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.

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.

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.

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

PubMed

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

2012-02-01

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

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

PubMed Central

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

2016-01-01

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

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

Size Effect on Specific Energy Distribution in Particle Comminution

NASA Astrophysics Data System (ADS)

Xu, Yongfu; Wang, Yidong

A theoretical study is made to derive an energy distribution equation for the size reduction process from the fractal model for the particle comminution. Fractal model is employed as a valid measure of the self-similar size distribution of comminution daughter products. The tensile strength of particles varies with particle size in the manner of a power function law. The energy consumption for comminuting single particle is found to be proportional to the 5(D-3)/3rd order of the particle size, D being the fractal dimension of particle comminution daughter. The Weibull statistics is applied to describe the relationship between the breakage probability and specific energy of particle comminution. A simple equation is derived for the breakage probability of particles in view of the dependence of fracture energy on particle size. The calculated exponents and Weibull coefficients are generally in conformity with published data for fracture of particles.

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

PubMed

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

2013-11-01

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

A quantum anharmonic oscillator model for the stock market

NASA Astrophysics Data System (ADS)

Gao, Tingting; Chen, Yu

2017-02-01

A financially interpretable quantum model is proposed to study the probability distributions of the stock price return. The dynamics of a quantum particle is considered an analog of the motion of stock price. Then the probability distributions of price return can be computed from the wave functions that evolve according to Schrodinger equation. Instead of a harmonic oscillator in previous studies, a quantum anharmonic oscillator is applied to the stock in liquid market. The leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed-state and multi-potential. The trend following dominant market, in which the price return follows a bimodal distribution, is discussed as a specific case of the illiquid market.

Translational Genomics Research Institute: Identification of Pathways Enriched with Condition-Specific Statistical Dependencies Across Four Subtypes of Glioblastoma Multiforme | Office of Cancer Genomics

Cancer.gov

Evaluation of Differential DependencY (EDDY) is a statistical test for the differential dependency relationship of a set of genes between two given conditions. For each condition, possible dependency network structures are enumerated and their likelihoods are computed to represent a probability distribution of dependency networks. The difference between the probability distributions of dependency networks is computed between conditions, and its statistical significance is evaluated with random permutations of condition labels on the samples.  

Translational Genomics Research Institute (TGen): Identification of Pathways Enriched with Condition-Specific Statistical Dependencies Across Four Subtypes of Glioblastoma Multiforme | Office of Cancer Genomics

Cancer.gov

Evaluation of Differential DependencY (EDDY) is a statistical test for the differential dependency relationship of a set of genes between two given conditions. For each condition, possible dependency network structures are enumerated and their likelihoods are computed to represent a probability distribution of dependency networks. The difference between the probability distributions of dependency networks is computed between conditions, and its statistical significance is evaluated with random permutations of condition labels on the samples.  

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.

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.

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

NASA Astrophysics Data System (ADS)

Geist, E. L.; Parsons, T.

2015-12-01

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

NEWTPOIS- NEWTON POISSON DISTRIBUTION PROGRAM

NASA Technical Reports Server (NTRS)

Bowerman, P. N.

1994-01-01

The cumulative poisson distribution program, NEWTPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714), can be used independently of one another. NEWTPOIS determines percentiles for gamma distributions with integer shape parameters and calculates percentiles for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. NEWTPOIS determines the Poisson parameter (lambda), that is; the mean (or expected) number of events occurring in a given unit of time, area, or space. Given that the user already knows the cumulative probability for a specific number of occurrences (n) it is usually a simple matter of substitution into the Poisson distribution summation to arrive at lambda. However, direct calculation of the Poisson parameter becomes difficult for small positive values of n and unmanageable for large values. NEWTPOIS uses Newton's iteration method to extract lambda from the initial value condition of the Poisson distribution where n=0, taking successive estimations until some user specified error term (epsilon) is reached. The NEWTPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting epsilon, n, and the cumulative probability of the occurrence of n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 30K. NEWTPOIS was developed in 1988.

Cumulative Poisson Distribution Program

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Scheuer, Ernest M.; Nolty, Robert

1990-01-01

Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

50 CFR 648.21 - Procedures for determining initial annual amounts.

Code of Federal Regulations, 2011 CFR

2011-10-01

... maximum probability of overfishing as informed by the OFL distribution will be 35 percent for stocks with... specifications established pursuant to this section may be adjusted by the Regional Administrator, in... the reasons for such an action and providing a 30-day public comment period. (f) Distribution of...

Application of the Bootstrap Statistical Method in Deriving Vibroacoustic Specifications

NASA Technical Reports Server (NTRS)

Hughes, William O.; Paez, Thomas L.

2006-01-01

This paper discusses the Bootstrap Method for specification of vibroacoustic test specifications. Vibroacoustic test specifications are necessary to properly accept or qualify a spacecraft and its components for the expected acoustic, random vibration and shock environments seen on an expendable launch vehicle. Traditionally, NASA and the U.S. Air Force have employed methods of Normal Tolerance Limits to derive these test levels based upon the amount of data available, and the probability and confidence levels desired. The Normal Tolerance Limit method contains inherent assumptions about the distribution of the data. The Bootstrap is a distribution-free statistical subsampling method which uses the measured data themselves to establish estimates of statistical measures of random sources. This is achieved through the computation of large numbers of Bootstrap replicates of a data measure of interest and the use of these replicates to derive test levels consistent with the probability and confidence desired. The comparison of the results of these two methods is illustrated via an example utilizing actual spacecraft vibroacoustic data.

Voronoi Cell Patterns: theoretical model and application to submonolayer growth

NASA Astrophysics Data System (ADS)

González, Diego Luis; Einstein, T. L.

2012-02-01

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We apply our model to describe the Voronoi cell patterns of island nucleation for critical island sizes i=0,1,2,3. Experimental results for the Voronoi cells of InAs/GaAs quantum dots are also described by our model.

Deep Learning Role in Early Diagnosis of Prostate Cancer

PubMed Central

Reda, Islam; Khalil, Ashraf; Elmogy, Mohammed; Abou El-Fetouh, Ahmed; Shalaby, Ahmed; Abou El-Ghar, Mohamed; Elmaghraby, Adel; Ghazal, Mohammed; El-Baz, Ayman

2018-01-01

The objective of this work is to develop a computer-aided diagnostic system for early diagnosis of prostate cancer. The presented system integrates both clinical biomarkers (prostate-specific antigen) and extracted features from diffusion-weighted magnetic resonance imaging collected at multiple b values. The presented system performs 3 major processing steps. First, prostate delineation using a hybrid approach that combines a level-set model with nonnegative matrix factorization. Second, estimation and normalization of diffusion parameters, which are the apparent diffusion coefficients of the delineated prostate volumes at different b values followed by refinement of those apparent diffusion coefficients using a generalized Gaussian Markov random field model. Then, construction of the cumulative distribution functions of the processed apparent diffusion coefficients at multiple b values. In parallel, a K-nearest neighbor classifier is employed to transform the prostate-specific antigen results into diagnostic probabilities. Finally, those prostate-specific antigen–based probabilities are integrated with the initial diagnostic probabilities obtained using stacked nonnegativity constraint sparse autoencoders that employ apparent diffusion coefficient–cumulative distribution functions for better diagnostic accuracy. Experiments conducted on 18 diffusion-weighted magnetic resonance imaging data sets achieved 94.4% diagnosis accuracy (sensitivity = 88.9% and specificity = 100%), which indicate the promising results of the presented computer-aided diagnostic system. PMID:29804518

Inverse statistics and information content

NASA Astrophysics Data System (ADS)

Ebadi, H.; Bolgorian, Meysam; Jafari, G. R.

2010-12-01

Inverse statistics analysis studies the distribution of investment horizons to achieve a predefined level of return. This distribution provides a maximum investment horizon which determines the most likely horizon for gaining a specific return. There exists a significant difference between inverse statistics of financial market data and a fractional Brownian motion (fBm) as an uncorrelated time-series, which is a suitable criteria to measure information content in financial data. In this paper we perform this analysis for the DJIA and S&P500 as two developed markets and Tehran price index (TEPIX) as an emerging market. We also compare these probability distributions with fBm probability, to detect when the behavior of the stocks are the same as fBm.

Calculation of the number of Monte Carlo histories for a planetary protection probability of impact estimation

NASA Astrophysics Data System (ADS)

Barengoltz, Jack

2016-07-01

Monte Carlo (MC) is a common method to estimate probability, effectively by a simulation. For planetary protection, it may be used to estimate the probability of impact P{}_{I} by a launch vehicle (upper stage) of a protected planet. The object of the analysis is to provide a value for P{}_{I} with a given level of confidence (LOC) that the true value does not exceed the maximum allowed value of P{}_{I}. In order to determine the number of MC histories required, one must also guess the maximum number of hits that will occur in the analysis. This extra parameter is needed because a LOC is desired. If more hits occur, the MC analysis would indicate that the true value may exceed the specification value with a higher probability than the LOC. (In the worst case, even the mean value of the estimated P{}_{I} might exceed the specification value.) After the analysis is conducted, the actual number of hits is, of course, the mean. The number of hits arises from a small probability per history and a large number of histories; these are the classic requirements for a Poisson distribution. For a known Poisson distribution (the mean is the only parameter), the probability for some interval in the number of hits is calculable. Before the analysis, this is not possible. Fortunately, there are methods that can bound the unknown mean for a Poisson distribution. F. Garwoodfootnote{ F. Garwood (1936), ``Fiduciary limits for the Poisson distribution.'' Biometrika 28, 437-442.} published an appropriate method that uses the Chi-squared function, actually its inversefootnote{ The integral chi-squared function would yield probability α as a function of the mean µ and an actual value n.} (despite the notation used): This formula for the upper and lower limits of the mean μ with the two-tailed probability 1-α depends on the LOC α and an estimated value of the number of "successes" n. In a MC analysis for planetary protection, only the upper limit is of interest, i.e., the single-tailed distribution. (Smaller actual P{}_{I }is no problem.) {}_{ } One advantage of this method is that this function is available in EXCEL. Note that care must be taken with the definition of the CHIINV function (the inverse of the integral chi-squared distribution). The equivalent inequality in EXCEL is μ < CHIINV[1-α, 2(n+1)] In practice, one calculates this upper limit for a specified LOC, α , and a guess of how many hits n will be found after the MC analysis. Then the estimate of the number of histories required is this upper limit divided by the specification for the allowed P{}_{I} (rounded up). However, if the number of hits actually exceeds the guess, the P{}_{I} requirement will be met only with a smaller LOC. A disadvantage is that the intervals about the mean are "in general too wide, yielding coverage probabilities much greater than 1- α ." footnote{ G. Casella and C. Robert (1988), Purdue University-Technical Report #88-7 or Cornell University-Technical Report BU-903-M.} For planetary protection, this technical issue means that the upper limit of the interval and the probability associated with the interval (i.e., the LOC) are conservative.

Estimation of distribution overlap of urn models.

PubMed

Hampton, Jerrad; Lladser, Manuel E

2012-01-01

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a draw from one distribution not being observed in [Formula: see text] draws from another distribution. We show our estimator of dissimilarity to be a [Formula: see text]-statistic and a uniformly minimum variance unbiased estimator of dissimilarity over the largest appropriate range of [Formula: see text]. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over [Formula: see text], we show it converges uniformly in probability to the dissimilarity parameter, and we present criteria when it is approximately normally distributed and admits a consistent jackknife estimator of its variance. As proof of concept, we analyze V35 16S rRNA data to discern between various microbial environments. Other potential applications concern any situation where dissimilarity of two discrete distributions may be of interest. For instance, in SELEX experiments, each urn could represent a random RNA pool and each draw a possible solution to a particular binding site problem over that pool. The dissimilarity of these pools is then related to the probability of finding binding site solutions in one pool that are absent in the other.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Optimal minimal measurements of mixed states

NASA Astrophysics Data System (ADS)

Vidal, G.; Latorre, J. I.; Pascual, P.; Tarrach, R.

1999-07-01

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized measurements, which turn out to be independent of the a priori probability distribution, obtaining the best guesses for the unknown state as well as a closed expression for the maximal mean-average fidelity. We do this for up to three copies of the unknown state in a way that leads to the generalization to any number of copies, which we then present and prove.

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.

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.

Using hidden Markov models to align multiple sequences.

PubMed

Mount, David W

2009-07-01

A hidden Markov model (HMM) is a probabilistic model of a multiple sequence alignment (msa) of proteins. In the model, each column of symbols in the alignment is represented by a frequency distribution of the symbols (called a "state"), and insertions and deletions are represented by other states. One moves through the model along a particular path from state to state in a Markov chain (i.e., random choice of next move), trying to match a given sequence. The next matching symbol is chosen from each state, recording its probability (frequency) and also the probability of going to that state from a previous one (the transition probability). State and transition probabilities are multiplied to obtain a probability of the given sequence. The hidden nature of the HMM is due to the lack of information about the value of a specific state, which is instead represented by a probability distribution over all possible values. This article discusses the advantages and disadvantages of HMMs in msa and presents algorithms for calculating an HMM and the conditions for producing the best HMM.

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

NASA Astrophysics Data System (ADS)

Lee, Jaeha; Tsutsui, Izumi

2017-05-01

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

Velocity distributions among colliding asteroids

NASA Technical Reports Server (NTRS)

Bottke, William F., Jr.; Nolan, Michael C.; Greenberg, Richard; Kolvoord, Robert A.

1994-01-01

The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.

C-5A Cargo Deck Low-Frequency Vibration Environment

DTIC Science & Technology

1975-02-01

SAMPLE VIBRATION CALCULATIONS 13 1. Normal Distribution 13 2. Binomial Distribution 15 IV CONCLUSIONS 17 -! V REFERENCES 18 t: FEiCENDIJJ PAGS 2LANKNOT...Calculation for Binomial Distribution 108 (Vertical Acceleration, Right Rear Cargo Deck) xi I. INTRODUCTION The availability of large transport...the end of taxi. These peaks could then be used directly to compile the probability of occurrence of specific values of acceleration using the binomial

Comparison of probability statistics for automated ship detection in SAR imagery

NASA Astrophysics Data System (ADS)

Henschel, Michael D.; Rey, Maria T.; Campbell, J. W. M.; Petrovic, D.

1998-12-01

This paper discuses the initial results of a recent operational trial of the Ocean Monitoring Workstation's (OMW) ship detection algorithm which is essentially a Constant False Alarm Rate filter applied to Synthetic Aperture Radar data. The choice of probability distribution and methodologies for calculating scene specific statistics are discussed in some detail. An empirical basis for the choice of probability distribution used is discussed. We compare the results using a l-look, k-distribution function with various parameter choices and methods of estimation. As a special case of sea clutter statistics the application of a (chi) 2-distribution is also discussed. Comparisons are made with reference to RADARSAT data collected during the Maritime Command Operation Training exercise conducted in Atlantic Canadian Waters in June 1998. Reference is also made to previously collected statistics. The OMW is a commercial software suite that provides modules for automated vessel detection, oil spill monitoring, and environmental monitoring. This work has been undertaken to fine tune the OMW algorithm's, with special emphasis on the false alarm rate of each algorithm.

Landscape-scale distribution and density of raptor populations wintering in anthropogenic-dominated desert landscapes

USGS Publications Warehouse

Duerr, Adam E.; Miller, Tricia A.; Cornell Duerr, Kerri L; Lanzone, Michael J.; Fesnock, Amy; Katzner, Todd E.

2015-01-01

Anthropogenic development has great potential to affect fragile desert environments. Large-scale development of renewable energy infrastructure is planned for many desert ecosystems. Development plans should account for anthropogenic effects to distributions and abundance of rare or sensitive wildlife; however, baseline data on abundance and distribution of such wildlife are often lacking. We surveyed for predatory birds in the Sonoran and Mojave Deserts of southern California, USA, in an area designated for protection under the “Desert Renewable Energy Conservation Plan”, to determine how these birds are distributed across the landscape and how this distribution is affected by existing development. We developed species-specific models of resight probability to adjust estimates of abundance and density of each individual common species. Second, we developed combined-species models of resight probability for common and rare species so that we could make use of sparse data on the latter. We determined that many common species, such as red-tailed hawks, loggerhead shrikes, and especially common ravens, are associated with human development and likely subsidized by human activity. Species-specific and combined-species models of resight probability performed similarly, although the former model type provided higher quality information. Comparing abundance estimates with past surveys in the Mojave Desert suggests numbers of predatory birds associated with human development have increased while other sensitive species not associated with development have decreased. This approach gave us information beyond what we would have collected by focusing either on common or rare species, thus it provides a low-cost framework for others conducting surveys in similar desert environments outside of California.

Skill of Ensemble Seasonal Probability Forecasts

NASA Astrophysics Data System (ADS)

Smith, Leonard A.; Binter, Roman; Du, Hailiang; Niehoerster, Falk

2010-05-01

In operational forecasting, the computational complexity of large simulation models is, ideally, justified by enhanced performance over simpler models. We will consider probability forecasts and contrast the skill of ENSEMBLES-based seasonal probability forecasts of interest to the finance sector (specifically temperature forecasts for Nino 3.4 and the Atlantic Main Development Region (MDR)). The ENSEMBLES model simulations will be contrasted against forecasts from statistical models based on the observations (climatological distributions) and empirical dynamics based on the observations but conditioned on the current state (dynamical climatology). For some start dates, individual ENSEMBLES models yield significant skill even at a lead-time of 14 months. The nature of this skill is discussed, and chances of application are noted. Questions surrounding the interpretation of probability forecasts based on these multi-model ensemble simulations are then considered; the distributions considered are formed by kernel dressing the ensemble and blending with the climatology. The sources of apparent (RMS) skill in distributions based on multi-model simulations is discussed, and it is demonstrated that the inclusion of "zero-skill" models in the long range can improve Root-Mean-Square-Error scores, casting some doubt on the common justification for the claim that all models should be included in forming an operational probability forecast. It is argued that the rational response varies with lead time.

The concept of entropy in landscape evolution

USGS Publications Warehouse

Leopold, Luna Bergere; Langbein, Walter Basil

1962-01-01

The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations equations for the longitudinal profiles of rivers are derived that are mathematically comparable to those observed in the field. The most probable river profiles approach the condition in which the downstream rate of production of entropy per unit mass is constant. Hydraulic equations are insufficient to determine the velocity, depths, and slopes of rivers that are themselves authors of their own hydraulic geometries. A solution becomes possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the hydraulic geometry of river channels that agrees closely with field observations. The most probable state for certain physical systems can also be illustrated by random-walk models. Average longitudinal profiles and drainage networks were so derived and these have the properties implied by the theory. The drainage networks derived from random walks have some of the principal properties demonstrated by the Horton analysis; specifically, the logarithms of stream length and stream numbers are proportional to stream order.

PSE-HMM: genome-wide CNV detection from NGS data using an HMM with Position-Specific Emission probabilities.

PubMed

Malekpour, Seyed Amir; Pezeshk, Hamid; Sadeghi, Mehdi

2016-11-03

Copy Number Variation (CNV) is envisaged to be a major source of large structural variations in the human genome. In recent years, many studies apply Next Generation Sequencing (NGS) data for the CNV detection. However, still there is a necessity to invent more accurate computational tools. In this study, mate pair NGS data are used for the CNV detection in a Hidden Markov Model (HMM). The proposed HMM has position specific emission probabilities, i.e. a Gaussian mixture distribution. Each component in the Gaussian mixture distribution captures a different type of aberration that is observed in the mate pairs, after being mapped to the reference genome. These aberrations may include any increase (decrease) in the insertion size or change in the direction of mate pairs that are mapped to the reference genome. This HMM with Position-Specific Emission probabilities (PSE-HMM) is utilized for the genome-wide detection of deletions and tandem duplications. The performance of PSE-HMM is evaluated on a simulated dataset and also on a real data of a Yoruban HapMap individual, NA18507. PSE-HMM is effective in taking observation dependencies into account and reaches a high accuracy in detecting genome-wide CNVs. MATLAB programs are available at http://bs.ipm.ir/softwares/PSE-HMM/ .

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

PubMed

Ikegami, A

1977-01-01

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

Ensemble learning and model averaging for material identification in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Basener, William F.

2017-05-01

In this paper we present a method for identifying the material contained in a pixel or region of pixels in a hyperspectral image. An identification process can be performed on a spectrum from an image from pixels that has been pre-determined to be of interest, generally comparing the spectrum from the image to spectra in an identification library. The metric for comparison used in this paper a Bayesian probability for each material. This probability can be computed either from Bayes' theorem applied to normal distributions for each library spectrum or using model averaging. Using probabilities has the advantage that the probabilities can be summed over spectra for any material class to obtain a class probability. For example, the probability that the spectrum of interest is a fabric is equal to the sum of all probabilities for fabric spectra in the library. We can do the same to determine the probability for a specific type of fabric, or any level of specificity contained in our library. Probabilities not only tell us which material is most likely, the tell us how confident we can be in the material presence; a probability close to 1 indicates near certainty of the presence of a material in the given class, and a probability close to 0.5 indicates that we cannot know if the material is present at the given level of specificity. This is much more informative than a detection score from a target detection algorithm or a label from a classification algorithm. In this paper we present results in the form of a hierarchical tree with probabilities for each node. We use Forest Radiance imagery with 159 bands.

Measurement of 240Pu Angular Momentum Dependent Fission Probabilities Using the (α ,α') Reaction

NASA Astrophysics Data System (ADS)

Koglin, Johnathon; Burke, Jason; Fisher, Scott; Jovanovic, Igor

2017-09-01

The surrogate reaction method often lacks the theoretical framework and necessary experimental data to constrain models especially when rectifying differences between angular momentum state differences between the desired and surrogate reaction. In this work, dual arrays of silicon telescope particle identification detectors and photovoltaic (solar) cell fission fragment detectors have been used to measure the fission probability of the 240Pu(α ,α' f) reaction - a surrogate for the 239Pu(n , f) - and fission fragment angular distributions. Fission probability measurements were performed at a beam energy of 35.9(2) MeV at eleven scattering angles from 40° to 140°e in 10° intervals and at nuclear excitation energies up to 16 MeV. Fission fragment angular distributions were measured in six bins from 4.5 MeV to 8.0 MeV and fit to expected distributions dependent on the vibrational and rotational excitations at the saddle point. In this way, the contributions to the total fission probability from specific states of K angular momentum projection on the symmetry axis are extracted. A sizable data collection is presented to be considered when constraining microscopic cross section calculations.

Host specificity and the probability of discovering species of helminth parasites.

PubMed

Poulin, R; Mouillot, D

2005-06-01

Different animal species have different probabilities of being discovered and described by scientists, and these probabilities are determined to a large extent by the biological characteristics of these species. For instance, species with broader geographical ranges are more likely to be encountered by collectors than species with restricted distributions; indeed, the size of the geographical range is often the best predictor of a species' date of description. For parasitic organisms, host specificity may be similarly linked to the probability of a species being found. Here, using data on 170 helminth species parasitic in freshwater fishes, we show that host specificity is associated with the year in which the helminths were described. Helminths that exploit more host species, and to a lesser degree those that exploit a broader taxonomic range of host species, tend to be discovered earlier than the more host-specific helminths. This pattern was observed across all helminth species, as well as within the different helminth taxa (trematodes, cestodes, nematodes and acanthocephalans). Our results demonstrate that the parasite species known at any given point in time are not a random subset of existing species, but rather a biased subset with respect to the parasites' biological properties.

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.

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.

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.

Axon and dendrite geography predict the specificity of synaptic connections in a functioning spinal cord network.

PubMed

Li, Wen-Chang; Cooke, Tom; Sautois, Bart; Soffe, Stephen R; Borisyuk, Roman; Roberts, Alan

2007-09-10

How specific are the synaptic connections formed as neuronal networks develop and can simple rules account for the formation of functioning circuits? These questions are assessed in the spinal circuits controlling swimming in hatchling frog tadpoles. This is possible because detailed information is now available on the identity and synaptic connections of the main types of neuron. The probabilities of synapses between 7 types of identified spinal neuron were measured directly by making electrical recordings from 500 pairs of neurons. For the same neuron types, the dorso-ventral distributions of axons and dendrites were measured and then used to calculate the probabilities that axons would encounter particular dendrites and so potentially form synaptic connections. Surprisingly, synapses were found between all types of neuron but contact probabilities could be predicted simply by the anatomical overlap of their axons and dendrites. These results suggested that synapse formation may not require axons to recognise specific, correct dendrites. To test the plausibility of simpler hypotheses, we first made computational models that were able to generate longitudinal axon growth paths and reproduce the axon distribution patterns and synaptic contact probabilities found in the spinal cord. To test if probabilistic rules could produce functioning spinal networks, we then made realistic computational models of spinal cord neurons, giving them established cell-specific properties and connecting them into networks using the contact probabilities we had determined. A majority of these networks produced robust swimming activity. Simple factors such as morphogen gradients controlling dorso-ventral soma, dendrite and axon positions may sufficiently constrain the synaptic connections made between different types of neuron as the spinal cord first develops and allow functional networks to form. Our analysis implies that detailed cellular recognition between spinal neuron types may not be necessary for the reliable formation of functional networks to generate early behaviour like swimming.

Predicting bottlenose dolphin distribution along Liguria coast (northwestern Mediterranean Sea) through different modeling techniques and indirect predictors.

PubMed

Marini, C; Fossa, F; Paoli, C; Bellingeri, M; Gnone, G; Vassallo, P

2015-03-01

Habitat modeling is an important tool to investigate the quality of the habitat for a species within a certain area, to predict species distribution and to understand the ecological processes behind it. Many species have been investigated by means of habitat modeling techniques mainly to address effective management and protection policies and cetaceans play an important role in this context. The bottlenose dolphin (Tursiops truncatus) has been investigated with habitat modeling techniques since 1997. The objectives of this work were to predict the distribution of bottlenose dolphin in a coastal area through the use of static morphological features and to compare the prediction performances of three different modeling techniques: Generalized Linear Model (GLM), Generalized Additive Model (GAM) and Random Forest (RF). Four static variables were tested: depth, bottom slope, distance from 100 m bathymetric contour and distance from coast. RF revealed itself both the most accurate and the most precise modeling technique with very high distribution probabilities predicted in presence cells (90.4% of mean predicted probabilities) and with 66.7% of presence cells with a predicted probability comprised between 90% and 100%. The bottlenose distribution obtained with RF allowed the identification of specific areas with particularly high presence probability along the coastal zone; the recognition of these core areas may be the starting point to develop effective management practices to improve T. truncatus protection. Copyright © 2014 Elsevier Ltd. All rights reserved.

Precipitation intensity probability distribution modelling for hydrological and construction design purposes

NASA Astrophysics Data System (ADS)

Koshinchanov, Georgy; Dimitrov, Dobri

2008-11-01

The characteristics of rainfall intensity are important for many purposes, including design of sewage and drainage systems, tuning flood warning procedures, etc. Those estimates are usually statistical estimates of the intensity of precipitation realized for certain period of time (e.g. 5, 10 min., etc) with different return period (e.g. 20, 100 years, etc). The traditional approach in evaluating the mentioned precipitation intensities is to process the pluviometer's records and fit probability distribution to samples of intensities valid for certain locations ore regions. Those estimates further become part of the state regulations to be used for various economic activities. Two problems occur using the mentioned approach: 1. Due to various factors the climate conditions are changed and the precipitation intensity estimates need regular update; 2. As far as the extremes of the probability distribution are of particular importance for the practice, the methodology of the distribution fitting needs specific attention to those parts of the distribution. The aim of this paper is to make review of the existing methodologies for processing the intensive rainfalls and to refresh some of the statistical estimates for the studied areas. The methodologies used in Bulgaria for analyzing the intensive rainfalls and produce relevant statistical estimates: The method of the maximum intensity, used in the National Institute of Meteorology and Hydrology to process and decode the pluviometer's records, followed by distribution fitting for each precipitation duration period; As the above, but with separate modeling of probability distribution for the middle and high probability quantiles. Method is similar to the first one, but with a threshold of 0,36 mm/min of intensity; Another method proposed by the Russian hydrologist G. A. Aleksiev for regionalization of estimates over some territory, improved and adapted by S. Gerasimov for Bulgaria; Next method is considering only the intensive rainfalls (if any) during the day with the maximal annual daily precipitation total for a given year; Conclusions are drown on the relevance and adequacy of the applied methods.

Streamflow distribution maps for the Cannon River drainage basin, southeast Minnesota, and the St. Louis River drainage basin, northeast Minnesota

USGS Publications Warehouse

Smith, Erik A.; Sanocki, Chris A.; Lorenz, David L.; Jacobsen, Katrin E.

2017-12-27

Streamflow distribution maps for the Cannon River and St. Louis River drainage basins were developed by the U.S. Geological Survey, in cooperation with the Legislative-Citizen Commission on Minnesota Resources, to illustrate relative and cumulative streamflow distributions. The Cannon River was selected to provide baseline data to assess the effects of potential surficial sand mining, and the St. Louis River was selected to determine the effects of ongoing Mesabi Iron Range mining. Each drainage basin (Cannon, St. Louis) was subdivided into nested drainage basins: the Cannon River was subdivided into 152 nested drainage basins, and the St. Louis River was subdivided into 353 nested drainage basins. For each smaller drainage basin, the estimated volumes of groundwater discharge (as base flow) and surface runoff flowing into all surface-water features were displayed under the following conditions: (1) extreme low-flow conditions, comparable to an exceedance-probability quantile of 0.95; (2) low-flow conditions, comparable to an exceedance-probability quantile of 0.90; (3) a median condition, comparable to an exceedance-probability quantile of 0.50; and (4) a high-flow condition, comparable to an exceedance-probability quantile of 0.02.Streamflow distribution maps were developed using flow-duration curve exceedance-probability quantiles in conjunction with Soil-Water-Balance model outputs; both the flow-duration curve and Soil-Water-Balance models were built upon previously published U.S. Geological Survey reports. The selected streamflow distribution maps provide a proactive water management tool for State cooperators by illustrating flow rates during a range of hydraulic conditions. Furthermore, after the nested drainage basins are highlighted in terms of surface-water flows, the streamflows can be evaluated in the context of meeting specific ecological flows under different flow regimes and potentially assist with decisions regarding groundwater and surface-water appropriations. Presented streamflow distribution maps are foundational work intended to support the development of additional streamflow distribution maps that include statistical constraints on the selected flow conditions.

Accreting SMBH in the COSMOS field: the connection to their host galaxies .

NASA Astrophysics Data System (ADS)

Merloni, A.; Bongiorno, A.

Using the rich multi-band photometry in the COSMOS field we explore the host galaxy properties of a large, complete, sample of X-ray and spectroscopically selected AGN. Based on a two-components fit to their Spectral Energy Distribution (SED) we derive rest-frame magnitudes, colours, stellar masses and star formation rates up to z˜ 3. The probability for a galaxy to host a black hole growing at any given specific accretion rate (the ratio of X-ray luminosity to the host stellar mass) is independent of the galaxy mass and follows a power-law distribution in L_X/M. By looking at the normalisation of such a probability distribution, we show how the incidence of AGN increases with redshift as rapidly as (1+z)4.2, in close resemblance with the overall evolution of the specific star formation rate. Although AGN activity and star formation appear to have a common triggering mechanism, we do not find any 'smoking gun' signalling powerful AGN influence on the global properties of their host galaxies.

Percolation

NASA Astrophysics Data System (ADS)

Dã¡Vila, Alã¡N.; Escudero, Christian; López, Jorge, , Dr.

2004-10-01

Several methods have been developed in order to study phase transitions in nuclear fragmentation. The one used in this research is Percolation. This method allows us to adjust resulting data to heavy ion collisions experiments. In systems, such as atomic nuclei or molecules, energy is put into the system. The system's particles move away from each other until their links are broken. Some particles will still be linked. The fragments' distribution is found to be a power law. We are witnessing then a critical phenomenon. In our model the particles are represented as occupied spaces in a cubical array. Each particle has a bound to each one of its 6 neighbors. Each bound can be active if the two particles are linked or inactive if they are not. When two or more particles are linked, a fragment is formed. The probability for a specific link to be broken cannot be calculated, so the probability for a bound to be active is going to be used as parameter when trying to adjust the data. For a given probability p several arrays are generated. The fragments are counted. The fragments' distribution is then adjusted to a power law. The probability that generates the better fit is going to be the critical probability that indicates a phase transition. The better fit is found by seeking the fragments' distribution that gives the minimal chi squared when compared to a power law. As additional evidence of criticality the entropy and normalized variance of the mass are also calculated for each probability.

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.

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.

Information retrieval from wide-band meteorological data - An example

NASA Technical Reports Server (NTRS)

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

1983-01-01

The methods proposed by Smith and Adelfang (1981) and Smith et al. (1982) are used to calculate probabilities over rectangles and sectors of the gust magnitude-gust length plane; probabilities over the same regions are also calculated from the observed distributions and a comparison is also presented to demonstrate the accuracy of the statistical model. These and other statistical results are calculated from samples of Jimsphere wind profiles at Cape Canaveral. The results are presented for a variety of wavelength bands, altitudes, and seasons. It is shown that wind perturbations observed in Jimsphere wind profiles in various wavelength bands can be analyzed by using digital filters. The relationship between gust magnitude and gust length is modeled with the bivariate gamma distribution. It is pointed out that application of the model to calculate probabilities over specific areas of the gust magnitude-gust length plane can be useful in aerospace design.

