journal of Animal Ecology © 2015 British Ecological Society.

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.

Predictive onboard flow control for packet switching satellites

NASA Technical Reports Server (NTRS)

Bobinsky, Eric A.

1992-01-01

We outline two alternate approaches to predicting the onset of congestion in a packet switching satellite, and argue that predictive, rather than reactive, flow control is necessary for the efficient operation of such a system. The first method discussed is based on standard, statistical techniques which are used to periodically calculate a probability of near-term congestion based on arrival rate statistics. If this probability exceeds a present threshold, the satellite would transmit a rate-reduction signal to all active ground stations. The second method discussed would utilize a neural network to periodically predict the occurrence of buffer overflow based on input data which would include, in addition to arrival rates, the distributions of packet lengths, source addresses, and destination addresses.

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.

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.

Beyond the swab: ecosystem sampling to understand the persistence of an amphibian pathogen.

PubMed

Mosher, Brittany A; Huyvaert, Kathryn P; Bailey, Larissa L

2018-06-02

Understanding the ecosystem-level persistence of pathogens is essential for predicting and measuring host-pathogen dynamics. However, this process is often masked, in part due to a reliance on host-based pathogen detection methods. The amphibian pathogens Batrachochytrium dendrobatidis (Bd) and B. salamandrivorans (Bsal) are pathogens of global conservation concern. Despite having free-living life stages, little is known about the distribution and persistence of these pathogens outside of their amphibian hosts. We combine historic amphibian monitoring data with contemporary host- and environment-based pathogen detection data to obtain estimates of Bd occurrence independent of amphibian host distributions. We also evaluate differences in filter- and swab-based detection probability and assess inferential differences arising from using different decision criteria used to classify samples as positive or negative. Water filtration-based detection probabilities were lower than those from swabs but were > 10%, and swab-based detection probabilities varied seasonally, declining in the early fall. The decision criterion used to classify samples as positive or negative was important; using a more liberal criterion yielded higher estimates of Bd occurrence than when a conservative criterion was used. Different covariates were important when using the liberal or conservative criterion in modeling Bd detection. We found evidence of long-term Bd persistence for several years after an amphibian host species of conservation concern, the boreal toad (Anaxyrus boreas boreas), was last detected. Our work provides evidence of long-term Bd persistence in the ecosystem, and underscores the importance of environmental samples for understanding and mitigating disease-related threats to amphibian biodiversity.

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.

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.

Distribution of arsenic and copper in sediment pore water: an ecological risk assessment case study for offshore drilling waste discharges.

PubMed

Sadiq, Rehan; Husain, Tahir; Veitch, Brian; Bose, Neil

2003-12-01

Due to the hydrophobic nature of synthetic based fluids (SBFs), drilling cuttings are not very dispersive in the water column and settle down close to the disposal site. Arsenic and copper are two important toxic heavy metals, among others, found in the drilling waste. In this article, the concentrations of heavy metals are determined using a steady state "aquivalence-based" fate model in a probabilistic mode. Monte Carlo simulations are employed to determine pore water concentrations. A hypothetical case study is used to determine the water quality impacts for two discharge options: 4% and 10% attached SBFs, which correspond to the best available technology option and the current discharge practice in the U.S. offshore. The exposure concentration (CE) is a predicted environmental concentration, which is adjusted for exposure probability and bioavailable fraction of heavy metals. The response of the ecosystem (RE) is defined by developing an empirical distribution function of predicted no-effect concentration. The pollutants' pore water concentrations within the radius of 750 m are estimated and cumulative distributions of risk quotient (RQ=CE/RE) are developed to determine the probability of RQ greater than 1.

Financial derivative pricing under probability operator via Esscher transfomation

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

Achi, Godswill U., E-mail: achigods@yahoo.com

2014-10-24

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing{sup 9} where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula usingmore » the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φ{sub x}(u) of X{sub t} we recuperate the Black-Scholes formula for financial derivative prices.« less

Application of Probabilistic Methods for the Determination of an Economically Robust HSCT Configuration

NASA Technical Reports Server (NTRS)

Mavris, Dimitri N.; Bandte, Oliver; Schrage, Daniel P.

1996-01-01

This paper outlines an approach for the determination of economically viable robust design solutions using the High Speed Civil Transport (HSCT) as a case study. Furthermore, the paper states the advantages of a probability based aircraft design over the traditional point design approach. It also proposes a new methodology called Robust Design Simulation (RDS) which treats customer satisfaction as the ultimate design objective. RDS is based on a probabilistic approach to aerospace systems design, which views the chosen objective as a distribution function introduced by so called noise or uncertainty variables. Since the designer has no control over these variables, a variability distribution is defined for each one of them. The cumulative effect of all these distributions causes the overall variability of the objective function. For cases where the selected objective function depends heavily on these noise variables, it may be desirable to obtain a design solution that minimizes this dependence. The paper outlines a step by step approach on how to achieve such a solution for the HSCT case study and introduces an evaluation criterion which guarantees the highest customer satisfaction. This customer satisfaction is expressed by the probability of achieving objective function values less than a desired target value.

Boosting with Averaged Weight Vectors

NASA Technical Reports Server (NTRS)

Oza, Nikunj C.; Clancy, Daniel (Technical Monitor)

2002-01-01

AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the previous base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. Some researchers have pointed out the intuition that it is probably better to construct a distribution that is orthogonal to the mistake vectors of all the previous base models, but that this is not always possible. We present an algorithm that attempts to come as close as possible to this goal in an efficient manner. We present experimental results demonstrating significant improvement over AdaBoost and the Totally Corrective boosting algorithm, which also attempts to satisfy this goal.

Gravity dual for a model of perception

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

Nakayama, Yu, E-mail: nakayama@berkeley.edu

2011-01-15

One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based onmore » a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution.« less

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

Xu, Xin-Ping, E-mail: xuxp@mail.ihep.ac.cn; Ide, Yusuke

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coinmore » and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.« less

Normal probabilities for Vandenberg AFB wind components - monthly reference periods for all flight azimuths, 0- to 70-km altitudes

NASA Technical Reports Server (NTRS)

Falls, L. W.

1975-01-01

Vandenberg Air Force Base (AFB), California, wind component statistics are presented to be used for aerospace engineering applications that require component wind probabilities for various flight azimuths and selected altitudes. The normal (Gaussian) distribution is presented as a statistical model to represent component winds at Vandenberg AFB. Head tail, and crosswind components are tabulated for all flight azimuths for altitudes from 0 to 70 km by monthly reference periods. Wind components are given for 11 selected percentiles ranging from 0.135 percent to 99.865 percent for each month. The results of statistical goodness-of-fit tests are presented to verify the use of the Gaussian distribution as an adequate model to represent component winds at Vandenberg AFB.

Connection between two statistical approaches for the modelling of particle velocity and concentration distributions in turbulent flow: The mesoscopic Eulerian formalism and the two-point probability density function method

NASA Astrophysics Data System (ADS)

Simonin, Olivier; Zaichik, Leonid I.; Alipchenkov, Vladimir M.; Février, Pierre

2006-12-01

The objective of the paper is to elucidate a connection between two approaches that have been separately proposed for modelling the statistical spatial properties of inertial particles in turbulent fluid flows. One of the approaches proposed recently by Février, Simonin, and Squires [J. Fluid Mech. 533, 1 (2005)] is based on the partitioning of particle turbulent velocity field into spatially correlated (mesoscopic Eulerian) and random-uncorrelated (quasi-Brownian) components. The other approach stems from a kinetic equation for the two-point probability density function of the velocity distributions of two particles [Zaichik and Alipchenkov, Phys. Fluids 15, 1776 (2003)]. Comparisons between these approaches are performed for isotropic homogeneous turbulence and demonstrate encouraging agreement.

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.

A Predictive Analysis of the Department of Defense Distribution System Utilizing Random Forests

DTIC Science & Technology

2016-06-01

resources capable of meeting both customer and individual resource constraints and goals while also maximizing the global benefit to the supply...and probability rules to determine the optimal red wine distribution network for an Italian-based wine producer. The decision support model for...combinations of factors that will result in delivery of the highest quality wines . The model’s first stage inputs basic logistics information to look

A New Self-Constrained Inversion Method of Potential Fields Based on Probability Tomography

NASA Astrophysics Data System (ADS)

Sun, S.; Chen, C.; WANG, H.; Wang, Q.

2014-12-01

The self-constrained inversion method of potential fields uses a priori information self-extracted from potential field data. Differing from external a priori information, the self-extracted information are generally parameters derived exclusively from the analysis of the gravity and magnetic data (Paoletti et al., 2013). Here we develop a new self-constrained inversion method based on probability tomography. Probability tomography doesn't need any priori information, as well as large inversion matrix operations. Moreover, its result can describe the sources, especially the distribution of which is complex and irregular, entirely and clearly. Therefore, we attempt to use the a priori information extracted from the probability tomography results to constrain the inversion for physical properties. The magnetic anomaly data was taken as an example in this work. The probability tomography result of magnetic total field anomaly(ΔΤ) shows a smoother distribution than the anomalous source and cannot display the source edges exactly. However, the gradients of ΔΤ are with higher resolution than ΔΤ in their own direction, and this characteristic is also presented in their probability tomography results. So we use some rules to combine the probability tomography results of ∂ΔΤ⁄∂x, ∂ΔΤ⁄∂y and ∂ΔΤ⁄∂z into a new result which is used for extracting a priori information, and then incorporate the information into the model objective function as spatial weighting functions to invert the final magnetic susceptibility. Some magnetic synthetic examples incorporated with and without a priori information extracted from the probability tomography results were made to do comparison, results of which show that the former are more concentrated and with higher resolution of the source body edges. This method is finally applied in an iron mine in China with field measured ΔΤ data and performs well. ReferencesPaoletti, V., Ialongo, S., Florio, G., Fedi, M. & Cella, F., 2013. Self-constrained inversion of potential fields, Geophys J Int.This research is supported by the Fundamental Research Funds for Institute for Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences (Grant Nos. WHS201210 and WHS201211).

Pan-European comparison of candidate distributions for climatological drought indices, SPI and SPEI

NASA Astrophysics Data System (ADS)

Stagge, James; Tallaksen, Lena; Gudmundsson, Lukas; Van Loon, Anne; Stahl, Kerstin

2013-04-01

Drought indices are vital to objectively quantify and compare drought severity, duration, and extent across regions with varied climatic and hydrologic regimes. The Standardized Precipitation Index (SPI), a well-reviewed meterological drought index recommended by the WMO, and its more recent water balance variant, the Standardized Precipitation-Evapotranspiration Index (SPEI) both rely on selection of univariate probability distributions to normalize the index, allowing for comparisons across climates. The SPI, considered a universal meteorological drought index, measures anomalies in precipitation, whereas the SPEI measures anomalies in climatic water balance (precipitation minus potential evapotranspiration), a more comprehensive measure of water availability that incorporates temperature. Many reviewers recommend use of the gamma (Pearson Type III) distribution for SPI normalization, while developers of the SPEI recommend use of the three parameter log-logistic distribution, based on point observation validation. Before the SPEI can be implemented at the pan-European scale, it is necessary to further validate the index using a range of candidate distributions to determine sensitivity to distribution selection, identify recommended distributions, and highlight those instances where a given distribution may not be valid. This study rigorously compares a suite of candidate probability distributions using WATCH Forcing Data, a global, historical (1958-2001) climate dataset based on ERA40 reanalysis with 0.5 x 0.5 degree resolution and bias-correction based on CRU-TS2.1 observations. Using maximum likelihood estimation, alternative candidate distributions are fit for the SPI and SPEI across the range of European climate zones. When evaluated at this scale, the gamma distribution for the SPI results in negatively skewed values, exaggerating the index severity of extreme dry conditions, while decreasing the index severity of extreme high precipitation. This bias is particularly notable for shorter aggregation periods (1-6 months) during the summer months in southern Europe (below 45° latitude), and can partially be attributed to distribution fitting difficulties in semi-arid regions where monthly precipitation totals cluster near zero. By contrast, the SPEI has potential for avoiding this fitting difficulty because it is not bounded by zero. However, the recommended log-logistic distribution produces index values with less variation than the standard normal distribution. Among the alternative candidate distributions, the best fit distribution and the distribution parameters vary in space and time, suggesting regional commonalities within hydroclimatic regimes, as discussed further in the presentation.

Conflict Probability Estimation for Free Flight

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Erzberger, Heinz

1996-01-01

The safety and efficiency of free flight will benefit from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method is developed in this paper to estimate that conflict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and Monte Carlo validation are presented.

The Forecast Interpretation Tool—a Monte Carlo technique for blending climatic distributions with probabilistic forecasts

USGS Publications Warehouse

Husak, Gregory J.; Michaelsen, Joel; Kyriakidis, P.; Verdin, James P.; Funk, Chris; Galu, Gideon

2011-01-01

Probabilistic forecasts are produced from a variety of outlets to help predict rainfall, and other meteorological events, for periods of 1 month or more. Such forecasts are expressed as probabilities of a rainfall event, e.g. being in the upper, middle, or lower third of the relevant distribution of rainfall in the region. The impact of these forecasts on the expectation for the event is not always clear or easily conveyed. This article proposes a technique based on Monte Carlo simulation for adjusting existing climatologic statistical parameters to match forecast information, resulting in new parameters defining the probability of events for the forecast interval. The resulting parameters are shown to approximate the forecasts with reasonable accuracy. To show the value of the technique as an application for seasonal rainfall, it is used with consensus forecast developed for the Greater Horn of Africa for the 2009 March-April-May season. An alternative, analytical approach is also proposed, and discussed in comparison to the first simulation-based technique.

Numerical Investigation of the Microscopic Heat Current Inside a Nanofluid System Based on Molecular Dynamics Simulation and Wavelet Analysis.

PubMed

Jia, Tao; Gao, Di

2018-04-03

Molecular dynamics simulation is employed to investigate the microscopic heat current inside an argon-copper nanofluid. Wavelet analysis of the microscopic heat current inside the nanofluid system is conducted. The signal of the microscopic heat current is decomposed into two parts: one is the approximation part; the other is the detail part. The approximation part is associated with the low-frequency part of the signal, and the detail part is associated with the high-frequency part of the signal. Both the probability distributions of the high-frequency and the low-frequency parts of the signals demonstrate Gaussian-like characteristics. The curves fit to data of the probability distribution of the microscopic heat current are established, and the parameters including the mean value and the standard deviation in the mathematical formulas of the curves show dramatic changes for the cases before and after adding copper nanoparticles into the argon base fluid.

Impact of Distributed Energy Resources on the Reliability of Critical Telecommunications Facilities: Preprint

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

Robinson, D. G.; Arent, D. J.; Johnson, L.

2006-06-01

This paper documents a probabilistic risk assessment of existing and alternative power supply systems at a large telecommunications office. The analysis characterizes the increase in the reliability of power supply through the use of two alternative power configurations. Failures in the power systems supporting major telecommunications service nodes are a main contributor to significant telecommunications outages. A logical approach to improving the robustness of telecommunication facilities is to increase the depth and breadth of technologies available to restore power during power outages. Distributed energy resources such as fuel cells and gas turbines could provide additional on-site electric power sources tomore » provide backup power, if batteries and diesel generators fail. The analysis is based on a hierarchical Bayesian approach and focuses on the failure probability associated with each of three possible facility configurations, along with assessment of the uncertainty or confidence level in the probability of failure. A risk-based characterization of final best configuration is presented.« less

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.

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.

Star Cluster Properties in Two LEGUS Galaxies Computed with Stochastic Stellar Population Synthesis Models

NASA Astrophysics Data System (ADS)

Krumholz, Mark R.; Adamo, Angela; Fumagalli, Michele; Wofford, Aida; Calzetti, Daniela; Lee, Janice C.; Whitmore, Bradley C.; Bright, Stacey N.; Grasha, Kathryn; Gouliermis, Dimitrios A.; Kim, Hwihyun; Nair, Preethi; Ryon, Jenna E.; Smith, Linda J.; Thilker, David; Ubeda, Leonardo; Zackrisson, Erik

2015-10-01

We investigate a novel Bayesian analysis method, based on the Stochastically Lighting Up Galaxies (slug) code, to derive the masses, ages, and extinctions of star clusters from integrated light photometry. Unlike many analysis methods, slug correctly accounts for incomplete initial mass function (IMF) sampling, and returns full posterior probability distributions rather than simply probability maxima. We apply our technique to 621 visually confirmed clusters in two nearby galaxies, NGC 628 and NGC 7793, that are part of the Legacy Extragalactic UV Survey (LEGUS). LEGUS provides Hubble Space Telescope photometry in the NUV, U, B, V, and I bands. We analyze the sensitivity of the derived cluster properties to choices of prior probability distribution, evolutionary tracks, IMF, metallicity, treatment of nebular emission, and extinction curve. We find that slug's results for individual clusters are insensitive to most of these choices, but that the posterior probability distributions we derive are often quite broad, and sometimes multi-peaked and quite sensitive to the choice of priors. In contrast, the properties of the cluster population as a whole are relatively robust against all of these choices. We also compare our results from slug to those derived with a conventional non-stochastic fitting code, Yggdrasil. We show that slug's stochastic models are generally a better fit to the observations than the deterministic ones used by Yggdrasil. However, the overall properties of the cluster populations recovered by both codes are qualitatively similar.

Probability-based nitrate contamination map of groundwater in Kinmen.

PubMed

Liu, Chen-Wuing; Wang, Yeuh-Bin; Jang, Cheng-Shin

2013-12-01

Groundwater supplies over 50% of drinking water in Kinmen. Approximately 16.8% of groundwater samples in Kinmen exceed the drinking water quality standard (DWQS) of NO3 (-)-N (10 mg/L). The residents drinking high nitrate-polluted groundwater pose a potential risk to health. To formulate effective water quality management plan and assure a safe drinking water in Kinmen, the detailed spatial distribution of nitrate-N in groundwater is a prerequisite. The aim of this study is to develop an efficient scheme for evaluating spatial distribution of nitrate-N in residential well water using logistic regression (LR) model. A probability-based nitrate-N contamination map in Kinmen is constructed. The LR model predicted the binary occurrence probability of groundwater nitrate-N concentrations exceeding DWQS by simple measurement variables as independent variables, including sampling season, soil type, water table depth, pH, EC, DO, and Eh. The analyzed results reveal that three statistically significant explanatory variables, soil type, pH, and EC, are selected for the forward stepwise LR analysis. The total ratio of correct classification reaches 92.7%. The highest probability of nitrate-N contamination map presents in the central zone, indicating that groundwater in the central zone should not be used for drinking purposes. Furthermore, a handy EC-pH-probability curve of nitrate-N exceeding the threshold of DWQS was developed. This curve can be used for preliminary screening of nitrate-N contamination in Kinmen groundwater. This study recommended that the local agency should implement the best management practice strategies to control nonpoint nitrogen sources and carry out a systematic monitoring of groundwater quality in residential wells of the high nitrate-N contamination zones.

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...

Optimal methods for fitting probability distributions to propagule retention time in studies of zoochorous dispersal.

PubMed

Viana, Duarte S; Santamaría, Luis; Figuerola, Jordi

2016-02-01

Propagule retention time is a key factor in determining propagule dispersal distance and the shape of "seed shadows". Propagules dispersed by animal vectors are either ingested and retained in the gut until defecation or attached externally to the body until detachment. Retention time is a continuous variable, but it is commonly measured at discrete time points, according to pre-established sampling time-intervals. Although parametric continuous distributions have been widely fitted to these interval-censored data, the performance of different fitting methods has not been evaluated. To investigate the performance of five different fitting methods, we fitted parametric probability distributions to typical discretized retention-time data with known distribution using as data-points either the lower, mid or upper bounds of sampling intervals, as well as the cumulative distribution of observed values (using either maximum likelihood or non-linear least squares for parameter estimation); then compared the estimated and original distributions to assess the accuracy of each method. We also assessed the robustness of these methods to variations in the sampling procedure (sample size and length of sampling time-intervals). Fittings to the cumulative distribution performed better for all types of parametric distributions (lognormal, gamma and Weibull distributions) and were more robust to variations in sample size and sampling time-intervals. These estimated distributions had negligible deviations of up to 0.045 in cumulative probability of retention times (according to the Kolmogorov-Smirnov statistic) in relation to original distributions from which propagule retention time was simulated, supporting the overall accuracy of this fitting method. In contrast, fitting the sampling-interval bounds resulted in greater deviations that ranged from 0.058 to 0.273 in cumulative probability of retention times, which may introduce considerable biases in parameter estimates. We recommend the use of cumulative probability to fit parametric probability distributions to propagule retention time, specifically using maximum likelihood for parameter estimation. Furthermore, the experimental design for an optimal characterization of unimodal propagule retention time should contemplate at least 500 recovered propagules and sampling time-intervals not larger than the time peak of propagule retrieval, except in the tail of the distribution where broader sampling time-intervals may also produce accurate fits.

How Can Histograms Be Useful for Introducing Continuous Probability Distributions?

ERIC Educational Resources Information Center

Derouet, Charlotte; Parzysz, Bernard

2016-01-01

The teaching of probability has changed a great deal since the end of the last century. The development of technologies is indeed part of this evolution. In France, continuous probability distributions began to be studied in 2002 by scientific 12th graders, but this subject was marginal and appeared only as an application of integral calculus.…

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…

Context-Based Intent Understanding for Autonomous Systems in Naval and Collaborative Robot Applications

DTIC Science & Technology

2013-10-29

COVERED (From - To) 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...based on contextual information, 3) develop vision-based techniques for learning of contextual information, and detection and identification of...that takes into account many possible contexts. The probability distributions of these contexts will be learned from existing databases on common sense

Predicting species distributions from checklist data using site-occupancy models

USGS Publications Warehouse

Kery, M.; Gardner, B.; Monnerat, C.