Quantum temporal probabilities in tunneling systems

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

Anastopoulos, Charis, E-mail: anastop@physics.upatras.gr; Savvidou, Ntina, E-mail: ksavvidou@physics.upatras.gr

We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines ‘classical’ time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlation functions of the quantum field associated with tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects ofmore » the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region. Finally, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems. -- Highlights: •Present a general methodology for deriving temporal probabilities in tunneling systems. •Treatment applies to relativistic particles interacting through quantum fields. •Derive a new expression for tunneling time. •Identify new time parameters relevant to tunneling. •Propose a resolution of the superluminality paradox in tunneling.« less

Evaluation of an Ensemble Dispersion Calculation.

NASA Astrophysics Data System (ADS)

Draxler, Roland R.

2003-02-01

A Lagrangian transport and dispersion model was modified to generate multiple simulations from a single meteorological dataset. Each member of the simulation was computed by assuming a ±1-gridpoint shift in the horizontal direction and a ±250-m shift in the vertical direction of the particle position, with respect to the meteorological data. The configuration resulted in 27 ensemble members. Each member was assumed to have an equal probability. The model was tested by creating an ensemble of daily average air concentrations for 3 months at 75 measurement locations over the eastern half of the United States during the Across North America Tracer Experiment (ANATEX). Two generic graphical displays were developed to summarize the ensemble prediction and the resulting concentration probabilities for a specific event: a probability-exceed plot and a concentration-probability plot. Although a cumulative distribution of the ensemble probabilities compared favorably with the measurement data, the resulting distribution was not uniform. This result was attributed to release height sensitivity. The trajectory ensemble approach accounts for about 41%-47% of the variance in the measurement data. This residual uncertainty is caused by other model and data errors that are not included in the ensemble design.

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

A statistical method for estimating rates of soil development and ages of geologic deposits: A design for soil-chronosequence studies

USGS Publications Warehouse

Switzer, P.; Harden, J.W.; Mark, R.K.

1988-01-01

A statistical method for estimating rates of soil development in a given region based on calibration from a series of dated soils is used to estimate ages of soils in the same region that are not dated directly. The method is designed specifically to account for sampling procedures and uncertainties that are inherent in soil studies. Soil variation and measurement error, uncertainties in calibration dates and their relation to the age of the soil, and the limited number of dated soils are all considered. Maximum likelihood (ML) is employed to estimate a parametric linear calibration curve, relating soil development to time or age on suitably transformed scales. Soil variation on a geomorphic surface of a certain age is characterized by replicate sampling of soils on each surface; such variation is assumed to have a Gaussian distribution. The age of a geomorphic surface is described by older and younger bounds. This technique allows age uncertainty to be characterized by either a Gaussian distribution or by a triangular distribution using minimum, best-estimate, and maximum ages. The calibration curve is taken to be linear after suitable (in certain cases logarithmic) transformations, if required, of the soil parameter and age variables. Soil variability, measurement error, and departures from linearity are described in a combined fashion using Gaussian distributions with variances particular to each sampled geomorphic surface and the number of sample replicates. Uncertainty in age of a geomorphic surface used for calibration is described using three parameters by one of two methods. In the first method, upper and lower ages are specified together with a coverage probability; this specification is converted to a Gaussian distribution with the appropriate mean and variance. In the second method, "absolute" older and younger ages are specified together with a most probable age; this specification is converted to an asymmetric triangular distribution with mode at the most probable age. The statistical variability of the ML-estimated calibration curve is assessed by a Monte Carlo method in which simulated data sets repeatedly are drawn from the distributional specification; calibration parameters are reestimated for each such simulation in order to assess their statistical variability. Several examples are used for illustration. The age of undated soils in a related setting may be estimated from the soil data using the fitted calibration curve. A second simulation to assess age estimate variability is described and applied to the examples. ?? 1988 International Association for Mathematical Geology.

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport.

PubMed

Zhang, Kejiang; Achari, Gopal; Li, Hua

2009-11-03

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.

Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform.

PubMed

Lange, K

1982-03-01

In a population of constant size every deleterious gene eventually attains a stochastic equilibrium between mutation and selection. The individual probabilities of this equilibrium distribution can be computed by an application of the finite Fourier transform to an appropriate branching process formula. Specific numerical examples are discussed for the autosomal dominants, Huntington's chorea and chondrodystrophy, and for the X-linked recessive, Becker's muscular dystrophy.

Modeling nonbreeding distributions of shorebirds and waterfowl in response to climate change

USGS Publications Warehouse

Reese, Gordon; Skagen, Susan K.

2017-01-01

To identify areas on the landscape that may contribute to a robust network of conservation areas, we modeled the probabilities of occurrence of several en route migratory shorebirds and wintering waterfowl in the southern Great Plains of North America, including responses to changing climate. We predominantly used data from the eBird citizen-science project to model probabilities of occurrence relative to land-use patterns, spatial distribution of wetlands, and climate. We projected models to potential future climate conditions using five representative general circulation models of the Coupled Model Intercomparison Project 5 (CMIP5). We used Random Forests to model probabilities of occurrence and compared the time periods 1981–2010 (hindcast) and 2041–2070 (forecast) in “model space.” Projected changes in shorebird probabilities of occurrence varied with species-specific general distribution pattern, migration distance, and spatial extent. Species using the western and northern portion of the study area exhibited the greatest likelihoods of decline, whereas species with more easterly occurrences, mostly long-distance migrants, had the greatest projected increases in probability of occurrence. At an ecoregional extent, differences in probabilities of shorebird occurrence ranged from −0.015 to 0.045 when averaged across climate models, with the largest increases occurring early in migration. Spatial shifts are predicted for several shorebird species. Probabilities of occurrence of wintering Mallards and Northern Pintail are predicted to increase by 0.046 and 0.061, respectively, with northward shifts projected for both species. When incorporated into partner land management decision tools, results at ecoregional extents can be used to identify wetland complexes with the greatest potential to support birds in the nonbreeding season under a wide range of future climate scenarios.

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2011-06-01

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

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.

Relating centrality to impact parameter in nucleus-nucleus collisions

NASA Astrophysics Data System (ADS)

Das, Sruthy Jyothi; Giacalone, Giuliano; Monard, Pierre-Amaury; Ollitrault, Jean-Yves

2018-01-01

In ultrarelativistic heavy-ion experiments, one estimates the centrality of a collision by using a single observable, say n , typically given by the transverse energy or the number of tracks observed in a dedicated detector. The correlation between n and the impact parameter b of the collision is then inferred by fitting a specific model of the collision dynamics, such as the Glauber model, to experimental data. The goal of this paper is to assess precisely which information about b can be extracted from data without any specific model of the collision. Under the sole assumption that the probability distribution of n for a fixed b is Gaussian, we show that the probability distribution of the impact parameter in a narrow centrality bin can be accurately reconstructed up to 5 % centrality. We apply our methodology to data from the Relativistic Heavy Ion Collider and the Large Hadron Collider. We propose a simple measure of the precision of the centrality determination, which can be used to compare different experiments.

Metocean design parameter estimation for fixed platform based on copula functions

NASA Astrophysics Data System (ADS)

Zhai, Jinjin; Yin, Qilin; Dong, Sheng

2017-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Probabilistic estimates of drought impacts on agricultural production

NASA Astrophysics Data System (ADS)

Madadgar, Shahrbanou; AghaKouchak, Amir; Farahmand, Alireza; Davis, Steven J.

2017-08-01

Increases in the severity and frequency of drought in a warming climate may negatively impact agricultural production and food security. Unlike previous studies that have estimated agricultural impacts of climate condition using single-crop yield distributions, we develop a multivariate probabilistic model that uses projected climatic conditions (e.g., precipitation amount or soil moisture) throughout a growing season to estimate the probability distribution of crop yields. We demonstrate the model by an analysis of the historical period 1980-2012, including the Millennium Drought in Australia (2001-2009). We find that precipitation and soil moisture deficit in dry growing seasons reduced the average annual yield of the five largest crops in Australia (wheat, broad beans, canola, lupine, and barley) by 25-45% relative to the wet growing seasons. Our model can thus produce region- and crop-specific agricultural sensitivities to climate conditions and variability. Probabilistic estimates of yield may help decision-makers in government and business to quantitatively assess the vulnerability of agriculture to climate variations. We develop a multivariate probabilistic model that uses precipitation to estimate the probability distribution of crop yields. The proposed model shows how the probability distribution of crop yield changes in response to droughts. During Australia's Millennium Drought precipitation and soil moisture deficit reduced the average annual yield of the five largest crops.

Measurement-device-independent quantum key distribution with source state errors and statistical fluctuation

NASA Astrophysics Data System (ADS)

Jiang, Cong; Yu, Zong-Wen; Wang, Xiang-Bin

2017-03-01

We show how to calculate the secure final key rate in the four-intensity decoy-state measurement-device-independent quantum key distribution protocol with both source errors and statistical fluctuations with a certain failure probability. Our results rely only on the range of only a few parameters in the source state. All imperfections in this protocol have been taken into consideration without assuming any specific error patterns of the source.

Automatically-generated rectal dose constraints in intensity-modulated radiation therapy for prostate cancer

NASA Astrophysics Data System (ADS)

Hwang, Taejin; Kim, Yong Nam; Kim, Soo Kon; Kang, Sei-Kwon; Cheong, Kwang-Ho; Park, Soah; Yoon, Jai-Woong; Han, Taejin; Kim, Haeyoung; Lee, Meyeon; Kim, Kyoung-Joo; Bae, Hoonsik; Suh, Tae-Suk

2015-06-01

The dose constraint during prostate intensity-modulated radiation therapy (IMRT) optimization should be patient-specific for better rectum sparing. The aims of this study are to suggest a novel method for automatically generating a patient-specific dose constraint by using an experience-based dose volume histogram (DVH) of the rectum and to evaluate the potential of such a dose constraint qualitatively. The normal tissue complication probabilities (NTCPs) of the rectum with respect to V %ratio in our study were divided into three groups, where V %ratio was defined as the percent ratio of the rectal volume overlapping the planning target volume (PTV) to the rectal volume: (1) the rectal NTCPs in the previous study (clinical data), (2) those statistically generated by using the standard normal distribution (calculated data), and (3) those generated by combining the calculated data and the clinical data (mixed data). In the calculated data, a random number whose mean value was on the fitted curve described in the clinical data and whose standard deviation was 1% was generated by using the `randn' function in the MATLAB program and was used. For each group, we validated whether the probability density function (PDF) of the rectal NTCP could be automatically generated with the density estimation method by using a Gaussian kernel. The results revealed that the rectal NTCP probability increased in proportion to V %ratio , that the predictive rectal NTCP was patient-specific, and that the starting point of IMRT optimization for the given patient might be different. The PDF of the rectal NTCP was obtained automatically for each group except that the smoothness of the probability distribution increased with increasing number of data and with increasing window width. We showed that during the prostate IMRT optimization, the patient-specific dose constraints could be automatically generated and that our method could reduce the IMRT optimization time as well as maintain the IMRT plan quality.

Estimating sales and sales market share from sales rank data for consumer appliances

NASA Astrophysics Data System (ADS)

Touzani, Samir; Van Buskirk, Robert

2016-06-01

Our motivation in this work is to find an adequate probability distribution to fit sales volumes of different appliances. This distribution allows for the translation of sales rank into sales volume. This paper shows that the log-normal distribution and specifically the truncated version are well suited for this purpose. We demonstrate that using sales proxies derived from a calibrated truncated log-normal distribution function can be used to produce realistic estimates of market average product prices, and product attributes. We show that the market averages calculated with the sales proxies derived from the calibrated, truncated log-normal distribution provide better market average estimates than sales proxies estimated with simpler distribution functions.

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

PubMed

Tygert, Mark

2010-09-21

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

Design of a sampling plan to detect ochratoxin A in green coffee.

PubMed

Vargas, E A; Whitaker, T B; Dos Santos, E A; Slate, A B; Lima, F B; Franca, R C A

2006-01-01

The establishment of maximum limits for ochratoxin A (OTA) in coffee by importing countries requires that coffee-producing countries develop scientifically based sampling plans to assess OTA contents in lots of green coffee before coffee enters the market thus reducing consumer exposure to OTA, minimizing the number of lots rejected, and reducing financial loss for producing countries. A study was carried out to design an official sampling plan to determine OTA in green coffee produced in Brazil. Twenty-five lots of green coffee (type 7 - approximately 160 defects) were sampled according to an experimental protocol where 16 test samples were taken from each lot (total of 16 kg) resulting in a total of 800 OTA analyses. The total, sampling, sample preparation, and analytical variances were 10.75 (CV = 65.6%), 7.80 (CV = 55.8%), 2.84 (CV = 33.7%), and 0.11 (CV = 6.6%), respectively, assuming a regulatory limit of 5 microg kg(-1) OTA and using a 1 kg sample, Romer RAS mill, 25 g sub-samples, and high performance liquid chromatography. The observed OTA distribution among the 16 OTA sample results was compared to several theoretical distributions. The 2 parameter-log normal distribution was selected to model OTA test results for green coffee as it gave the best fit across all 25 lot distributions. Specific computer software was developed using the variance and distribution information to predict the probability of accepting or rejecting coffee lots at specific OTA concentrations. The acceptation probability was used to compute an operating characteristic (OC) curve specific to a sampling plan design. The OC curve was used to predict the rejection of good lots (sellers' or exporters' risk) and the acceptance of bad lots (buyers' or importers' risk).

Trending in Probability of Collision Measurements via a Bayesian Zero-Inflated Beta Mixed Model

NASA Technical Reports Server (NTRS)

Vallejo, Jonathon; Hejduk, Matt; Stamey, James

2015-01-01

We investigate the performance of a generalized linear mixed model in predicting the Probabilities of Collision (Pc) for conjunction events. Specifically, we apply this model to the log(sub 10) transformation of these probabilities and argue that this transformation yields values that can be considered bounded in practice. Additionally, this bounded random variable, after scaling, is zero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, and utilize the Bayesian paradigm and the mixed model framework to borrow information from past and current events. This provides a natural way to model the data and provides a basis for answering questions of interest, such as what is the likelihood of observing a probability of collision equal to the effective value of zero on a subsequent observation.

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.

CUMPOIS- CUMULATIVE POISSON DISTRIBUTION PROGRAM

NASA Technical Reports Server (NTRS)

Bowerman, P. N.

1994-01-01

The Cumulative Poisson distribution program, CUMPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), can be used independently of one another. CUMPOIS determines the approximate cumulative binomial distribution, evaluates the cumulative distribution function (cdf) for gamma distributions with integer shape parameters, and evaluates the cdf for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. CUMPOIS calculates the probability that n or less events (ie. cumulative) will occur within any unit when the expected number of events is given as lambda. Normally, this probability is calculated by a direct summation, from i=0 to n, of terms involving the exponential function, lambda, and inverse factorials. This approach, however, eventually fails due to underflow for sufficiently large values of n. Additionally, when the exponential term is moved outside of the summation for simplification purposes, there is a risk that the terms remaining within the summation, and the summation itself, will overflow for certain values of i and lambda. CUMPOIS eliminates these possibilities by multiplying an additional exponential factor into the summation terms and the partial sum whenever overflow/underflow situations threaten. The reciprocal of this term is then multiplied into the completed sum giving the cumulative probability. The CUMPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting lambda and n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 26K. CUMPOIS was developed in 1988.

Diagnostic accuracy of enzyme-linked immunosorbent assay (ELISA) and immunoblot (IB) for the detection of antibodies against Neospora caninum in milk from dairy cows.

PubMed

Chatziprodromidou, I P; Apostolou, T

2018-04-01

The aim of the study was to estimate the sensitivity and specificity of enzyme-linked immunosorbent assay (ELISA) and immunoblot (IB) for detecting antibodies of Neospora caninum in dairy cows, in the absence of a gold standard. The study complies with STRADAS-paratuberculosis guidelines for reporting the accuracy of the test. We tried to apply Bayesian models that do not require conditional independence of the tests under evaluation, but as convergence problems appeared, we used Bayesian methodology, that does not assume conditional dependence of the tests. Informative prior probability distributions were constructed, based on scientific inputs regarding sensitivity and specificity of the IB test and the prevalence of disease in the studied populations. IB sensitivity and specificity were estimated to be 98.8% and 91.3%, respectively, while the respective estimates for ELISA were 60% and 96.7%. A sensitivity analysis, where modified prior probability distributions concerning IB diagnostic accuracy applied, showed a limited effect in posterior assessments. We concluded that ELISA can be used to screen the bulk milk and secondly, IB can be used whenever needed.

Prediction of fatty acid-binding residues on protein surfaces with three-dimensional probability distributions of interacting atoms.

PubMed

Mahalingam, Rajasekaran; Peng, Hung-Pin; Yang, An-Suei

2014-08-01

Protein-fatty acid interaction is vital for many cellular processes and understanding this interaction is important for functional annotation as well as drug discovery. In this work, we present a method for predicting the fatty acid (FA)-binding residues by using three-dimensional probability density distributions of interacting atoms of FAs on protein surfaces which are derived from the known protein-FA complex structures. A machine learning algorithm was established to learn the characteristic patterns of the probability density maps specific to the FA-binding sites. The predictor was trained with five-fold cross validation on a non-redundant training set and then evaluated with an independent test set as well as on holo-apo pair's dataset. The results showed good accuracy in predicting the FA-binding residues. Further, the predictor developed in this study is implemented as an online server which is freely accessible at the following website, http://ismblab.genomics.sinica.edu.tw/. Copyright © 2014 Elsevier B.V. All rights reserved.

A multimodal detection model of dolphins to estimate abundance validated by field experiments.

PubMed

Akamatsu, Tomonari; Ura, Tamaki; Sugimatsu, Harumi; Bahl, Rajendar; Behera, Sandeep; Panda, Sudarsan; Khan, Muntaz; Kar, S K; Kar, C S; Kimura, Satoko; Sasaki-Yamamoto, Yukiko

2013-09-01

Abundance estimation of marine mammals requires matching of detection of an animal or a group of animal by two independent means. A multimodal detection model using visual and acoustic cues (surfacing and phonation) that enables abundance estimation of dolphins is proposed. The method does not require a specific time window to match the cues of both means for applying mark-recapture method. The proposed model was evaluated using data obtained in field observations of Ganges River dolphins and Irrawaddy dolphins, as examples of dispersed and condensed distributions of animals, respectively. The acoustic detection probability was approximately 80%, 20% higher than that of visual detection for both species, regardless of the distribution of the animals in present study sites. The abundance estimates of Ganges River dolphins and Irrawaddy dolphins fairly agreed with the numbers reported in previous monitoring studies. The single animal detection probability was smaller than that of larger cluster size, as predicted by the model and confirmed by field data. However, dense groups of Irrawaddy dolphins showed difference in cluster sizes observed by visual and acoustic methods. Lower detection probability of single clusters of this species seemed to be caused by the clumped distribution of this species.

Generative adversarial networks for brain lesion detection

NASA Astrophysics Data System (ADS)

Alex, Varghese; Safwan, K. P. Mohammed; Chennamsetty, Sai Saketh; Krishnamurthi, Ganapathy

2017-02-01

Manual segmentation of brain lesions from Magnetic Resonance Images (MRI) is cumbersome and introduces errors due to inter-rater variability. This paper introduces a semi-supervised technique for detection of brain lesion from MRI using Generative Adversarial Networks (GANs). GANs comprises of a Generator network and a Discriminator network which are trained simultaneously with the objective of one bettering the other. The networks were trained using non lesion patches (n=13,000) from 4 different MR sequences. The network was trained on BraTS dataset and patches were extracted from regions excluding tumor region. The Generator network generates data by modeling the underlying probability distribution of the training data, (PData). The Discriminator learns the posterior probability P (Label Data) by classifying training data and generated data as "Real" or "Fake" respectively. The Generator upon learning the joint distribution, produces images/patches such that the performance of the Discriminator on them are random, i.e. P (Label Data = GeneratedData) = 0.5. During testing, the Discriminator assigns posterior probability values close to 0.5 for patches from non lesion regions, while patches centered on lesion arise from a different distribution (PLesion) and hence are assigned lower posterior probability value by the Discriminator. On the test set (n=14), the proposed technique achieves whole tumor dice score of 0.69, sensitivity of 91% and specificity of 59%. Additionally the generator network was capable of generating non lesion patches from various MR sequences.

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.

Dependency of outbreaks distribution from insects - defoliators' seasonal development

Treesearch

Valentina Meshkova

2003-01-01

Analysis of data on the population dynamics of foliage browsing insects in time and space was conducted in the Ukraine. For each of the main species, correlation indices were calculated between outbreak characteristics (mean and specific foci area, outbreak probability), weather elements (air temperature, precipitation), indices (hydrothermal coefficient, winter...

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

PubMed

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

2009-07-01

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

Monte Carlo simulation of single accident airport risk profile

NASA Technical Reports Server (NTRS)

1979-01-01

A computer simulation model was developed for estimating the potential economic impacts of a carbon fiber release upon facilities within an 80 kilometer radius of a major airport. The model simulated the possible range of release conditions and the resulting dispersion of the carbon fibers. Each iteration of the model generated a specific release scenario, which would cause a specific amount of dollar loss to the surrounding community. By repeated iterations, a risk profile was generated, showing the probability distribution of losses from one accident. Using accident probability estimates, the risks profile for annual losses was derived. The mechanics are described of the simulation model, the required input data, and the risk profiles generated for the 26 large hub airports.

Preferences for equity in health behind a veil of ignorance.

PubMed

Andersson, F; Lyttkens, C H

1999-08-01

Individual attitudes to distributions of life years between two groups in a society are explored by means of an experiment. Subjects are asked to place themselves behind a veil of ignorance which is specified in terms of risk (known probabilities) for some subjects and in terms of uncertainty (unknown probabilities) for some subjects. The latter is argued to be the appropriate interpretation of Rawls' notion. It is found that subjects exhibit convex preferences over life years for the two groups, and that preferences do not differ between the risk and the uncertainty specifications.

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.

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

PubMed

Garriguet, Didier

2016-04-01

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

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.

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.

Gravity and count probabilities in an expanding universe

NASA Technical Reports Server (NTRS)

Bouchet, Francois R.; Hernquist, Lars

1992-01-01

The time evolution of nonlinear clustering on large scales in cold dark matter, hot dark matter, and white noise models of the universe is investigated using N-body simulations performed with a tree code. Count probabilities in cubic cells are determined as functions of the cell size and the clustering state (redshift), and comparisons are made with various theoretical models. We isolate the features that appear to be the result of gravitational instability, those that depend on the initial conditions, and those that are likely a consequence of numerical limitations. More specifically, we study the development of skewness, kurtosis, and the fifth moment in relation to variance, the dependence of the void probability on time as well as on sparseness of sampling, and the overall shape of the count probability distribution. Implications of our results for theoretical and observational studies are discussed.

Understanding the complexity of the Lévy-walk nature of human mobility with a multi-scale cost∕benefit model.

PubMed

Scafetta, Nicola

2011-12-01

Probability distributions of human displacements have been fit with exponentially truncated Lévy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the city of residence), but with a non-vanishing frequency they visit nearby or far locations too. Herein, we show that an important empirical distribution of human displacements (range: from 1 to 1000 km) can be well fit by three consecutive Pareto distributions with simple integer exponents equal to 1, 2, and (>) 3. These three exponents correspond to three displacement range zones of about 1 km ≲Δr≲10 km, 10 km ≲Δr≲300 km, and 300 km ≲Δr≲1000 km, respectively. These three zones can be geographically and physically well determined as displacements within a city, visits to nearby cities that may occur within just one-day trips, and visit to far locations that may require multi-days trips. The incremental integer values of the three exponents can be easily explained with a three-scale mobility cost∕benefit model for human displacements based on simple geometrical constrains. Essentially, people would divide the space into three major regions (close, medium, and far distances) and would assume that the travel benefits are randomly∕uniformly distributed mostly only within specific urban-like areas. The three displacement distribution zones appear to be characterized by an integer (1, 2, or >3) inverse power exponent because of the specific number (1, 2, or >3) of cost mechanisms (each of which is proportional to the displacement length). The distributions in the first two zones would be associated to Pareto distributions with exponent β = 1 and β = 2 because of simple geometrical statistical considerations due to the a priori assumption that most benefits are searched in the urban area of the city of residence or in the urban area of specific nearby cities. We also show, by using independent records of human mobility, that the proposed model predicts the statistical properties of human mobility below 1 km ranges, where people just walk. In the latter case, the threshold between zone 1 and zone 2 may be around 100-200 m and, perhaps, may have been evolutionary determined by the natural human high resolution visual range, which characterizes an area of interest where the benefits are assumed to be randomly and uniformly distributed. This rich and suggestive interpretation of human mobility may characterize other complex random walk phenomena that may also be described by a N-piece fit Pareto distributions with increasing integer exponents. This study also suggests that distribution functions used to fit experimental probability distributions must be carefully chosen for not improperly obscuring the physics underlying a phenomenon.

Use of the gamma distribution to represent monthly rainfall in Africa for drought monitoring applications

USGS Publications Warehouse

Husak, Gregory J.; Michaelsen, Joel C.; Funk, Christopher C.

2007-01-01

Evaluating a range of scenarios that accurately reflect precipitation variability is critical for water resource applications. Inputs to these applications can be provided using location- and interval-specific probability distributions. These distributions make it possible to estimate the likelihood of rainfall being within a specified range. In this paper, we demonstrate the feasibility of fitting cell-by-cell probability distributions to grids of monthly interpolated, continent-wide data. Future work will then detail applications of these grids to improved satellite-remote sensing of drought and interpretations of probabilistic climate outlook forum forecasts. The gamma distribution is well suited to these applications because it is fairly familiar to African scientists, and capable of representing a variety of distribution shapes. This study tests the goodness-of-fit using the Kolmogorov–Smirnov (KS) test, and compares these results against another distribution commonly used in rainfall events, the Weibull. The gamma distribution is suitable for roughly 98% of the locations over all months. The techniques and results presented in this study provide a foundation for use of the gamma distribution to generate drivers for various rain-related models. These models are used as decision support tools for the management of water and agricultural resources as well as food reserves by providing decision makers with ways to evaluate the likelihood of various rainfall accumulations and assess different scenarios in Africa. 

How to Introduce Historically the Normal Distribution in Engineering Education: A Classroom Experiment

ERIC Educational Resources Information Center

Blanco, Monica; Ginovart, Marta

2010-01-01

Little has been explored with regard to introducing historical aspects in the undergraduate statistics classroom in engineering studies. This article focuses on the design, implementation and assessment of a specific activity concerning the introduction of the normal probability curve and related aspects from a historical dimension. Following a…

DNS of moderate-temperature gaseous mixing layers laden with multicomponent-fuel drops

NASA Technical Reports Server (NTRS)

Clercq, P. C. Le; Bellan, J.

2004-01-01

A formulation representing multicomponent-fuel (MC-fuel) composition as a Probability Distribution Function (PDF) depending on the molar weight is used to construct a model of a large number of MC-fuel drops evaporating in a gas flow, so as to assess the extent of fuel specificity on the vapor composition.

Neural response to reward anticipation under risk is nonlinear in probabilities.

PubMed

Hsu, Ming; Krajbich, Ian; Zhao, Chen; Camerer, Colin F

2009-02-18

A widely observed phenomenon in decision making under risk is the apparent overweighting of unlikely events and the underweighting of nearly certain events. This violates standard assumptions in expected utility theory, which requires that expected utility be linear (objective) in probabilities. Models such as prospect theory have relaxed this assumption and introduced the notion of a "probability weighting function," which captures the key properties found in experimental data. This study reports functional magnetic resonance imaging (fMRI) data that neural response to expected reward is nonlinear in probabilities. Specifically, we found that activity in the striatum during valuation of monetary gambles are nonlinear in probabilities in the pattern predicted by prospect theory, suggesting that probability distortion is reflected at the level of the reward encoding process. The degree of nonlinearity reflected in individual subjects' decisions is also correlated with striatal activity across subjects. Our results shed light on the neural mechanisms of reward processing, and have implications for future neuroscientific studies of decision making involving extreme tails of the distribution, where probability weighting provides an explanation for commonly observed behavioral anomalies.

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

Adaptability and phenotypic stability of common bean genotypes through Bayesian inference.

PubMed

Corrêa, A M; Teodoro, P E; Gonçalves, M C; Barroso, L M A; Nascimento, M; Santos, A; Torres, F E

2016-04-27

This study used Bayesian inference to investigate the genotype x environment interaction in common bean grown in Mato Grosso do Sul State, and it also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 13 common bean genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian inference was effective for the selection of upright common bean genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions. According to Bayesian inference, the EMGOPA-201, BAMBUÍ, CNF 4999, CNF 4129 A 54, and CNFv 8025 genotypes had specific adaptability to favorable environments, while the IAPAR 14 and IAC CARIOCA ETE genotypes had specific adaptability to unfavorable environments.

Using Multi-Scenario Tsunami Modelling Results combined with Probabilistic Analyses to provide Hazard Information for the South-WestCoast of Indonesia

NASA Astrophysics Data System (ADS)

Zosseder, K.; Post, J.; Steinmetz, T.; Wegscheider, S.; Strunz, G.

2009-04-01

Indonesia is located at one of the most active geological subduction zones in the world. Following the most recent seaquakes and their subsequent tsunamis in December 2004 and July 2006 it is expected that also in the near future tsunamis are likely to occur due to increased tectonic tensions leading to abrupt vertical seafloor alterations after a century of relative tectonic silence. To face this devastating threat tsunami hazard maps are very important as base for evacuation planning and mitigation strategies. In terms of a tsunami impact the hazard assessment is mostly covered by numerical modelling because the model results normally offer the most precise database for a hazard analysis as they include spatially distributed data and their influence to the hydraulic dynamics. Generally a model result gives a probability for the intensity distribution of a tsunami at the coast (or run up) and the spatial distribution of the maximum inundation area depending on the location and magnitude of the tsunami source used. The boundary condition of the source used for the model is mostly chosen by a worst case approach. Hence the location and magnitude which are likely to occur and which are assumed to generate the worst impact are used to predict the impact at a specific area. But for a tsunami hazard assessment covering a large coastal area, as it is demanded in the GITEWS (German Indonesian Tsunami Early Warning System) project in which the present work is embedded, this approach is not practicable because a lot of tsunami sources can cause an impact at the coast and must be considered. Thus a multi-scenario tsunami model approach is developed to provide a reliable hazard assessment covering large areas. For the Indonesian Early Warning System many tsunami scenarios were modelled by the Alfred Wegener Institute (AWI) at different probable tsunami sources and with different magnitudes along the Sunda Trench. Every modelled scenario delivers the spatial distribution of the inundation for a specific area, the wave height at coast at this area and the estimated times of arrival (ETAs) of the waves, caused by one tsunamigenic source with a specific magnitude. These parameters from the several scenarios can overlap each other along the coast and must be combined to get one comprehensive hazard assessment for all possible future tsunamis at the region under observation. The simplest way to derive the inundation probability along the coast using the multiscenario approach is to overlay all scenario inundation results and to determine how often a point on land will be significantly inundated from the various scenarios. But this does not take into account that the used tsunamigenic sources for the modeled scenarios have different likelihoods of causing a tsunami. Hence a statistical analysis of historical data and geophysical investigation results based on numerical modelling results is added to the hazard assessment, which clearly improves the significance of the hazard assessment. For this purpose the present method is developed and contains a complex logical combination of the diverse probabilities assessed like probability of occurrence for different earthquake magnitudes at different localities, probability of occurrence for a specific wave height at the coast and the probability for every point on land likely to get hit by a tsunami. The values are combined by a logical tree technique and quantified by statistical analysis of historical data and of the tsunami modelling results as mentioned before. This results in a tsunami inundation probability map covering the South West Coast of Indonesia which nevertheless shows a significant spatial diversity offering a good base for evacuation planning and mitigation strategies. Keywords: tsunami hazard assessment, tsunami modelling, probabilistic analysis, early warning

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

PubMed

Yura, Harold T; Hanson, Steen G

2012-04-01

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

The global impact distribution of Near-Earth objects

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob; Englander, Arnold

2014-01-01

Trajectory optimization methods using MBH have become well developed during the past decade. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing RVs from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by Englander significantly improves MBH performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness, where efficiency is finding better solutions in less time, and robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive RWs originally developed in the field of statistical physics.

Contrast statistics for foveated visual systems: fixation selection by minimizing contrast entropy

NASA Astrophysics Data System (ADS)

Raj, Raghu; Geisler, Wilson S.; Frazor, Robert A.; Bovik, Alan C.

2005-10-01

The human visual system combines a wide field of view with a high-resolution fovea and uses eye, head, and body movements to direct the fovea to potentially relevant locations in the visual scene. This strategy is sensible for a visual system with limited neural resources. However, for this strategy to be effective, the visual system needs sophisticated central mechanisms that efficiently exploit the varying spatial resolution of the retina. To gain insight into some of the design requirements of these central mechanisms, we have analyzed the effects of variable spatial resolution on local contrast in 300 calibrated natural images. Specifically, for each retinal eccentricity (which produces a certain effective level of blur), and for each value of local contrast observed at that eccentricity, we measured the probability distribution of the local contrast in the unblurred image. These conditional probability distributions can be regarded as posterior probability distributions for the ``true'' unblurred contrast, given an observed contrast at a given eccentricity. We find that these conditional probability distributions are adequately described by a few simple formulas. To explore how these statistics might be exploited by central perceptual mechanisms, we consider the task of selecting successive fixation points, where the goal on each fixation is to maximize total contrast information gained about the image (i.e., minimize total contrast uncertainty). We derive an entropy minimization algorithm and find that it performs optimally at reducing total contrast uncertainty and that it also works well at reducing the mean squared error between the original image and the image reconstructed from the multiple fixations. Our results show that measurements of local contrast alone could efficiently drive the scan paths of the eye when the goal is to gain as much information about the spatial structure of a scene as possible.