2010-01-01

Aim: (1) To increase awareness of the challenges induced by imperfect detection, which is a fundamental issue in species distribution modelling; (2) to emphasize the value of replicate observations for species distribution modelling; and (3) to show how 'cheap' checklist data in faunal/floral databases may be used for the rigorous modelling of distributions by site-occupancy models. Location: Switzerland. Methods: We used checklist data collected by volunteers during 1999 and 2000 to analyse the distribution of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly in Switzerland. We used data from repeated visits to 1-ha pixels to derive 'detection histories' and apply site-occupancy models to estimate the 'true' species distribution, i.e. corrected for imperfect detection. We modelled blue hawker distribution as a function of elevation and year and its detection probability of elevation, year and season. Results: The best model contained cubic polynomial elevation effects for distribution and quadratic effects of elevation and season for detectability. We compared the site-occupancy model with a conventional distribution model based on a generalized linear model, which assumes perfect detectability (p = 1). The conventional distribution map looked very different from the distribution map obtained using site-occupancy models that accounted for the imperfect detection. The conventional model underestimated the species distribution by 60%, and the slope parameters of the occurrence-elevation relationship were also underestimated when assuming p = 1. Elevation was not only an important predictor of blue hawker occurrence, but also of the detection probability, with a bell-shaped relationship. Furthermore, detectability increased over the season. The average detection probability was estimated at only 0.19 per survey. Main conclusions: Conventional species distribution models do not model species distributions per se but rather the apparent distribution, i.e. an unknown proportion of species distributions. That unknown proportion is equivalent to detectability. Imperfect detection in conventional species distribution models yields underestimates of the extent of distributions and covariate effects that are biased towards zero. In addition, patterns in detectability will erroneously be ascribed to species distributions. In contrast, site-occupancy models applied to replicated detection/non-detection data offer a powerful framework for making inferences about species distributions corrected for imperfect detection. The use of 'cheap' checklist data greatly enhances the scope of applications of this useful class of models. ?? 2010 Blackwell Publishing Ltd.

A SAS-based solution to evaluate study design efficiency of phase I pediatric oncology trials via discrete event simulation.

PubMed

Barrett, Jeffrey S; Jayaraman, Bhuvana; Patel, Dimple; Skolnik, Jeffrey M

2008-06-01

Previous exploration of oncology study design efficiency has focused on Markov processes alone (probability-based events) without consideration for time dependencies. Barriers to study completion include time delays associated with patient accrual, inevaluability (IE), time to dose limiting toxicities (DLT) and administrative and review time. Discrete event simulation (DES) can incorporate probability-based assignment of DLT and IE frequency, correlated with cohort in the case of DLT, with time-based events defined by stochastic relationships. A SAS-based solution to examine study efficiency metrics and evaluate design modifications that would improve study efficiency is presented. Virtual patients are simulated with attributes defined from prior distributions of relevant patient characteristics. Study population datasets are read into SAS macros which select patients and enroll them into a study based on the specific design criteria if the study is open to enrollment. Waiting times, arrival times and time to study events are also sampled from prior distributions; post-processing of study simulations is provided within the decision macros and compared across designs in a separate post-processing algorithm. This solution is examined via comparison of the standard 3+3 decision rule relative to the "rolling 6" design, a newly proposed enrollment strategy for the phase I pediatric oncology setting.

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

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.

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.

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.

Uncertainty squared: Choosing among multiple input probability distributions and interpreting multiple output probability distributions in Monte Carlo climate risk models

NASA Astrophysics Data System (ADS)

Baer, P.; Mastrandrea, M.

2006-12-01

Simple probabilistic models which attempt to estimate likely transient temperature change from specified CO2 emissions scenarios must make assumptions about at least six uncertain aspects of the causal chain between emissions and temperature: current radiative forcing (including but not limited to aerosols), current land use emissions, carbon sinks, future non-CO2 forcing, ocean heat uptake, and climate sensitivity. Of these, multiple PDFs (probability density functions) have been published for the climate sensitivity, a couple for current forcing and ocean heat uptake, one for future non-CO2 forcing, and none for current land use emissions or carbon cycle uncertainty (which are interdependent). Different assumptions about these parameters, as well as different model structures, will lead to different estimates of likely temperature increase from the same emissions pathway. Thus policymakers will be faced with a range of temperature probability distributions for the same emissions scenarios, each described by a central tendency and spread. Because our conventional understanding of uncertainty and probability requires that a probabilistically defined variable of interest have only a single mean (or median, or modal) value and a well-defined spread, this "multidimensional" uncertainty defies straightforward utilization in policymaking. We suggest that there are no simple solutions to the questions raised. Crucially, we must dispel the notion that there is a "true" probability probabilities of this type are necessarily subjective, and reasonable people may disagree. Indeed, we suggest that what is at stake is precisely the question, what is it reasonable to believe, and to act as if we believe? As a preliminary suggestion, we demonstrate how the output of a simple probabilistic climate model might be evaluated regarding the reasonableness of the outputs it calculates with different input PDFs. We suggest further that where there is insufficient evidence to clearly favor one range of probabilistic projections over another, that the choice of results on which to base policy must necessarily involve ethical considerations, as they have inevitable consequences for the distribution of risk In particular, the choice to use a more "optimistic" PDF for climate sensitivity (or other components of the causal chain) leads to the allowance of higher emissions consistent with any specified goal for risk reduction, and thus leads to higher climate impacts, in exchange for lower mitigation costs.

Uncertainty Analysis via Failure Domain Characterization: Unrestricted Requirement Functions

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2011-01-01

This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. The methods developed herein, which are based on nonlinear constrained optimization, are applicable to requirement functions whose functional dependency on the uncertainty is arbitrary and whose explicit form may even be unknown. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the assumed uncertainty model (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.

Scale Dependence of Spatiotemporal Intermittence of Rain

NASA Technical Reports Server (NTRS)

Kundu, Prasun K.; Siddani, Ravi K.

2011-01-01

It is a common experience that rainfall is intermittent in space and time. This is reflected by the fact that the statistics of area- and/or time-averaged rain rate is described by a mixed distribution with a nonzero probability of having a sharp value zero. In this paper we have explored the dependence of the probability of zero rain on the averaging space and time scales in large multiyear data sets based on radar and rain gauge observations. A stretched exponential fannula fits the observed scale dependence of the zero-rain probability. The proposed formula makes it apparent that the space-time support of the rain field is not quite a set of measure zero as is sometimes supposed. We also give an ex.planation of the observed behavior in tenus of a simple probabilistic model based on the premise that rainfall process has an intrinsic memory.

Exact and Approximate Probabilistic Symbolic Execution

NASA Technical Reports Server (NTRS)

Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem

2014-01-01

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Distribution, characterization, and exposure of MC252 oil in the supratidal beach environment.

PubMed

Lemelle, Kendall R; Elango, Vijaikrishnah; Pardue, John H

2014-07-01

The distribution and characteristics of MC252 oil:sand aggregates, termed surface residue balls (SRBs), were measured on the supratidal beach environment of oil-impacted Fourchon Beach in Louisiana (USA). Probability distributions of 4 variables, surface coverage (%), size of SRBs (mm(2) of projected area), mass of SRBs per m(2) (g/m(2)), and concentrations of polycyclic aromatic hydrocarbons (PAHs) and n-alkanes in the SRBs (mg of crude oil component per kg of SRB) were determined using parametric and nonparametric statistical techniques. Surface coverage of SRBs, an operational remedial standard for the beach surface, was a gamma-distributed variable ranging from 0.01% to 8.1%. The SRB sizes had a mean of 90.7 mm(2) but fit no probability distribution, and a nonparametric ranking was used to describe the size distributions. Concentrations of total PAHs ranged from 2.5 mg/kg to 126 mg/kg of SRB. Individual PAH concentration distributions, consisting primarily of alkylated phenanthrenes, dibenzothiophenes, and chrysenes, did not consistently fit a parametric distribution. Surface coverage was correlated with an oil mass per unit area but with a substantial error at lower coverage (i.e., <2%). These data provide probabilistic risk assessors with the ability to specify uncertainty in PAH concentration, exposure frequency, and ingestion rate, based on SRB characteristics for the dominant oil form on beaches along the US Gulf Coast. © 2014 SETAC.

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.

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.

Security evaluation of the quantum key distribution system with two-mode squeezed states

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

Osaki, M.; Ban, M.

2003-08-01

The quantum key distribution (QKD) system with two-mode squeezed states has been demonstrated by Pereira et al. [Phys. Rev. A 62, 042311 (2000)]. They evaluate the security of the system based on the signal to noise ratio attained by a homodyne detector. In this paper, we discuss its security based on the error probability individually attacked by eavesdropper with the unambiguous or the error optimum detection. The influence of the energy loss at transmission channels is also taken into account. It will be shown that the QKD system is secure under these conditions.

Tolerancing aspheres based on manufacturing knowledge

NASA Astrophysics Data System (ADS)

Wickenhagen, S.; Kokot, S.; Fuchs, U.

2017-10-01

A standard way of tolerancing optical elements or systems is to perform a Monte Carlo based analysis within a common optical design software package. Although, different weightings and distributions are assumed they are all counting on statistics, which usually means several hundreds or thousands of systems for reliable results. Thus, employing these methods for small batch sizes is unreliable, especially when aspheric surfaces are involved. The huge database of asphericon was used to investigate the correlation between the given tolerance values and measured data sets. The resulting probability distributions of these measured data were analyzed aiming for a robust optical tolerancing process.

Tolerancing aspheres based on manufacturing statistics

NASA Astrophysics Data System (ADS)

Wickenhagen, S.; Möhl, A.; Fuchs, U.

2017-11-01

A standard way of tolerancing optical elements or systems is to perform a Monte Carlo based analysis within a common optical design software package. Although, different weightings and distributions are assumed they are all counting on statistics, which usually means several hundreds or thousands of systems for reliable results. Thus, employing these methods for small batch sizes is unreliable, especially when aspheric surfaces are involved. The huge database of asphericon was used to investigate the correlation between the given tolerance values and measured data sets. The resulting probability distributions of these measured data were analyzed aiming for a robust optical tolerancing process.

Forecasting the Rupture Directivity of Large Earthquakes: Centroid Bias of the Conditional Hypocenter Distribution

NASA Astrophysics Data System (ADS)

Donovan, J.; Jordan, T. H.