Data Applicability of Heritage and New Hardware For Launch Vehicle Reliability Models

NASA Technical Reports Server (NTRS)

Al Hassan, Mohammad; Novack, Steven

2015-01-01

Bayesian reliability requires the development of a prior distribution to represent degree of belief about the value of a parameter (such as a component's failure rate) before system specific data become available from testing or operations. Generic failure data are often provided in reliability databases as point estimates (mean or median). A component's failure rate is considered a random variable where all possible values are represented by a probability distribution. The applicability of the generic data source is a significant source of uncertainty that affects the spread of the distribution. This presentation discusses heuristic guidelines for quantifying uncertainty due to generic data applicability when developing prior distributions mainly from reliability predictions.

Site specific probability of passive acoustic detection of humpback whale calls from single fixed hydrophones.

PubMed

Helble, Tyler A; D'Spain, Gerald L; Hildebrand, John A; Campbell, Gregory S; Campbell, Richard L; Heaney, Kevin D

2013-09-01

Passive acoustic monitoring of marine mammal calls is an increasingly important method for assessing population numbers, distribution, and behavior. A common mistake in the analysis of marine mammal acoustic data is formulating conclusions about these animals without first understanding how environmental properties such as bathymetry, sediment properties, water column sound speed, and ocean acoustic noise influence the detection and character of vocalizations in the acoustic data. The approach in this paper is to use Monte Carlo simulations with a full wave field acoustic propagation model to characterize the site specific probability of detection of six types of humpback whale calls at three passive acoustic monitoring locations off the California coast. Results show that the probability of detection can vary by factors greater than ten when comparing detections across locations, or comparing detections at the same location over time, due to environmental effects. Effects of uncertainties in the inputs to the propagation model are also quantified, and the model accuracy is assessed by comparing calling statistics amassed from 24,690 humpback units recorded in the month of October 2008. Under certain conditions, the probability of detection can be estimated with uncertainties sufficiently small to allow for accurate density estimates.

Detection of mastitis in dairy cattle by use of mixture models for repeated somatic cell scores: a Bayesian approach via Gibbs sampling.

PubMed

Odegård, J; Jensen, J; Madsen, P; Gianola, D; Klemetsdal, G; Heringstad, B

2003-11-01

The distribution of somatic cell scores could be regarded as a mixture of at least two components depending on a cow's udder health status. A heteroscedastic two-component Bayesian normal mixture model with random effects was developed and implemented via Gibbs sampling. The model was evaluated using datasets consisting of simulated somatic cell score records. Somatic cell score was simulated as a mixture representing two alternative udder health statuses ("healthy" or "diseased"). Animals were assigned randomly to the two components according to the probability of group membership (Pm). Random effects (additive genetic and permanent environment), when included, had identical distributions across mixture components. Posterior probabilities of putative mastitis were estimated for all observations, and model adequacy was evaluated using measures of sensitivity, specificity, and posterior probability of misclassification. Fitting different residual variances in the two mixture components caused some bias in estimation of parameters. When the components were difficult to disentangle, so were their residual variances, causing bias in estimation of Pm and of location parameters of the two underlying distributions. When all variance components were identical across mixture components, the mixture model analyses returned parameter estimates essentially without bias and with a high degree of precision. Including random effects in the model increased the probability of correct classification substantially. No sizable differences in probability of correct classification were found between models in which a single cow effect (ignoring relationships) was fitted and models where this effect was split into genetic and permanent environmental components, utilizing relationship information. When genetic and permanent environmental effects were fitted, the between-replicate variance of estimates of posterior means was smaller because the model accounted for random genetic drift.

Evaluation of Gas Phase Dispersion in Flotation under Predetermined Hydrodynamic Conditions

NASA Astrophysics Data System (ADS)

Młynarczykowska, Anna; Oleksik, Konrad; Tupek-Murowany, Klaudia

2018-03-01

Results of various investigations shows the relationship between the flotation parameters and gas distribution in a flotation cell. The size of gas bubbles is a random variable with a specific distribution. The analysis of this distribution is useful to make mathematical description of the flotation process. The flotation process depends on many variable factors. These are mainly occurrences like collision of single particle with gas bubble, adhesion of particle to the surface of bubble and detachment process. These factors are characterized by randomness. Because of that it is only possible to talk about the probability of occurence of one of these events which directly affects the speed of the process, thus a constant speed of flotation process. Probability of the bubble-particle collision in the flotation chamber with mechanical pulp agitation depends on the surface tension of the solution, air consumption, degree of pul aeration, energy dissipation and average feed particle size. Appropriate identification and description of the parameters of the dispersion of gas bubbles helps to complete the analysis of the flotation process in a specific physicochemical conditions and hydrodynamic for any raw material. The article presents the results of measurements and analysis of the gas phase dispersion by the size distribution of air bubbles in a flotation chamber under fixed hydrodynamic conditions. The tests were carried out in the Laboratory of Instrumental Methods in Department of Environmental Engineering and Mineral Processing, Faculty of Mining and Geoengineerin, AGH Univeristy of Science and Technology in Krakow.

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.

Gravitational wave hotspots: Ranking potential locations of single-source gravitational wave emission

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

Simon, Joseph; Polin, Abigail; Lommen, Andrea

2014-03-20

The steadily improving sensitivity of pulsar timing arrays (PTAs) suggests that gravitational waves (GWs) from supermassive black hole binary (SMBHB) systems in the nearby universe will be detectable sometime during the next decade. Currently, PTAs assume an equal probability of detection from every sky position, but as evidence grows for a non-isotropic distribution of sources, is there a most likely sky position for a detectable single source of GWs? In this paper, a collection of Galactic catalogs is used to calculate various metrics related to the detectability of a single GW source resolvable above a GW background, assuming that everymore » galaxy has the same probability of containing an SMBHB. Our analyses of these data reveal small probabilities that one of these sources is currently in the PTA band, but as sensitivity is improved regions of consistent probability density are found in predictable locations, specifically around local galaxy clusters.« less

A Classroom Note on the Binomial and Poisson Distributions: Biomedical Examples for Use in Teaching Introductory Statistics

ERIC Educational Resources Information Center

Holland, Bart K.

2006-01-01

A generally-educated individual should have some insight into how decisions are made in the very wide range of fields that employ statistical and probabilistic reasoning. Also, students of introductory probability and statistics are often best motivated by specific applications rather than by theory and mathematical development, because most…

PresenceAbsence: An R package for presence absence analysis

Treesearch

Elizabeth A. Freeman; Gretchen Moisen

2008-01-01

The PresenceAbsence package for R provides a set of functions useful when evaluating the results of presence-absence analysis, for example, models of species distribution or the analysis of diagnostic tests. The package provides a toolkit for selecting the optimal threshold for translating a probability surface into presence-absence maps specifically tailored to their...

A statistical treatment of bioassay pour fractions

NASA Astrophysics Data System (ADS)

Barengoltz, Jack; Hughes, David

A bioassay is a method for estimating the number of bacterial spores on a spacecraft surface for the purpose of demonstrating compliance with planetary protection (PP) requirements (Ref. 1). The details of the process may be seen in the appropriate PP document (e.g., for NASA, Ref. 2). In general, the surface is mechanically sampled with a damp sterile swab or wipe. The completion of the process is colony formation in a growth medium in a plate (Petri dish); the colonies are counted. Consider a set of samples from randomly selected, known areas of one spacecraft surface, for simplicity. One may calculate the mean and standard deviation of the bioburden density, which is the ratio of counts to area sampled. The standard deviation represents an estimate of the variation from place to place of the true bioburden density commingled with the precision of the individual sample counts. The accuracy of individual sample results depends on the equipment used, the collection method, and the culturing method. One aspect that greatly influences the result is the pour fraction, which is the quantity of fluid added to the plates divided by the total fluid used in extracting spores from the sampling equipment. In an analysis of a single sample’s counts due to the pour fraction, one seeks to answer the question: What is the probability that if a certain number of spores are counted with a known pour fraction, that there are an additional number of spores in the part of the rinse not poured. This is given for specific values by the binomial distribution density, where detection (of culturable spores) is success and the probability of success is the pour fraction. A special summation over the binomial distribution, equivalent to adding for all possible values of the true total number of spores, is performed. This distribution when normalized will almost yield the desired quantity. It is the probability that the additional number of spores does not exceed a certain value. Of course, for a desired value of uncertainty, one must invert the calculation. However, this probability of finding exactly the number of spores in the poured part is correct only in the case where all values of the true number of spores greater than or equal to the adjusted count are equally probable. This is not realistic, of course, but the result can only overestimate the uncertainty. So it is useful. In probability speak, one has the conditional probability given any true total number of spores. Therefore one must multiply it by the probability of each possible true count, before the summation. If the counts for a sample set (of which this is one sample) are available, one may use the calculated variance and the normal probability distribution. In this approach, one assumes a normal distribution and neglects the contribution from spatial variation. The former is a common assumption. The latter can only add to the conservatism (over estimate the number of spores at some level of confidence). A more straightforward approach is to assume a Poisson probability distribution for the measured total sample set counts, and use the product of the number of samples and the mean number of counts per sample as the mean of the Poisson distribution. It is necessary to set the total count to 1 in the Poisson distribution when actual total count is zero. Finally, even when the planetary protection requirements for spore burden refer only to the mean values, they require an adjustment for pour fraction and method efficiency (a PP specification based on independent data). The adjusted mean values are a 50/50 proposition (e.g., the probability of the true total counts in the sample set exceeding the estimate is 0.50). However, this is highly unconservative when the total counts are zero. No adjustment to the mean values occurs for either pour fraction or efficiency. The recommended approach is once again to set the total counts to 1, but now applied to the mean values. Then one may apply the corrections to the revised counts. It can be shown by the methods developed in this work that this change is usually conservative enough to increase the level of confidence in the estimate to 0.5. 1. NASA. (2005) Planetary protection provisions for robotic extraterrestrial missions. NPR 8020.12C, April 2005, National Aeronautics and Space Administration, Washington, DC. 2. NASA. (2010) Handbook for the Microbiological Examination of Space Hardware, NASA-HDBK-6022, National Aeronautics and Space Administration, Washington, DC.

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.

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

PubMed

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

2013-11-01

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

The Statistics of Urban Scaling and Their Connection to Zipf’s Law

PubMed Central

Gomez-Lievano, Andres; Youn, HyeJin; Bettencourt, Luís M. A.

2012-01-01

Urban scaling relations characterizing how diverse properties of cities vary on average with their population size have recently been shown to be a general quantitative property of many urban systems around the world. However, in previous studies the statistics of urban indicators were not analyzed in detail, raising important questions about the full characterization of urban properties and how scaling relations may emerge in these larger contexts. Here, we build a self-consistent statistical framework that characterizes the joint probability distributions of urban indicators and city population sizes across an urban system. To develop this framework empirically we use one of the most granular and stochastic urban indicators available, specifically measuring homicides in cities of Brazil, Colombia and Mexico, three nations with high and fast changing rates of violent crime. We use these data to derive the conditional probability of the number of homicides per year given the population size of a city. To do this we use Bayes’ rule together with the estimated conditional probability of city size given their number of homicides and the distribution of total homicides. We then show that scaling laws emerge as expectation values of these conditional statistics. Knowledge of these distributions implies, in turn, a relationship between scaling and population size distribution exponents that can be used to predict Zipf’s exponent from urban indicator statistics. Our results also suggest how a general statistical theory of urban indicators may be constructed from the stochastic dynamics of social interaction processes in cities. PMID:22815745

ProbOnto: ontology and knowledge base of probability distributions.

PubMed

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

2016-09-01

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

Living with marginal coral communities: Diversity and host-specificity in coral-associated barnacles in the northern coral distribution limit of the East China Sea.

PubMed

Chan, Benny K K; Xu, Guang; Kim, Hyun Kyong; Park, Jin-Ho; Kim, Won

2018-01-01

Corals and their associated fauna are extremely diverse in tropical waters and form major reefs. In the high-latitude temperate zone, corals living near their distribution limit are considered marginal communities because they are particularly extremely sensitive to environmental and climatic changes. In this study, we examined the diversity and host usage of coral-associated barnacles on Jeju Island, Korea, the northern coral distribution limit in the East China Sea. In this study, only three coral-associated barnacles-from two genera in two subfamilies-were collected. The Pyrgomatinid barnacles Cantellius arcuatus and Cantellius cf. euspinulosum were found only on the corals Montipora millepora and Alveopora japonica, respectively. The Megatrematinid barnacle Pyrgomina oulastreae, relatively a generalist, was found on Psammocora spp. (both profundacella and albopicta) and Oulastrea crispata corals. The host usage of these three barnacles does not overlap. DNA barcode sequences of the C. arcuatus specimens collected in the present study matched those collected in Kochi in Japan, Taiwan, Malaysia and Papua New Guinea, suggesting that this species has a wide geographical distribution. C. arcuatus covers a wider host range in Taiwan waters, inhabiting Montipora spp. and Porites spp., which suggests that the host specificity of coral-associated barnacles varies with host availability. C. cf. euspinulosum probably has a very narrow distribution and host usage. The sequences of C. cf. euspinulosum on Jeju Island do not match those of any known sequences of Cantellius barnacles in the Indo-Pacific region. P. oulastreae probably prefers cold water because it has been reported in temperate regions. Coral-associated barnacles in marginal communities have considerably lower diversity than their subtropical and tropical counterparts. When host availability is limited, marginal coral-associated barnacles exhibit higher host specificity than those in subtropical and tropical reef systems.

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

Quantitative histogram analysis of images

NASA Astrophysics Data System (ADS)

Holub, Oliver; Ferreira, Sérgio T.

2006-11-01

A routine for histogram analysis of images has been written in the object-oriented, graphical development environment LabVIEW. The program converts an RGB bitmap image into an intensity-linear greyscale image according to selectable conversion coefficients. This greyscale image is subsequently analysed by plots of the intensity histogram and probability distribution of brightness, and by calculation of various parameters, including average brightness, standard deviation, variance, minimal and maximal brightness, mode, skewness and kurtosis of the histogram and the median of the probability distribution. The program allows interactive selection of specific regions of interest (ROI) in the image and definition of lower and upper threshold levels (e.g., to permit the removal of a constant background signal). The results of the analysis of multiple images can be conveniently saved and exported for plotting in other programs, which allows fast analysis of relatively large sets of image data. The program file accompanies this manuscript together with a detailed description of two application examples: The analysis of fluorescence microscopy images, specifically of tau-immunofluorescence in primary cultures of rat cortical and hippocampal neurons, and the quantification of protein bands by Western-blot. The possibilities and limitations of this kind of analysis are discussed. Program summaryTitle of program: HAWGC Catalogue identifier: ADXG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXG_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: Mobile Intel Pentium III, AMD Duron Installations: No installation necessary—Executable file together with necessary files for LabVIEW Run-time engine Operating systems or monitors under which the program has been tested: WindowsME/2000/XP Programming language used: LabVIEW 7.0 Memory required to execute with typical data:˜16MB for starting and ˜160MB used for loading of an image No. of bits in a word: 32 No. of processors used: 1 Has the code been vectorized or parallelized?: No No of lines in distributed program, including test data, etc.:138 946 No. of bytes in distributed program, including test data, etc.:15 166 675 Distribution format: tar.gz Nature of physical problem: Quantification of image data (e.g., for discrimination of molecular species in gels or fluorescent molecular probes in cell cultures) requires proprietary or complex software packages, which might not include the relevant statistical parameters or make the analysis of multiple images a tedious procedure for the general user. Method of solution: Tool for conversion of RGB bitmap image into luminance-linear image and extraction of luminance histogram, probability distribution, and statistical parameters (average brightness, standard deviation, variance, minimal and maximal brightness, mode, skewness and kurtosis of histogram and median of probability distribution) with possible selection of region of interest (ROI) and lower and upper threshold levels. Restrictions on the complexity of the problem: Does not incorporate application-specific functions (e.g., morphometric analysis) Typical running time: Seconds (depending on image size and processor speed) Unusual features of the program: None

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

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.

Probability analysis of the relation of salinity to freshwater discharge in the St. Sebastian River, Florida

USGS Publications Warehouse

Wicklein, S.M.; Gain, W.S.

1999-01-01

The St. Sebastian River lies in the southern part of the Indian River basin on the east coast of Florida. Increases in freshwater discharge due to urbanization and changes in land use have reduced salinity in the St. Sebastian River and, consequently, salinity in the Indian River, affecting the commercial fishing industry. Wind, water temperature, tidal flux, freshwater discharge, and downstream salinity all affect salinity in the St. Sebastian River estuary, but freshwater discharge is the only one of these hydrologic factors which might be affected by water-management practices. A probability analysis of salinity conditions in the St. Sebastian River estuary, taking into account the effects of freshwater discharge over a period from May 1992 to March 1996, was used to determine the likelihood (probability) that salinities, as represented by daily mean specific- conductance values, will fall below a given threshold. The effects of freshwater discharge on salinities were evaluated with a simple volumetric model fitted to time series of measured specific conductance, by using nonlinear optimization techniques. Specific-conductance values for two depths at monitored sites represent stratified flow which results from differences in salt concentration between freshwater and saltwater. Layering of freshwater and saltwater is assumed, and the model is applied independently to each layer with the assumption that the water within the layer is well mixed. The model of specific conductance as a function of discharge (a salinity response model) was combined with a model of residual variation to produce a total probability model. Flow distributions and model residuals were integrated to produce a salinity distribution and determine differences in salinity probabilities as a result of changes in water-management practices. Two possible management alternatives were analyzed: stormwater detention (reducing the peak rate of discharge but not reducing the overall flow volume) and stormwater retention (reducing peak discharges without later release). Detention of freshwater discharges increased the probability of specific- conductance values falling below a given limit (20,000 microsiemens per centimeter) for all sites but one. The retention of freshwater input to the system decreased the likelihood of falling below a selected limit of specific conductance at all sites. For limits of specific conductance (1,000 microsiemens per centimeter or 20,000 microsiemens per centimeter, depending on the site), the predicted days of occurrence below a limit decreased ranging from 17 to 68 percent of the predicted days of occurrence for unregulated flow. The primary finding to be drawn from the discharge-salinity analysis is that an empirical-response model alone does not provide adequate information to assess the response of the system to changes in flow regime. Whether a given level of discharge can produce a given response on a given day is not as important as the probability of that response on a given day and over a period of many days. A deterministic model of the St. Sebastian River estuary based only on discharge would predict that retention of discharge peaks should increase the average salinity conditions in the St. Sebastian River estuary. The probabilistic model produces a very different response indicating that salinity can decrease by a power of three as discharges increase, and that random factors can predominate and control salinity until discharges increase sufficiently to flush the entire system of saltwater.

Probability distributions of whisker-surface contact: quantifying elements of the rat vibrissotactile natural scene.

PubMed

Hobbs, Jennifer A; Towal, R Blythe; Hartmann, Mitra J Z

2015-08-01

Analysis of natural scene statistics has been a powerful approach for understanding neural coding in the auditory and visual systems. In the field of somatosensation, it has been more challenging to quantify the natural tactile scene, in part because somatosensory signals are so tightly linked to the animal's movements. The present work takes a step towards quantifying the natural tactile scene for the rat vibrissal system by simulating rat whisking motions to systematically investigate the probabilities of whisker-object contact in naturalistic environments. The simulations permit an exhaustive search through the complete space of possible contact patterns, thereby allowing for the characterization of the patterns that would most likely occur during long sequences of natural exploratory behavior. We specifically quantified the probabilities of 'concomitant contact', that is, given that a particular whisker makes contact with a surface during a whisk, what is the probability that each of the other whiskers will also make contact with the surface during that whisk? Probabilities of concomitant contact were quantified in simulations that assumed increasingly naturalistic conditions: first, the space of all possible head poses; second, the space of behaviorally preferred head poses as measured experimentally; and third, common head poses in environments such as cages and burrows. As environments became more naturalistic, the probability distributions shifted from exhibiting a 'row-wise' structure to a more diagonal structure. Results also reveal that the rat appears to use motor strategies (e.g. head pitches) that generate contact patterns that are particularly well suited to extract information in the presence of uncertainty. © 2015. Published by The Company of Biologists Ltd.

Metabolic networks evolve towards states of maximum entropy production.

PubMed

Unrean, Pornkamol; Srienc, Friedrich

2011-11-01

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

A random walk rule for phase I clinical trials.

PubMed

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

1997-06-01

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

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

Does prevalence matter to physicians in estimating post-test probability of disease? A randomized trial.

PubMed

Agoritsas, Thomas; Courvoisier, Delphine S; Combescure, Christophe; Deom, Marie; Perneger, Thomas V

2011-04-01

The probability of a disease following a diagnostic test depends on the sensitivity and specificity of the test, but also on the prevalence of the disease in the population of interest (or pre-test probability). How physicians use this information is not well known. To assess whether physicians correctly estimate post-test probability according to various levels of prevalence and explore this skill across respondent groups. Randomized trial. Population-based sample of 1,361 physicians of all clinical specialties. We described a scenario of a highly accurate screening test (sensitivity 99% and specificity 99%) in which we randomly manipulated the prevalence of the disease (1%, 2%, 10%, 25%, 95%, or no information). We asked physicians to estimate the probability of disease following a positive test (categorized as <60%, 60-79%, 80-94%, 95-99.9%, and >99.9%). Each answer was correct for a different version of the scenario, and no answer was possible in the "no information" scenario. We estimated the proportion of physicians proficient in assessing post-test probability as the proportion of correct answers beyond the distribution of answers attributable to guessing. Most respondents in each of the six groups (67%-82%) selected a post-test probability of 95-99.9%, regardless of the prevalence of disease and even when no information on prevalence was provided. This answer was correct only for a prevalence of 25%. We estimated that 9.1% (95% CI 6.0-14.0) of respondents knew how to assess correctly the post-test probability. This proportion did not vary with clinical experience or practice setting. Most physicians do not take into account the prevalence of disease when interpreting a positive test result. This may cause unnecessary testing and diagnostic errors.

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.

Time-specific ecological niche modeling predicts spatial dynamics of vector insects and human dengue cases.

PubMed

Peterson, A Townsend; Martínez-Campos, Carmen; Nakazawa, Yoshinori; Martínez-Meyer, Enrique

2005-09-01

Numerous human diseases-malaria, dengue, yellow fever and leishmaniasis, to name a few-are transmitted by insect vectors with brief life cycles and biting activity that varies in both space and time. Although the general geographic distributions of these epidemiologically important species are known, the spatiotemporal variation in their emergence and activity remains poorly understood. We used ecological niche modeling via a genetic algorithm to produce time-specific predictive models of monthly distributions of Aedes aegypti in Mexico in 1995. Significant predictions of monthly mosquito activity and distributions indicate that predicting spatiotemporal dynamics of disease vector species is feasible; significant coincidence with human cases of dengue indicate that these dynamics probably translate directly into transmission of dengue virus to humans. This approach provides new potential for optimizing use of resources for disease prevention and remediation via automated forecasting of disease transmission risk.

Multi-scale occupancy estimation and modelling using multiple detection methods

USGS Publications Warehouse

Nichols, James D.; Bailey, Larissa L.; O'Connell, Allan F.; Talancy, Neil W.; Grant, Evan H. Campbell; Gilbert, Andrew T.; Annand, Elizabeth M.; Husband, Thomas P.; Hines, James E.

2008-01-01

Occupancy estimation and modelling based on detection–nondetection data provide an effective way of exploring change in a species’ distribution across time and space in cases where the species is not always detected with certainty. Today, many monitoring programmes target multiple species, or life stages within a species, requiring the use of multiple detection methods. When multiple methods or devices are used at the same sample sites, animals can be detected by more than one method.We develop occupancy models for multiple detection methods that permit simultaneous use of data from all methods for inference about method-specific detection probabilities. Moreover, the approach permits estimation of occupancy at two spatial scales: the larger scale corresponds to species’ use of a sample unit, whereas the smaller scale corresponds to presence of the species at the local sample station or site.We apply the models to data collected on two different vertebrate species: striped skunks Mephitis mephitis and red salamanders Pseudotriton ruber. For striped skunks, large-scale occupancy estimates were consistent between two sampling seasons. Small-scale occupancy probabilities were slightly lower in the late winter/spring when skunks tend to conserve energy, and movements are limited to males in search of females for breeding. There was strong evidence of method-specific detection probabilities for skunks. As anticipated, large- and small-scale occupancy areas completely overlapped for red salamanders. The analyses provided weak evidence of method-specific detection probabilities for this species.Synthesis and applications. Increasingly, many studies are utilizing multiple detection methods at sampling locations. The modelling approach presented here makes efficient use of detections from multiple methods to estimate occupancy probabilities at two spatial scales and to compare detection probabilities associated with different detection methods. The models can be viewed as another variation of Pollock's robust design and may be applicable to a wide variety of scenarios where species occur in an area but are not always near the sampled locations. The estimation approach is likely to be especially useful in multispecies conservation programmes by providing efficient estimates using multiple detection devices and by providing device-specific detection probability estimates for use in survey design.

Accounting for length-bias and selection effects in estimating the distribution of menstrual cycle length

PubMed Central

Lum, Kirsten J.; Sundaram, Rajeshwari; Louis, Thomas A.

2015-01-01

Prospective pregnancy studies are a valuable source of longitudinal data on menstrual cycle length. However, care is needed when making inferences of such renewal processes. For example, accounting for the sampling plan is necessary for unbiased estimation of the menstrual cycle length distribution for the study population. If couples can enroll when they learn of the study as opposed to waiting for the start of a new menstrual cycle, then due to length-bias, the enrollment cycle will be stochastically larger than the general run of cycles, a typical property of prevalent cohort studies. Furthermore, the probability of enrollment can depend on the length of time since a woman’s last menstrual period (a backward recurrence time), resulting in selection effects. We focus on accounting for length-bias and selection effects in the likelihood for enrollment menstrual cycle length, using a recursive two-stage approach wherein we first estimate the probability of enrollment as a function of the backward recurrence time and then use it in a likelihood with sampling weights that account for length-bias and selection effects. To broaden the applicability of our methods, we augment our model to incorporate a couple-specific random effect and time-independent covariate. A simulation study quantifies performance for two scenarios of enrollment probability when proper account is taken of sampling plan features. In addition, we estimate the probability of enrollment and the distribution of menstrual cycle length for the study population of the Longitudinal Investigation of Fertility and the Environment Study. PMID:25027273

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

PubMed

Gragg, Jared; Yang, James

2016-01-01

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

Integrated-Circuit Pseudorandom-Number Generator

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Risk of false decision on conformity of a multicomponent material when test results of the components' content are correlated.

PubMed

Kuselman, Ilya; Pennecchi, Francesca R; da Silva, Ricardo J N B; Hibbert, D Brynn

2017-11-01

The probability of a false decision on conformity of a multicomponent material due to measurement uncertainty is discussed when test results are correlated. Specification limits of the components' content of such a material generate a multivariate specification interval/domain. When true values of components' content and corresponding test results are modelled by multivariate distributions (e.g. by multivariate normal distributions), a total global risk of a false decision on the material conformity can be evaluated based on calculation of integrals of their joint probability density function. No transformation of the raw data is required for that. A total specific risk can be evaluated as the joint posterior cumulative function of true values of a specific batch or lot lying outside the multivariate specification domain, when the vector of test results, obtained for the lot, is inside this domain. It was shown, using a case study of four components under control in a drug, that the correlation influence on the risk value is not easily predictable. To assess this influence, the evaluated total risk values were compared with those calculated for independent test results and also with those assuming much stronger correlation than that observed. While the observed statistically significant correlation did not lead to a visible difference in the total risk values in comparison to the independent test results, the stronger correlation among the variables caused either the total risk decreasing or its increasing, depending on the actual values of the test results. Copyright © 2017 Elsevier B.V. All rights reserved.

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

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

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

USGS Publications Warehouse

Geist, E.L.; Parsons, T.

2009-01-01

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

Multinomial mixture model with heterogeneous classification probabilities

USGS Publications Warehouse

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

2011-01-01

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

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.

Decentralized Routing and Diameter Bounds in Entangled Quantum Networks

NASA Astrophysics Data System (ADS)

Gyongyosi, Laszlo; Imre, Sandor

2017-04-01

Entangled quantum networks are a necessity for any future quantum internet, long-distance quantum key distribution, and quantum repeater networks. The entangled quantum nodes can communicate through several different levels of entanglement, leading to a heterogeneous, multi-level entangled network structure. The level of entanglement between the quantum nodes determines the hop distance, the number of spanned nodes, and the probability of the existence of an entangled link in the network. In this work we define a decentralized routing for entangled quantum networks. We show that the probability distribution of the entangled links can be modeled by a specific distribution in a base-graph. The results allow us to perform efficient routing to find the shortest paths in entangled quantum networks by using only local knowledge of the quantum nodes. We give bounds on the maximum value of the total number of entangled links of a path. The proposed scheme can be directly applied in practical quantum communications and quantum networking scenarios. This work was partially supported by the Hungarian Scientific Research Fund - OTKA K-112125.

Complementarity between entanglement-assisted and quantum distributed random access code

NASA Astrophysics Data System (ADS)

Hameedi, Alley; Saha, Debashis; Mironowicz, Piotr; Pawłowski, Marcin; Bourennane, Mohamed

2017-05-01

Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific cases where one outperforms the other. In this article, we study a family of 3 →1 distributed RACs [J. Bowles, N. Brunner, and M. Pawłowski, Phys. Rev. A 92, 022351 (2015), 10.1103/PhysRevA.92.022351] and present its general construction of both the QRAC and the EARAC. We demonstrate that, depending on the function of inputs that is sought, if QRAC achieves the maximal success probability then EARAC fails to do so and vice versa. Moreover, a tripartite Bell-type inequality associated with the EARAC variants reveals the genuine multipartite nonlocality exhibited by our protocol. We conclude with an experimental realization of the 3 →1 distributed QRAC that achieves higher success probabilities than the maximum possible with EARACs for a number of tasks.

Semiparametric Bayesian classification with longitudinal markers

PubMed Central

De la Cruz-Mesía, Rolando; Quintana, Fernando A.; Müller, Peter

2013-01-01

Summary We analyse data from a study involving 173 pregnant women. The data are observed values of the β human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random-effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods. PMID:24368871

Discriminative Bayesian Dictionary Learning for Classification.

PubMed

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.

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

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Englander, Arnold C.

2014-01-01

Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics.

Anurans in a Subarctic Tundra Landscape Near Cape Churchill, Manitoba

USGS Publications Warehouse

Reiter, M.E.; Boal, C.W.; Andersen, D.E.

2008-01-01

Distribution, abundance, and habitat relationships of anurans inhabiting subarctic regions are poorly understood, and anuran monitoring protocols developed for temperate regions may not be applicable across large roadless areas of northern landscapes. In addition, arctic and subarctic regions of North America are predicted to experience changes in climate and, in some areas, are experiencing habitat alteration due to high rates of herbivory by breeding and migrating waterfowl. To better understand subarctic anuran abundance, distribution, and habitat associations, we conducted anuran calling surveys in the Cape Churchill region of Wapusk National Park, Manitoba, Canada, in 2004 and 2005. We conducted surveys along ~l-km transects distributed across three landscape types (coastal tundra, interior sedge meadow-tundra, and boreal forest-tundra interface) to estimate densities and probabilities of detection of Boreal Chorus Frogs (Pseudacris maculata) and Wood Frogs (Lithobates sylvaticus). We detected a Wood Frog or Boreal Chorus Frog on 22 (87%) of 26 transects surveyed, but probability of detection varied between years and species and among landscape types. Estimated densities of both species increased from the coastal zone inland toward the boreal forest edge. Our results suggest anurans occur across all three landscape types in our study area, but that species-specific spatial patterns exist in their abundances. Considerations for both spatial and temporal variation in abundance and detection probability need to be incorporated into surveys and monitoring programs for subarctic anurans.

Distribution of tsunami interevent times

NASA Astrophysics Data System (ADS)

Geist, Eric L.; Parsons, Tom

2008-01-01

The distribution of tsunami interevent times is analyzed using global and site-specific (Hilo, Hawaii) tsunami catalogs. An empirical probability density distribution is determined by binning the observed interevent times during a period in which the observation rate is approximately constant. The empirical distributions for both catalogs exhibit non-Poissonian behavior in which there is an abundance of short interevent times compared to an exponential distribution. Two types of statistical distributions are used to model this clustering behavior: (1) long-term clustering described by a universal scaling law, and (2) Omori law decay of aftershocks and triggered sources. The empirical and theoretical distributions all imply an increased hazard rate after a tsunami, followed by a gradual decrease with time approaching a constant hazard rate. Examination of tsunami sources suggests that many of the short interevent times are caused by triggered earthquakes, though the triggered events are not necessarily on the same fault.