2012-12-01

Forecasting the rupture directivity of large earthquakes is an important problem in probabilistic seismic hazard analysis (PSHA), because directivity is known to strongly influence ground motions. We describe how rupture directivity can be forecast in terms of the "conditional hypocenter distribution" or CHD, defined to be the probability distribution of a hypocenter given the spatial distribution of moment release (fault slip). The simplest CHD is a uniform distribution, in which the hypocenter probability density equals the moment-release probability density. For rupture models in which the rupture velocity and rise time depend only on the local slip, the CHD completely specifies the distribution of the directivity parameter D, defined in terms of the degree-two polynomial moments of the source space-time function. This parameter, which is zero for a bilateral rupture and unity for a unilateral rupture, can be estimated from finite-source models or by the direct inversion of seismograms (McGuire et al., 2002). We compile D-values from published studies of 65 large earthquakes and show that these data are statistically inconsistent with the uniform CHD advocated by McGuire et al. (2002). Instead, the data indicate a "centroid biased" CHD, in which the expected distance between the hypocenter and the hypocentroid is less than that of a uniform CHD. In other words, the observed directivities appear to be closer to bilateral than predicted by this simple model. We discuss the implications of these results for rupture dynamics and fault-zone heterogeneities. We also explore their PSHA implications by modifying the CyberShake simulation-based hazard model for the Los Angeles region, which assumed a uniform CHD (Graves et al., 2011).

Flow-duration-frequency behaviour of British rivers based on annual minima data

NASA Astrophysics Data System (ADS)

Zaidman, Maxine D.; Keller, Virginie; Young, Andrew R.; Cadman, Daniel

2003-06-01

A comparison of different probability distribution models for describing the flow-duration-frequency behaviour of annual minima flow events in British rivers is reported. Twenty-five catchments were included in the study, each having stable and natural flow records of at least 30 years in length. Time series of annual minima D-day average flows were derived for each record using durations ( D) of 1, 7, 30, 60, 90, and 365 days and used to construct low flow frequency curves. In each case the Gringorten plotting position formula was used to determine probabilities (of non-exceedance). Four distribution types—Generalised Extreme Value (GEV), Generalised Logistic (GL), Pearson Type-3 (PE3) and Generalised Pareto (GP)—were used to model the probability distribution function for each site. L-moments were used to parameterise individual models, whilst goodness-of-fit tests were used to assess their match to the sample data. The study showed that where short durations (i.e. 60 days or less) were considered, high storage catchments tended to be best represented by GL and GEV distribution models whilst low storage catchments were best described by PE3 or GEV models. However, these models produced reasonable results only within a limited range (e.g. models for high storage catchments did not produce sensible estimates of return periods where the prescribed flow was less than 10% of the mean flow). For annual minima series derived using long duration flow averages (e.g. more than 90 days), GP and GEV models were generally more applicable. The study suggests that longer duration minima do not conform to the same distribution types as short durations, and that catchment properties can influence the type of distribution selected.

Communicating the risk of injury in schoolboy rugby: using Poisson probability as an alternative presentation of the epidemiology.

PubMed

Parekh, Nikesh; Hodges, Stewart D; Pollock, Allyson M; Kirkwood, Graham

2012-06-01

The communication of injury risk in rugby and other sports is underdeveloped and parents, children and coaches need to be better informed about risk. A Poisson distribution was used to transform population based incidence of injury into average probabilities of injury to individual players. The incidence of injury in schoolboy rugby matches range from 7 to 129.8 injuries per 1000 player-hours; these rates translate to average probabilities of injury to a player of between 12% and 90% over a season. Incidence of injury and average probabilities of injury over a season should be published together in all future epidemiological studies on school rugby and other sports. More research is required on informing and communicating injury risks to parents, staff and children and how it affects monitoring, decision making and prevention strategies.

Functional aging in pilots : an examination of a mathematical model based on medical data on general aviation pilots.

DOT National Transportation Integrated Search

1982-06-01

The purpose of this study was to apply mathematical procedures to the Federal Aviation Administration (FAA) pilot medical data to examine the feasibility of devising a linear numbering system such that (1) the cumulative probability distribution func...

Load sharing in distributed real-time systems with state-change broadcasts

NASA Technical Reports Server (NTRS)

Shin, Kang G.; Chang, Yi-Chieh

1989-01-01

A decentralized dynamic load-sharing (LS) method based on state-change broadcasts is proposed for a distributed real-time system. Whenever the state of a node changes from underloaded to fully loaded and vice versa, the node broadcasts this change to a set of nodes, called a buddy set, in the system. The performance of the method is evaluated with both analytic modeling and simulation. It is modeled first by an embedded Markov chain for which numerical solutions are derived. The model solutions are then used to calculate the distribution of queue lengths at the nodes and the probability of meeting task deadlines. The analytical results show that buddy sets of 10 nodes outperform those of less than 10 nodes, and the incremental benefit gained from increasing the buddy set size beyond 15 nodes is insignificant. These and other analytical results are verified by simulation. The proposed LS method is shown to meet task deadlines with a very high probability.

Mean, covariance, and effective dimension of stochastic distributed delay dynamics

NASA Astrophysics Data System (ADS)

René, Alexandre; Longtin, André

2017-11-01

Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.

Post-glacial redistribution and shifts in productivity of giant kelp forests

PubMed Central

Graham, Michael H.; Kinlan, Brian P.; Grosberg, Richard K.

2010-01-01

Quaternary glacial–interglacial cycles create lasting biogeographic, demographic and genetic effects on ecosystems, yet the ecological effects of ice ages on benthic marine communities are unknown. We analysed long-term datasets to develop a niche-based model of southern Californian giant kelp (Macrocystis pyrifera) forest distribution as a function of oceanography and geomorphology, and synthesized palaeo-oceanographic records to show that late Quaternary climate change probably drove high millennial variability in the distribution and productivity of this foundation species. Our predictions suggest that kelp forest biomass increased up to threefold from the glacial maximum to the mid-Holocene, then rapidly declined by 40–70 per cent to present levels. The peak in kelp forest productivity would have coincided with the earliest coastal archaeological sites in the New World. Similar late Quaternary changes in kelp forest distribution and productivity probably occurred in coastal upwelling systems along active continental margins worldwide, which would have resulted in complex shifts in the relative productivity of terrestrial and marine components of coastal ecosystems. PMID:19846450

Universality in survivor distributions: Characterizing the winners of competitive dynamics

NASA Astrophysics Data System (ADS)

Luck, J. M.; Mehta, A.

2015-11-01

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept—the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node becomes independent of network geometry and assumes a simple form which depends only on its mass and degree.

Target Tracking Using SePDAF under Ambiguous Angles for Distributed Array Radar.

PubMed

Long, Teng; Zhang, Honggang; Zeng, Tao; Chen, Xinliang; Liu, Quanhua; Zheng, Le

2016-09-09

Distributed array radar can improve radar detection capability and measurement accuracy. However, it will suffer cyclic ambiguity in its angle estimates according to the spatial Nyquist sampling theorem since the large sparse array is undersampling. Consequently, the state estimation accuracy and track validity probability degrades when the ambiguous angles are directly used for target tracking. This paper proposes a second probability data association filter (SePDAF)-based tracking method for distributed array radar. Firstly, the target motion model and radar measurement model is built. Secondly, the fusion result of each radar's estimation is employed to the extended Kalman filter (EKF) to finish the first filtering. Thirdly, taking this result as prior knowledge, and associating with the array-processed ambiguous angles, the SePDAF is applied to accomplish the second filtering, and then achieving a high accuracy and stable trajectory with relatively low computational complexity. Moreover, the azimuth filtering accuracy will be promoted dramatically and the position filtering accuracy will also improve. Finally, simulations illustrate the effectiveness of the proposed method.

Probability distribution of haplotype frequencies under the two-locus Wright-Fisher model by diffusion approximation.

PubMed

Boitard, Simon; Loisel, Patrice

2007-05-01

The probability distribution of haplotype frequencies in a population, and the way it is influenced by genetical forces such as recombination, selection, random drift ...is a question of fundamental interest in population genetics. For large populations, the distribution of haplotype frequencies for two linked loci under the classical Wright-Fisher model is almost impossible to compute because of numerical reasons. However the Wright-Fisher process can in such cases be approximated by a diffusion process and the transition density can then be deduced from the Kolmogorov equations. As no exact solution has been found for these equations, we developed a numerical method based on finite differences to solve them. It applies to transient states and models including selection or mutations. We show by several tests that this method is accurate for computing the conditional joint density of haplotype frequencies given that no haplotype has been lost. We also prove that it is far less time consuming than other methods such as Monte Carlo simulations.

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis

PubMed Central

Dumitrascu, Adela-Eliza; Lepadatescu, Badea; Dumitrascu, Dorin-Ion; Nedelcu, Anisor; Ciobanu, Doina Valentina

2015-01-01

Due to the prolonged use of wind turbines they must be characterized by high reliability. This can be achieved through a rigorous design, appropriate simulation and testing, and proper construction. The reliability prediction and analysis of these systems will lead to identifying the critical components, increasing the operating time, minimizing failure rate, and minimizing maintenance costs. To estimate the produced energy by the wind turbine, an evaluation approach based on the Monte Carlo simulation model is developed which enables us to estimate the probability of minimum and maximum parameters. In our simulation process we used triangular distributions. The analysis of simulation results has been focused on the interpretation of the relative frequency histograms and cumulative distribution curve (ogive diagram), which indicates the probability of obtaining the daily or annual energy output depending on wind speed. The experimental researches consist in estimation of the reliability and unreliability functions and hazard rate of the helical vertical axis wind turbine designed and patented to climatic conditions for Romanian regions. Also, the variation of power produced for different wind speeds, the Weibull distribution of wind probability, and the power generated were determined. The analysis of experimental results indicates that this type of wind turbine is efficient at low wind speed. PMID:26167524

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis.

PubMed

Dumitrascu, Adela-Eliza; Lepadatescu, Badea; Dumitrascu, Dorin-Ion; Nedelcu, Anisor; Ciobanu, Doina Valentina

2015-01-01

Due to the prolonged use of wind turbines they must be characterized by high reliability. This can be achieved through a rigorous design, appropriate simulation and testing, and proper construction. The reliability prediction and analysis of these systems will lead to identifying the critical components, increasing the operating time, minimizing failure rate, and minimizing maintenance costs. To estimate the produced energy by the wind turbine, an evaluation approach based on the Monte Carlo simulation model is developed which enables us to estimate the probability of minimum and maximum parameters. In our simulation process we used triangular distributions. The analysis of simulation results has been focused on the interpretation of the relative frequency histograms and cumulative distribution curve (ogive diagram), which indicates the probability of obtaining the daily or annual energy output depending on wind speed. The experimental researches consist in estimation of the reliability and unreliability functions and hazard rate of the helical vertical axis wind turbine designed and patented to climatic conditions for Romanian regions. Also, the variation of power produced for different wind speeds, the Weibull distribution of wind probability, and the power generated were determined. The analysis of experimental results indicates that this type of wind turbine is efficient at low wind speed.

Driven fragmentation of granular gases.

PubMed

Cruz Hidalgo, Raúl; Pagonabarraga, Ignacio

2008-06-01

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the long velocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f(c) approximately exp(-cn) , with n approximately 1.2 , regarding less the fragmentation mechanisms.

Transmission characteristics of Bessel-Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

NASA Astrophysics Data System (ADS)

Wang, Xiaohui; Song, Yingxiong

2018-02-01

By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.

A New Bond Albedo for Performing Orbital Debris Brightness to Size Transformations

NASA Technical Reports Server (NTRS)

Mulrooney, Mark K.; Matney, Mark J.

2008-01-01

We have developed a technique for estimating the intrinsic size distribution of orbital debris objects via optical measurements alone. The process is predicated on the empirically observed power-law size distribution of debris (as indicated by radar RCS measurements) and the log-normal probability distribution of optical albedos as ascertained from phase (Lambertian) and range-corrected telescopic brightness measurements. Since the observed distribution of optical brightness is the product integral of the size distribution of the parent [debris] population with the albedo probability distribution, it is a straightforward matter to transform a given distribution of optical brightness back to a size distribution by the appropriate choice of a single albedo value. This is true because the integration of a powerlaw with a log-normal distribution (Fredholm Integral of the First Kind) yields a Gaussian-blurred power-law distribution with identical power-law exponent. Application of a single albedo to this distribution recovers a simple power-law [in size] which is linearly offset from the original distribution by a constant whose value depends on the choice of the albedo. Significantly, there exists a unique Bond albedo which, when applied to an observed brightness distribution, yields zero offset and therefore recovers the original size distribution. For physically realistic powerlaws of negative slope, the proper choice of albedo recovers the parent size distribution by compensating for the observational bias caused by the large number of small objects that appear anomalously large (bright) - and thereby skew the small population upward by rising above the detection threshold - and the lower number of large objects that appear anomalously small (dim). Based on this comprehensive analysis, a value of 0.13 should be applied to all orbital debris albedo-based brightness-to-size transformations regardless of data source. Its prima fascia genesis, derived and constructed from the current RCS to size conversion methodology (SiBAM Size-Based Estimation Model) and optical data reduction standards, assures consistency in application with the prior canonical value of 0.1. Herein we present the empirical and mathematical arguments for this approach and by example apply it to a comprehensive set of photometric data acquired via NASA's Liquid Mirror Telescopes during the 2000-2001 observing season.

An approach to evaluating reactive airborne wind shear systems

NASA Technical Reports Server (NTRS)

Gibson, Joseph P., Jr.

1992-01-01

An approach to evaluating reactive airborne windshear detection systems was developed to support a deployment study for future FAA ground-based windshear detection systems. The deployment study methodology assesses potential future safety enhancements beyond planned capabilities. The reactive airborne systems will be an integral part of planned windshear safety enhancements. The approach to evaluating reactive airborne systems involves separate analyses for both landing and take-off scenario. The analysis estimates the probability of effective warning considering several factors including NASA energy height loss characteristics, reactive alert timing, and a probability distribution for microburst strength.

Evolution of ion emission yield of alloys with the nature of the solute. 2: Interpretation

NASA Technical Reports Server (NTRS)

Blaise, G.; Slodzian, G.

1977-01-01

Solid solutions of transition elements in copper, nickel, cobalt, iron, and aluminum matrices were analyzed by observing secondary ion emissions under bombardment with 6.2-keV argon ions. Enchancement of the production of solute-element ions was observed. An ion emission model is proposed according to which the ion yield is governed by the probability of an atom leaving the metal in a preionized state. The energy distribution of the valence electrons of the solute atoms is the bases of the probability calculation.

Change Point Problems in Regression

DTIC Science & Technology

1988-06-01

equals W at i/m (i = 1,...,m) and is linear in each interval (i/m, (i + 1)/m). I!,. Section 2.2: Asymptotic Behavior of Test Statistics 13 Lemma ...Numbers implies that Qzz.vn/m - 1, QZV,/m --+ 0 in probability. By the previous lemma . B’-- W1, B’- W2 in distribution, and hence Dm - 1 in probability...2 converges to the same limit as in (2.5) by the Slutsky’s Lemma . I S Now we will consider the conditional test for HO. This conditional test is based

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.

Heterogeneous Data Fusion Method to Estimate Travel Time Distributions in Congested Road Networks

PubMed Central

Lam, William H. K.; Li, Qingquan

2017-01-01

Travel times in congested urban road networks are highly stochastic. Provision of travel time distribution information, including both mean and variance, can be very useful for travelers to make reliable path choice decisions to ensure higher probability of on-time arrival. To this end, a heterogeneous data fusion method is proposed to estimate travel time distributions by fusing heterogeneous data from point and interval detectors. In the proposed method, link travel time distributions are first estimated from point detector observations. The travel time distributions of links without point detectors are imputed based on their spatial correlations with links that have point detectors. The estimated link travel time distributions are then fused with path travel time distributions obtained from the interval detectors using Dempster-Shafer evidence theory. Based on fused path travel time distribution, an optimization technique is further introduced to update link travel time distributions and their spatial correlations. A case study was performed using real-world data from Hong Kong and showed that the proposed method obtained accurate and robust estimations of link and path travel time distributions in congested road networks. PMID:29210978

Heterogeneous Data Fusion Method to Estimate Travel Time Distributions in Congested Road Networks.

PubMed

Shi, Chaoyang; Chen, Bi Yu; Lam, William H K; Li, Qingquan

2017-12-06

Travel times in congested urban road networks are highly stochastic. Provision of travel time distribution information, including both mean and variance, can be very useful for travelers to make reliable path choice decisions to ensure higher probability of on-time arrival. To this end, a heterogeneous data fusion method is proposed to estimate travel time distributions by fusing heterogeneous data from point and interval detectors. In the proposed method, link travel time distributions are first estimated from point detector observations. The travel time distributions of links without point detectors are imputed based on their spatial correlations with links that have point detectors. The estimated link travel time distributions are then fused with path travel time distributions obtained from the interval detectors using Dempster-Shafer evidence theory. Based on fused path travel time distribution, an optimization technique is further introduced to update link travel time distributions and their spatial correlations. A case study was performed using real-world data from Hong Kong and showed that the proposed method obtained accurate and robust estimations of link and path travel time distributions in congested road networks.

Balancing exploration and exploitation in population-based sampling improves fragment-based de novo protein structure prediction.

PubMed

Simoncini, David; Schiex, Thomas; Zhang, Kam Y J

2017-05-01

Conformational search space exploration remains a major bottleneck for protein structure prediction methods. Population-based meta-heuristics typically enable the possibility to control the search dynamics and to tune the balance between local energy minimization and search space exploration. EdaFold is a fragment-based approach that can guide search by periodically updating the probability distribution over the fragment libraries used during model assembly. We implement the EdaFold algorithm as a Rosetta protocol and provide two different probability update policies: a cluster-based variation (EdaRose c ) and an energy-based one (EdaRose en ). We analyze the search dynamics of our new Rosetta protocols and show that EdaRose c is able to provide predictions with lower C αRMSD to the native structure than EdaRose en and Rosetta AbInitio Relax protocol. Our software is freely available as a C++ patch for the Rosetta suite and can be downloaded from http://www.riken.jp/zhangiru/software/. Our protocols can easily be extended in order to create alternative probability update policies and generate new search dynamics. Proteins 2017; 85:852-858. © 2016 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

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.

An understanding of human dynamics in urban subway traffic from the Maximum Entropy Principle

NASA Astrophysics Data System (ADS)

Yong, Nuo; Ni, Shunjiang; Shen, Shifei; Ji, Xuewei

2016-08-01

We studied the distribution of entry time interval in Beijing subway traffic by analyzing the smart card transaction data, and then deduced the probability distribution function of entry time interval based on the Maximum Entropy Principle. Both theoretical derivation and data statistics indicated that the entry time interval obeys power-law distribution with an exponential cutoff. In addition, we pointed out the constraint conditions for the distribution form and discussed how the constraints affect the distribution function. It is speculated that for bursts and heavy tails in human dynamics, when the fitted power exponent is less than 1.0, it cannot be a pure power-law distribution, but with an exponential cutoff, which may be ignored in the previous studies.

Ridit Analysis for Cooper-Harper and Other Ordinal Ratings for Sparse Data - A Distance-based Approach

DTIC Science & Technology

2016-09-01

is to fit empirical Beta distributions to observed data, and then to use a randomization approach to make inferences on the difference between...a Ridit analysis on the often sparse data sets in many Flying Qualities applicationsi. The method of this paper is to fit empirical Beta ...One such measure is the discrete- probability-distribution version of the (squared) ‘Hellinger Distance’ (Yang & Le Cam , 2000) 2(, ) = 1

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

Chertkov, Michael; Turitsyn, Konstantin; Sulc, Petr

The anticipated increase in the number of plug-in electric vehicles (EV) will put additional strain on electrical distribution circuits. Many control schemes have been proposed to control EV charging. Here, we develop control algorithms based on randomized EV charging start times and simple one-way broadcast communication allowing for a time delay between communication events. Using arguments from queuing theory and statistical analysis, we seek to maximize the utilization of excess distribution circuit capacity while keeping the probability of a circuit overload negligible.

Spatial distribution of sand fly species (Psychodidae: Phlebtominae), ecological niche, and climatic regionalization in zoonotic foci of cutaneous leishmaniasis, southwest of Iran.

PubMed

Ebrahimi, Sahar; Bordbar, Ali; Rastaghi, Ahmad R Esmaeili; Parvizi, Parviz

2016-06-01

Cutaneous leishmaniasis (CL) is a complex vector-borne disease caused by Leishmania parasites that are transmitted by the bite of several species of infected female phlebotomine sand flies. Monthly factor analysis of climatic variables indicated fundamental variables. Principal component-based regionalization was used for recognition of climatic zones using a clustering integrated method that identified five climatic zones based on factor analysis. To investigate spatial distribution of the sand fly species, the kriging method was used as an advanced geostatistical procedure in the ArcGIS modeling system that is beneficial to design measurement plans and to predict the transmission cycle in various regions of Khuzestan province, southwest of Iran. However, more than an 80% probability of P. papatasi was observed in rainy and temperate bio-climatic zones with a high potential of CL transmission. Finding P. sergenti revealed the probability of transmission and distribution patterns of a non-native vector of CL in related zones. These findings could be used as models indicating climatic zones and environmental variables connected to sand fly presence and vector distribution. Furthermore, this information is appropriate for future research efforts into the ecology of Phlebotomine sand flies and for the prevention of CL vector transmission as a public health priority. © 2016 The Society for Vector Ecology.

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.

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.