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.

The exact probability distribution of the rank product statistics for replicated experiments.

PubMed

Eisinga, Rob; Breitling, Rainer; Heskes, Tom

2013-03-18

The rank product method is a widely accepted technique for detecting differentially regulated genes in replicated microarray experiments. To approximate the sampling distribution of the rank product statistic, the original publication proposed a permutation approach, whereas recently an alternative approximation based on the continuous gamma distribution was suggested. However, both approximations are imperfect for estimating small tail probabilities. In this paper we relate the rank product statistic to number theory and provide a derivation of its exact probability distribution and the true tail probabilities. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Reconstructing missing information on precipitation datasets: impact of tails on adopted statistical distributions.

NASA Astrophysics Data System (ADS)

Pedretti, Daniele; Beckie, Roger Daniel

2014-05-01

Missing data in hydrological time-series databases are ubiquitous in practical applications, yet it is of fundamental importance to make educated decisions in problems involving exhaustive time-series knowledge. This includes precipitation datasets, since recording or human failures can produce gaps in these time series. For some applications, directly involving the ratio between precipitation and some other quantity, lack of complete information can result in poor understanding of basic physical and chemical dynamics involving precipitated water. For instance, the ratio between precipitation (recharge) and outflow rates at a discharge point of an aquifer (e.g. rivers, pumping wells, lysimeters) can be used to obtain aquifer parameters and thus to constrain model-based predictions. We tested a suite of methodologies to reconstruct missing information in rainfall datasets. The goal was to obtain a suitable and versatile method to reduce the errors given by the lack of data in specific time windows. Our analyses included both a classical chronologically-pairing approach between rainfall stations and a probability-based approached, which accounted for the probability of exceedence of rain depths measured at two or multiple stations. Our analyses proved that it is not clear a priori which method delivers the best methodology. Rather, this selection should be based considering the specific statistical properties of the rainfall dataset. In this presentation, our emphasis is to discuss the effects of a few typical parametric distributions used to model the behavior of rainfall. Specifically, we analyzed the role of distributional "tails", which have an important control on the occurrence of extreme rainfall events. The latter strongly affect several hydrological applications, including recharge-discharge relationships. The heavy-tailed distributions we considered were parametric Log-Normal, Generalized Pareto, Generalized Extreme and Gamma distributions. The methods were first tested on synthetic examples, to have a complete control of the impact of several variables such as minimum amount of data required to obtain reliable statistical distributions from the selected parametric functions. Then, we applied the methodology to precipitation datasets collected in the Vancouver area and on a mining site in Peru.

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

PubMed Central

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

2015-01-01

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

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.

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.

Substrate preferences of epiphytic bromeliads: an experimental approach

NASA Astrophysics Data System (ADS)

Zotz, Gerhard; Vollrath, Birgit

2002-05-01

Based on the known vertical distributions of three epiphyte species we tested the hypothesis that observed interspecific differences are determined at a very early ontogenetic stage. We attached 1296 first-year seedlings of the three species Guzmania monostachya, Tillandsia fasciculata, and Vriesea sanguinolenta (Bromeliaceae) to substrates differing in orientation and relative position within the crown of the host tree, Annona glabra. Surprisingly, we found no evidence for differential mortality on different substrate types for any of the three species. Hence, differences in vertical distribution cannot be explained by interspecific differences in site-specific survival at this stage. This suggests that spatial distribution patterns are determined even earlier, probably resulting from species differences in seed dispersal or during germination.

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.

Several Modified Goodness-Of-Fit Tests for the Cauchy Distribution with Unknown Scale and Location Parameters

DTIC Science & Technology

1994-03-01

labels of a, which is called significance levels. The hypothesis tests are done based on the a levels . The maximum probabilities of making type II error...critical values at specific a levels . This procedure is done for each of the 50,000 samples. The number of the samples passing each test at those specific... a levels is counted. The ratio of the number of accepted samples to 50,000 gives the percentage point. Then, subtracting that value from one would

Reliability of programs specified with equational specifications

NASA Astrophysics Data System (ADS)

Nikolik, Borislav

Ultrareliability is desirable (and sometimes a demand of regulatory authorities) for safety-critical applications, such as commercial flight-control programs, medical applications, nuclear reactor control programs, etc. A method is proposed, called the Term Redundancy Method (TRM), for obtaining ultrareliable programs through specification-based testing. Current specification-based testing schemes need a prohibitively large number of testcases for estimating ultrareliability. They assume availability of an accurate program-usage distribution prior to testing, and they assume the availability of a test oracle. It is shown how to obtain ultrareliable programs (probability of failure near zero) with a practical number of testcases, without accurate usage distribution, and without a test oracle. TRM applies to the class of decision Abstract Data Type (ADT) programs specified with unconditional equational specifications. TRM is restricted to programs that do not exceed certain efficiency constraints in generating testcases. The effectiveness of TRM in failure detection and recovery is demonstrated on formulas from the aircraft collision avoidance system TCAS.

Probability differently modulating the effects of reward and punishment on visuomotor adaptation.

PubMed

Song, Yanlong; Smiley-Oyen, Ann L

2017-12-01

Recent human motor learning studies revealed that punishment seemingly accelerated motor learning but reward enhanced consolidation of motor memory. It is not evident how intrinsic properties of reward and punishment modulate the potentially dissociable effects of reward and punishment on motor learning and motor memory. It is also not clear what causes the dissociation of the effects of reward and punishment. By manipulating probability of distribution, a critical property of reward and punishment, the present study demonstrated that probability had distinct modulation on the effects of reward and punishment in adapting to a sudden visual rotation and consolidation of the adaptation memory. Specifically, two probabilities of monetary reward and punishment distribution, 50 and 100%, were applied during young adult participants adapting to a sudden visual rotation. Punishment and reward showed distinct effects on motor adaptation and motor memory. The group that received punishments in 100% of the adaptation trials adapted significantly faster than the other three groups, but the group that received rewards in 100% of the adaptation trials showed marked savings in re-adapting to the same rotation. In addition, the group that received punishments in 50% of the adaptation trials that were randomly selected also had savings in re-adapting to the same rotation. Sensitivity to sensory prediction error or difference in explicit process induced by reward and punishment may likely contribute to the distinct effects of reward and punishment.

Orchestrating Semiotic Leaps from Tacit to Cultural Quantitative Reasoning--The Case of Anticipating Experimental Outcomes of a Quasi-Binomial Random Generator

ERIC Educational Resources Information Center

Abrahamson, Dor

2009-01-01

This article reports on a case study from a design-based research project that investigated how students make sense of the disciplinary tools they are taught to use, and specifically, what personal, interpersonal, and material resources support this process. The probability topic of binomial distribution was selected due to robust documentation of…

On the extinction probability in models of within-host infection: the role of latency and immunity.

PubMed

Yan, Ada W C; Cao, Pengxing; McCaw, James M

2016-10-01

Not every exposure to virus establishes infection in the host; instead, the small amount of initial virus could become extinct due to stochastic events. Different diseases and routes of transmission have a different average number of exposures required to establish an infection. Furthermore, the host immune response and antiviral treatment affect not only the time course of the viral load provided infection occurs, but can prevent infection altogether by increasing the extinction probability. We show that the extinction probability when there is a time-dependent immune response depends on the chosen form of the model-specifically, on the presence or absence of a delay between infection of a cell and production of virus, and the distribution of latent and infectious periods of an infected cell. We hypothesise that experimentally measuring the extinction probability when the virus is introduced at different stages of the immune response, alongside the viral load which is usually measured, will improve parameter estimates and determine the most suitable mathematical form of the model.

Estimating the Attack Ratio of Dengue Epidemics under Time-varying Force of Infection using Aggregated Notification Data

NASA Astrophysics Data System (ADS)

Coelho, Flavio Codeço; Carvalho, Luiz Max De

2015-12-01

Quantifying the attack ratio of disease is key to epidemiological inference and public health planning. For multi-serotype pathogens, however, different levels of serotype-specific immunity make it difficult to assess the population at risk. In this paper we propose a Bayesian method for estimation of the attack ratio of an epidemic and the initial fraction of susceptibles using aggregated incidence data. We derive the probability distribution of the effective reproductive number, Rt, and use MCMC to obtain posterior distributions of the parameters of a single-strain SIR transmission model with time-varying force of infection. Our method is showcased in a data set consisting of 18 years of dengue incidence in the city of Rio de Janeiro, Brazil. We demonstrate that it is possible to learn about the initial fraction of susceptibles and the attack ratio even in the absence of serotype specific data. On the other hand, the information provided by this approach is limited, stressing the need for detailed serological surveys to characterise the distribution of serotype-specific immunity in the population.

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.

Ignition probability of polymer-bonded explosives accounting for multiple sources of material stochasticity

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

Kim, S.; Barua, A.; Zhou, M., E-mail: min.zhou@me.gatech.edu

2014-05-07

Accounting for the combined effect of multiple sources of stochasticity in material attributes, we develop an approach that computationally predicts the probability of ignition of polymer-bonded explosives (PBXs) under impact loading. The probabilistic nature of the specific ignition processes is assumed to arise from two sources of stochasticity. The first source involves random variations in material microstructural morphology; the second source involves random fluctuations in grain-binder interfacial bonding strength. The effect of the first source of stochasticity is analyzed with multiple sets of statistically similar microstructures and constant interfacial bonding strength. Subsequently, each of the microstructures in the multiple setsmore » is assigned multiple instantiations of randomly varying grain-binder interfacial strengths to analyze the effect of the second source of stochasticity. Critical hotspot size-temperature states reaching the threshold for ignition are calculated through finite element simulations that explicitly account for microstructure and bulk and interfacial dissipation to quantify the time to criticality (t{sub c}) of individual samples, allowing the probability distribution of the time to criticality that results from each source of stochastic variation for a material to be analyzed. Two probability superposition models are considered to combine the effects of the multiple sources of stochasticity. The first is a parallel and series combination model, and the second is a nested probability function model. Results show that the nested Weibull distribution provides an accurate description of the combined ignition probability. The approach developed here represents a general framework for analyzing the stochasticity in the material behavior that arises out of multiple types of uncertainty associated with the structure, design, synthesis and processing of materials.« less

Seismic quiescence in a frictional earthquake model

NASA Astrophysics Data System (ADS)

Braun, Oleg M.; Peyrard, Michel

2018-04-01

We investigate the origin of seismic quiescence with a generalized version of the Burridge-Knopoff model for earthquakes and show that it can be generated by a multipeaked probability distribution of the thresholds at which contacts break. Such a distribution is not assumed a priori but naturally results from the aging of the contacts. We show that the model can exhibit quiescence as well as enhanced foreshock activity, depending on the value of some parameters. This provides a generic understanding for seismic quiescence, which encompasses earlier specific explanations and could provide a pathway for a classification of faults.

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

Sampling in health geography: reconciling geographical objectives and probabilistic methods. An example of a health survey in Vientiane (Lao PDR)

PubMed Central

Vallée, Julie; Souris, Marc; Fournet, Florence; Bochaton, Audrey; Mobillion, Virginie; Peyronnie, Karine; Salem, Gérard

2007-01-01

Background Geographical objectives and probabilistic methods are difficult to reconcile in a unique health survey. Probabilistic methods focus on individuals to provide estimates of a variable's prevalence with a certain precision, while geographical approaches emphasise the selection of specific areas to study interactions between spatial characteristics and health outcomes. A sample selected from a small number of specific areas creates statistical challenges: the observations are not independent at the local level, and this results in poor statistical validity at the global level. Therefore, it is difficult to construct a sample that is appropriate for both geographical and probability methods. Methods We used a two-stage selection procedure with a first non-random stage of selection of clusters. Instead of randomly selecting clusters, we deliberately chose a group of clusters, which as a whole would contain all the variation in health measures in the population. As there was no health information available before the survey, we selected a priori determinants that can influence the spatial homogeneity of the health characteristics. This method yields a distribution of variables in the sample that closely resembles that in the overall population, something that cannot be guaranteed with randomly-selected clusters, especially if the number of selected clusters is small. In this way, we were able to survey specific areas while minimising design effects and maximising statistical precision. Application We applied this strategy in a health survey carried out in Vientiane, Lao People's Democratic Republic. We selected well-known health determinants with unequal spatial distribution within the city: nationality and literacy. We deliberately selected a combination of clusters whose distribution of nationality and literacy is similar to the distribution in the general population. Conclusion This paper describes the conceptual reasoning behind the construction of the survey sample and shows that it can be advantageous to choose clusters using reasoned hypotheses, based on both probability and geographical approaches, in contrast to a conventional, random cluster selection strategy. PMID:17543100

Sampling in health geography: reconciling geographical objectives and probabilistic methods. An example of a health survey in Vientiane (Lao PDR).

PubMed

Vallée, Julie; Souris, Marc; Fournet, Florence; Bochaton, Audrey; Mobillion, Virginie; Peyronnie, Karine; Salem, Gérard

2007-06-01

Geographical objectives and probabilistic methods are difficult to reconcile in a unique health survey. Probabilistic methods focus on individuals to provide estimates of a variable's prevalence with a certain precision, while geographical approaches emphasise the selection of specific areas to study interactions between spatial characteristics and health outcomes. A sample selected from a small number of specific areas creates statistical challenges: the observations are not independent at the local level, and this results in poor statistical validity at the global level. Therefore, it is difficult to construct a sample that is appropriate for both geographical and probability methods. We used a two-stage selection procedure with a first non-random stage of selection of clusters. Instead of randomly selecting clusters, we deliberately chose a group of clusters, which as a whole would contain all the variation in health measures in the population. As there was no health information available before the survey, we selected a priori determinants that can influence the spatial homogeneity of the health characteristics. This method yields a distribution of variables in the sample that closely resembles that in the overall population, something that cannot be guaranteed with randomly-selected clusters, especially if the number of selected clusters is small. In this way, we were able to survey specific areas while minimising design effects and maximising statistical precision. We applied this strategy in a health survey carried out in Vientiane, Lao People's Democratic Republic. We selected well-known health determinants with unequal spatial distribution within the city: nationality and literacy. We deliberately selected a combination of clusters whose distribution of nationality and literacy is similar to the distribution in the general population. This paper describes the conceptual reasoning behind the construction of the survey sample and shows that it can be advantageous to choose clusters using reasoned hypotheses, based on both probability and geographical approaches, in contrast to a conventional, random cluster selection strategy.

Minimizing predation risk in a landscape of multiple predators: effects on the spatial distribution of African ungulates.

PubMed

Thaker, Maria; Vanak, Abi T; Owen, Cailey R; Ogden, Monika B; Niemann, Sophie M; Slotow, Rob

2011-02-01

Studies that focus on single predator-prey interactions can be inadequate for understanding antipredator responses in multi-predator systems. Yet there is still a general lack of information about the strategies of prey to minimize predation risk from multiple predators at the landscape level. Here we examined the distribution of seven African ungulate species in the fenced Karongwe Game Reserve (KGR), South Africa, as a function of predation risk from all large carnivore species (lion, leopard, cheetah, African wild dog, and spotted hyena). Using observed kill data, we generated ungulate-specific predictions of relative predation risk and of riskiness of habitats. To determine how ungulates minimize predation risk at the landscape level, we explicitly tested five hypotheses consisting of strategies that reduce the probability of encountering predators, and the probability of being killed. All ungulate species avoided risky habitats, and most selected safer habitats, thus reducing their probability of being killed. To reduce the probability of encountering predators, most of the smaller prey species (impala, warthog, waterbuck, kudu) avoided the space use of all predators, while the larger species (wildebeest, zebra, giraffe) only avoided areas where lion and leopard space use were high. The strength of avoidance for the space use of predators generally did not correspond to the relative predation threat from those predators. Instead, ungulates used a simpler behavioral rule of avoiding the activity areas of sit-and-pursue predators (lion and leopard), but not those of cursorial predators (cheetah and African wild dog). In general, selection and avoidance of habitats was stronger than avoidance of the predator activity areas. We expect similar decision rules to drive the distribution pattern of ungulates in other African savannas and in other multi-predator systems, especially where predators differ in their hunting modes.

Accounting for length-bias and selection effects in estimating the distribution of menstrual cycle length.

PubMed

Lum, Kirsten J; Sundaram, Rajeshwari; Louis, Thomas A

2015-01-01

Prospective pregnancy studies are a valuable source of longitudinal data on menstrual cycle length. However, care is needed when making inferences of such renewal processes. For example, accounting for the sampling plan is necessary for unbiased estimation of the menstrual cycle length distribution for the study population. If couples can enroll when they learn of the study as opposed to waiting for the start of a new menstrual cycle, then due to length-bias, the enrollment cycle will be stochastically larger than the general run of cycles, a typical property of prevalent cohort studies. Furthermore, the probability of enrollment can depend on the length of time since a woman's last menstrual period (a backward recurrence time), resulting in selection effects. We focus on accounting for length-bias and selection effects in the likelihood for enrollment menstrual cycle length, using a recursive two-stage approach wherein we first estimate the probability of enrollment as a function of the backward recurrence time and then use it in a likelihood with sampling weights that account for length-bias and selection effects. To broaden the applicability of our methods, we augment our model to incorporate a couple-specific random effect and time-independent covariate. A simulation study quantifies performance for two scenarios of enrollment probability when proper account is taken of sampling plan features. In addition, we estimate the probability of enrollment and the distribution of menstrual cycle length for the study population of the Longitudinal Investigation of Fertility and the Environment Study. Published by Oxford University Press 2014. This work is written by (a) US Government employee(s) and is in the public domain in the US.

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.

Quantitative assessment of direct and indirect landslide risk along transportation lines in southern India

NASA Astrophysics Data System (ADS)

Jaiswal, P.; van Westen, C. J.; Jetten, V.

2010-06-01

A quantitative approach for landslide risk assessment along transportation lines is presented and applied to a road and a railway alignment in the Nilgiri hills in southern India. The method allows estimating direct risk affecting the alignments, vehicles and people, and indirect risk resulting from the disruption of economic activities. The data required for the risk estimation were obtained from historical records. A total of 901 landslides were catalogued initiating from cut slopes along the railway and road alignment. The landslides were grouped into three magnitude classes based on the landslide type, volume, scar depth, run-out distance, etc and their probability of occurrence was obtained using frequency-volume distribution. Hazard, for a given return period, expressed as the number of landslides of a given magnitude class per kilometre of cut slopes, was obtained using Gumbel distribution and probability of landslide magnitude. In total 18 specific hazard scenarios were generated using the three magnitude classes and six return periods (1, 3, 5, 15, 25, and 50 years). The assessment of the vulnerability of the road and railway line was based on damage records whereas the vulnerability of different types of vehicles and people was subjectively assessed based on limited historic incidents. Direct specific loss for the alignments (railway line and road), vehicles (train, bus, lorry, car and motorbike) was expressed in monetary value (US), and direct specific loss of life of commuters was expressed in annual probability of death. Indirect specific loss (US) derived from the traffic interruption was evaluated considering alternative driving routes, and includes losses resulting from additional fuel consumption, additional travel cost, loss of income to the local business, and loss of revenue to the railway department. The results indicate that the total loss, including both direct and indirect loss, from 1 to 50 years return period, varies from US 90 840 to US 779 500 and the average annual total loss was estimated as US 35 000. The annual probability of a person most at risk travelling in a bus, lorry, car, motorbike and train is less than 10-4/annum in all the time periods considered. The detailed estimation of direct and indirect risk will facilitate developing landslide risk mitigation and management strategies for transportation lines in the study area.

N-mixture models for estimating population size from spatially replicated counts

USGS Publications Warehouse

Royle, J. Andrew

2004-01-01

Spatial replication is a common theme in count surveys of animals. Such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability. In this article, i describe a class of models (n-mixture models) which allow for estimation of population size from such data. The key idea is to view site-specific population sizes, n, as independent random variables distributed according to some mixing distribution (e.g., Poisson). Prior parameters are estimated from the marginal likelihood of the data, having integrated over the prior distribution for n. Carroll and lombard (1985, journal of american statistical association 80, 423-426) proposed a class of estimators based on mixing over a prior distribution for detection probability. Their estimator can be applied in limited settings, but is sensitive to prior parameter values that are fixed a priori. Spatial replication provides additional information regarding the parameters of the prior distribution on n that is exploited by the n-mixture models and which leads to reasonable estimates of abundance from sparse data. A simulation study demonstrates superior operating characteristics (bias, confidence interval coverage) of the n-mixture estimator compared to the caroll and lombard estimator. Both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence.

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.

Identifying early-warning signals of critical transitions with strong noise by dynamical network markers

PubMed Central

Liu, Rui; Chen, Pei; Aihara, Kazuyuki; Chen, Luonan

2015-01-01

Identifying early-warning signals of a critical transition for a complex system is difficult, especially when the target system is constantly perturbed by big noise, which makes the traditional methods fail due to the strong fluctuations of the observed data. In this work, we show that the critical transition is not traditional state-transition but probability distribution-transition when the noise is not sufficiently small, which, however, is a ubiquitous case in real systems. We present a model-free computational method to detect the warning signals before such transitions. The key idea behind is a strategy: “making big noise smaller” by a distribution-embedding scheme, which transforms the data from the observed state-variables with big noise to their distribution-variables with small noise, and thus makes the traditional criteria effective because of the significantly reduced fluctuations. Specifically, increasing the dimension of the observed data by moment expansion that changes the system from state-dynamics to probability distribution-dynamics, we derive new data in a higher-dimensional space but with much smaller noise. Then, we develop a criterion based on the dynamical network marker (DNM) to signal the impending critical transition using the transformed higher-dimensional data. We also demonstrate the effectiveness of our method in biological, ecological and financial systems. PMID:26647650

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

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

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

2012-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Reproductive maturation and senescence in the female brown bear

USGS Publications Warehouse

Schwartz, Charles C.; Keating, Kim A.; Reynolds III, Harry V.; Barnes, Victor G.; Sellers, Richard A.; Swenson, J.E.; Miller, Sterling D.; McLellan, B.N.; Keay, Jeffrey A.; McCann, Robert; Gibeau, Michael; Wakkinen, Wayne F.; Mace, Richard D.; Kasworm, Wayne; Smith, Rodger; Herrero, Steven

2003-01-01

Changes in age-specific reproductive rates can have important implications for managing populations, but the number of female brown (grizzly) bears (Ursus arctos) observed in any one study is usually inadequate to quantify such patterns, especially for older females and in hunted areas. We examined patterns of reproductive maturation and senescence in female brown bears by combining data from 20 study areas from Sweden, Alaska, Canada, and the continental United States. We assessed reproductive performance based on 4,726 radiocollared years for free-ranging female brown bears (age 3); 482 of these were for bears 20 years of age. We modeled age-specific probability of litter production using extreme value distributions to describe probabilities for young- and old-age classes, and a power distribution function to describe probabilities for prime-aged animals. We then fit 4 models to pooled observations from our 20 study areas. We used Akaike’s Information Criterion (AIC) to select the best model. Inflection points suggest that major shifts in litter production occur at 4–5 and 28–29 years of age. The estimated model asymptote (0.332, 95% CI ¼ 0.319–0.344) was consistent with the expected reproductive cycle of a cub litter every 3 years (0.333). We discuss assumptions and biases in data collection relative to the shape of the model curve. Our results conform to senescence theory and suggest that female age structure in contemporary brown bear populations is considerably younger than would be expected in the absence of modern man. This implies that selective pressures today differ from those that influenced brown bear evolution.

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.

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…

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.

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.

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

PubMed

Nakamura, Yoshihiro; Hasegawa, Osamu

2017-01-01

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

Probabilistic forecasting for extreme NO2 pollution episodes.

PubMed

Aznarte, José L

2017-10-01

In this study, we investigate the convenience of quantile regression to predict extreme concentrations of NO 2 . Contrarily to the usual point-forecasting, where a single value is forecast for each horizon, probabilistic forecasting through quantile regression allows for the prediction of the full probability distribution, which in turn allows to build models specifically fit for the tails of this distribution. Using data from the city of Madrid, including NO 2 concentrations as well as meteorological measures, we build models that predict extreme NO 2 concentrations, outperforming point-forecasting alternatives, and we prove that the predictions are accurate, reliable and sharp. Besides, we study the relative importance of the independent variables involved, and show how the important variables for the median quantile are different than those important for the upper quantiles. Furthermore, we present a method to compute the probability of exceedance of thresholds, which is a simple and comprehensible manner to present probabilistic forecasts maximizing their usefulness. Copyright © 2017 Elsevier Ltd. All rights reserved.

Reasoning and choice in the Monty Hall Dilemma (MHD): implications for improving Bayesian reasoning

PubMed Central

Tubau, Elisabet; Aguilar-Lleyda, David; Johnson, Eric D.

2015-01-01

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning. PMID:25873906

Plow Shop Pond Supplemental Investigation Work Plan

DTIC Science & Technology

1994-09-01

the results of the TIE, major contributors to sediment toxicity in Plow I Shop will be identified. Site-specific numerical criteria for contaminants in...consume Plow Shop Pond fish is less than 1.3". ABB-ES would use an available software package to generate the probability distributions. 5 If...Fort Devens project. The Project Manager is responsible for confirming the appropriateness and adequacy of the technical or engineering services

Traffic-Adaptive, Flow-Specific Medium Access for Wireless Networks

DTIC Science & Technology

2009-09-01

hybrid, contention and non-contention schemes are shown to be special cases. This work also compares the energy efficiency of centralized and distributed...solutions and proposes an energy efficient version of traffic-adaptive CWS-MAC that includes an adaptive sleep cycle coordinated through the use of...preamble sampling. A preamble sampling probability parameter is introduced to manage the trade-off between energy efficiency and throughput and delay

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.

Extinction probabilities and stationary distributions of mobile genetic elements in prokaryotes: The birth-death-diversification model.

PubMed

Drakos, Nicole E; Wahl, Lindi M

2015-12-01

Theoretical approaches are essential to our understanding of the complex dynamics of mobile genetic elements (MGEs) within genomes. Recently, the birth-death-diversification model was developed to describe the dynamics of mobile promoters (MPs), a particular class of MGEs in prokaryotes. A unique feature of this model is that genetic diversification of elements was included. To explore the implications of diversification on the longterm fate of MGE lineages, in this contribution we analyze the extinction probabilities, extinction times and equilibrium solutions of the birth-death-diversification model. We find that diversification increases both the survival and growth rate of MGE families, but the strength of this effect depends on the rate of horizontal gene transfer (HGT). We also find that the distribution of MGE families per genome is not necessarily monotonically decreasing, as observed for MPs, but may have a peak in the distribution that is related to the HGT rate. For MPs specifically, we find that new families have a high extinction probability, and predict that the number of MPs is increasing, albeit at a very slow rate. Additionally, we develop an extension of the birth-death-diversification model which allows MGEs in different regions of the genome, for example coding and non-coding, to be described by different rates. This extension may offer a potential explanation as to why the majority of MPs are located in non-promoter regions of the genome. Copyright © 2015 Elsevier Inc. All rights reserved.

Partitioning into hazard subregions for regional peaks-over-threshold modeling of heavy precipitation

NASA Astrophysics Data System (ADS)

Carreau, J.; Naveau, P.; Neppel, L.

2017-05-01

The French Mediterranean is subject to intense precipitation events occurring mostly in autumn. These can potentially cause flash floods, the main natural danger in the area. The distribution of these events follows specific spatial patterns, i.e., some sites are more likely to be affected than others. The peaks-over-threshold approach consists in modeling extremes, such as heavy precipitation, by the generalized Pareto (GP) distribution. The shape parameter of the GP controls the probability of extreme events and can be related to the hazard level of a given site. When interpolating across a region, the shape parameter should reproduce the observed spatial patterns of the probability of heavy precipitation. However, the shape parameter estimators have high uncertainty which might hide the underlying spatial variability. As a compromise, we choose to let the shape parameter vary in a moderate fashion. More precisely, we assume that the region of interest can be partitioned into subregions with constant hazard level. We formalize the model as a conditional mixture of GP distributions. We develop a two-step inference strategy based on probability weighted moments and put forward a cross-validation procedure to select the number of subregions. A synthetic data study reveals that the inference strategy is consistent and not very sensitive to the selected number of subregions. An application on daily precipitation data from the French Mediterranean shows that the conditional mixture of GPs outperforms two interpolation approaches (with constant or smoothly varying shape parameter).

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.

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.

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.

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.

Alternative Derivations of the Statistical Mechanical Distribution Laws

PubMed Central

Wall, Frederick T.

1971-01-01

A new approach is presented for the derivation of statistical mechanical distribution laws. The derivations are accomplished by minimizing the Helmholtz free energy under constant temperature and volume, instead of maximizing the entropy under constant energy and volume. An alternative method involves stipulating equality of chemical potential, or equality of activity, for particles in different energy levels. This approach leads to a general statement of distribution laws applicable to all systems for which thermodynamic probabilities can be written. The methods also avoid use of the calculus of variations, Lagrangian multipliers, and Stirling's approximation for the factorial. The results are applied specifically to Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. The special significance of chemical potential and activity is discussed for microscopic systems. PMID:16578712

Alternative derivations of the statistical mechanical distribution laws.

PubMed

Wall, F T

1971-08-01

A new approach is presented for the derivation of statistical mechanical distribution laws. The derivations are accomplished by minimizing the Helmholtz free energy under constant temperature and volume, instead of maximizing the entropy under constant energy and volume. An alternative method involves stipulating equality of chemical potential, or equality of activity, for particles in different energy levels. This approach leads to a general statement of distribution laws applicable to all systems for which thermodynamic probabilities can be written. The methods also avoid use of the calculus of variations, Lagrangian multipliers, and Stirling's approximation for the factorial. The results are applied specifically to Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. The special significance of chemical potential and activity is discussed for microscopic systems.

A randomised approach for NARX model identification based on a multivariate Bernoulli distribution

NASA Astrophysics Data System (ADS)

Bianchi, F.; Falsone, A.; Prandini, M.; Piroddi, L.

2017-04-01

The identification of polynomial NARX models is typically performed by incremental model building techniques. These methods assess the importance of each regressor based on the evaluation of partial individual models, which may ultimately lead to erroneous model selections. A more robust assessment of the significance of a specific model term can be obtained by considering ensembles of models, as done by the RaMSS algorithm. In that context, the identification task is formulated in a probabilistic fashion and a Bernoulli distribution is employed to represent the probability that a regressor belongs to the target model. Then, samples of the model distribution are collected to gather reliable information to update it, until convergence to a specific model. The basic RaMSS algorithm employs multiple independent univariate Bernoulli distributions associated to the different candidate model terms, thus overlooking the correlations between different terms, which are typically important in the selection process. Here, a multivariate Bernoulli distribution is employed, in which the sampling of a given term is conditioned by the sampling of the others. The added complexity inherent in considering the regressor correlation properties is more than compensated by the achievable improvements in terms of accuracy of the model selection process.

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

PubMed

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

2013-11-01

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

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

NASA Technical Reports Server (NTRS)

Bogdan, V. M.

1981-01-01

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

An exactly solvable coarse-grained model for species diversity

NASA Astrophysics Data System (ADS)

Suweis, Samir; Rinaldo, Andrea; Maritan, Amos

2012-07-01

We present novel analytical results concerning ecosystem species diversity that stem from a proposed coarse-grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results from ecological neutral theory and empirical evidence on species diversity preservation. The neutral model of biodiversity deals with ecosystems at the same trophic level, where per capita vital rates are assumed to be species independent. Closed-form analytical solutions for the neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain to: the probability distribution function of the number of species in the ecosystem, both in transient and in stationary states; the n-point connected time correlation function; and the survival probability, defined as the distribution of time spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from an estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications for biodiversity and conservation biology.

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

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

1991-01-01

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

Force Density Function Relationships in 2-D Granular Media

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

Quantifying seining detection probability for fishes of Great Plains sand‐bed rivers

USGS Publications Warehouse

Mollenhauer, Robert; Logue, Daniel R.; Brewer, Shannon K.

2018-01-01

Species detection error (i.e., imperfect and variable detection probability) is an essential consideration when investigators map distributions and interpret habitat associations. When fish detection error that is due to highly variable instream environments needs to be addressed, sand‐bed streams of the Great Plains represent a unique challenge. We quantified seining detection probability for diminutive Great Plains fishes across a range of sampling conditions in two sand‐bed rivers in Oklahoma. Imperfect detection resulted in underestimates of species occurrence using naïve estimates, particularly for less common fishes. Seining detection probability also varied among fishes and across sampling conditions. We observed a quadratic relationship between water depth and detection probability, in which the exact nature of the relationship was species‐specific and dependent on water clarity. Similarly, the direction of the relationship between water clarity and detection probability was species‐specific and dependent on differences in water depth. The relationship between water temperature and detection probability was also species dependent, where both the magnitude and direction of the relationship varied among fishes. We showed how ignoring detection error confounded an underlying relationship between species occurrence and water depth. Despite imperfect and heterogeneous detection, our results support that determining species absence can be accomplished with two to six spatially replicated seine hauls per 200‐m reach under average sampling conditions; however, required effort would be higher under certain conditions. Detection probability was low for the Arkansas River Shiner Notropis girardi, which is federally listed as threatened, and more than 10 seine hauls per 200‐m reach would be required to assess presence across sampling conditions. Our model allows scientists to estimate sampling effort to confidently assess species occurrence, which maximizes the use of available resources. Increased implementation of approaches that consider detection error promote ecological advancements and conservation and management decisions that are better informed.