End-to-end distance and contour length distribution functions of DNA helices

NASA Astrophysics Data System (ADS)

Zoli, Marco

2018-06-01

I present a computational method to evaluate the end-to-end and the contour length distribution functions of short DNA molecules described by a mesoscopic Hamiltonian. The method generates a large statistical ensemble of possible configurations for each dimer in the sequence, selects the global equilibrium twist conformation for the molecule, and determines the average base pair distances along the molecule backbone. Integrating over the base pair radial and angular fluctuations, I derive the room temperature distribution functions as a function of the sequence length. The obtained values for the most probable end-to-end distance and contour length distance, providing a measure of the global molecule size, are used to examine the DNA flexibility at short length scales. It is found that, also in molecules with less than ˜60 base pairs, coiled configurations maintain a large statistical weight and, consistently, the persistence lengths may be much smaller than in kilo-base DNA.

Distributed Synchronization Technique for OFDMA-Based Wireless Mesh Networks Using a Bio-Inspired Algorithm

PubMed Central

Kim, Mi Jeong; Maeng, Sung Joon; Cho, Yong Soo

2015-01-01

In this paper, a distributed synchronization technique based on a bio-inspired algorithm is proposed for an orthogonal frequency division multiple access (OFDMA)-based wireless mesh network (WMN) with a time difference of arrival. The proposed time- and frequency-synchronization technique uses only the signals received from the neighbor nodes, by considering the effect of the propagation delay between the nodes. It achieves a fast synchronization with a relatively low computational complexity because it is operated in a distributed manner, not requiring any feedback channel for the compensation of the propagation delays. In addition, a self-organization scheme that can be effectively used to construct 1-hop neighbor nodes is proposed for an OFDMA-based WMN with a large number of nodes. The performance of the proposed technique is evaluated with regard to the convergence property and synchronization success probability using a computer simulation. PMID:26225974

Distributed Synchronization Technique for OFDMA-Based Wireless Mesh Networks Using a Bio-Inspired Algorithm.

PubMed

Kim, Mi Jeong; Maeng, Sung Joon; Cho, Yong Soo

2015-07-28

In this paper, a distributed synchronization technique based on a bio-inspired algorithm is proposed for an orthogonal frequency division multiple access (OFDMA)-based wireless mesh network (WMN) with a time difference of arrival. The proposed time- and frequency-synchronization technique uses only the signals received from the neighbor nodes, by considering the effect of the propagation delay between the nodes. It achieves a fast synchronization with a relatively low computational complexity because it is operated in a distributed manner, not requiring any feedback channel for the compensation of the propagation delays. In addition, a self-organization scheme that can be effectively used to construct 1-hop neighbor nodes is proposed for an OFDMA-based WMN with a large number of nodes. The performance of the proposed technique is evaluated with regard to the convergence property and synchronization success probability using a computer simulation.

Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events.

PubMed

Shahi, Mina; van Vreeswijk, Carl; Pipa, Gordon

2016-01-01

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate.

Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events

PubMed Central

Shahi, Mina; van Vreeswijk, Carl; Pipa, Gordon

2016-01-01

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate. PMID:28066225

Hantavirus reservoir Oligoryzomys longicaudatus spatial distribution sensitivity to climate change scenarios in Argentine Patagonia

PubMed Central

Carbajo, Aníbal E; Vera, Carolina; González, Paula LM

2009-01-01

Background Oligoryzomys longicaudatus (colilargo) is the rodent responsible for hantavirus pulmonary syndrome (HPS) in Argentine Patagonia. In past decades (1967–1998), trends of precipitation reduction and surface air temperature increase have been observed in western Patagonia. We explore how the potential distribution of the hantavirus reservoir would change under different climate change scenarios based on the observed trends. Methods Four scenarios of potential climate change were constructed using temperature and precipitation changes observed in Argentine Patagonia between 1967 and 1998: Scenario 1 assumed no change in precipitation but a temperature trend as observed; scenario 2 assumed no changes in temperature but a precipitation trend as observed; Scenario 3 included changes in both temperature and precipitation trends as observed; Scenario 4 assumed changes in both temperature and precipitation trends as observed but doubled. We used a validated spatial distribution model of O. longicaudatus as a function of temperature and precipitation. From the model probability of the rodent presence was calculated for each scenario. Results If changes in precipitation follow previous trends, the probability of the colilargo presence would fall in the HPS transmission zone of northern Patagonia. If temperature and precipitation trends remain at current levels for 60 years or double in the future 30 years, the probability of the rodent presence and the associated total area of potential distribution would diminish throughout Patagonia; the areas of potential distribution for colilargos would shift eastwards. These results suggest that future changes in Patagonia climate may lower transmission risk through a reduction in the potential distribution of the rodent reservoir. Conclusion According to our model the rates of temperature and precipitation changes observed between 1967 and 1998 may produce significant changes in the rodent distribution in an equivalent period of time only in certain areas. Given that changes maintain for 60 years or double in 30 years, the hantavirus reservoir Oligoryzomys longicaudatus may contract its distribution in Argentine Patagonia extensively. PMID:19607707

Quantum supremacy in constant-time measurement-based computation: A unified architecture for sampling and verification

NASA Astrophysics Data System (ADS)

Miller, Jacob; Sanders, Stephen; Miyake, Akimasa

2017-12-01

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable advantage in quantum devices without demanding quantum error correction, which is crucial for prolonging the coherence time of qubits. We propose a model device made of locally interacting multiple qubits, designed such that simultaneous single-qubit measurements on it can output probability distributions whose average-case sampling is classically intractable, under similar assumptions as the sampling of noninteracting bosons and instantaneous quantum circuits. Notably, in contrast to these previous unitary-based realizations, our measurement-based implementation has two distinctive features. (i) Our implementation involves no adaptation of measurement bases, leading output probability distributions to be generated in constant time, independent of the system size. Thus, it could be implemented in principle without quantum error correction. (ii) Verifying the classical intractability of our sampling is done by changing the Pauli measurement bases only at certain output qubits. Our usage of random commuting quantum circuits in place of computationally universal circuits allows a unique unification of sampling and verification, so they require the same physical resource requirements in contrast to the more demanding verification protocols seen elsewhere in the literature.

Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling

PubMed Central

Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno

2016-01-01

Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision. PMID:27303323

Stability metrics for multi-source biomedical data based on simplicial projections from probability distribution distances.

PubMed

Sáez, Carlos; Robles, Montserrat; García-Gómez, Juan M

2017-02-01

Biomedical data may be composed of individuals generated from distinct, meaningful sources. Due to possible contextual biases in the processes that generate data, there may exist an undesirable and unexpected variability among the probability distribution functions (PDFs) of the source subsamples, which, when uncontrolled, may lead to inaccurate or unreproducible research results. Classical statistical methods may have difficulties to undercover such variabilities when dealing with multi-modal, multi-type, multi-variate data. This work proposes two metrics for the analysis of stability among multiple data sources, robust to the aforementioned conditions, and defined in the context of data quality assessment. Specifically, a global probabilistic deviation and a source probabilistic outlyingness metrics are proposed. The first provides a bounded degree of the global multi-source variability, designed as an estimator equivalent to the notion of normalized standard deviation of PDFs. The second provides a bounded degree of the dissimilarity of each source to a latent central distribution. The metrics are based on the projection of a simplex geometrical structure constructed from the Jensen-Shannon distances among the sources PDFs. The metrics have been evaluated and demonstrated their correct behaviour on a simulated benchmark and with real multi-source biomedical data using the UCI Heart Disease data set. The biomedical data quality assessment based on the proposed stability metrics may improve the efficiency and effectiveness of biomedical data exploitation and research.

The 1996 Leonid shower as studied with a potassium lidar: Observations and inferred meteoroid sizes

NASA Astrophysics Data System (ADS)

Höffner, Josef; von Zahn, Ulf; McNeil, William J.; Murad, Edmond

1999-02-01

We report on the observation and analysis of meteor trails that are detected by ground-based lidar tuned to the D1 fine structure line of K. The lidar is located at Kühlungsborn, Germany. The echo profiles are analyzed with a temporal resolution of about 1 s and altitude resolution of 200 m. Identification of meteor trails in the large archive of raw data is performed with help of an automated computer search code. During the peak of the Lenoid meteor shower on the morning of November 17, 1996, we observed seven meteor trails between 0245 and 0445 UT. Their mean altitude was 89.0 km. The duration of observation of individual trails ranges from 3 s to ~30 min. We model the probability of observing a meteor trail by ground-based lidar as a function of both altitude distribution and duration of the trails. These distributions depend on the mass distribution, entry velocity, and entry angle of the meteoroids, on the altitude-dependent chemical and dynamical lifetimes of the released K atom, and on the absolute detection sensitivity of our lidar experiment. From the modeling, we derive the statistical likelihood of detection of trails from meteoroids of a particular size. These bracket quite well the observed trails. The model also gives estimates of the probable size of the meteoroids based on characteristics of individual trails.

Using optimal transport theory to estimate transition probabilities in metapopulation dynamics

USGS Publications Warehouse

Nichols, Jonathan M.; Spendelow, Jeffrey A.; Nichols, James D.

2017-01-01

This work considers the estimation of transition probabilities associated with populations moving among multiple spatial locations based on numbers of individuals at each location at two points in time. The problem is generally underdetermined as there exists an extremely large number of ways in which individuals can move from one set of locations to another. A unique solution therefore requires a constraint. The theory of optimal transport provides such a constraint in the form of a cost function, to be minimized in expectation over the space of possible transition matrices. We demonstrate the optimal transport approach on marked bird data and compare to the probabilities obtained via maximum likelihood estimation based on marked individuals. It is shown that by choosing the squared Euclidean distance as the cost, the estimated transition probabilities compare favorably to those obtained via maximum likelihood with marked individuals. Other implications of this cost are discussed, including the ability to accurately interpolate the population's spatial distribution at unobserved points in time and the more general relationship between the cost and minimum transport energy.

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.