Compensating for geographic variation in detection probability with water depth improves abundance estimates of coastal marine megafauna.

PubMed

Hagihara, Rie; Jones, Rhondda E; Sobtzick, Susan; Cleguer, Christophe; Garrigue, Claire; Marsh, Helene

2018-01-01

The probability of an aquatic animal being available for detection is typically <1. Accounting for covariates that reduce the probability of detection is important for obtaining robust estimates of the population abundance and determining its status and trends. The dugong (Dugong dugon) is a bottom-feeding marine mammal and a seagrass community specialist. We hypothesized that the probability of a dugong being available for detection is dependent on water depth and that dugongs spend more time underwater in deep-water seagrass habitats than in shallow-water seagrass habitats. We tested this hypothesis by quantifying the depth use of 28 wild dugongs fitted with GPS satellite transmitters and time-depth recorders (TDRs) at three sites with distinct seagrass depth distributions: 1) open waters supporting extensive seagrass meadows to 40 m deep (Torres Strait, 6 dugongs, 2015); 2) a protected bay (average water depth 6.8 m) with extensive shallow seagrass beds (Moreton Bay, 13 dugongs, 2011 and 2012); and 3) a mixture of lagoon, coral and seagrass habitats to 60 m deep (New Caledonia, 9 dugongs, 2013). The fitted instruments were used to measure the times the dugongs spent in the experimentally determined detection zones under various environmental conditions. The estimated probability of detection was applied to aerial survey data previously collected at each location. In general, dugongs were least available for detection in Torres Strait, and the population estimates increased 6-7 fold using depth-specific availability correction factors compared with earlier estimates that assumed homogeneous detection probability across water depth and location. Detection probabilities were higher in Moreton Bay and New Caledonia than Torres Strait because the water transparency in these two locations was much greater than in Torres Strait and the effect of correcting for depth-specific detection probability much less. The methodology has application to visual survey of coastal megafauna including surveys using Unmanned Aerial Vehicles.

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.

SU-D-303-01: Spatial Distribution of Bone Metastases In Metastatic Castrate-Resistant Prostate Cancer

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

Perk, T; Bradshaw, T; Harmon, S

2015-06-15

Purpose: Identification of metastatic bone lesions is critical in prostate cancer, where treatments may be more effective in patients with fewer lesions. This study aims characterize the distribution and spread of bone lesions and create a probability map of metastatic spread in bone. Methods: Fifty-five metastatic castrate-resistant prostate cancer patients received up to 3 whole-body [F-18]NaF PET/CT scans. Lesions were identified by physician on PET/CT and contoured using a threshold of SUV>15. An atlas-based segmentation method was used to create CT regions, which determined skeletal location of lesions. Patients were divided into 3 groups with low (N<40), medium (40100) numbersmore » of lesions. A combination of articulated and deformable registrations was used to register the skeletal segments and lesions of each patient to a single skeleton. All the lesion data was then combined to make a probability map. Results: A total of 4038 metastatic lesions (mean 74, range 2–304) were identified. Skeletal regions with highest occurrence of lesions included ribs, thoracic spine, and pelvis with 21%, 19%, and 15% of the total number lesions and 8%, 18%, and 31 % of the total lesion volume, respectively. Interestingly, patients with fewer lesions were found to have a lower proportion of lesions in the ribs (9% in low vs. 27% in high number of lesions). Additionally, the probability map showed specific areas in the spine and pelvis where over 75% of patients had metastases, and other areas in the skeleton with a less than 2% of metastases. Conclusion: We identified skeletal regions with higher incidence of metastases and specific sub-regions in the skeleton that had high or low probability of occurrence of metastases. Additionally, we found that metastatic lesions in the ribs and skull occur more commonly in advanced disease. These results may have future applications in computer-aided diagnosis. Funding from the Prostate Cancer Foundation.« less

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

NASA Astrophysics Data System (ADS)

Katz, Yuri A.; Tian, Li

2013-10-01

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

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

USGS Publications Warehouse

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

1979-01-01

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

Univariate Probability Distributions

ERIC Educational Resources Information Center

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

2012-01-01

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

Estimating site occupancy and detection probability parameters for meso- and large mammals in a coastal eosystem

USGS Publications Warehouse

O'Connell, Allan F.; Talancy, Neil W.; Bailey, Larissa L.; Sauer, John R.; Cook, Robert; Gilbert, Andrew T.

2006-01-01

Large-scale, multispecies monitoring programs are widely used to assess changes in wildlife populations but they often assume constant detectability when documenting species occurrence. This assumption is rarely met in practice because animal populations vary across time and space. As a result, detectability of a species can be influenced by a number of physical, biological, or anthropogenic factors (e.g., weather, seasonality, topography, biological rhythms, sampling methods). To evaluate some of these influences, we estimated site occupancy rates using species-specific detection probabilities for meso- and large terrestrial mammal species on Cape Cod, Massachusetts, USA. We used model selection to assess the influence of different sampling methods and major environmental factors on our ability to detect individual species. Remote cameras detected the most species (9), followed by cubby boxes (7) and hair traps (4) over a 13-month period. Estimated site occupancy rates were similar among sampling methods for most species when detection probabilities exceeded 0.15, but we question estimates obtained from methods with detection probabilities between 0.05 and 0.15, and we consider methods with lower probabilities unacceptable for occupancy estimation and inference. Estimated detection probabilities can be used to accommodate variation in sampling methods, which allows for comparison of monitoring programs using different protocols. Vegetation and seasonality produced species-specific differences in detectability and occupancy, but differences were not consistent within or among species, which suggests that our results should be considered in the context of local habitat features and life history traits for the target species. We believe that site occupancy is a useful state variable and suggest that monitoring programs for mammals using occupancy data consider detectability prior to making inferences about species distributions or population change.

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.

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.

Representation of analysis results involving aleatory and epistemic uncertainty.

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

Johnson, Jay Dean; Helton, Jon Craig; Oberkampf, William Louis

2008-08-01

Procedures are described for the representation of results in analyses that involve both aleatory uncertainty and epistemic uncertainty, with aleatory uncertainty deriving from an inherent randomness in the behavior of the system under study and epistemic uncertainty deriving from a lack of knowledge about the appropriate values to use for quantities that are assumed to have fixed but poorly known values in the context of a specific study. Aleatory uncertainty is usually represented with probability and leads to cumulative distribution functions (CDFs) or complementary cumulative distribution functions (CCDFs) for analysis results of interest. Several mathematical structures are available for themore » representation of epistemic uncertainty, including interval analysis, possibility theory, evidence theory and probability theory. In the presence of epistemic uncertainty, there is not a single CDF or CCDF for a given analysis result. Rather, there is a family of CDFs and a corresponding family of CCDFs that derive from epistemic uncertainty and have an uncertainty structure that derives from the particular uncertainty structure (i.e., interval analysis, possibility theory, evidence theory, probability theory) used to represent epistemic uncertainty. Graphical formats for the representation of epistemic uncertainty in families of CDFs and CCDFs are investigated and presented for the indicated characterizations of epistemic uncertainty.« less

Hybrid computer technique yields random signal probability distributions

NASA Technical Reports Server (NTRS)

Cameron, W. D.

1965-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

Code of Federal Regulations, 2014 CFR

2014-07-01

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

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

Code of Federal Regulations, 2011 CFR

2011-07-01

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

Knock probability estimation through an in-cylinder temperature model with exogenous noise

NASA Astrophysics Data System (ADS)

Bares, P.; Selmanaj, D.; Guardiola, C.; Onder, C.

2018-01-01

This paper presents a new knock model which combines a deterministic knock model based on the in-cylinder temperature and an exogenous noise disturbing this temperature. The autoignition of the end-gas is modelled by an Arrhenius-like function and the knock probability is estimated by propagating a virtual error probability distribution. Results show that the random nature of knock can be explained by uncertainties at the in-cylinder temperature estimation. The model only has one parameter for calibration and thus can be easily adapted online. In order to reduce the measurement uncertainties associated with the air mass flow sensor, the trapped mass is derived from the in-cylinder pressure resonance, which improves the knock probability estimation and reduces the number of sensors needed for the model. A four stroke SI engine was used for model validation. By varying the intake temperature, the engine speed, the injected fuel mass, and the spark advance, specific tests were conducted, which furnished data with various knock intensities and probabilities. The new model is able to predict the knock probability within a sufficient range at various operating conditions. The trapped mass obtained by the acoustical model was compared in steady conditions by using a fuel balance and a lambda sensor and differences below 1 % were found.

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

PubMed Central

Baumann, Hendrik; Sandmann, Werner

2016-01-01

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

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

PubMed

Baumann, Hendrik; Sandmann, Werner

2016-01-01

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

3D radiation belt diffusion model results using new empirical models of whistler chorus and hiss

NASA Astrophysics Data System (ADS)

Cunningham, G.; Chen, Y.; Henderson, M. G.; Reeves, G. D.; Tu, W.

2012-12-01

3D diffusion codes model the energization, radial transport, and pitch angle scattering due to wave-particle interactions. Diffusion codes are powerful but are limited by the lack of knowledge of the spatial & temporal distribution of waves that drive the interactions for a specific event. We present results from the 3D DREAM model using diffusion coefficients driven by new, activity-dependent, statistical models of chorus and hiss waves. Most 3D codes parameterize the diffusion coefficients or wave amplitudes as functions of magnetic activity indices like Kp, AE, or Dst. These functional representations produce the average value of the wave intensities for a given level of magnetic activity; however, the variability of the wave population at a given activity level is lost with such a representation. Our 3D code makes use of the full sample distributions contained in a set of empirical wave databases (one database for each wave type, including plasmaspheric hiss, lower and upper hand chorus) that were recently produced by our team using CRRES and THEMIS observations. The wave databases store the full probability distribution of observed wave intensity binned by AE, MLT, MLAT and L*. In this presentation, we show results that make use of the wave intensity sample probability distributions for lower-band and upper-band chorus by sampling the distributions stochastically during a representative CRRES-era storm. The sampling of the wave intensity probability distributions produces a collection of possible evolutions of the phase space density, which quantifies the uncertainty in the model predictions caused by the uncertainty of the chorus wave amplitudes for a specific event. A significant issue is the determination of an appropriate model for the spatio-temporal correlations of the wave intensities, since the diffusion coefficients are computed as spatio-temporal averages of the waves over MLT, MLAT and L*. The spatiotemporal correlations cannot be inferred from the wave databases. In this study we use a temporal correlation of ~1 hour for the sampled wave intensities that is informed by the observed autocorrelation in the AE index, a spatial correlation length of ~100 km in the two directions perpendicular to the magnetic field, and a spatial correlation length of 5000 km in the direction parallel to the magnetic field, according to the work of Santolik et al (2003), who used multi-spacecraft measurements from Cluster to quantify the correlation length scales for equatorial chorus . We find that, despite the small correlation length scale for chorus, there remains significant variability in the model outcomes driven by variability in the chorus wave intensities.

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…

Element specificity of ortho-positronium annihilation for alkali-metal loaded SiO2 glasses.

PubMed

Sato, K; Hatta, T

2015-03-07

Momentum distributions associated with ortho-positronium (o-Ps) pick-off annihilation photon are often influenced by light elements, as, e.g., carbon, oxygen, and fluorine. This phenomenon, so-called element specificity of o-Ps pick-off annihilation, has been utilized for studying the elemental environment around the open spaces. To gain an insight into the element specificity of o-Ps pick-off annihilation, the chemical shift of oxygen 1s binding energy and the momentum distributions associated with o-Ps pick-off annihilation were systematically investigated for alkali-metal loaded SiO2 glasses by means of X-ray photoelectron spectroscopy and positron-age-momentum correlation spectroscopy, respectively. Alkali metals introduced into the open spaces surrounded by oxygen atoms cause charge transfer from alkali metals to oxygen atoms, leading to the lower chemical shift for the oxygen 1s binding energy. The momentum distribution of o-Ps localized into the open spaces is found to be closely correlated with the oxygen 1s chemical shift. This correlation with the deepest 1s energy level evidences that the element specificity of o-Ps originates from pick-off annihilation with orbital electrons, i.e., dominantly with oxygen 2p valence electrons and s electrons with lower probability.

Probabilistic estimation of residential air exchange rates for ...

EPA Pesticide Factsheets

Residential air exchange rates (AERs) are a key determinant in the infiltration of ambient air pollution indoors. Population-based human exposure models using probabilistic approaches to estimate personal exposure to air pollutants have relied on input distributions from AER measurements. An algorithm for probabilistically estimating AER was developed based on the Lawrence Berkley National Laboratory Infiltration model utilizing housing characteristics and meteorological data with adjustment for window opening behavior. The algorithm was evaluated by comparing modeled and measured AERs in four US cities (Los Angeles, CA; Detroit, MI; Elizabeth, NJ; and Houston, TX) inputting study-specific data. The impact on the modeled AER of using publically available housing data representative of the region for each city was also assessed. Finally, modeled AER based on region-specific inputs was compared with those estimated using literature-based distributions. While modeled AERs were similar in magnitude to the measured AER they were consistently lower for all cities except Houston. AERs estimated using region-specific inputs were lower than those using study-specific inputs due to differences in window opening probabilities. The algorithm produced more spatially and temporally variable AERs compared with literature-based distributions reflecting within- and between-city differences, helping reduce error in estimates of air pollutant exposure. Published in the Journal of

Failure probability under parameter uncertainty.

PubMed

Gerrard, R; Tsanakas, A

2011-05-01

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

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

NASA Astrophysics Data System (ADS)

Wilks, Daniel S.

1993-10-01

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

A case cluster of variant Creutzfeldt-Jakob disease linked to the Kingdom of Saudi Arabia.

PubMed

Coulthart, Michael B; Geschwind, Michael D; Qureshi, Shireen; Phielipp, Nicolas; Demarsh, Alex; Abrams, Joseph Y; Belay, Ermias; Gambetti, Pierluigi; Jansen, Gerard H; Lang, Anthony E; Schonberger, Lawrence B

2016-10-01

As of mid-2016, 231 cases of variant Creutzfeldt-Jakob disease-the human form of a prion disease of cattle, bovine spongiform encephalopathy-have been reported from 12 countries. With few exceptions, the affected individuals had histories of extended residence in the UK or other Western European countries during the period (1980-96) of maximum global risk for human exposure to bovine spongiform encephalopathy. However, the possibility remains that other geographic foci of human infection exist, identification of which may help to foreshadow the future of the epidemic. We report results of a quantitative analysis of country-specific relative risks of infection for three individuals diagnosed with variant Creutzfeldt-Jakob disease in the USA and Canada. All were born and raised in Saudi Arabia, but had histories of residence and travel in other countries. To calculate country-specific relative probabilities of infection, we aligned each patient's life history with published estimates of probability distributions of incubation period and age at infection parameters from a UK cohort of 171 variant Creutzfeldt-Jakob disease cases. The distributions were then partitioned into probability density fractions according to time intervals of the patient's residence and travel history, and the density fractions were combined by country. This calculation was performed for incubation period alone, age at infection alone, and jointly for incubation and age at infection. Country-specific fractions were normalized either to the total density between the individual's dates of birth and symptom onset ('lifetime'), or to that between 1980 and 1996, for a total of six combinations of parameter and interval. The country-specific relative probability of infection for Saudi Arabia clearly ranked highest under each of the six combinations of parameter × interval for Patients 1 and 2, with values ranging from 0.572 to 0.998, respectively, for Patient 2 (age at infection × lifetime) and Patient 1 (joint incubation and age at infection × 1980-96). For Patient 3, relative probabilities for Saudi Arabia were not as distinct from those for other countries using the lifetime interval: 0.394, 0.360 and 0.378, respectively, for incubation period, age at infection and jointly for incubation and age at infection. However, for this patient Saudi Arabia clearly ranked highest within the 1980-96 period: 0.859, 0.871 and 0.865, respectively, for incubation period, age at infection and jointly for incubation and age at infection. These findings support the hypothesis that human infection with bovine spongiform encephalopathy occurred in Saudi Arabia. © Her Majesty the Queen in Right of Canada 2016. Reproduced with the permission of the Minister of Public Health.

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.

Completion of the Edward Air Force Base Statistical Guidance Wind Tool

NASA Technical Reports Server (NTRS)

Dreher, Joseph G.

2008-01-01

The goal of this task was to develop a GUI using EAFB wind tower data similar to the KSC SLF peak wind tool that is already in operations at SMG. In 2004, MSFC personnel began work to replicate the KSC SLF tool using several wind towers at EAFB. They completed the analysis and QC of the data, but due to higher priority work did not start development of the GUI. MSFC personnel calculated wind climatologies and probabilities of 10-minute peak wind occurrence based on the 2-minute average wind speed for several EAFB wind towers. Once the data were QC'ed and analyzed the climatologies were calculated following the methodology outlined in Lambert (2003). The climatologies were calculated for each tower and month, and then were stratified by hour, direction (10" sectors), and direction (45" sectors)/hour. For all climatologies, MSFC calculated the mean, standard deviation and observation counts of the Zminute average and 10-minute peak wind speeds. MSFC personnel also calculated empirical and modeled probabilities of meeting or exceeding specific 10- minute peak wind speeds using PDFs. The empirical PDFs were asymmetrical and bounded on the left by the 2- minute average wind speed. They calculated the parametric PDFs by fitting the GEV distribution to the empirical distributions. Parametric PDFs were calculated in order to smooth and interpolate over variations in the observed values due to possible under-sampling of certain peak winds and to estimate probabilities associated with average winds outside the observed range. MSFC calculated the individual probabilities of meeting or exceeding specific 10- minute peak wind speeds by integrating the area under each curve. The probabilities assist SMG forecasters in assessing the shuttle FR for various Zminute average wind speeds. The A M ' obtained the processed EAFB data from Dr. Lee Bums of MSFC and reformatted them for input to Excel PivotTables, which allow users to display different values with point-click-drag techniques. The GUI was created from the PivotTables using VBA code. It is run through a macro within Excel and allows forecasters to quickly display and interpret peak wind climatology and probabilities in a fast-paced operational environment. The GUI was designed to look and operate exactly the same as the KSC SLF tool since SMG forecasters were already familiar with that product. SMG feedback was continually incorporated into the GUI ensuring the end product met their needs. The final version of the GUI along with all climatologies, PDFs, and probabilities has been delivered to SMG and will be put into operational use.

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.

Task specificity of attention training: the case of probability cuing

PubMed Central

Jiang, Yuhong V.; Swallow, Khena M.; Won, Bo-Yeong; Cistera, Julia D.; Rosenbaum, Gail M.

2014-01-01

Statistical regularities in our environment enhance perception and modulate the allocation of spatial attention. Surprisingly little is known about how learning-induced changes in spatial attention transfer across tasks. In this study, we investigated whether a spatial attentional bias learned in one task transfers to another. Most of the experiments began with a training phase in which a search target was more likely to be located in one quadrant of the screen than in the other quadrants. An attentional bias toward the high-probability quadrant developed during training (probability cuing). In a subsequent, testing phase, the target's location distribution became random. In addition, the training and testing phases were based on different tasks. Probability cuing did not transfer between visual search and a foraging-like task. However, it did transfer between various types of visual search tasks that differed in stimuli and difficulty. These data suggest that different visual search tasks share a common and transferrable learned attentional bias. However, this bias is not shared by high-level, decision-making tasks such as foraging. PMID:25113853

Probabilistic approach to lysozyme crystal nucleation kinetics.

PubMed

Dimitrov, Ivaylo L; Hodzhaoglu, Feyzim V; Koleva, Dobryana P

2015-09-01

Nucleation of lysozyme crystals in quiescent solutions at a regime of progressive nucleation is investigated under an optical microscope at conditions of constant supersaturation. A method based on the stochastic nature of crystal nucleation and using discrete time sampling of small solution volumes for the presence or absence of detectable crystals is developed. It allows probabilities for crystal detection to be experimentally estimated. One hundred single samplings were used for each probability determination for 18 time intervals and six lysozyme concentrations. Fitting of a particular probability function to experimentally obtained data made possible the direct evaluation of stationary rates for lysozyme crystal nucleation, the time for growth of supernuclei to a detectable size and probability distribution of nucleation times. Obtained stationary nucleation rates were then used for the calculation of other nucleation parameters, such as the kinetic nucleation factor, nucleus size, work for nucleus formation and effective specific surface energy of the nucleus. The experimental method itself is simple and adaptable and can be used for crystal nucleation studies of arbitrary soluble substances with known solubility at particular solution conditions.

Hypothesis testing and earthquake prediction.

PubMed

Jackson, D D

1996-04-30

Requirements for testing include advance specification of the conditional rate density (probability per unit time, area, and magnitude) or, alternatively, probabilities for specified intervals of time, space, and magnitude. Here I consider testing fully specified hypotheses, with no parameter adjustments or arbitrary decisions allowed during the test period. Because it may take decades to validate prediction methods, it is worthwhile to formulate testable hypotheses carefully in advance. Earthquake prediction generally implies that the probability will be temporarily higher than normal. Such a statement requires knowledge of "normal behavior"--that is, it requires a null hypothesis. Hypotheses can be tested in three ways: (i) by comparing the number of actual earth-quakes to the number predicted, (ii) by comparing the likelihood score of actual earthquakes to the predicted distribution, and (iii) by comparing the likelihood ratio to that of a null hypothesis. The first two tests are purely self-consistency tests, while the third is a direct comparison of two hypotheses. Predictions made without a statement of probability are very difficult to test, and any test must be based on the ratio of earthquakes in and out of the forecast regions.

Hypothesis testing and earthquake prediction.

PubMed Central

Jackson, D D

1996-01-01

Requirements for testing include advance specification of the conditional rate density (probability per unit time, area, and magnitude) or, alternatively, probabilities for specified intervals of time, space, and magnitude. Here I consider testing fully specified hypotheses, with no parameter adjustments or arbitrary decisions allowed during the test period. Because it may take decades to validate prediction methods, it is worthwhile to formulate testable hypotheses carefully in advance. Earthquake prediction generally implies that the probability will be temporarily higher than normal. Such a statement requires knowledge of "normal behavior"--that is, it requires a null hypothesis. Hypotheses can be tested in three ways: (i) by comparing the number of actual earth-quakes to the number predicted, (ii) by comparing the likelihood score of actual earthquakes to the predicted distribution, and (iii) by comparing the likelihood ratio to that of a null hypothesis. The first two tests are purely self-consistency tests, while the third is a direct comparison of two hypotheses. Predictions made without a statement of probability are very difficult to test, and any test must be based on the ratio of earthquakes in and out of the forecast regions. PMID:11607663

Measurement of Plutonium-240 Angular Momentum Dependent Fission Probabilities Using the Alpha-Alpha' Reaction

NASA Astrophysics Data System (ADS)

Koglin, Johnathon

Accurate nuclear reaction data from a few keV to tens of MeV and across the table of nuclides is essential to a number of applications of nuclear physics, including national security, nuclear forensics, nuclear astrophysics, and nuclear energy. Precise determination of (n, f) and neutron capture cross sections for reactions in high- ux environments are particularly important for a proper understanding of nuclear reactor performance and stellar nucleosynthesis. In these extreme environments reactions on short-lived and otherwise difficult-to-produce isotopes play a significant role in system evolution and provide insights into the types of nuclear processes taking place; a detailed understanding of these processes is necessary to properly determine cross sections far from stability. Indirect methods are often attempted to measure cross sections on isotopes that are difficult to separate in a laboratory setting. Using the surrogate approach, the same compound nucleus from the reaction of interest is created through a "surrogate" reaction on a different isotope and the resulting decay is measured. This result is combined with appropriate reaction theory for compound nucleus population, from which the desired cross sections can be inferred. This method has shown promise, but the theoretical framework often lacks necessary experimental data to constrain models. In this work, dual arrays of silicon telescope particle identification detectors and photovoltaic (solar) cell fission fragment detectors have been used to measure the fission probability of the 240Pu(alpha, alpha'f) reaction - a surrogate for the 239Pu(n, f) - and fission of 35.9(2)MeV at eleven scattering angles from 40° to 140° in 10° intervals and at nuclear excitation energies up to 16MeV. Within experimental uncertainty, the maximum fission probability was observed at the neutron separation energy for each alpha scattering angle. Fission probabilities were separated into five 500 keV bins from 5:5MeV to 8:0MeV and one bin from 4:5MeV to 5:5MeV. Across energy bins the fission probability increases approximately linearly with increasing alpha' scattering angle. At 90° the fission probability increases from 0:069(6) in the lowest energy bin to 0:59(2) in the highest. Likewise, within a single energy bin the fission probability increases with alpha' scattering angle. Within the 6:5MeV and 7:0MeV energy bin, the fission probability increased from 0:41(1) at 60° to 0:81(10) at 140°. Fission fragment angular distributions were also measured integrated over each energy bin. These distributions were fit to theoretical distributions based on combinations of transitional nuclear vibrational and rotational excitations at the saddle point. Contributions from specific K vibrational states were extracted and combined with fission probability measurements to determine the relative fission probability of each state as a function of nuclear excitation energy. Within a given excitation energy bin, it is found that contributions from K states greater than the minimum K = 0 state tend to increase with the increasing alpha' scattering angle. This is attributed to an increase in the transferred angular momentum associated with larger scattering angles. The 90° alpha' scattering angle produced the highest quality results. The relative contributions of K states do not show a discernible trend across the energy spectrum. The energy-binned results confirm existing measurements that place a K = 2 state in the first energy bin with the opening of K = 1 and K = 4 states at energies above 5:5MeV. This experiment represents the first of its kind in which fission probabilities and angular distributions are simultaneously measured at a large number of scattering angles. The acquired fission probability, angular distribution, and K state contribution provide a diverse dataset against which microscopic fission models can be constrained and further the understanding of the properties of the 240Pu fission.

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.

Dealing with non-unique and non-monotonic response in particle sizing instruments

NASA Astrophysics Data System (ADS)

Rosenberg, Phil

2017-04-01

A number of instruments used as de-facto standards for measuring particle size distributions are actually incapable of uniquely determining the size of an individual particle. This is due to non-unique or non-monotonic response functions. Optical particle counters have non monotonic response due to oscillations in the Mie response curves, especially for large aerosol and small cloud droplets. Scanning mobility particle sizers respond identically to two particles where the ratio of particle size to particle charge is approximately the same. Images of two differently sized cloud or precipitation particles taken by an optical array probe can have similar dimensions or shadowed area depending upon where they are in the imaging plane. A number of methods exist to deal with these issues, including assuming that positive and negative errors cancel, smoothing response curves, integrating regions in measurement space before conversion to size space and matrix inversion. Matrix inversion (also called kernel inversion) has the advantage that it determines the size distribution which best matches the observations, given specific information about the instrument (a matrix which specifies the probability that a particle of a given size will be measured in a given instrument size bin). In this way it maximises use of the information in the measurements. However this technique can be confused by poor counting statistics which can cause erroneous results and negative concentrations. Also an effective method for propagating uncertainties is yet to be published or routinely implemented. Her we present a new alternative which overcomes these issues. We use Bayesian methods to determine the probability that a given size distribution is correct given a set of instrument data and then we use Markov Chain Monte Carlo methods to sample this many dimensional probability distribution function to determine the expectation and (co)variances - hence providing a best guess and an uncertainty for the size distribution which includes contributions from the non-unique response curve, counting statistics and can propagate calibration uncertainties.

The Integrated Medical Model: A Probabilistic Simulation Model for Predicting In-Flight Medical Risks

NASA Technical Reports Server (NTRS)

Keenan, Alexandra; Young, Millennia; Saile, Lynn; Boley, Lynn; Walton, Marlei; Kerstman, Eric; Shah, Ronak; Goodenow, Debra A.; Myers, Jerry G.

2015-01-01

The Integrated Medical Model (IMM) is a probabilistic model that uses simulation to predict mission medical risk. Given a specific mission and crew scenario, medical events are simulated using Monte Carlo methodology to provide estimates of resource utilization, probability of evacuation, probability of loss of crew, and the amount of mission time lost due to illness. Mission and crew scenarios are defined by mission length, extravehicular activity (EVA) schedule, and crew characteristics including: sex, coronary artery calcium score, contacts, dental crowns, history of abdominal surgery, and EVA eligibility. The Integrated Medical Evidence Database (iMED) houses the model inputs for one hundred medical conditions using in-flight, analog, and terrestrial medical data. Inputs include incidence, event durations, resource utilization, and crew functional impairment. Severity of conditions is addressed by defining statistical distributions on the dichotomized best and worst-case scenarios for each condition. The outcome distributions for conditions are bounded by the treatment extremes of the fully treated scenario in which all required resources are available and the untreated scenario in which no required resources are available. Upon occurrence of a simulated medical event, treatment availability is assessed, and outcomes are generated depending on the status of the affected crewmember at the time of onset, including any pre-existing functional impairments or ongoing treatment of concurrent conditions. The main IMM outcomes, including probability of evacuation and loss of crew life, time lost due to medical events, and resource utilization, are useful in informing mission planning decisions. To date, the IMM has been used to assess mission-specific risks with and without certain crewmember characteristics, to determine the impact of eliminating certain resources from the mission medical kit, and to design medical kits that maximally benefit crew health while meeting mass and volume constraints.

The Integrated Medical Model: A Probabilistic Simulation Model Predicting In-Flight Medical Risks

NASA Technical Reports Server (NTRS)

Keenan, Alexandra; Young, Millennia; Saile, Lynn; Boley, Lynn; Walton, Marlei; Kerstman, Eric; Shah, Ronak; Goodenow, Debra A.; Myers, Jerry G., Jr.

2015-01-01

The Integrated Medical Model (IMM) is a probabilistic model that uses simulation to predict mission medical risk. Given a specific mission and crew scenario, medical events are simulated using Monte Carlo methodology to provide estimates of resource utilization, probability of evacuation, probability of loss of crew, and the amount of mission time lost due to illness. Mission and crew scenarios are defined by mission length, extravehicular activity (EVA) schedule, and crew characteristics including: sex, coronary artery calcium score, contacts, dental crowns, history of abdominal surgery, and EVA eligibility. The Integrated Medical Evidence Database (iMED) houses the model inputs for one hundred medical conditions using in-flight, analog, and terrestrial medical data. Inputs include incidence, event durations, resource utilization, and crew functional impairment. Severity of conditions is addressed by defining statistical distributions on the dichotomized best and worst-case scenarios for each condition. The outcome distributions for conditions are bounded by the treatment extremes of the fully treated scenario in which all required resources are available and the untreated scenario in which no required resources are available. Upon occurrence of a simulated medical event, treatment availability is assessed, and outcomes are generated depending on the status of the affected crewmember at the time of onset, including any pre-existing functional impairments or ongoing treatment of concurrent conditions. The main IMM outcomes, including probability of evacuation and loss of crew life, time lost due to medical events, and resource utilization, are useful in informing mission planning decisions. To date, the IMM has been used to assess mission-specific risks with and without certain crewmember characteristics, to determine the impact of eliminating certain resources from the mission medical kit, and to design medical kits that maximally benefit crew health while meeting mass and volume constraints.

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.

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.

Relaxation of ferroelectric states in 2D distributions of quantum dots: EELS simulation

NASA Astrophysics Data System (ADS)

Cortés, C. M.; Meza-Montes, L.; Moctezuma, R. E.; Carrillo, J. L.

2016-06-01

The relaxation time of collective electronic states in a 2D distribution of quantum dots is investigated theoretically by simulating EELS experiments. From the numerical calculation of the probability of energy loss of an electron beam, traveling parallel to the distribution, it is possible to estimate the damping time of ferroelectric-like states. We generate this collective response of the distribution by introducing a mean field interaction among the quantum dots, and then, the model is extended incorporating effects of long-range correlations through a Bragg-Williams approximation. The behavior of the dielectric function, the energy loss function, and the relaxation time of ferroelectric-like states is then investigated as a function of the temperature of the distribution and the damping constant of the electronic states in the single quantum dots. The robustness of the trends and tendencies of our results indicate that this scheme of analysis can guide experimentalists to develop tailored quantum dots distributions for specific applications.

Optimal Operation of Energy Storage in Power Transmission and Distribution

NASA Astrophysics Data System (ADS)

Akhavan Hejazi, Seyed Hossein

In this thesis, we investigate optimal operation of energy storage units in power transmission and distribution grids. At transmission level, we investigate the problem where an investor-owned independently-operated energy storage system seeks to offer energy and ancillary services in the day-ahead and real-time markets. We specifically consider the case where a significant portion of the power generated in the grid is from renewable energy resources and there exists significant uncertainty in system operation. In this regard, we formulate a stochastic programming framework to choose optimal energy and reserve bids for the storage units that takes into account the fluctuating nature of the market prices due to the randomness in the renewable power generation availability. At distribution level, we develop a comprehensive data set to model various stochastic factors on power distribution networks, with focus on networks that have high penetration of electric vehicle charging load and distributed renewable generation. Furthermore, we develop a data-driven stochastic model for energy storage operation at distribution level, where the distribution of nodal voltage and line power flow are modelled as stochastic functions of the energy storage unit's charge and discharge schedules. In particular, we develop new closed-form stochastic models for such key operational parameters in the system. Our approach is analytical and allows formulating tractable optimization problems. Yet, it does not involve any restricting assumption on the distribution of random parameters, hence, it results in accurate modeling of uncertainties. By considering the specific characteristics of random variables, such as their statistical dependencies and often irregularly-shaped probability distributions, we propose a non-parametric chance-constrained optimization approach to operate and plan energy storage units in power distribution girds. In the proposed stochastic optimization, we consider uncertainty from various elements, such as solar photovoltaic , electric vehicle chargers, and residential baseloads, in the form of discrete probability functions. In the last part of this thesis we address some other resources and concepts for enhancing the operation of power distribution and transmission systems. In particular, we proposed a new framework to determine the best sites, sizes, and optimal payment incentives under special contracts for committed-type DG projects to offset distribution network investment costs. In this framework, the aim is to allocate DGs such that the profit gained by the distribution company is maximized while each DG unit's individual profit is also taken into account to assure that private DG investment remains economical.

Incorporating expert judgments in utility evaluation of bacteroidales qPCR assays for microbial source tracking in a drinking water source.

PubMed

Åström, Johan; Pettersson, Thomas J R; Reischer, Georg H; Norberg, Tommy; Hermansson, Malte

2015-02-03

Several assays for the detection of host-specific genetic markers of the order Bacteroidales have been developed and used for microbial source tracking (MST) in environmental waters. It is recognized that the source-sensitivity and source-specificity are unknown and variable when introducing these assays in new geographic regions, which reduces their reliability and use. A Bayesian approach was developed to incorporate expert judgments with regional assay sensitivity and specificity assessments in a utility evaluation of a human and a ruminant-specific qPCR assay for MST in a drinking water source. Water samples from Lake Rådasjön were analyzed for E. coli, intestinal enterococci and somatic coliphages through cultivation and for human (BacH) and ruminant-specific (BacR) markers through qPCR assays. Expert judgments were collected regarding the probability of human and ruminant fecal contamination based on fecal indicator organism data and subjective information. Using Bayes formula, the conditional probability of a true human or ruminant fecal contamination given the presence of BacH or BacR was determined stochastically from expert judgments and regional qPCR assay performance, using Beta distributions to represent uncertainties. A web-based computational tool was developed for the procedure, which provides a measure of confidence to findings of host-specific markers and demonstrates the information value from these assays.

Incorporating Expert Judgments in Utility Evaluation of Bacteroidales qPCR Assays for Microbial Source Tracking in a Drinking Water Source

PubMed Central

Åström, Johan; Pettersson, Thomas J. R.; Reischer, Georg H.; Norberg, Tommy; Hermansson, Malte

2017-01-01

Several assays for the detection of host-specific genetic markers of the order Bacteroidales have been developed and used for microbial source tracking (MST) in environmental waters. It is recognized that the source-sensitivity and source-specificity are unknown and variable when introducing these assays in new geographic regions, which reduces their reliability and use. A Bayesian approach was developed to incorporate expert judgments with regional assay sensitivity and specificity assessments in a utility evaluation of a human and a ruminant-specific qPCR assay for MST in a drinking water source. Water samples from Lake Rådasjön were analyzed for E. coli, intestinal enterococci and somatic coliphages through cultivation and for human (BacH) and ruminant-specific (BacR) markers through qPCR assays. Expert judgments were collected regarding the probability of human and ruminant fecal contamination based on fecal indicator organism data and subjective information. Using Bayes formula, the conditional probability of a true human or ruminant fecal contamination given the presence of BacH or BacR was determined stochastically from expert judgments and regional qPCR assay performance, using Beta distributions to represent uncertainties. A web-based computational tool was developed for the procedure, which provides a measure of confidence to findings of host-specific markers and demonstrates the information value from these assays. PMID:25545113

A local approach for focussed Bayesian fusion

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael; Goussev, Igor; Beyerer, Jürgen

2009-04-01

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential.

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.

Directional data analysis under the general projected normal distribution

PubMed Central

Wang, Fangpo; Gelfand, Alan E.

2013-01-01

The projected normal distribution is an under-utilized model for explaining directional data. In particular, the general version provides flexibility, e.g., asymmetry and possible bimodality along with convenient regression specification. Here, we clarify the properties of this general class. We also develop fully Bayesian hierarchical models for analyzing circular data using this class. We show how they can be fit using MCMC methods with suitable latent variables. We show how posterior inference for distributional features such as the angular mean direction and concentration can be implemented as well as how prediction within the regression setting can be handled. With regard to model comparison, we argue for an out-of-sample approach using both a predictive likelihood scoring loss criterion and a cumulative rank probability score criterion. PMID:24046539

Site occupancy models with heterogeneous detection probabilities

USGS Publications Warehouse

Royle, J. Andrew

2006-01-01

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

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

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

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

2012-06-15

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

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.

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

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

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.

General formulation of long-range degree correlations in complex networks

NASA Astrophysics Data System (ADS)

Fujiki, Yuka; Takaguchi, Taro; Yakubo, Kousuke

2018-06-01

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

Stochastic analysis of particle movement over a dune bed

USGS Publications Warehouse

Lee, Baum K.; Jobson, Harvey E.

1977-01-01

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

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

PubMed

Wang, Jihan; Yang, Kai

2014-07-01

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

Derivation of Hunt equation for suspension distribution using Shannon entropy theory

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2017-12-01

In this study, the Hunt equation for computing suspension concentration in sediment-laden flows is derived using Shannon entropy theory. Considering the inverse of the void ratio as a random variable and using principle of maximum entropy, probability density function and cumulative distribution function of suspension concentration is derived. A new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of CDF reported in literature. This general form of cumulative distribution function also helps to derive the Rouse equation. The entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory. Finally model parameters in the entropy based model are also expressed as functions of the Rouse number to establish a link between the parameters of the deterministic and probabilistic approaches.

More Intense Experiences, Less Intense Forecasts: Why People Overweight Probability Specifications in Affective Forecasts

PubMed Central

Buechel, Eva C.; Zhang, Jiao; Morewedge, Carey K.; Vosgerau, Joachim

2014-01-01

We propose that affective forecasters overestimate the extent to which experienced hedonic responses to an outcome are influenced by the probability of its occurrence. The experience of an outcome (e.g., winning a gamble) is typically more affectively intense than the simulation of that outcome (e.g., imagining winning a gamble) upon which the affective forecast for it is based. We suggest that, as a result, experiencers allocate a larger share of their attention toward the outcome (e.g., winning the gamble) and less to its probability specifications than do affective forecasters. Consequently, hedonic responses to an outcome are less sensitive to its probability specifications than are affective forecasts for that outcome. The results of 6 experiments provide support for our theory. Affective forecasters overestimated how sensitive experiencers would be to the probability of positive and negative outcomes (Experiments 1 and 2). Consistent with our attentional account, differences in sensitivity to probability specifications disappeared when the attention of forecasters was diverted from probability specifications (Experiment 3) or when the attention of experiencers was drawn toward probability specifications (Experiment 4). Finally, differences in sensitivity to probability specifications between forecasters and experiencers were diminished when the forecasted outcome was more affectively intense (Experiments 5 and 6). PMID:24128184

More intense experiences, less intense forecasts: why people overweight probability specifications in affective forecasts.

PubMed

Buechel, Eva C; Zhang, Jiao; Morewedge, Carey K; Vosgerau, Joachim

2014-01-01

We propose that affective forecasters overestimate the extent to which experienced hedonic responses to an outcome are influenced by the probability of its occurrence. The experience of an outcome (e.g., winning a gamble) is typically more affectively intense than the simulation of that outcome (e.g., imagining winning a gamble) upon which the affective forecast for it is based. We suggest that, as a result, experiencers allocate a larger share of their attention toward the outcome (e.g., winning the gamble) and less to its probability specifications than do affective forecasters. Consequently, hedonic responses to an outcome are less sensitive to its probability specifications than are affective forecasts for that outcome. The results of 6 experiments provide support for our theory. Affective forecasters overestimated how sensitive experiencers would be to the probability of positive and negative outcomes (Experiments 1 and 2). Consistent with our attentional account, differences in sensitivity to probability specifications disappeared when the attention of forecasters was diverted from probability specifications (Experiment 3) or when the attention of experiencers was drawn toward probability specifications (Experiment 4). Finally, differences in sensitivity to probability specifications between forecasters and experiencers were diminished when the forecasted outcome was more affectively intense (Experiments 5 and 6).

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

PubMed

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

2017-01-01

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

Lognormal Approximations of Fault Tree Uncertainty Distributions.

PubMed

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

2018-01-26

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

Quantum key distribution without the wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

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

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

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

Proceedings of a Hydrology and Hydraulics Workshop on Riverine Levee Freeboard Held in Monticello, Minnesota on 27-29 August 1991

DTIC Science & Technology

1991-12-10

necessary to plan the location and manner of overtopping. Freeboard is to be designed and the final results supported and documented. Site specific...elevation resulting from incorporating values that represent reasonably high conveyance losses that could occur given the uncertainty of the best estimates...in the relationships. The result of the risk analysis framework approach is a matrix of levee height, probability distributions of the several

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.

Parkinson Disease Detection from Speech Articulation Neuromechanics.

PubMed

Gómez-Vilda, Pedro; Mekyska, Jiri; Ferrández, José M; Palacios-Alonso, Daniel; Gómez-Rodellar, Andrés; Rodellar-Biarge, Victoria; Galaz, Zoltan; Smekal, Zdenek; Eliasova, Ilona; Kostalova, Milena; Rektorova, Irena

2017-01-01

Aim: The research described is intended to give a description of articulation dynamics as a correlate of the kinematic behavior of the jaw-tongue biomechanical system, encoded as a probability distribution of an absolute joint velocity. This distribution may be used in detecting and grading speech from patients affected by neurodegenerative illnesses, as Parkinson Disease. Hypothesis: The work hypothesis is that the probability density function of the absolute joint velocity includes information on the stability of phonation when applied to sustained vowels, as well as on fluency if applied to connected speech. Methods: A dataset of sustained vowels recorded from Parkinson Disease patients is contrasted with similar recordings from normative subjects. The probability distribution of the absolute kinematic velocity of the jaw-tongue system is extracted from each utterance. A Random Least Squares Feed-Forward Network (RLSFN) has been used as a binary classifier working on the pathological and normative datasets in a leave-one-out strategy. Monte Carlo simulations have been conducted to estimate the influence of the stochastic nature of the classifier. Two datasets for each gender were tested (males and females) including 26 normative and 53 pathological subjects in the male set, and 25 normative and 38 pathological in the female set. Results: Male and female data subsets were tested in single runs, yielding equal error rates under 0.6% (Accuracy over 99.4%). Due to the stochastic nature of each experiment, Monte Carlo runs were conducted to test the reliability of the methodology. The average detection results after 200 Montecarlo runs of a 200 hyperplane hidden layer RLSFN are given in terms of Sensitivity (males: 0.9946, females: 0.9942), Specificity (males: 0.9944, females: 0.9941) and Accuracy (males: 0.9945, females: 0.9942). The area under the ROC curve is 0.9947 (males) and 0.9945 (females). The equal error rate is 0.0054 (males) and 0.0057 (females). Conclusions: The proposed methodology avails that the use of highly normalized descriptors as the probability distribution of kinematic variables of vowel articulation stability, which has some interesting properties in terms of information theory, boosts the potential of simple yet powerful classifiers in producing quite acceptable detection results in Parkinson Disease.

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

NASA Astrophysics Data System (ADS)

Kacker, Raghu N.

2006-02-01

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

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

PubMed Central

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

2013-01-01

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

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

PubMed

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

2013-01-01

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

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

PubMed Central

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

2010-01-01

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

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

PubMed

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

2008-09-01

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

Comparative analysis through probability distributions of a data set

NASA Astrophysics Data System (ADS)

Cristea, Gabriel; Constantinescu, Dan Mihai

2018-02-01

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

Incorporating uncertainty regarding applicability of evidence from meta-analyses into clinical decision making.

PubMed

Kriston, Levente; Meister, Ramona

2014-03-01

Judging applicability (relevance) of meta-analytical findings to particular clinical decision-making situations remains challenging. We aimed to describe an evidence synthesis method that accounts for possible uncertainty regarding applicability of the evidence. We conceptualized uncertainty regarding applicability of the meta-analytical estimates to a decision-making situation as the result of uncertainty regarding applicability of the findings of the trials that were included in the meta-analysis. This trial-level applicability uncertainty can be directly assessed by the decision maker and allows for the definition of trial inclusion probabilities, which can be used to perform a probabilistic meta-analysis with unequal probability resampling of trials (adaptive meta-analysis). A case study with several fictitious decision-making scenarios was performed to demonstrate the method in practice. We present options to elicit trial inclusion probabilities and perform the calculations. The result of an adaptive meta-analysis is a frequency distribution of the estimated parameters from traditional meta-analysis that provides individually tailored information according to the specific needs and uncertainty of the decision maker. The proposed method offers a direct and formalized combination of research evidence with individual clinical expertise and may aid clinicians in specific decision-making situations. Copyright © 2014 Elsevier Inc. All rights reserved.

Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency

NASA Astrophysics Data System (ADS)

Papalexiou, Simon Michael

2018-05-01

Hydroclimatic processes come in all "shapes and sizes". They are characterized by different spatiotemporal correlation structures and probability distributions that can be continuous, mixed-type, discrete or even binary. Simulating such processes by reproducing precisely their marginal distribution and linear correlation structure, including features like intermittency, can greatly improve hydrological analysis and design. Traditionally, modelling schemes are case specific and typically attempt to preserve few statistical moments providing inadequate and potentially risky distribution approximations. Here, a single framework is proposed that unifies, extends, and improves a general-purpose modelling strategy, based on the assumption that any process can emerge by transforming a specific "parent" Gaussian process. A novel mathematical representation of this scheme, introducing parametric correlation transformation functions, enables straightforward estimation of the parent-Gaussian process yielding the target process after the marginal back transformation, while it provides a general description that supersedes previous specific parameterizations, offering a simple, fast and efficient simulation procedure for every stationary process at any spatiotemporal scale. This framework, also applicable for cyclostationary and multivariate modelling, is augmented with flexible parametric correlation structures that parsimoniously describe observed correlations. Real-world simulations of various hydroclimatic processes with different correlation structures and marginals, such as precipitation, river discharge, wind speed, humidity, extreme events per year, etc., as well as a multivariate example, highlight the flexibility, advantages, and complete generality of the method.

Estimating reach-specific fish movement probabilities in rivers with a Bayesian state-space model: application to sea lamprey passage and capture at dams

USGS Publications Warehouse

Holbrook, Christopher M.; Johnson, Nicholas S.; Steibel, Juan P.; Twohey, Michael B.; Binder, Thomas R.; Krueger, Charles C.; Jones, Michael L.

2014-01-01

Improved methods are needed to evaluate barriers and traps for control and assessment of invasive sea lamprey (Petromyzon marinus) in the Great Lakes. A Bayesian state-space model provided reach-specific probabilities of movement, including trap capture and dam passage, for 148 acoustic tagged invasive sea lamprey in the lower Cheboygan River, Michigan, a tributary to Lake Huron. Reach-specific movement probabilities were combined to obtain estimates of spatial distribution and abundance needed to evaluate a barrier and trap complex for sea lamprey control and assessment. Of an estimated 21 828 – 29 300 adult sea lampreys in the river, 0%–2%, or 0–514 untagged lampreys, could have passed upstream of the dam, and 46%–61% were caught in the trap. Although no tagged lampreys passed above the dam (0/148), our sample size was not sufficient to consider the lock and dam a complete barrier to sea lamprey. Results also showed that existing traps are in good locations because 83%–96% of the population was vulnerable to existing traps. However, only 52%–69% of lampreys vulnerable to traps were caught, suggesting that traps can be improved. The approach used in this study was a novel use of Bayesian state-space models that may have broader applications, including evaluation of barriers for other invasive species (e.g., Asian carp (Hypophthalmichthys spp.)) and fish passage structures for other diadromous fishes.

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

NASA Astrophysics Data System (ADS)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

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

Net present value probability distributions from decline curve reserves estimates

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

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

1995-12-31

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

Optimal random search for a single hidden target.

PubMed

Snider, Joseph

2011-01-01

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

Application of Monte Carlo Method for Evaluation of Uncertainties of ITS-90 by Standard Platinum Resistance Thermometer

NASA Astrophysics Data System (ADS)

Palenčár, Rudolf; Sopkuliak, Peter; Palenčár, Jakub; Ďuriš, Stanislav; Suroviak, Emil; Halaj, Martin

2017-06-01

Evaluation of uncertainties of the temperature measurement by standard platinum resistance thermometer calibrated at the defining fixed points according to ITS-90 is a problem that can be solved in different ways. The paper presents a procedure based on the propagation of distributions using the Monte Carlo method. The procedure employs generation of pseudo-random numbers for the input variables of resistances at the defining fixed points, supposing the multivariate Gaussian distribution for input quantities. This allows taking into account the correlations among resistances at the defining fixed points. Assumption of Gaussian probability density function is acceptable, with respect to the several sources of uncertainties of resistances. In the case of uncorrelated resistances at the defining fixed points, the method is applicable to any probability density function. Validation of the law of propagation of uncertainty using the Monte Carlo method is presented on the example of specific data for 25 Ω standard platinum resistance thermometer in the temperature range from 0 to 660 °C. Using this example, we demonstrate suitability of the method by validation of its results.

Genogroup distribution of F-specific coliphages in wastewater and river water in the Kofu basin in Japan.

PubMed

Haramoto, E; Otagiri, M; Morita, H; Kitajima, M

2012-04-01

To determine the genogroup distribution of F-specific coliphages in aquatic environments using the plaque isolation procedure combined with genogroup-specific real-time PCR. Thirty water samples were collected from a wastewater treatment plant and a river in the Kofu basin in Japan on fine weather days. F-specific coliphages were detected in all tested samples, 187 (82%) of 227 phage plaques isolated were classified into one of the 4 F-specific RNA (F-RNA) coliphage genogroups and 24 (11%) plaques were F-specific DNA coliphages. Human genogroups II and III F-RNA coliphages were more abundant in raw sewage than animal genogroups I and IV, excluding one sample that was suspected to be heavily contaminated with sporadic heavy animal faeces. The secondary-treated sewage samples were highly contaminated with genogroup I F-RNA coliphages, probably because of different behaviours among the coliphage genogroups during wastewater treatment. The river water samples were expected to be mainly contaminated with human faeces, independent of rainfall effects. A wide range of F-specific coliphage genogroups were successfully identified in wastewater and river water samples. Our results clearly show the usefulness of the genogroup-specific real-time PCR for determining the genogroups of F-specific coliphages present in aquatic environments. © 2012 The Authors. Letters in Applied Microbiology © 2012 The Society for Applied Microbiology.

Smart sensing surveillance system

NASA Astrophysics Data System (ADS)

Hsu, Charles; Chu, Kai-Dee; O'Looney, James; Blake, Michael; Rutar, Colleen

2010-04-01

An effective public safety sensor system for heavily-populated applications requires sophisticated and geographically-distributed infrastructures, centralized supervision, and deployment of large-scale security and surveillance networks. Artificial intelligence in sensor systems is a critical design to raise awareness levels, improve the performance of the system and adapt to a changing scenario and environment. In this paper, a highly-distributed, fault-tolerant, and energy-efficient Smart Sensing Surveillance System (S4) is presented to efficiently provide a 24/7 and all weather security operation in crowded environments or restricted areas. Technically, the S4 consists of a number of distributed sensor nodes integrated with specific passive sensors to rapidly collect, process, and disseminate heterogeneous sensor data from near omni-directions. These distributed sensor nodes can cooperatively work to send immediate security information when new objects appear. When the new objects are detected, the S4 will smartly select the available node with a Pan- Tilt- Zoom- (PTZ) Electro-Optics EO/IR camera to track the objects and capture associated imagery. The S4 provides applicable advanced on-board digital image processing capabilities to detect and track the specific objects. The imaging detection operations include unattended object detection, human feature and behavior detection, and configurable alert triggers, etc. Other imaging processes can be updated to meet specific requirements and operations. In the S4, all the sensor nodes are connected with a robust, reconfigurable, LPI/LPD (Low Probability of Intercept/ Low Probability of Detect) wireless mesh network using Ultra-wide band (UWB) RF technology. This UWB RF technology can provide an ad-hoc, secure mesh network and capability to relay network information, communicate and pass situational awareness and messages. The Service Oriented Architecture of S4 enables remote applications to interact with the S4 network and use the specific presentation methods. In addition, the S4 is compliant with Open Geospatial Consortium - Sensor Web Enablement (OGC-SWE) standards to efficiently discover, access, use, and control heterogeneous sensors and their metadata. These S4 capabilities and technologies have great potential for both military and civilian applications, enabling highly effective security support tools for improving surveillance activities in densely crowded environments. The S4 system is directly applicable to solutions for emergency response personnel, law enforcement, and other homeland security missions, as well as in applications requiring the interoperation of sensor networks with handheld or body-worn interface devices.

An economic evaluation of home management of malaria in Uganda: an interactive Markov model.

PubMed

Lubell, Yoel; Mills, Anne J; Whitty, Christopher J M; Staedke, Sarah G

2010-08-27

Home management of malaria (HMM), promoting presumptive treatment of febrile children in the community, is advocated to improve prompt appropriate treatment of malaria in Africa. The cost-effectiveness of HMM is likely to vary widely in different settings and with the antimalarial drugs used. However, no data on the cost-effectiveness of HMM programmes are available. A Markov model was constructed to estimate the cost-effectiveness of HMM as compared to conventional care for febrile illnesses in children without HMM. The model was populated with data from Uganda, but is designed to be interactive, allowing the user to adjust certain parameters, including the antimalarials distributed. The model calculates the cost per disability adjusted life year averted and presents the incremental cost-effectiveness ratio compared to a threshold value. Model output is stratified by level of malaria transmission and the probability that a child would receive appropriate care from a health facility, to indicate the circumstances in which HMM is likely to be cost-effective. The model output suggests that the cost-effectiveness of HMM varies with malaria transmission, the probability of appropriate care, and the drug distributed. Where transmission is high and the probability of appropriate care is limited, HMM is likely to be cost-effective from a provider perspective. Even with the most effective antimalarials, HMM remains an attractive intervention only in areas of high malaria transmission and in medium transmission areas with a lower probability of appropriate care. HMM is generally not cost-effective in low transmission areas, regardless of which antimalarial is distributed. Considering the analysis from the societal perspective decreases the attractiveness of HMM. Syndromic HMM for children with fever may be a useful strategy for higher transmission settings with limited health care and diagnosis, but is not appropriate for all settings. HMM may need to be tailored to specific settings, accounting for local malaria transmission intensity and availability of health services.

Assessment of local variability by high-throughput e-beam metrology for prediction of patterning defect probabilities

NASA Astrophysics Data System (ADS)

Wang, Fuming; Hunsche, Stefan; Anunciado, Roy; Corradi, Antonio; Tien, Hung Yu; Tang, Peng; Wei, Junwei; Wang, Yongjun; Fang, Wei; Wong, Patrick; van Oosten, Anton; van Ingen Schenau, Koen; Slachter, Bram

2018-03-01

We present an experimental study of pattern variability and defectivity, based on a large data set with more than 112 million SEM measurements from an HMI high-throughput e-beam tool. The test case is a 10nm node SRAM via array patterned with a DUV immersion LELE process, where we see a variation in mean size and litho sensitivities between different unique via patterns that leads to a seemingly qualitative differences in defectivity. The large available data volume enables further analysis to reliably distinguish global and local CDU variations, including a breakdown into local systematics and stochastics. A closer inspection of the tail end of the distributions and estimation of defect probabilities concludes that there is a common defect mechanism and defect threshold despite the observed differences of specific pattern characteristics. We expect that the analysis methodology can be applied for defect probability modeling as well as general process qualification in the future.

A probabilistic safety analysis of incidents in nuclear research reactors.

PubMed

Lopes, Valdir Maciel; Agostinho Angelo Sordi, Gian Maria; Moralles, Mauricio; Filho, Tufic Madi

2012-06-01

This work aims to evaluate the potential risks of incidents in nuclear research reactors. For its development, two databases of the International Atomic Energy Agency (IAEA) were used: the Research Reactor Data Base (RRDB) and the Incident Report System for Research Reactor (IRSRR). For this study, the probabilistic safety analysis (PSA) was used. To obtain the result of the probability calculations for PSA, the theory and equations in the paper IAEA TECDOC-636 were used. A specific program to analyse the probabilities was developed within the main program, Scilab 5.1.1. for two distributions, Fischer and chi-square, both with the confidence level of 90 %. Using Sordi equations, the maximum admissible doses to compare with the risk limits established by the International Commission on Radiological Protection (ICRP) were obtained. All results achieved with this probability analysis led to the conclusion that the incidents which occurred had radiation doses within the stochastic effects reference interval established by the ICRP-64.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

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

NASA Technical Reports Server (NTRS)

Lanzi, R. James; Vincent, Brett T.

1993-01-01

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

Probability and the changing shape of response distributions for orientation.

PubMed

Anderson, Britt

2014-11-18

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

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

NASA Technical Reports Server (NTRS)

Smith, O. E.

1976-01-01

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

Joint probabilities and quantum cognition

NASA Astrophysics Data System (ADS)

de Barros, J. Acacio

2012-12-01

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

When violence pays: a cost-benefit analysis of aggressive behavior in animals and humans.

PubMed

Georgiev, Alexander V; Klimczuk, Amanda C E; Traficonte, Daniel M; Maestripieri, Dario

2013-07-18

An optimization analysis of human behavior from a comparative perspective can improve our understanding of the adaptiveness of human nature. Intra-specific competition for resources provides the main selective pressure for the evolution of violent aggression toward conspecifics, and variation in the fitness benefits and costs of aggression can account for inter-specific and inter-individual differences in aggressiveness. When aggression reflects competition for resources, its benefits vary in relation to the characteristics of the resources (their intrinsic value, abundance, spatial distribution, and controllability) while its costs vary in relation to the characteristics of organisms and how they fight (which, in turn, affects the extent to which aggression entails risk of physical injury or death, energetic depletion, exposure to predation, psychological and physiological stress, or damage to social relationships). Humans are a highly aggressive species in comparison to other animals, probably as a result of an unusually high benefit-to-cost ratio for intra-specific aggression. This conclusion is supported by frequent and widespread occurrence of male-male coalitionary killing and by male-female sexual coercion. Sex differences in violent aggression in humans and other species probably evolved by sexual selection and reflect different optimal competitive strategies for males and females.

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

PubMed

Zhuang, Jiancang; Ogata, Yosihiko

2006-04-01

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

Multi-Scale Particle Size Distributions of Mars, Moon and Itokawa based on a time-maturation dependent fragmentation model

NASA Astrophysics Data System (ADS)

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

2013-12-01

We present the development of a soil evolution framework and multiscale modelling of the surface of Mars, Moon and Itokawa thus providing an atlas of extra-terrestrial Particle Size Distributions (PSD). These PSDs are profoundly based on a tailoring method which interconnects several datasets from different sites captured by the various missions. The final integrated product is then fully justified through a soil evolution analysis model mathematically constructed via fundamental physical principles (Charalambous, 2013). The construction of the PSD takes into account the macroscale fresh primary impacts and their products, the mesoscale distributions obtained by the in-situ data of surface missions (Golombek et al., 1997, 2012) and finally the microscopic scale distributions provided by Curiosity and Phoenix Lander (Pike, 2011). The distribution naturally extends at the magnitudinal scales at which current data does not exist due to the lack of scientific instruments capturing the populations at these data absent scales. The extension is based on the model distribution (Charalambous, 2013) which takes as parameters known values of material specific probabilities of fragmentation and grinding limits. Additionally, the establishment of a closed-form statistical distribution provides a quantitative description of the soil's structure. Consequently, reverse engineering of the model distribution allows the synthesis of soil that faithfully represents the particle population at the studied sites (Charalambous, 2011). Such representation essentially delivers a virtual soil environment to work with for numerous applications. A specific application demonstrated here will be the information that can directly be extracted for the successful drilling probability as a function of distance in an effort to aid the HP3 instrument of the 2016 Insight Mission to Mars. Pike, W. T., et al. "Quantification of the dry history of the Martian soil inferred from in situ microscopy." Geophysical Research Letters 38.24 (2011). C. A. Charalambous and W. T. Pike (2013). 'Evolution of Particle Size Distributions in Fragmentation Over Time' Abstract Submitted to the AGU 46th Fall Meeting. Charalambous, C., Pike, W. T., Goetz, W., Hecht, M. H., & Staufer, U. (2011, December). 'A Digital Martian Soil based on In-Situ Data.' In AGU Fall Meeting Abstracts (Vol. 1, p. 1669). Golombek, M., & Rapp, D. (1997). 'Size-frequency distributions of rocks on Mars and Earth analog sites: Implications for future landed missions.' Journal of Geophysical Research, 102(E2), 4117-4129. Golombek, M., Huertas, A., Kipp, D., & Calef, F. (2012). 'Detection and characterization of rocks and rock size-frequency distributions at the final four Mars Science Laboratory landing sites.' Mars, 7, 1-22.

How extreme is extreme hourly precipitation?

NASA Astrophysics Data System (ADS)

Papalexiou, Simon Michael; Dialynas, Yannis G.; Pappas, Christoforos

2016-04-01

The importance of accurate representation of precipitation at fine time scales (e.g., hourly), directly associated with flash flood events, is crucial in hydrological design and prediction. The upper part of a probability distribution, known as the distribution tail, determines the behavior of extreme events. In general, and loosely speaking, tails can be categorized in two families: the subexponential and the hyperexponential family, with the first generating more intense and more frequent extremes compared to the latter. In past studies, the focus has been mainly on daily precipitation, with the Gamma distribution being the most popular model. Here, we investigate the behaviour of tails of hourly precipitation by comparing the upper part of empirical distributions of thousands of records with three general types of tails corresponding to the Pareto, Lognormal, and Weibull distributions. Specifically, we use thousands of hourly rainfall records from all over the USA. The analysis indicates that heavier-tailed distributions describe better the observed hourly rainfall extremes in comparison to lighter tails. Traditional representations of the marginal distribution of hourly rainfall may significantly deviate from observed behaviours of extremes, with direct implications on hydroclimatic variables modelling and engineering design.

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

PubMed

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

2016-12-01

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

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

PubMed Central

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Effects of variability in probable maximum precipitation patterns on flood losses

NASA Astrophysics Data System (ADS)

Zischg, Andreas Paul; Felder, Guido; Weingartner, Rolf; Quinn, Niall; Coxon, Gemma; Neal, Jeffrey; Freer, Jim; Bates, Paul

2018-05-01

The assessment of the impacts of extreme floods is important for dealing with residual risk, particularly for critical infrastructure management and for insurance purposes. Thus, modelling of the probable maximum flood (PMF) from probable maximum precipitation (PMP) by coupling hydrological and hydraulic models has gained interest in recent years. Herein, we examine whether variability in precipitation patterns exceeds or is below selected uncertainty factors in flood loss estimation and if the flood losses within a river basin are related to the probable maximum discharge at the basin outlet. We developed a model experiment with an ensemble of probable maximum precipitation scenarios created by Monte Carlo simulations. For each rainfall pattern, we computed the flood losses with a model chain and benchmarked the effects of variability in rainfall distribution with other model uncertainties. The results show that flood losses vary considerably within the river basin and depend on the timing and superimposition of the flood peaks from the basin's sub-catchments. In addition to the flood hazard component, the other components of flood risk, exposure, and vulnerability contribute remarkably to the overall variability. This leads to the conclusion that the estimation of the probable maximum expectable flood losses in a river basin should not be based exclusively on the PMF. Consequently, the basin-specific sensitivities to different precipitation patterns and the spatial organization of the settlements within the river basin need to be considered in the analyses of probable maximum flood losses.

Aneuploidy theory explains tumor formation, the absence of immune surveillance, and the failure of chemotherapy.

PubMed

Rasnick, David

2002-07-01

The autocatalyzed progression of aneuploidy accounts for all cancer-specific phenotypes, the Hayflick limit of cultured cells, carcinogen-induced tumors in mice, the age distribution of human cancer, and multidrug-resistance. Here aneuploidy theory addresses tumor formation. The logistic equation, phi(n)(+1) = rphi(n) (1 - phi(n)), models the autocatalyzed progression of aneuploidy in vivo and in vitro. The variable phi(n)(+1) is the average aneuploid fraction of a population of cells at the n+1 cell division and is determined by the value at the nth cell division. The value r is the growth control parameter. The logistic equation was used to compute the probability distribution for values of phi after numerous divisions of aneuploid cells. The autocatalyzed progression of aneuploidy follows the laws of deterministic chaos, which means that certain values of phi are more probable than others. The probability map of the logistic equation shows that: 1) an aneuploid fraction of at least 0.30 is necessary to sustain a population of cancer cells; and 2) the most likely aneuploid fraction after many population doublings is 0.70, which is equivalent to a DNA(index)=1.7, the point of maximum disorder of the genome that still sustains life. Aneuploidy theory also explains the lack of immune surveillance and the failure of chemotherapy.

Role of social environment and social clustering in spread of opinions in coevolving networks.

PubMed

Malik, Nishant; Mucha, Peter J

2013-12-01

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the coevolving network voter model of opinion formation studied by Holme and Newman [Phys. Rev. E 74, 056108 (2006)]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for heterogeneity and asymmetric influences in relationships between individuals. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus, allowing for the existence of diverse opinions, and the other having a single dominant connected component with each node within that dominant component having the same opinion. Furthermore, more importantly, we found that the initial clustering in the network can also induce similar transitions. Our investigation also indicates that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes.