Exceedance probability map: a tool helping the definition of arsenic Natural Background Level (NBL) within the Drainage Basin to the Venice Lagoon (NE Italy)

NASA Astrophysics Data System (ADS)

Dalla Libera, Nico; Fabbri, Paolo; Mason, Leonardo; Piccinini, Leonardo; Pola, Marco

2017-04-01

Arsenic groundwater contamination affects worldwide shallower groundwater bodies. Starting from the actual knowledges around arsenic origin into groundwater, we know that the major part of dissolved arsenic is naturally occurring through the dissolution of As-bearing minerals and ores. Several studies on the shallow aquifers of both the regional Venetian Plain (NE Italy) and the local Drainage Basin to the Venice Lagoon (DBVL) show local high arsenic concentration related to peculiar geochemical conditions, which drive arsenic mobilization. The uncertainty of arsenic spatial distribution makes difficult both the evaluation of the processes involved in arsenic mobilization and the stakeholders' decision about environmental management. Considering the latter aspect, the present study treats the problem of the Natural Background Level (NBL) definition as the threshold discriminating the natural contamination from the anthropogenic pollution. Actually, the UE's Directive 2006/118/EC suggests the procedures and criteria to set up the water quality standards guaranteeing a healthy status and reversing any contamination trends. In addition, the UE's BRIDGE project proposes some criteria, based on the 90th percentile of the contaminant's concentrations dataset, to estimate the NBL. Nevertheless, these methods provides just a statistical NBL for the whole area without considering the spatial variation of the contaminant's concentration. In this sense, we would reinforce the NBL concept using a geostatistical approach, which is able to give some detailed information about the distribution of arsenic concentrations and unveiling zones with high concentrations referred to the Italian drinking water standard (IDWS = 10 µg/liter). Once obtained the spatial information about arsenic distribution, we can apply the 90th percentile methods to estimate some Local NBL referring to every zones with arsenic higher than IDWS. The indicator kriging method was considered because it estimates the spatial distribution of the exceedance probabilities respect some pre-defined thresholds. This approach is largely mentioned in literature to face similar environmental problems. To test the validity of the procedure, we used the dataset from "A.Li.Na" project (founded by the Regional Environmental Agency) that defined regional NBLs of As, Fe, Mn and NH4+ into DBVL's groundwater. Primarily, we defined two thresholds corresponding respectively to the IDWS and the median of the data over the IDWS. These values were decided basing on the dataset's statistical structure and the quality criteria of the GWD 2006/118/EC. Subsequently, we evaluated the spatial distribution of the probability to exceed the defined thresholds using the Indicator kriging. The results highlight different zones with high exceedance probability ranging from 75% to 95% respect both the IDWS and the median value. Considering the geological setting of the DBVL, these probability values correspond with the occurrence of both organic matter and reducing conditions. In conclusion, the spatial prediction of the exceedance probability could be useful to define the areas in which estimate the local NBLs, enhancing the procedure of NBL definition. In that way, the NBL estimation could be more realistic because it considers the spatial distribution of the studied contaminant, distinguishing areas with high natural concentrations from polluted ones.

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.

Beta Regression Finite Mixture Models of Polarization and Priming

ERIC Educational Resources Information Center

Smithson, Michael; Merkle, Edgar C.; Verkuilen, Jay

2011-01-01

This paper describes the application of finite-mixture general linear models based on the beta distribution to modeling response styles, polarization, anchoring, and priming effects in probability judgments. These models, in turn, enhance our capacity for explicitly testing models and theories regarding the aforementioned phenomena. The mixture…

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).

BAT - The Bayesian analysis toolkit

NASA Astrophysics Data System (ADS)

Caldwell, Allen; Kollár, Daniel; Kröninger, Kevin

2009-11-01

We describe the development of a new toolkit for data analysis. The analysis package is based on Bayes' Theorem, and is realized with the use of Markov Chain Monte Carlo. This gives access to the full posterior probability distribution. Parameter estimation, limit setting and uncertainty propagation are implemented in a straightforward manner.

A Riemannian framework for orientation distribution function computing.

PubMed

Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid

2009-01-01

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H1/2 of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation.

Water shortage risk assessment considering large-scale regional transfers: a copula-based uncertainty case study in Lunan, China.

PubMed

Gao, Xueping; Liu, Yinzhu; Sun, Bowen

2018-06-05

The risk of water shortage caused by uncertainties, such as frequent drought, varied precipitation, multiple water resources, and different water demands, brings new challenges to the water transfer projects. Uncertainties exist for transferring water and local surface water; therefore, the relationship between them should be thoroughly studied to prevent water shortage. For more effective water management, an uncertainty-based water shortage risk assessment model (UWSRAM) is developed to study the combined effect of multiple water resources and analyze the shortage degree under uncertainty. The UWSRAM combines copula-based Monte Carlo stochastic simulation and the chance-constrained programming-stochastic multiobjective optimization model, using the Lunan water-receiving area in China as an example. Statistical copula functions are employed to estimate the joint probability of available transferring water and local surface water and sampling from the multivariate probability distribution, which are used as inputs for the optimization model. The approach reveals the distribution of water shortage and is able to emphasize the importance of improving and updating transferring water and local surface water management, and examine their combined influence on water shortage risk assessment. The possible available water and shortages can be calculated applying the UWSRAM, also with the corresponding allocation measures under different water availability levels and violating probabilities. The UWSRAM is valuable for mastering the overall multi-water resource and water shortage degree, adapting to the uncertainty surrounding water resources, establishing effective water resource planning policies for managers and achieving sustainable development.

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.

Prediction of future asset prices

NASA Astrophysics Data System (ADS)

Seong, Ng Yew; Hin, Pooi Ah; Ching, Soo Huei

2014-12-01

This paper attempts to incorporate trading volumes as an additional predictor for predicting asset prices. Denoting r(t) as the vector consisting of the time-t values of the trading volume and price of a given asset, we model the time-(t+1) asset price to be dependent on the present and l-1 past values r(t), r(t-1), ....., r(t-1+1) via a conditional distribution which is derived from a (2l+1)-dimensional power-normal distribution. A prediction interval based on the 100(α/2)% and 100(1-α/2)% points of the conditional distribution is then obtained. By examining the average lengths of the prediction intervals found by using the composite indices of the Malaysia stock market for the period 2008 to 2013, we found that the value 2 appears to be a good choice for l. With the omission of the trading volume in the vector r(t), the corresponding prediction interval exhibits a slightly longer average length, showing that it might be desirable to keep trading volume as a predictor. From the above conditional distribution, the probability that the time-(t+1) asset price will be larger than the time-t asset price is next computed. When the probability differs from 0 (or 1) by less than 0.03, the observed time-(t+1) increase in price tends to be negative (or positive). Thus the above probability has a good potential of being used as a market indicator in technical analysis.

Distribution pattern of public transport passenger in Yogyakarta, Indonesia

NASA Astrophysics Data System (ADS)

Narendra, Alfa; Malkhamah, Siti; Sopha, Bertha Maya

2018-03-01

The arrival and departure distribution pattern of Trans Jogja bus passenger is one of the fundamental model for simulation. The purpose of this paper is to build models of passengers flows. This research used passengers data from January to May 2014. There is no policy that change the operation system affecting the nature of this pattern nowadays. The roads, buses, land uses, schedule, and people are relatively still the same. The data then categorized based on the direction, days, and location. Moreover, each category was fitted into some well-known discrete distributions. Those distributions are compared based on its AIC value and BIC. The chosen distribution model has the smallest AIC and BIC value and the negative binomial distribution found has the smallest AIC and BIC value. Probability mass function (PMF) plots of those models were compared to draw generic model from each categorical negative binomial distribution models. The value of accepted generic negative binomial distribution is 0.7064 and 1.4504 of mu. The minimum and maximum passenger vector value of distribution are is 0 and 41.

On the optimal identification of tag sets in time-constrained RFID configurations.

PubMed

Vales-Alonso, Javier; Bueno-Delgado, María Victoria; Egea-López, Esteban; Alcaraz, Juan José; Pérez-Mañogil, Juan Manuel

2011-01-01

In Radio Frequency Identification facilities the identification delay of a set of tags is mainly caused by the random access nature of the reading protocol, yielding a random identification time of the set of tags. In this paper, the cumulative distribution function of the identification time is evaluated using a discrete time Markov chain for single-set time-constrained passive RFID systems, namely those ones where a single group of tags is assumed to be in the reading area and only for a bounded time (sojourn time) before leaving. In these scenarios some tags in a set may leave the reader coverage area unidentified. The probability of this event is obtained from the cumulative distribution function of the identification time as a function of the sojourn time. This result provides a suitable criterion to minimize the probability of losing tags. Besides, an identification strategy based on splitting the set of tags in smaller subsets is also considered. Results demonstrate that there are optimal splitting configurations that reduce the overall identification time while keeping the same probability of losing tags.

Development of a European Ensemble System for Seasonal Prediction: Application to crop yield

NASA Astrophysics Data System (ADS)

Terres, J. M.; Cantelaube, P.

2003-04-01

Western European agriculture is highly intensive and the weather is the main source of uncertainty for crop yield assessment and for crop management. In the current system, at the time when a crop yield forecast is issued, the weather conditions leading up to harvest time are unknown and are therefore a major source of uncertainty. The use of seasonal weather forecast would bring additional information for the remaining crop season and has valuable benefit for improving the management of agricultural markets and environmentally sustainable farm practices. An innovative method for supplying seasonal forecast information to crop simulation models has been developed in the frame of the EU funded research project DEMETER. It consists in running a crop model on each individual member of the seasonal hindcasts to derive a probability distribution of crop yield. Preliminary results of cumulative probability function of wheat yield provides information on both the yield anomaly and the reliability of the forecast. Based on the spread of the probability distribution, the end-user can directly quantify the benefits and risks of taking weather-sensitive decisions.

Spacing distribution functions for 1D point island model with irreversible attachment

NASA Astrophysics Data System (ADS)

Gonzalez, Diego; Einstein, Theodore; Pimpinelli, Alberto

2011-03-01

We study the configurational structure of the point island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p xy n (x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for p xy n (x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system. This work was supported by the NSF-MRSEC at the University of Maryland, Grant No. DMR 05-20471, with ancillary support from the Center for Nanophysics and Advanced Materials (CNAM).

Distributed Storage Algorithm for Geospatial Image Data Based on Data Access Patterns.

PubMed

Pan, Shaoming; Li, Yongkai; Xu, Zhengquan; Chong, Yanwen

2015-01-01

Declustering techniques are widely used in distributed environments to reduce query response time through parallel I/O by splitting large files into several small blocks and then distributing those blocks among multiple storage nodes. Unfortunately, however, many small geospatial image data files cannot be further split for distributed storage. In this paper, we propose a complete theoretical system for the distributed storage of small geospatial image data files based on mining the access patterns of geospatial image data using their historical access log information. First, an algorithm is developed to construct an access correlation matrix based on the analysis of the log information, which reveals the patterns of access to the geospatial image data. Then, a practical heuristic algorithm is developed to determine a reasonable solution based on the access correlation matrix. Finally, a number of comparative experiments are presented, demonstrating that our algorithm displays a higher total parallel access probability than those of other algorithms by approximately 10-15% and that the performance can be further improved by more than 20% by simultaneously applying a copy storage strategy. These experiments show that the algorithm can be applied in distributed environments to help realize parallel I/O and thereby improve system performance.

Distributed decision-making in electric power system transmission maintenance scheduling using multi-agent systems (MAS)

NASA Astrophysics Data System (ADS)

Zhang, Zhong

In this work, motivated by the need to coordinate transmission maintenance scheduling among a multiplicity of self-interested entities in restructured power industry, a distributed decision support framework based on multiagent negotiation systems (MANS) is developed. An innovative risk-based transmission maintenance optimization procedure is introduced. Several models for linking condition monitoring information to the equipment's instantaneous failure probability are presented, which enable quantitative evaluation of the effectiveness of maintenance activities in terms of system cumulative risk reduction. Methodologies of statistical processing, equipment deterioration evaluation and time-dependent failure probability calculation are also described. A novel framework capable of facilitating distributed decision-making through multiagent negotiation is developed. A multiagent negotiation model is developed and illustrated that accounts for uncertainty and enables social rationality. Some issues of multiagent negotiation convergence and scalability are discussed. The relationships between agent-based negotiation and auction systems are also identified. A four-step MAS design methodology for constructing multiagent systems for power system applications is presented. A generic multiagent negotiation system, capable of inter-agent communication and distributed decision support through inter-agent negotiations, is implemented. A multiagent system framework for facilitating the automated integration of condition monitoring information and maintenance scheduling for power transformers is developed. Simulations of multiagent negotiation-based maintenance scheduling among several independent utilities are provided. It is shown to be a viable alternative solution paradigm to the traditional centralized optimization approach in today's deregulated environment. This multiagent system framework not only facilitates the decision-making among competing power system entities, but also provides a tool to use in studying competitive industry relative to monopolistic industry.

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.

Specifying the Probability Characteristics of Funnel Plot Control Limits: An Investigation of Three Approaches

PubMed Central

Manktelow, Bradley N.; Seaton, Sarah E.

2012-01-01

Background Emphasis is increasingly being placed on the monitoring and comparison of clinical outcomes between healthcare providers. Funnel plots have become a standard graphical methodology to identify outliers and comprise plotting an outcome summary statistic from each provider against a specified ‘target’ together with upper and lower control limits. With discrete probability distributions it is not possible to specify the exact probability that an observation from an ‘in-control’ provider will fall outside the control limits. However, general probability characteristics can be set and specified using interpolation methods. Guidelines recommend that providers falling outside such control limits should be investigated, potentially with significant consequences, so it is important that the properties of the limits are understood. Methods Control limits for funnel plots for the Standardised Mortality Ratio (SMR) based on the Poisson distribution were calculated using three proposed interpolation methods and the probability calculated of an ‘in-control’ provider falling outside of the limits. Examples using published data were shown to demonstrate the potential differences in the identification of outliers. Results The first interpolation method ensured that the probability of an observation of an ‘in control’ provider falling outside either limit was always less than a specified nominal probability (p). The second method resulted in such an observation falling outside either limit with a probability that could be either greater or less than p, depending on the expected number of events. The third method led to a probability that was always greater than, or equal to, p. Conclusion The use of different interpolation methods can lead to differences in the identification of outliers. This is particularly important when the expected number of events is small. We recommend that users of these methods be aware of the differences, and specify which interpolation method is to be used prior to any analysis. PMID:23029202

Average BER and outage probability of the ground-to-train OWC link in turbulence with rain

NASA Astrophysics Data System (ADS)

Zhang, Yixin; Yang, Yanqiu; Hu, Beibei; Yu, Lin; Hu, Zheng-Da

2017-09-01

The bit-error rate (BER) and outage probability of optical wireless communication (OWC) link for the ground-to-train of the curved track in turbulence with rain is evaluated. Considering the re-modulation effects of raining fluctuation on optical signal modulated by turbulence, we set up the models of average BER and outage probability in the present of pointing errors, based on the double inverse Gaussian (IG) statistical distribution model. The numerical results indicate that, for the same covered track length, the larger curvature radius increases the outage probability and average BER. The performance of the OWC link in turbulence with rain is limited mainly by the rain rate and pointing errors which are induced by the beam wander and train vibration. The effect of the rain rate on the performance of the link is more severe than the atmospheric turbulence, but the fluctuation owing to the atmospheric turbulence affects the laser beam propagation more greatly than the skewness of the rain distribution. Besides, the turbulence-induced beam wander has a more significant impact on the system in heavier rain. We can choose the size of transmitting and receiving apertures and improve the shockproof performance of the tracks to optimize the communication performance of the system.

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.

A comparison of two methods for expert elicitation in health technology assessments.

PubMed

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

2016-07-26

When data needed to inform parameters in decision models are lacking, formal elicitation of expert judgement can be used to characterise parameter uncertainty. Although numerous methods for eliciting expert opinion as probability distributions exist, there is little research to suggest whether one method is more useful than any other method. This study had three objectives: (i) to obtain subjective probability distributions characterising parameter uncertainty in the context of a health technology assessment; (ii) to compare two elicitation methods by eliciting the same parameters in different ways; (iii) to collect subjective preferences of the experts for the different elicitation methods used. Twenty-seven clinical experts were invited to participate in an elicitation exercise to inform a published model-based cost-effectiveness analysis of alternative treatments for prostate cancer. Participants were individually asked to express their judgements as probability distributions using two different methods - the histogram and hybrid elicitation methods - presented in a random order. Individual distributions were mathematically aggregated across experts with and without weighting. The resulting combined distributions were used in the probabilistic analysis of the decision model and mean incremental cost-effectiveness ratios and the expected values of perfect information (EVPI) were calculated for each method, and compared with the original cost-effectiveness analysis. Scores on the ease of use of the two methods and the extent to which the probability distributions obtained from each method accurately reflected the expert's opinion were also recorded. Six experts completed the task. Mean ICERs from the probabilistic analysis ranged between £162,600-£175,500 per quality-adjusted life year (QALY) depending on the elicitation and weighting methods used. Compared to having no information, use of expert opinion decreased decision uncertainty: the EVPI value at the £30,000 per QALY threshold decreased by 74-86 % from the original cost-effectiveness analysis. Experts indicated that the histogram method was easier to use, but attributed a perception of more accuracy to the hybrid method. Inclusion of expert elicitation can decrease decision uncertainty. Here, choice of method did not affect the overall cost-effectiveness conclusions, but researchers intending to use expert elicitation need to be aware of the impact different methods could have.

Development and application of a probability distribution retrieval scheme to the remote sensing of clouds and precipitation

NASA Astrophysics Data System (ADS)

McKague, Darren Shawn

2001-12-01

The statistical properties of clouds and precipitation on a global scale are important to our understanding of climate. Inversion methods exist to retrieve the needed cloud and precipitation properties from satellite data pixel-by-pixel that can then be summarized over large data sets to obtain the desired statistics. These methods can be quite computationally expensive, and typically don't provide errors on the statistics. A new method is developed to directly retrieve probability distributions of parameters from the distribution of measured radiances. The method also provides estimates of the errors on the retrieved distributions. The method can retrieve joint distributions of parameters that allows for the study of the connection between parameters. A forward radiative transfer model creates a mapping from retrieval parameter space to radiance space. A Monte Carlo procedure uses the mapping to transform probability density from the observed radiance histogram to a two- dimensional retrieval property probability distribution function (PDF). An estimate of the uncertainty in the retrieved PDF is calculated from random realizations of the radiance to retrieval parameter PDF transformation given the uncertainty of the observed radiances, the radiance PDF, the forward radiative transfer, the finite number of prior state vectors, and the non-unique mapping to retrieval parameter space. The retrieval method is also applied to the remote sensing of precipitation from SSM/I microwave data. A method of stochastically generating hydrometeor fields based on the fields from a numerical cloud model is used to create the precipitation parameter radiance space transformation. The impact of vertical and horizontal variability within the hydrometeor fields has a significant impact on algorithm performance. Beamfilling factors are computed from the simulated hydrometeor fields. The beamfilling factors vary quite a bit depending upon the horizontal structure of the rain. The algorithm is applied to SSM/I images from the eastern tropical Pacific and is compared to PDFs of rain rate computed using pixel-by-pixel retrievals from Wilheit and from Liu and Curry. Differences exist between the three methods, but good general agreement is seen between the PDF retrieval algorithm and the algorithm of Liu and Curry. (Abstract shortened by UMI.)

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.

Understanding interaction effects of climate change and fire management on bird distributions through combined process and habitat models

USGS Publications Warehouse

White, Joseph D.; Gutzwiller, Kevin J.; Barrow, Wylie C.; Johnson-Randall, Lori; Zygo, Lisa; Swint, Pamela

2011-01-01

Avian conservation efforts must account for changes in vegetation composition and structure associated with climate change. We modeled vegetation change and the probability of occurrence of birds to project changes in winter bird distributions associated with climate change and fire management in the northern Chihuahuan Desert (southwestern U.S.A.). We simulated vegetation change in a process-based model (Landscape and Fire Simulator) in which anticipated climate change was associated with doubling of current atmospheric carbon dioxide over the next 50 years. We estimated the relative probability of bird occurrence on the basis of statistical models derived from field observations of birds and data on vegetation type, topography, and roads. We selected 3 focal species, Scaled Quail (Callipepla squamata), Loggerhead Shrike (Lanius ludovicianus), and Rock Wren (Salpinctes obsoletus), that had a range of probabilities of occurrence for our study area. Our simulations projected increases in relative probability of bird occurrence in shrubland and decreases in grassland and Yucca spp. and ocotillo (Fouquieria splendens) vegetation. Generally, the relative probability of occurrence of all 3 species was highest in shrubland because leaf-area index values were lower in shrubland. This high probability of occurrence likely is related to the species' use of open vegetation for foraging. Fire suppression had little effect on projected vegetation composition because as climate changed there was less fuel and burned area. Our results show that if future water limits on plant type are considered, models that incorporate spatial data may suggest how and where different species of birds may respond to vegetation changes.

Understanding interaction effects of climate change and fire management on bird distributions through combined process and habitat models

USGS Publications Warehouse

White, Joseph D.; Gutzwiller, Kevin J.; Barrow, Wylie C.; Johnson-Randall, Lori; Zygo, Lisa; Swint, Pamela

2011-01-01

Avian conservation efforts must account for changes in vegetation composition and structure associated with climate change. We modeled vegetation change and the probability of occurrence of birds to project changes in winter bird distributions associated with climate change and fire management in the northern Chihuahuan Desert (southwestern U.S.A.). We simulated vegetation change in a process-based model (Landscape and Fire Simulator) in which anticipated climate change was associated with doubling of current atmospheric carbon dioxide over the next 50 years. We estimated the relative probability of bird occurrence on the basis of statistical models derived from field observations of birds and data on vegetation type, topography, and roads. We selected 3 focal species, Scaled Quail (Callipepla squamata), Loggerhead Shrike (Lanius ludovicianus), and Rock Wren (Salpinctes obsoletus), that had a range of probabilities of occurrence for our study area. Our simulations projected increases in relative probability of bird occurrence in shrubland and decreases in grassland and Yucca spp. and ocotillo (Fouquieria splendens) vegetation. Generally, the relative probability of occurrence of all 3 species was highest in shrubland because leaf-area index values were lower in shrubland. This high probability of occurrence likely is related to the species' use of open vegetation for foraging. Fire suppression had little effect on projected vegetation composition because as climate changed there was less fuel and burned area. Our results show that if future water limits on plant type are considered, models that incorporate spatial data may suggest how and where different species of birds may respond to vegetation changes. ??2011 Society for Conservation Biology.

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.