Quantitative assessment of building fire risk to life safety.

PubMed

Guanquan, Chu; Jinhua, Sun

2008-06-01

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

On probability-possibility transformations

NASA Technical Reports Server (NTRS)

Klir, George J.; Parviz, Behzad

1992-01-01

Several probability-possibility transformations are compared in terms of the closeness of preserving second-order properties. The comparison is based on experimental results obtained by computer simulation. Two second-order properties are involved in this study: noninteraction of two distributions and projections of a joint distribution.

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

PubMed

Reed, William J; Hughes, Barry D

2007-03-22

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

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

PubMed

Ben-David, Avishai; Davidson, Charles E

2012-04-23

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

Sampling probability distributions of lesions in mammograms

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Probabilistic storm surge inundation maps for Metro Manila based on Philippine public storm warning signals

NASA Astrophysics Data System (ADS)

Tablazon, J.; Caro, C. V.; Lagmay, A. M. F.; Briones, J. B. L.; Dasallas, L.; Lapidez, J. P.; Santiago, J.; Suarez, J. K.; Ladiero, C.; Gonzalo, L. A.; Mungcal, M. T. F.; Malano, V.

2015-03-01

A storm surge is the sudden rise of sea water over the astronomical tides, generated by an approaching storm. This event poses a major threat to the Philippine coastal areas, as manifested by Typhoon Haiyan on 8 November 2013. This hydro-meteorological hazard is one of the main reasons for the high number of casualties due to the typhoon, with 6300 deaths. It became evident that the need to develop a storm surge inundation map is of utmost importance. To develop these maps, the Nationwide Operational Assessment of Hazards under the Department of Science and Technology (DOST-Project NOAH) simulated historical tropical cyclones that entered the Philippine Area of Responsibility. The Japan Meteorological Agency storm surge model was used to simulate storm surge heights. The frequency distribution of the maximum storm surge heights was calculated using simulation results of tropical cyclones under a specific public storm warning signal (PSWS) that passed through a particular coastal area. This determines the storm surge height corresponding to a given probability of occurrence. The storm surge heights from the model were added to the maximum astronomical tide data from WXTide software. The team then created maps of inundation for a specific PSWS using the probability of exceedance derived from the frequency distribution. Buildings and other structures were assigned a probability of exceedance depending on their occupancy category, i.e., 1% probability of exceedance for critical facilities, 10% probability of exceedance for special occupancy structures, and 25% for standard occupancy and miscellaneous structures. The maps produced show the storm-surge-vulnerable areas in Metro Manila, illustrated by the flood depth of up to 4 m and extent of up to 6.5 km from the coastline. This information can help local government units in developing early warning systems, disaster preparedness and mitigation plans, vulnerability assessments, risk-sensitive land use plans, shoreline defense efforts, and coastal protection measures. These maps can also determine the best areas to build critical structures, or at least determine the level of protection of these structures should they be built in hazard areas. Moreover, these will support the local government units' mandate to raise public awareness, disseminate information about storm surge hazards, and implement appropriate countermeasures for a given PSWS.

Brownian excursions on combs

NASA Astrophysics Data System (ADS)

Dean, David S.; Jansons, Kalvis M.

1993-03-01

In this paper we use techniques from Ito excursion theory to analyze Brownian motion on generalized combs. Ito excursion theory is a little-known area of probability theory and we therefore present a brief introduction for the uninitiated. A general method for analyzing transport along the backbone of the comb is demonstrated and the specific case of a comb whose teeth are scaling branching trees is examined. We then present a recursive method for evaluating the distribution of the first passage times on hierarchical combs.

Clustering and optimal arrangement of enzymes in reaction-diffusion systems.

PubMed

Buchner, Alexander; Tostevin, Filipe; Gerland, Ulrich

2013-05-17

Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.

Multi-Step Fibrinogen Binding to the Integrin αIIbβ3 Detected Using Force Spectroscopy

PubMed Central

Litvinov, Rustem I.; Bennett, Joel S.; Weisel, John W.; Shuman, Henry

2005-01-01

The regulated ability of integrin αIIbβ3 to bind fibrinogen plays a crucial role in platelet aggregation and hemostasis. We have developed a model system based on laser tweezers, enabling us to measure specific rupture forces needed to separate single receptor-ligand complexes. First of all, we performed a thorough and statistically representative analysis of nonspecific protein-protein binding versus specific αIIbβ3-fibrinogen interactions in combination with experimental evidence for single-molecule measurements. The rupture force distribution of purified αIIbβ3 and fibrinogen, covalently attached to underlying surfaces, ranged from ∼20 to 150 pN. This distribution could be fit with a sum of an exponential curve for weak to moderate (20–60 pN) forces, and a Gaussian curve for strong (>60 pN) rupture forces that peaked at 80–90 pN. The interactions corresponding to these rupture force regimes differed in their susceptibility to αIIbβ3 antagonists or Mn2+, an αIIbβ3 activator. Varying the surface density of fibrinogen changed the total binding probability linearly >3.5-fold but did not affect the shape of the rupture force distribution, indicating that the measurements represent single-molecule binding. The yield strength of αIIbβ3-fibrinogen interactions was independent of the loading rate (160–16,000 pN/s), whereas their binding probability markedly correlated with the duration of contact. The aggregate of data provides evidence for complex multi-step binding/unbinding pathways of αIIbβ3 and fibrinogen revealed at the single-molecule level. PMID:16040750

Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

NASA Astrophysics Data System (ADS)

Massiot, Cécile; Townend, John; Nicol, Andrew; McNamara, David D.

2017-08-01

Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one-dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K-means, fuzzy K-means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high-temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

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

PubMed

Powell, Mark R

2013-06-01

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

Fourier Method for Calculating Fission Chain Neutron Multiplicity Distributions

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

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

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

Fourier Method for Calculating Fission Chain Neutron Multiplicity Distributions

DOE PAGES

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

2017-03-27

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

Teaching Uncertainties

ERIC Educational Resources Information Center

Duerdoth, Ian

2009-01-01

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

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

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

NASA Astrophysics Data System (ADS)

van Lith, Janneke

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

p-adic stochastic hidden variable model

NASA Astrophysics Data System (ADS)

Khrennikov, Andrew

1998-03-01

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

Biodiversity of free-living marine nematodes in the southern Yellow Sea, China

NASA Astrophysics Data System (ADS)

Liu, Xiaoshou; Xu, Man; Hua, Er; Zhang, Zhinan

2016-02-01

Biodiversity patterns of free-living marine nematodes were studied using specific, taxonomic and phylogenetic diversity measures in the southern Yellow Sea, China. The results showed that the average of Shannon-Wiener diversity index ( H') in the study area was 3.17. The higher values were distributed in the east part of Shandong coastal waters and north part of Jiangsu coastal waters, while the lower values were distributed in the southern Yellow Sea Cold Water Mass (YSCWM). The average of taxonomic diversity ( Δ) was 62.09 in the study region. The higher values were distributed in the transitional areas between the coastal areas and the southern YSCWM, while the lower values were distributed near the north part of Jiangsu coastal waters and the YSCWM. Results of correlation analysis of species diversity and taxonomic diversity showed that some of the two kinds of diversity index were independent, which suggested that combining the two kinds of diversity indices can reflect the ecological characteristics better. A test for 95% probability funnels of average taxonomic distinctness and variation in taxonomic distinctness suggested that Station 8794 (in the YSCWM) was outside of the 95% probability funnels, which may be due to the environmental stress. Results of correlation analysis between marine nematodes biodiversity and environmental variables showed that the sediment characteristics (Mdø and Silt-clay fraction) and phaeophorbide a (Pha- a) were the most important factors to determine the biodiversity patterns of marine nematodes.

Stationary properties of maximum-entropy random walks.

PubMed

Dixit, Purushottam D

2015-10-01

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

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.

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.

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.

Application of wildfire simulation methods to assess wildfire exposure in a Mediterranean fire-prone area (Sardinia, Italy)

NASA Astrophysics Data System (ADS)

Salis, M.; Ager, A.; Arca, B.; Finney, M.; Bacciu, V. M.; Spano, D.; Duce, P.

2012-12-01

Spatial and temporal patterns of fire spread and behavior are dependent on interactions among climate, topography, vegetation and fire suppression efforts (Pyne et al. 1996; Viegas 2006; Falk et al. 2007). Humans also play a key role in determining frequency and spatial distribution of ignitions (Bar Massada et al, 2011), and thus influence fire regimes as well. The growing incidence of catastrophic wildfires has led to substantial losses for important ecological and human values within many areas of the Mediterranean basin (Moreno et al. 1998; Mouillot et al. 2005; Viegas et al. 2006a; Riaño et al. 2007). The growing fire risk issue has led to many new programs and policies of fuel management and risk mitigation by environmental and fire agencies. However, risk-based methodologies to help identify areas characterized by high potential losses and prioritize fuel management have been lacking for the region. Formal risk assessment requires the joint consideration of likelihood, intensity, and susceptibility, the product of which estimates the chance of a specific loss (Brillinger 2003; Society of Risk Analysis, 2006). Quantifying fire risk therefore requires estimates of a) the probability of a specific location burning at a specific intensity and location, and b) the resulting change in financial or ecological value (Finney 2005; Scott 2006). When large fires are the primary cause of damage, the application of this risk formulation requires modeling fire spread to capture landscape properties that affect burn probability. Recently, the incorporation of large fire spread into risk assessment systems has become feasible with the development of high performance fire simulation systems (Finney et al. 2011) that permit the simulation of hundreds of thousands of fires to generate fine scale maps of burn probability, flame length, and fire size, while considering the combined effects of weather, fuels, and topography (Finney 2002; Andrews et al. 2007; Ager and Finney 2009; Finney et al. 2009; Salis et al. 2012 accepted). In this work, we employed wildfire simulation methods to quantify wildfire exposure to human and ecological values for the island of Sardinia, Italy. The work was focused on the risk and exposure posed by large fires (e.g. 100 - 10,000 ha), and considers historical weather, ignition patterns and fuels. We simulated 100,000 fires using burn periods that replicated the historical size distribution on the Island, and an ignition probability grid derived from historic ignition data. We then examine spatial variation in three exposure components (burn probability, flame length, fire size) among important human and ecological values. The results allowed us to contract exposure among and within the various features examined, and highlighted the importance of human factors in shaping wildfire exposure in Sardinia. The work represents the first application of burn probability modeling in the Mediterranean region, and sets the stage for expanded work in the region to quantify risk from large fires

AUTOCLASS III - AUTOMATIC CLASS DISCOVERY FROM DATA

NASA Technical Reports Server (NTRS)

Cheeseman, P. C.

1994-01-01

The program AUTOCLASS III, Automatic Class Discovery from Data, uses Bayesian probability theory to provide a simple and extensible approach to problems such as classification and general mixture separation. Its theoretical basis is free from ad hoc quantities, and in particular free of any measures which alter the data to suit the needs of the program. As a result, the elementary classification model used lends itself easily to extensions. The standard approach to classification in much of artificial intelligence and statistical pattern recognition research involves partitioning of the data into separate subsets, known as classes. AUTOCLASS III uses the Bayesian approach in which classes are described by probability distributions over the attributes of the objects, specified by a model function and its parameters. The calculation of the probability of each object's membership in each class provides a more intuitive classification than absolute partitioning techniques. AUTOCLASS III is applicable to most data sets consisting of independent instances, each described by a fixed length vector of attribute values. An attribute value may be a number, one of a set of attribute specific symbols, or omitted. The user specifies a class probability distribution function by associating attribute sets with supplied likelihood function terms. AUTOCLASS then searches in the space of class numbers and parameters for the maximally probable combination. It returns the set of class probability function parameters, and the class membership probabilities for each data instance. AUTOCLASS III is written in Common Lisp, and is designed to be platform independent. This program has been successfully run on Symbolics and Explorer Lisp machines. It has been successfully used with the following implementations of Common LISP on the Sun: Franz Allegro CL, Lucid Common Lisp, and Austin Kyoto Common Lisp and similar UNIX platforms; under the Lucid Common Lisp implementations on VAX/VMS v5.4, VAX/Ultrix v4.1, and MIPS/Ultrix v4, rev. 179; and on the Macintosh personal computer. The minimum Macintosh required is the IIci. This program will not run under CMU Common Lisp or VAX/VMS DEC Common Lisp. A minimum of 8Mb of RAM is required for Macintosh platforms and 16Mb for workstations. The standard distribution medium for this program is a .25 inch streaming magnetic tape cartridge in UNIX tar format. It is also available on a 3.5 inch diskette in UNIX tar format and a 3.5 inch diskette in Macintosh format. An electronic copy of the documentation is included on the distribution medium. AUTOCLASS was developed between March 1988 and March 1992. It was initially released in May 1991. Sun is a trademark of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories. DEC, VAX, VMS, and ULTRIX are trademarks of Digital Equipment Corporation. Macintosh is a trademark of Apple Computer, Inc. Allegro CL is a registered trademark of Franz, Inc.

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

NASA Astrophysics Data System (ADS)

Perline, Richard; Perline, Ron

2016-03-01

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

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

USGS Publications Warehouse

Kirby, W.

1983-01-01

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

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

USGS Publications Warehouse

Kirby, W.H.

1980-01-01

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

Universal laws of human society's income distribution

NASA Astrophysics Data System (ADS)

Tao, Yong

2015-10-01

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

Polynomial chaos representation of databases on manifolds

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

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

2017-04-15

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

Gravitational lensing, time delay, and gamma-ray bursts

NASA Technical Reports Server (NTRS)

Mao, Shude

1992-01-01

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

A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations.

PubMed

Dai, Huanping; Micheyl, Christophe

2015-05-01

Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.

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

PubMed Central

Reed, William J; Hughes, Barry D

2007-01-01

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

Probability distributions of continuous measurement results for conditioned quantum evolution

NASA Astrophysics Data System (ADS)

Franquet, A.; Nazarov, Yuli V.

2017-02-01

We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the latter is achieved by the postselection in the end of the evolution. The statistics may drastically differ from the nonconditioned case, and the interference between initial and final states can be observed in the probability distributions of measurement outcomes as well as in the average values exceeding the conventional range of nonconditioned averages. We develop a proper formalism to compute the distributions of measurement outcomes, and evaluate and discuss the distributions in experimentally relevant setups. We demonstrate the manifestations of the interference between initial and final states in various regimes. We consider analytically simple examples of nontrivial probability distributions. We reveal peaks (or dips) at half-quantized values of the measurement outputs. We discuss in detail the case of zero overlap between initial and final states demonstrating anomalously big average outputs and sudden jump in time-integrated output. We present and discuss the numerical evaluation of the probability distribution aiming at extending the analytical results and describing a realistic experimental situation of a qubit in the regime of resonant fluorescence.

Parasites as biological tags for stock discrimination in marine fish from South American Atlantic waters.

PubMed

Timi, Juan T

2007-06-01

The use of parasites as biological tags in population studies of marine fish in the south-western Atlantic has proved to be a successful tool for discriminating stocks for all species to which it has been applied, namely: Scomber japonicus, Engraulis anchoita, Merluccius hubbsi and Cynoscion guatucupa, the latter studied on a broader geographic scale, including samples from Uruguayan and Brazilian waters. The distribution patterns of marine parasites are determined mainly by temperature-salinity profiles and by their association with specific masses of water. Analyses of distribution patterns of some parasite species in relation to gradients in environmental (oceanographic) conditions showed that latitudinal gradients in parasite distribution are common in the study area, and are probably directly related to water temperature. Indeed, temperature, which is a good predictor of latitudinal gradients of richness and diversity of species, shows a latitudinal pattern in south-western Atlantic coasts, decreasing southwards, due to the influence of subtropical and subantarctic marine currents flowing along the edge of the continental slope. This pattern also determines the distribution of zooplankton, with a characteristic specific composition in different water masses. The gradient in the distribution of parasites determines differential compositions of their communities at different latitudes, which makes possible the identification of different stocks of their fish hosts. Other features of the host-parasite systems contributing to the success of the parasitological method are: (1) parasites identified as good biological tags (i.e. anisakids) are widely distributed in the local fauna; (2) many of these species show low specificity and use paratenic hosts; and (3) the structure of parasite communities are, to a certain degree, predictable in time and space.

A discussion on the origin of quantum probabilities

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

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

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

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

PubMed

Takemura, Kazuhisa; Murakami, Hajime

2016-01-01

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

Hybrid Approaches and Industrial Applications of Pattern Recognition,

DTIC Science & Technology

1980-10-01

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

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

ERIC Educational Resources Information Center

Egghe, Leo; Rousseau, Ronald

1995-01-01

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

The beta distribution: A statistical model for world cloud cover

NASA Technical Reports Server (NTRS)

Falls, L. W.

1973-01-01

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

Macroscopic relationship in primal-dual portfolio optimization problem

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-02-01

In the present paper, using a replica analysis, we examine the portfolio optimization problem handled in previous work and discuss the minimization of investment risk under constraints of budget and expected return for the case that the distribution of the hyperparameters of the mean and variance of the return rate of each asset are not limited to a specific probability family. Findings derived using our proposed method are compared with those in previous work to verify the effectiveness of our proposed method. Further, we derive a Pythagorean theorem of the Sharpe ratio and macroscopic relations of opportunity loss. Using numerical experiments, the effectiveness of our proposed method is demonstrated for a specific situation.

A new approach to estimate time-to-cure from cancer registries data.

PubMed

Boussari, Olayidé; Romain, Gaëlle; Remontet, Laurent; Bossard, Nadine; Mounier, Morgane; Bouvier, Anne-Marie; Binquet, Christine; Colonna, Marc; Jooste, Valérie

2018-04-01

Cure models have been adapted to net survival context to provide important indicators from population-based cancer data, such as the cure fraction and the time-to-cure. However existing methods for computing time-to-cure suffer from some limitations. Cure models in net survival framework were briefly overviewed and a new definition of time-to-cure was introduced as the time TTC at which P(t), the estimated covariate-specific probability of being cured at a given time t after diagnosis, reaches 0.95. We applied flexible parametric cure models to data of four cancer sites provided by the French network of cancer registries (FRANCIM). Then estimates of the time-to-cure by TTC and by two existing methods were derived and compared. Cure fractions and probabilities P(t) were also computed. Depending on the age group, TTC ranged from to 8 to 10 years for colorectal and pancreatic cancer and was nearly 12 years for breast cancer. In thyroid cancer patients under 55 years at diagnosis, TTC was strikingly 0: the probability of being cured was >0.95 just after diagnosis. This is an interesting result regarding the health insurance premiums of these patients. The estimated values of time-to-cure from the three approaches were close for colorectal cancer only. We propose a new approach, based on estimated covariate-specific probability of being cured, to estimate time-to-cure. Compared to two existing methods, the new approach seems to be more intuitive and natural and less sensitive to the survival time distribution. Copyright © 2018 Elsevier Ltd. All rights reserved.

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.

Development and Application of a New Method for Specific and Sensitive Enumeration of Spores of Nonproteolytic Clostridium botulinum Types B, E, and F in Foods and Food Materials ▿

PubMed Central

Peck, Michael W.; Plowman, June; Aldus, Clare F.; Wyatt, Gary M.; Penaloza Izurieta, Walter; Stringer, Sandra C.; Barker, Gary C.

2010-01-01

The highly potent botulinum neurotoxins are responsible for botulism, a severe neuroparalytic disease. Strains of nonproteolytic Clostridium botulinum form neurotoxins of types B, E, and F and are the main hazard associated with minimally heated refrigerated foods. Recent developments in quantitative microbiological risk assessment (QMRA) and food safety objectives (FSO) have made food safety more quantitative and include, as inputs, probability distributions for the contamination of food materials and foods. A new method that combines a selective enrichment culture with multiplex PCR has been developed and validated to enumerate specifically the spores of nonproteolytic C. botulinum. Key features of this new method include the following: (i) it is specific for nonproteolytic C. botulinum (and does not detect proteolytic C. botulinum), (ii) the detection limit has been determined for each food tested (using carefully structured control samples), and (iii) a low detection limit has been achieved by the use of selective enrichment and large test samples. The method has been used to enumerate spores of nonproteolytic C. botulinum in 637 samples of 19 food materials included in pasta-based minimally heated refrigerated foods and in 7 complete foods. A total of 32 samples (5 egg pastas and 27 scallops) contained spores of nonproteolytic C. botulinum type B or F. The majority of samples contained <100 spores/kg, but one sample of scallops contained 444 spores/kg. Nonproteolytic C. botulinum type E was not detected. Importantly, for QMRA and FSO, the construction of probability distributions will enable the frequency of packs containing particular levels of contamination to be determined. PMID:20709854

Development and application of a new method for specific and sensitive enumeration of spores of nonproteolytic Clostridium botulinum types B, E, and F in foods and food materials.

PubMed

Peck, Michael W; Plowman, June; Aldus, Clare F; Wyatt, Gary M; Izurieta, Walter Penaloza; Stringer, Sandra C; Barker, Gary C

2010-10-01

The highly potent botulinum neurotoxins are responsible for botulism, a severe neuroparalytic disease. Strains of nonproteolytic Clostridium botulinum form neurotoxins of types B, E, and F and are the main hazard associated with minimally heated refrigerated foods. Recent developments in quantitative microbiological risk assessment (QMRA) and food safety objectives (FSO) have made food safety more quantitative and include, as inputs, probability distributions for the contamination of food materials and foods. A new method that combines a selective enrichment culture with multiplex PCR has been developed and validated to enumerate specifically the spores of nonproteolytic C. botulinum. Key features of this new method include the following: (i) it is specific for nonproteolytic C. botulinum (and does not detect proteolytic C. botulinum), (ii) the detection limit has been determined for each food tested (using carefully structured control samples), and (iii) a low detection limit has been achieved by the use of selective enrichment and large test samples. The method has been used to enumerate spores of nonproteolytic C. botulinum in 637 samples of 19 food materials included in pasta-based minimally heated refrigerated foods and in 7 complete foods. A total of 32 samples (5 egg pastas and 27 scallops) contained spores of nonproteolytic C. botulinum type B or F. The majority of samples contained <100 spores/kg, but one sample of scallops contained 444 spores/kg. Nonproteolytic C. botulinum type E was not detected. Importantly, for QMRA and FSO, the construction of probability distributions will enable the frequency of packs containing particular levels of contamination to be determined.

Computed Tomography-Based Biomarker for Longitudinal Assessment of Disease Burden in Pulmonary Tuberculosis.

PubMed

Gordaliza, P M; Muñoz-Barrutia, A; Via, L E; Sharpe, S; Desco, M; Vaquero, J J

2018-05-29

Computed tomography (CT) images enable capturing specific manifestations of tuberculosis (TB) that are undetectable using common diagnostic tests, which suffer from limited specificity. In this study, we aimed to automatically quantify the burden of Mycobacterium tuberculosis (Mtb) using biomarkers extracted from x-ray CT images. Nine macaques were aerosol-infected with Mtb and treated with various antibiotic cocktails. Chest CT scans were acquired in all animals at specific times independently of disease progression. First, a fully automatic segmentation of the healthy lungs from the acquired chest CT volumes was performed and air-like structures were extracted. Next, unsegmented pulmonary regions corresponding to damaged parenchymal tissue and TB lesions were included. CT biomarkers were extracted by classification of the probability distribution of the intensity of the segmented images into three tissue types: (1) Healthy tissue, parenchyma free from infection; (2) soft diseased tissue, and (3) hard diseased tissue. The probability distribution of tissue intensities was assumed to follow a Gaussian mixture model. The thresholds identifying each region were automatically computed using an expectation-maximization algorithm. The estimated longitudinal course of TB infection shows that subjects that have followed the same antibiotic treatment present a similar response (relative change in the diseased volume) with respect to baseline. More interestingly, the correlation between the diseased volume (soft tissue + hard tissue), which was manually delineated by an expert, and the automatically extracted volume with the proposed method was very strong (R 2  ≈ 0.8). We present a methodology that is suitable for automatic extraction of a radiological biomarker from CT images for TB disease burden. The method could be used to describe the longitudinal evolution of Mtb infection in a clinical trial devoted to the design of new drugs.

Quantum work in the Bohmian framework

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Glomerular epithelial foot processes in normal man and rats. Distribution of true width and its intra- and inter-individual variation.

PubMed

Gundersen, H J; Seefeldt, T; Osterby, R

1980-01-01

The width of individual glomerular epithelial foot processes appears very different on electron micrographs. A method for obtainining distributions of the true width of foot processes from that of their apparent width on electron micrographs has been developed based on geometric probability theory pertaining to a specific geometric model. Analyses of foot process width in humans and rats show a remarkable interindividual invariance implying rigid control and therefore great biological significance of foot process width or a derivative thereof. The very low inter-individual variation of the true width, shown in the present paper, makes it possible to demonstrate slight changes in rather small groups of patients or experimental animals.

Statistical Characterization and Classification of Edge-Localized Plasma Instabilities

NASA Astrophysics Data System (ADS)

Webster, A. J.; Dendy, R. O.

2013-04-01

The statistics of edge-localized plasma instabilities (ELMs) in toroidal magnetically confined fusion plasmas are considered. From first principles, standard experimentally motivated assumptions are shown to determine a specific probability distribution for the waiting times between ELMs: the Weibull distribution. This is confirmed empirically by a statistically rigorous comparison with a large data set from the Joint European Torus. The successful characterization of ELM waiting times enables future work to progress in various ways. Here we present a quantitative classification of ELM types, complementary to phenomenological approaches. It also informs us about the nature of ELM processes, such as whether they are random or deterministic. The methods are extremely general and can be applied to numerous other quasiperiodic intermittent phenomena.

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.

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

NASA Technical Reports Server (NTRS)

Vitali, Roberto; Lutomski, Michael G.

2004-01-01

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

Assessment of fragment projection hazard: probability distributions for the initial direction of fragments.

PubMed

Tugnoli, Alessandro; Gubinelli, Gianfilippo; Landucci, Gabriele; Cozzani, Valerio

2014-08-30

The evaluation of the initial direction and velocity of the fragments generated in the fragmentation of a vessel due to internal pressure is an important information in the assessment of damage caused by fragments, in particular within the quantitative risk assessment (QRA) of chemical and process plants. In the present study an approach is proposed to the identification and validation of probability density functions (pdfs) for the initial direction of the fragments. A detailed review of a large number of past accidents provided the background information for the validation procedure. A specific method was developed for the validation of the proposed pdfs. Validated pdfs were obtained for both the vertical and horizontal angles of projection and for the initial velocity of the fragments. Copyright © 2014 Elsevier B.V. All rights reserved.

Revision to flood hazard evaluation for the Savannah River Site

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

Buckley, R.; Werth, D.

Requirements for the Natural Phenomena Hazard (NPH) mitigation for new and existing Department of Energy (DOE) facilities are outlined in DOE Order 420.1. This report examines the hazards posed by potential flooding and represents an update to two previous reports. The facility-specific probabilistic flood hazard curve is defined as the water elevation for each annual probability of precipitation occurrence (or inversely, the return period in years). New design hyetographs for both 6-hr and 24-hr precipitation distributions were used in conjunction with hydrological models of various basins within the Savannah River Site (SRS). For numerous locations of interest, peak flow dischargemore » and flood water elevation were determined. In all cases, the probability of flooding of these facilities for a 100,000 year precipitation event is negligible.« less

The Spiral of Life

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

PubMed

Schmidt, Benedikt R

2003-08-01

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

Bayesian data analysis tools for atomic physics

NASA Astrophysics Data System (ADS)

Trassinelli, Martino

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Altering spatial priority maps via statistical learning of target selection and distractor filtering.

PubMed

Ferrante, Oscar; Patacca, Alessia; Di Caro, Valeria; Della Libera, Chiara; Santandrea, Elisa; Chelazzi, Leonardo

2018-05-01

The cognitive system has the capacity to learn and make use of environmental regularities - known as statistical learning (SL), including for the implicit guidance of attention. For instance, it is known that attentional selection is biased according to the spatial probability of targets; similarly, changes in distractor filtering can be triggered by the unequal spatial distribution of distractors. Open questions remain regarding the cognitive/neuronal mechanisms underlying SL of target selection and distractor filtering. Crucially, it is unclear whether the two processes rely on shared neuronal machinery, with unavoidable cross-talk, or they are fully independent, an issue that we directly addressed here. In a series of visual search experiments, participants had to discriminate a target stimulus, while ignoring a task-irrelevant salient distractor (when present). We systematically manipulated spatial probabilities of either one or the other stimulus, or both. We then measured performance to evaluate the direct effects of the applied contingent probability distribution (e.g., effects on target selection of the spatial imbalance in target occurrence across locations) as well as its indirect or "transfer" effects (e.g., effects of the same spatial imbalance on distractor filtering across locations). By this approach, we confirmed that SL of both target and distractor location implicitly bias attention. Most importantly, we described substantial indirect effects, with the unequal spatial probability of the target affecting filtering efficiency and, vice versa, the unequal spatial probability of the distractor affecting target selection efficiency across locations. The observed cross-talk demonstrates that SL of target selection and distractor filtering are instantiated via (at least partly) shared neuronal machinery, as further corroborated by strong correlations between direct and indirect effects at the level of individual participants. Our findings are compatible with the notion that both kinds of SL adjust the priority of specific locations within attentional priority maps of space. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Characterising RNA secondary structure space using information entropy

PubMed Central

2013-01-01

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

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

PubMed

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

2003-01-01

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

Probability of lek collapse is lower inside sage-grouse Core Areas: Effectiveness of conservation policy for a landscape species.

PubMed

Spence, Emma Suzuki; Beck, Jeffrey L; Gregory, Andrew J

2017-01-01

Greater sage-grouse (Centrocercus urophasianus) occupy sagebrush (Artemisia spp.) habitats in 11 western states and 2 Canadian provinces. In September 2015, the U.S. Fish and Wildlife Service announced the listing status for sage-grouse had changed from warranted but precluded to not warranted. The primary reason cited for this change of status was that the enactment of new regulatory mechanisms was sufficient to protect sage-grouse populations. One such plan is the 2008, Wyoming Sage Grouse Executive Order (SGEO), enacted by Governor Freudenthal. The SGEO identifies "Core Areas" that are to be protected by keeping them relatively free from further energy development and limiting other forms of anthropogenic disturbances near active sage-grouse leks. Using the Wyoming Game and Fish Department's sage-grouse lek count database and the Wyoming Oil and Gas Conservation Commission database of oil and gas well locations, we investigated the effectiveness of Wyoming's Core Areas, specifically: 1) how well Core Areas encompass the distribution of sage-grouse in Wyoming, 2) whether Core Area leks have a reduced probability of lek collapse, and 3) what, if any, edge effects intensification of oil and gas development adjacent to Core Areas may be having on Core Area populations. Core Areas contained 77% of male sage-grouse attending leks and 64% of active leks. Using Bayesian binomial probability analysis, we found an average 10.9% probability of lek collapse in Core Areas and an average 20.4% probability of lek collapse outside Core Areas. Using linear regression, we found development density outside Core Areas was related to the probability of lek collapse inside Core Areas. Specifically, probability of collapse among leks >4.83 km from inside Core Area boundaries was significantly related to well density within 1.61 km (1-mi) and 4.83 km (3-mi) outside of Core Area boundaries. Collectively, these data suggest that the Wyoming Core Area Strategy has benefited sage-grouse and sage-grouse habitat conservation; however, additional guidelines limiting development densities adjacent to Core Areas may be necessary to effectively protect Core Area populations.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Note on Two-Phase Phenomena in Financial Markets

NASA Astrophysics Data System (ADS)

Jiang, Shi-Mei; Cai, Shi-Min; Zhou, Tao; Zhou, Pei-Ling

2008-06-01

The two-phase behaviour in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. We investigate the bifurcation phenomenon in Hang-Seng index. It is observed that the bifurcation phenomenon in financial index is not universal, but specific under certain conditions. For Hang-Seng index and randomly generated time series, the phenomenon just emerges when the power-law exponent of absolute increment distribution is between 1 and 2 with appropriate period. Simulations on a randomly generated time series suggest the bifurcation phenomenon itself is subject to the statistics of absolute increment, thus it may not be able to reflect essential financial behaviours. However, even under the same distribution of absolute increment, the range where bifurcation phenomenon occurs is far different from real market to artificial data, which may reflect certain market information.

A model independent search for new physics in final states containing leptons at the DO experiment

NASA Astrophysics Data System (ADS)

Piper, Joel M.

The standard model is known to be the low energy limit of a more general theory. Several consequences of the standard model point to a strong probability of new physics becoming experimentally visible in high energy collisions of a few TeV, resulting in high momentum objects. The specific signatures of these collisions are topics of much debate. Rather than choosing a specific signature, this analysis broadly searches the data, preferring breadth over sensitivity. In searching for new physics, several different approaches are used. These include the comparison of data with standard model background expectation in overall number of events, comparisons of distributions of many kinematic variables, and finally comparisons on the tails of distributions that sum the momenta of the objects in an event. With 1.07 fb-1 at the DO experiment, we find no evidence of physics beyond the standard model. Several discrepancies from the standard model were found, but none of these provide a compelling case for new physics.

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.

Root anatomy and element distribution vary between two Salix caprea isolates with different Cd accumulation capacities

PubMed Central

Vaculík, Marek; Konlechner, Cornelia; Langer, Ingrid; Adlassnig, Wolfram; Puschenreiter, Markus; Lux, Alexander; Hauser, Marie-Theres

2012-01-01

The understanding of the influence of toxic elements on root anatomy and element distribution is still limited. This study describes anatomical responses, metal accumulation and element distribution of rooted cuttings of Salix caprea after exposure to Cd and/or Zn. Differences in the development of apoplastic barriers and tissue organization in roots between two distinct S. caprea isolates with divergent Cd uptake and accumulation capacities in leaves might reflect an adaptive predisposition based on different natural origins. Energy-dispersive X-ray spectroscopy (EDX) revealed that Cd and Zn interfered with the distribution of elements in a tissue- and isolate-specific manner. Zinc, Ca, Mg, Na and Si were enriched in the peripheral bark, K and S in the phloem and Cd in both vascular tissues. Si levels were lower in the superior Cd translocator. Since the cuttings originated from stocks isolated from polluted and unpolluted sites we probably uncovered different strategies against toxic elements. PMID:22325439

Delayed fission and multifragmentation in sub-keV C60 - Au(0 0 1) collisions via molecular dynamics simulations: Mass distributions and activated statistical decay

NASA Astrophysics Data System (ADS)

Bernstein, V.; Kolodney, E.

2017-10-01

We have recently observed, both experimentally and computationally, the phenomenon of postcollision multifragmentation in sub-keV surface collisions of a C60 projectile. Namely, delayed multiparticle breakup of a strongly impact deformed and vibrationally excited large cluster collider into several large fragments, after leaving the surface. Molecular dynamics simulations with extensive statistics revealed a nearly simultaneous event, within a sub-psec time window. Here we study, computationally, additional essential aspects of this new delayed collisional fragmentation which were not addressed before. Specifically, we study here the delayed (binary) fission channel for different impact energies both by calculating mass distributions over all fission events and by calculating and analyzing lifetime distributions of the scattered projectile. We observe an asymmetric fission resulting in a most probable fission channel and we find an activated exponential (statistical) decay. Finally, we also calculate and discuss the fragment mass distribution in (triple) multifragmentation over different time windows, in terms of most abundant fragments.

Mapping risk of plague in Qinghai-Tibetan Plateau, China.

PubMed

Qian, Quan; Zhao, Jian; Fang, Liqun; Zhou, Hang; Zhang, Wenyi; Wei, Lan; Yang, Hong; Yin, Wenwu; Cao, Wuchun; Li, Qun

2014-07-10

Qinghai-Tibetan Plateau of China is known to be the plague endemic region where marmot (Marmota himalayana) is the primary host. Human plague cases are relatively low incidence but high mortality, which presents unique surveillance and public health challenges, because early detection through surveillance may not always be feasible and infrequent clinical cases may be misdiagnosed. Based on plague surveillance data and environmental variables, Maxent was applied to model the presence probability of plague host. 75% occurrence points were randomly selected for training model, and the rest 25% points were used for model test and validation. Maxent model performance was measured as test gain and test AUC. The optimal probability cut-off value was chosen by maximizing training sensitivity and specificity simultaneously. We used field surveillance data in an ecological niche modeling (ENM) framework to depict spatial distribution of natural foci of plague in Qinghai-Tibetan Plateau. Most human-inhabited areas at risk of exposure to enzootic plague are distributed in the east and south of the Plateau. Elevation, temperature of land surface and normalized difference vegetation index play a large part in determining the distribution of the enzootic plague. This study provided a more detailed view of spatial pattern of enzootic plague and human-inhabited areas at risk of plague. The maps could help public health authorities decide where to perform plague surveillance and take preventive measures in Qinghai-Tibetan Plateau.

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.

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

PubMed

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

2010-11-01

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

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

PubMed

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

2016-10-01

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

The Detection of Signals in Impulsive Noise.

DTIC Science & Technology

1983-06-01

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

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

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

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

Nondeterministic data base for computerized visual perception

NASA Technical Reports Server (NTRS)

Yakimovsky, Y.

1976-01-01

A description is given of the knowledge representation data base in the perception subsystem of the Mars robot vehicle prototype. Two types of information are stored. The first is generic information that represents general rules that are conformed to by structures in the expected environments. The second kind of information is a specific description of a structure, i.e., the properties and relations of objects in the specific case being analyzed. The generic knowledge is represented so that it can be applied to extract and infer the description of specific structures. The generic model of the rules is substantially a Bayesian representation of the statistics of the environment, which means it is geared to representation of nondeterministic rules relating properties of, and relations between, objects. The description of a specific structure is also nondeterministic in the sense that all properties and relations may take a range of values with an associated probability distribution.

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

NASA Astrophysics Data System (ADS)

Salama, Paul

2008-02-01

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

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

NASA Astrophysics Data System (ADS)

Hannay, J. H.

2018-04-01

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

A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

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

On Orbital Elements of Extrasolar Planetary Candidates and Spectroscopic Binaries

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

Steady-state distributions of probability fluxes on complex networks

NASA Astrophysics Data System (ADS)

Chełminiak, Przemysław; Kurzyński, Michał

2017-02-01

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

Time-dependent landslide probability mapping

USGS Publications Warehouse

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

1993-01-01

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

Generalized Wishart Mixtures for Unsupervised Classification of PolSAR Data

NASA Astrophysics Data System (ADS)

Li, Lan; Chen, Erxue; Li, Zengyuan

2013-01-01

This paper presents an unsupervised clustering algorithm based upon the expectation maximization (EM) algorithm for finite mixture modelling, using the complex wishart probability density function (PDF) for the probabilities. The mixture model enables to consider heterogeneous thematic classes which could not be better fitted by the unimodal wishart distribution. In order to make it fast and robust to calculate, we use the recently proposed generalized gamma distribution (GΓD) for the single polarization intensity data to make the initial partition. Then we use the wishart probability density function for the corresponding sample covariance matrix to calculate the posterior class probabilities for each pixel. The posterior class probabilities are used for the prior probability estimates of each class and weights for all class parameter updates. The proposed method is evaluated and compared with the wishart H-Alpha-A classification. Preliminary results show that the proposed method has better performance.

Oil spill contamination probability in the southeastern Levantine basin.

PubMed

Goldman, Ron; Biton, Eli; Brokovich, Eran; Kark, Salit; Levin, Noam

2015-02-15

Recent gas discoveries in the eastern Mediterranean Sea led to multiple operations with substantial economic interest, and with them there is a risk of oil spills and their potential environmental impacts. To examine the potential spatial distribution of this threat, we created seasonal maps of the probability of oil spill pollution reaching an area in the Israeli coastal and exclusive economic zones, given knowledge of its initial sources. We performed simulations of virtual oil spills using realistic atmospheric and oceanic conditions. The resulting maps show dominance of the alongshore northerly current, which causes the high probability areas to be stretched parallel to the coast, increasing contamination probability downstream of source points. The seasonal westerly wind forcing determines how wide the high probability areas are, and may also restrict these to a small coastal region near source points. Seasonal variability in probability distribution, oil state, and pollution time is also discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Estimating the empirical probability of submarine landslide occurrence

USGS Publications Warehouse

Geist, Eric L.; Parsons, Thomas E.; Mosher, David C.; Shipp, Craig; Moscardelli, Lorena; Chaytor, Jason D.; Baxter, Christopher D. P.; Lee, Homa J.; Urgeles, Roger

2010-01-01

The empirical probability for the occurrence of submarine landslides at a given location can be estimated from age dates of past landslides. In this study, tools developed to estimate earthquake probability from paleoseismic horizons are adapted to estimate submarine landslide probability. In both types of estimates, one has to account for the uncertainty associated with age-dating individual events as well as the open time intervals before and after the observed sequence of landslides. For observed sequences of submarine landslides, we typically only have the age date of the youngest event and possibly of a seismic horizon that lies below the oldest event in a landslide sequence. We use an empirical Bayes analysis based on the Poisson-Gamma conjugate prior model specifically applied to the landslide probability problem. This model assumes that landslide events as imaged in geophysical data are independent and occur in time according to a Poisson distribution characterized by a rate parameter λ. With this method, we are able to estimate the most likely value of λ and, importantly, the range of uncertainty in this estimate. Examples considered include landslide sequences observed in the Santa Barbara Channel, California, and in Port Valdez, Alaska. We confirm that given the uncertainties of age dating that landslide complexes can be treated as single events by performing statistical test of age dates representing the main failure episode of the Holocene Storegga landslide complex.

Disturbance frequency and vertical distribution of seeds affect long-term population dynamics: a mechanistic seed bank model.

PubMed

Eager, Eric Alan; Haridas, Chirakkal V; Pilson, Diana; Rebarber, Richard; Tenhumberg, Brigitte

2013-08-01

Seed banks are critically important for disturbance specialist plants because seeds of these species germinate only in disturbed soil. Disturbance and seed depth affect the survival and germination probability of seeds in the seed bank, which in turn affect population dynamics. We develop a density-dependent stochastic integral projection model to evaluate the effect of stochastic soil disturbances on plant population dynamics with an emphasis on mimicking how disturbances vertically redistribute seeds within the seed bank. We perform a simulation analysis of the effect of the frequency and mean depth of disturbances on the population's quasi-extinction probability, as well as the long-term mean and variance of the total density of seeds in the seed bank. We show that increasing the frequency of disturbances increases the long-term viability of the population, but the relationship between the mean depth of disturbance and the long-term viability of the population are not necessarily monotonic for all parameter combinations. Specifically, an increase in the probability of disturbance increases the long-term viability of the total seed bank population. However, if the probability of disturbance is too low, a shallower mean depth of disturbance can increase long-term viability, a relationship that switches as the probability of disturbance increases. However, a shallow disturbance depth is beneficial only in scenarios with low survival in the seed bank.

Probability density function of non-reactive solute concentration in heterogeneous porous formations.

PubMed

Bellin, Alberto; Tonina, Daniele

2007-10-30

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.

A Performance Comparison on the Probability Plot Correlation Coefficient Test using Several Plotting Positions for GEV Distribution.

NASA Astrophysics Data System (ADS)

Ahn, Hyunjun; Jung, Younghun; Om, Ju-Seong; Heo, Jun-Haeng

2014-05-01

It is very important to select the probability distribution in Statistical hydrology. Goodness of fit test is a statistical method that selects an appropriate probability model for a given data. The probability plot correlation coefficient (PPCC) test as one of the goodness of fit tests was originally developed for normal distribution. Since then, this test has been widely applied to other probability models. The PPCC test is known as one of the best goodness of fit test because it shows higher rejection powers among them. In this study, we focus on the PPCC tests for the GEV distribution which is widely used in the world. For the GEV model, several plotting position formulas are suggested. However, the PPCC statistics are derived only for the plotting position formulas (Goel and De, In-na and Nguyen, and Kim et al.) in which the skewness coefficient (or shape parameter) are included. And then the regression equations are derived as a function of the shape parameter and sample size for a given significance level. In addition, the rejection powers of these formulas are compared using Monte-Carlo simulation. Keywords: Goodness-of-fit test, Probability plot correlation coefficient test, Plotting position, Monte-Carlo Simulation ACKNOWLEDGEMENTS This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-12-NH-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

Group elicitations yield more consistent, yet more uncertain experts in understanding risks to ecosystem services in New Zealand bays

PubMed Central

Sinner, Jim; Ellis, Joanne; Kandlikar, Milind; Halpern, Benjamin S.; Satterfield, Terre; Chan, Kai

2017-01-01

The elicitation of expert judgment is an important tool for assessment of risks and impacts in environmental management contexts, and especially important as decision-makers face novel challenges where prior empirical research is lacking or insufficient. Evidence-driven elicitation approaches typically involve techniques to derive more accurate probability distributions under fairly specific contexts. Experts are, however, prone to overconfidence in their judgements. Group elicitations with diverse experts can reduce expert overconfidence by allowing cross-examination and reassessment of prior judgements, but groups are also prone to uncritical “groupthink” errors. When the problem context is underspecified the probability that experts commit groupthink errors may increase. This study addresses how structured workshops affect expert variability among and certainty within responses in a New Zealand case study. We find that experts’ risk estimates before and after a workshop differ, and that group elicitations provided greater consistency of estimates, yet also greater uncertainty among experts, when addressing prominent impacts to four different ecosystem services in coastal New Zealand. After group workshops, experts provided more consistent ranking of risks and more consistent best estimates of impact through increased clarity in terminology and dampening of extreme positions, yet probability distributions for impacts widened. The results from this case study suggest that group elicitations have favorable consequences for the quality and uncertainty of risk judgments within and across experts, making group elicitation techniques invaluable tools in contexts of limited data. PMID:28767694

Quantum Walks on the Line with Phase Parameters

NASA Astrophysics Data System (ADS)

Villagra, Marcos; Nakanishi, Masaki; Yamashita, Shigeru; Nakashima, Yasuhiko

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step toward this objective, the following question is being addressed: Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps? This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin operator (Hadamard operator) for walks on the line. Even considering only walks on lines, generalizing these computations to a general SU(2) coin operator is a complex task. The main contribution is a closed-form formula for the amplitudes of the state of the walk (which includes the question above) for a general symmetric SU(2) operator for walks on the line. To this end, a coin operator with parameters that alters the phase of the state of the walk is defined. Then, closed-form solutions are computed by means of Fourier analysis and asymptotic approximation methods. We also present some basic properties of the walk which can be deducted using weak convergence theorems for quantum walks. In particular, the support of the induced probability distribution of the walk is calculated. Then, it is shown how changing the parameters in the coin operator affects the resulting probability distribution.

When Violence Pays: A Cost-Benefit Analysis of Aggressive Behavior in Animals and Humans

PubMed Central

Georgiev, Alexander V.; Klimczuk, Amanda C. E.; Traficonte, Daniel M.

2013-01-01

An optimization analysis of human behavior from a comparative perspective can improve our understanding of the adaptiveness of human nature. Intra-specific competition for resources provides the main selective pressure for the evolution of violent aggression toward conspecifics, and variation in the fitness benefits and costs of aggression can account for inter-specific and inter-individual differences in aggressiveness. When aggression reflects competition for resources, its benefits vary in relation to the characteristics of the resources (their intrinsic value, abundance, spatial distribution, and controllability) while its costs vary in relation to the characteristics of organisms and how they fight (which, in turn, affects the extent to which aggression entails risk of physical injury or death, energetic depletion, exposure to predation, psychological and physiological stress, or damage to social relationships). Humans are a highly aggressive species in comparison to other animals, probably as a result of an unusually high benefit-to-cost ratio for intra-specific aggression. This conclusion is supported by frequent and widespread occurrence of male-male coalitionary killing and by male-female sexual coercion. Sex differences in violent aggression in humans and other species probably evolved by sexual selection and reflect different optimal competitive strategies for males and females. PMID:23864299

An avoidance behavior model for migrating whale populations

NASA Astrophysics Data System (ADS)

Buck, John R.; Tyack, Peter L.

2003-04-01

A new model is presented for the avoidance behavior of migrating marine mammals in the presence of a noise stimulus. This model assumes that each whale will adjust its movement pattern near a sound source to maintain its exposure below its own individually specific maximum received sound-pressure level, called its avoidance threshold. The probability distribution function (PDF) of this avoidance threshold across individuals characterizes the migrating population. The avoidance threshold PDF may be estimated by comparing the distribution of migrating whales during playback and control conditions at their closest point of approach to the sound source. The proposed model was applied to the January 1998 experiment which placed a single acoustic source from the U.S. Navy SURTASS-LFA system in the migration corridor of grey whales off the California coast. This analysis found that the median avoidance threshold for this migrating grey whale population was 135 dB, with 90% confidence that the median threshold was within +/-3 dB of this value. This value is less than the 141 dB value for 50% avoidance obtained when the 1984 ``Probability of Avoidance'' model of Malme et al.'s was applied to the same data. [Work supported by ONR.

Stochastic Analysis of Orbital Lifetimes of Spacecraft

NASA Technical Reports Server (NTRS)

Sasamoto, Washito; Goodliff, Kandyce; Cornelius, David

2008-01-01

A document discusses (1) a Monte-Carlo-based methodology for probabilistic prediction and analysis of orbital lifetimes of spacecraft and (2) Orbital Lifetime Monte Carlo (OLMC)--a Fortran computer program, consisting of a previously developed long-term orbit-propagator integrated with a Monte Carlo engine. OLMC enables modeling of variances of key physical parameters that affect orbital lifetimes through the use of probability distributions. These parameters include altitude, speed, and flight-path angle at insertion into orbit; solar flux; and launch delays. The products of OLMC are predicted lifetimes (durations above specified minimum altitudes) for the number of user-specified cases. Histograms generated from such predictions can be used to determine the probabilities that spacecraft will satisfy lifetime requirements. The document discusses uncertainties that affect modeling of orbital lifetimes. Issues of repeatability, smoothness of distributions, and code run time are considered for the purpose of establishing values of code-specific parameters and number of Monte Carlo runs. Results from test cases are interpreted as demonstrating that solar-flux predictions are primary sources of variations in predicted lifetimes. Therefore, it is concluded, multiple sets of predictions should be utilized to fully characterize the lifetime range of a spacecraft.

From image captioning to video summary using deep recurrent networks and unsupervised segmentation

NASA Astrophysics Data System (ADS)

Morosanu, Bogdan-Andrei; Lemnaru, Camelia

2018-04-01

Automatic captioning systems based on recurrent neural networks have been tremendously successful at providing realistic natural language captions for complex and varied image data. We explore methods for adapting existing models trained on large image caption data sets to a similar problem, that of summarising videos using natural language descriptions and frame selection. These architectures create internal high level representations of the input image that can be used to define probability distributions and distance metrics on these distributions. Specifically, we interpret each hidden unit inside a layer of the caption model as representing the un-normalised log probability of some unknown image feature of interest for the caption generation process. We can then apply well understood statistical divergence measures to express the difference between images and create an unsupervised segmentation of video frames, classifying consecutive images of low divergence as belonging to the same context, and those of high divergence as belonging to different contexts. To provide a final summary of the video, we provide a group of selected frames and a text description accompanying them, allowing a user to perform a quick exploration of large unlabeled video databases.

On Applying the Prognostic Performance Metrics

NASA Technical Reports Server (NTRS)

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

2009-01-01

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

How likely are constituent quanta to initiate inflation?

DOE PAGES

Berezhiani, Lasha; Trodden, Mark

2015-08-06

In this study, we propose an intuitive framework for studying the problem of initial conditions in slow-roll inflation. In particular, we consider a universe at high, but sub-Planckian energy density and analyze the circumstances under which it is plausible for it to become dominated by inflated patches at late times, without appealing to the idea of self-reproduction. Our approach is based on defining a prior probability distribution for the constituent quanta of the pre-inflationary universe. To test the idea that inflation can begin under very generic circumstances, we make specific – yet quite general and well grounded – assumptions onmore » the prior distribution. As a result, we are led to the conclusion that the probability for a given region to ignite inflation at sub-Planckian densities is extremely small. Furthermore, if one chooses to use the enormous volume factor that inflation yields as an appropriate measure, we find that the regions of the universe which started inflating at densities below the self-reproductive threshold nevertheless occupy a negligible physical volume in the present universe as compared to those domains that have never inflated.« less

Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

PubMed Central

Legenstein, Robert; Maass, Wolfgang

2014-01-01

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information. PMID:25340749

Estimating individual benefits of medical or behavioral treatments in severely ill patients.

PubMed

Diaz, Francisco J

2017-01-01

There is a need for statistical methods appropriate for the analysis of clinical trials from a personalized-medicine viewpoint as opposed to the common statistical practice that simply examines average treatment effects. This article proposes an approach to quantifying, reporting and analyzing individual benefits of medical or behavioral treatments to severely ill patients with chronic conditions, using data from clinical trials. The approach is a new development of a published framework for measuring the severity of a chronic disease and the benefits treatments provide to individuals, which utilizes regression models with random coefficients. Here, a patient is considered to be severely ill if the patient's basal severity is close to one. This allows the derivation of a very flexible family of probability distributions of individual benefits that depend on treatment duration and the covariates included in the regression model. Our approach may enrich the statistical analysis of clinical trials of severely ill patients because it allows investigating the probability distribution of individual benefits in the patient population and the variables that influence it, and we can also measure the benefits achieved in specific patients including new patients. We illustrate our approach using data from a clinical trial of the anti-depressant imipramine.

Effect of Patient Set-up and Respiration motion on Defining Biological Targets for Image-Guided Targeted Radiotherapy

NASA Astrophysics Data System (ADS)

McCall, Keisha C.

Identification and monitoring of sub-tumor targets will be a critical step for optimal design and evaluation of cancer therapies in general and biologically targeted radiotherapy (dose-painting) in particular. Quantitative PET imaging may be an important tool for these applications. Currently radiotherapy planning accounts for tumor motion by applying geometric margins. These margins create a motion envelope to encompass the most probable positions of the tumor, while also maintaining the appropriate tumor control and normal tissue complication probabilities. This motion envelope is effective for uniform dose prescriptions where the therapeutic dose is conformed to the external margins of the tumor. However, much research is needed to establish the equivalent margins for non-uniform fields, where multiple biological targets are present and each target is prescribed its own dose level. Additionally, the size of the biological targets and close proximity make it impractical to apply planning margins on the sub-tumor level. Also, the extent of high dose regions must be limited to avoid excessive dose to the surrounding tissue. As such, this research project is an investigation of the uncertainty within quantitative PET images of moving and displaced dose-painting targets, and an investigation of the residual errors that remain after motion management. This included characterization of the changes in PET voxel-values as objects are moved relative to the discrete sampling interval of PET imaging systems (SPECIFIC AIM 1). Additionally, the repeatability of PET distributions and the delineating dose-painting targets were measured (SPECIFIC AIM 2). The effect of imaging uncertainty on the dose distributions designed using these images (SPECIFIC AIM 3) has also been investigated. This project also included analysis of methods to minimize motion during PET imaging and reduce the dosimetric impact of motion/position-induced imaging uncertainty (SPECIFIC AIM 4).

Classic maximum entropy recovery of the average joint distribution of apparent FRET efficiency and fluorescence photons for single-molecule burst measurements.

PubMed

DeVore, Matthew S; Gull, Stephen F; Johnson, Carey K

2012-04-05

We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions.

Improved first-order uncertainty method for water-quality modeling

USGS Publications Warehouse

Melching, C.S.; Anmangandla, S.

1992-01-01

Uncertainties are unavoidable in water-quality modeling and subsequent management decisions. Monte Carlo simulation and first-order uncertainty analysis (involving linearization at central values of the uncertain variables) have been frequently used to estimate probability distributions for water-quality model output due to their simplicity. Each method has its drawbacks: Monte Carlo simulation's is mainly computational time; and first-order analysis are mainly questions of accuracy and representativeness, especially for nonlinear systems and extreme conditions. An improved (advanced) first-order method is presented, where the linearization point varies to match the output level whose exceedance probability is sought. The advanced first-order method is tested on the Streeter-Phelps equation to estimate the probability distribution of critical dissolved-oxygen deficit and critical dissolved oxygen using two hypothetical examples from the literature. The advanced first-order method provides a close approximation of the exceedance probability for the Streeter-Phelps model output estimated by Monte Carlo simulation using less computer time - by two orders of magnitude - regardless of the probability distributions assumed for the uncertain model parameters.

Measures for a multidimensional multiverse

NASA Astrophysics Data System (ADS)

Chung, Hyeyoun

2015-04-01

We explore the phenomenological implications of generalizing the causal patch and fat geodesic measures to a multidimensional multiverse, where the vacua can have differing numbers of large dimensions. We consider a simple model in which the vacua are nucleated from a D -dimensional parent spacetime through dynamical compactification of the extra dimensions, and compute the geometric contribution to the probability distribution of observations within the multiverse for each measure. We then study how the shape of this probability distribution depends on the time scales for the existence of observers, for vacuum domination, and for curvature domination (tobs,tΛ , and tc, respectively.) In this work we restrict ourselves to bubbles with positive cosmological constant, Λ . We find that in the case of the causal patch cutoff, when the bubble universes have p +1 large spatial dimensions with p ≥2 , the shape of the probability distribution is such that we obtain the coincidence of time scales tobs˜tΛ˜tc . Moreover, the size of the cosmological constant is related to the size of the landscape. However, the exact shape of the probability distribution is different in the case p =2 , compared to p ≥3 . In the case of the fat geodesic measure, the result is even more robust: the shape of the probability distribution is the same for all p ≥2 , and we once again obtain the coincidence tobs˜tΛ˜tc . These results require only very mild conditions on the prior probability of the distribution of vacua in the landscape. Our work shows that the observed double coincidence of time scales is a robust prediction even when the multiverse is generalized to be multidimensional; that this coincidence is not a consequence of our particular Universe being (3 +1 )-dimensional; and that this observable cannot be used to preferentially select one measure over another in a multidimensional multiverse.

Use of attribute association error probability estimates to evaluate quality of medical record geocodes.

PubMed

Klaus, Christian A; Carrasco, Luis E; Goldberg, Daniel W; Henry, Kevin A; Sherman, Recinda L

2015-09-15

The utility of patient attributes associated with the spatiotemporal analysis of medical records lies not just in their values but also the strength of association between them. Estimating the extent to which a hierarchy of conditional probability exists between patient attribute associations such as patient identifying fields, patient and date of diagnosis, and patient and address at diagnosis is fundamental to estimating the strength of association between patient and geocode, and patient and enumeration area. We propose a hierarchy for the attribute associations within medical records that enable spatiotemporal relationships. We also present a set of metrics that store attribute association error probability (AAEP), to estimate error probability for all attribute associations upon which certainty in a patient geocode depends. A series of experiments were undertaken to understand how error estimation could be operationalized within health data and what levels of AAEP in real data reveal themselves using these methods. Specifically, the goals of this evaluation were to (1) assess if the concept of our error assessment techniques could be implemented by a population-based cancer registry; (2) apply the techniques to real data from a large health data agency and characterize the observed levels of AAEP; and (3) demonstrate how detected AAEP might impact spatiotemporal health research. We present an evaluation of AAEP metrics generated for cancer cases in a North Carolina county. We show examples of how we estimated AAEP for selected attribute associations and circumstances. We demonstrate the distribution of AAEP in our case sample across attribute associations, and demonstrate ways in which disease registry specific operations influence the prevalence of AAEP estimates for specific attribute associations. The effort to detect and store estimates of AAEP is worthwhile because of the increase in confidence fostered by the attribute association level approach to the assessment of uncertainty in patient geocodes, relative to existing geocoding related uncertainty metrics.

Shape of growth-rate distribution determines the type of Non-Gibrat’s Property

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki

2011-11-01

In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and business growth trends. Here, profits denote net profits. First, detailed balance is observed not only in profits data but also in sales data. Furthermore, the growth-rate distribution of sales has wider tails than the linear growth-rate distribution of profits in log-log scale. On the one hand, in the mid-scale range of profits, the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases. This is called Non-Gibrat’s First Property. On the other hand, in the mid-scale range of sales, the probability of positive growth decreases as the initial value increases, while the probability of negative growth hardly changes. This is called Non-Gibrat’s Second Property. Under detailed balance, Non-Gibrat’s First and Second Properties are analytically derived from the linear and quadratic growth-rate distributions in log-log scale, respectively. In both cases, the log-normal distribution is inferred from Non-Gibrat’s Properties and detailed balance. These analytic results are verified by empirical data. Consequently, this clarifies the notion that the difference in shapes between growth-rate distributions of sales and profits is closely related to the difference between the two Non-Gibrat’s Properties in the mid-scale range.

Developing a Peak Wind Probability Forecast Tool for Kennedy Space Center and Cape Canaveral Air Force Station

NASA Technical Reports Server (NTRS)

Lambert, WInifred; Roeder, William

2007-01-01

This conference presentation describes the development of a peak wind forecast tool to assist forecasters in determining the probability of violating launch commit criteria (LCC) at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) in east-central Florida. The peak winds are an important forecast element for both the Space Shuttle and Expendable Launch Vehicle (ELV) programs. The LCC define specific peak wind thresholds for each launch operation that cannot be exceeded in order to ensure the safety of the vehicle. The 45th Weather Squadron (45 WS) has found that peak winds are a challenging parameter to forecast, particularly in the cool season months of October through April. Based on the importance of forecasting peak winds, the 45 WS tasked the Applied Meteorology Unit (AMU) to develop a short-range peak-wind forecast tool to assist in forecasting LCC violations. The tool will include climatologies of the 5-minute mean and peak winds by month, hour, and direction, and probability distributions of the peak winds as a function of the 5-minute mean wind speeds.

A Peak Wind Probability Forecast Tool for Kennedy Space Center and Cape Canaveral Air Force Station

NASA Technical Reports Server (NTRS)

Crawford, Winifred; Roeder, William

2008-01-01

This conference abstract describes the development of a peak wind forecast tool to assist forecasters in determining the probability of violating launch commit criteria (LCC) at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) in east-central Florida. The peak winds are an important forecast element for both the Space Shuttle and Expendable Launch Vehicle (ELV) programs. The LCC define specific peak wind thresholds for each launch operation that cannot be exceeded in order to ensure the safety of the vehicle. The 45th Weather Squadron (45 WS) has found that peak winds are a challenging parameter to forecast, particularly in the cool season months of October through April. Based on the importance of forecasting peak winds, the 45 WS tasked the Applied Meteorology Unit (AMU) to develop a short-range peak-wind forecast tool to assist in forecasting LCC violatioas.The tool will include climatologies of the 5-minute mean end peak winds by month, hour, and direction, and probability distributions of the peak winds as a function of the 5-minute mean wind speeds.

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

NASA Astrophysics Data System (ADS)

Ballard, T.; Diffenbaugh, N. S.

2016-12-01

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

Diffusion of active chiral particles

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.

2016-12-01

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v ̂ at time t , and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

A Search Model for Imperfectly Detected Targets

NASA Technical Reports Server (NTRS)

Ahumada, Albert

2012-01-01

Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.

Optimizing probability of detection point estimate demonstration

NASA Astrophysics Data System (ADS)

Koshti, Ajay M.

2017-04-01

The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using point estimate method. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. Traditionally largest flaw size in the set is considered to be a conservative estimate of the flaw size with minimum 90% probability and 95% confidence. The flaw size is denoted as α90/95PE. The paper investigates relationship between range of flaw sizes in relation to α90, i.e. 90% probability flaw size, to provide a desired PPD. The range of flaw sizes is expressed as a proportion of the standard deviation of the probability density distribution. Difference between median or average of the 29 flaws and α90 is also expressed as a proportion of standard deviation of the probability density distribution. In general, it is concluded that, if probability of detection increases with flaw size, average of 29 flaw sizes would always be larger than or equal to α90 and is an acceptable measure of α90/95PE. If NDE technique has sufficient sensitivity and signal-to-noise ratio, then the 29 flaw-set can be optimized to meet requirements of minimum required PPD, maximum allowable POF, requirements on flaw size tolerance about mean flaw size and flaw size detectability requirements. The paper provides procedure for optimizing flaw sizes in the point estimate demonstration flaw-set.

Guest Editor's Introduction: Special section on dependable distributed systems

NASA Astrophysics Data System (ADS)

Fetzer, Christof

1999-09-01

We rely more and more on computers. For example, the Internet reshapes the way we do business. A `computer outage' can cost a company a substantial amount of money. Not only with respect to the business lost during an outage, but also with respect to the negative publicity the company receives. This is especially true for Internet companies. After recent computer outages of Internet companies, we have seen a drastic fall of the shares of the affected companies. There are multiple causes for computer outages. Although computer hardware becomes more reliable, hardware related outages remain an important issue. For example, some of the recent computer outages of companies were caused by failed memory and system boards, and even by crashed disks - a failure type which can easily be masked using disk mirroring. Transient hardware failures might also look like software failures and, hence, might be incorrectly classified as such. However, many outages are software related. Faulty system software, middleware, and application software can crash a system. Dependable computing systems are systems we can rely on. Dependable systems are, by definition, reliable, available, safe and secure [3]. This special section focuses on issues related to dependable distributed systems. Distributed systems have the potential to be more dependable than a single computer because the probability that all computers in a distributed system fail is smaller than the probability that a single computer fails. However, if a distributed system is not built well, it is potentially less dependable than a single computer since the probability that at least one computer in a distributed system fails is higher than the probability that one computer fails. For example, if the crash of any computer in a distributed system can bring the complete system to a halt, the system is less dependable than a single-computer system. Building dependable distributed systems is an extremely difficult task. There is no silver bullet solution. Instead one has to apply a variety of engineering techniques [2]: fault-avoidance (minimize the occurrence of faults, e.g. by using a proper design process), fault-removal (remove faults before they occur, e.g. by testing), fault-evasion (predict faults by monitoring and reconfigure the system before failures occur), and fault-tolerance (mask and/or contain failures). Building a system from scratch is an expensive and time consuming effort. To reduce the cost of building dependable distributed systems, one would choose to use commercial off-the-shelf (COTS) components whenever possible. The usage of COTS components has several potential advantages beyond minimizing costs. For example, through the widespread usage of a COTS component, design failures might be detected and fixed before the component is used in a dependable system. Custom-designed components have to mature without the widespread in-field testing of COTS components. COTS components have various potential disadvantages when used in dependable systems. For example, minimizing the time to market might lead to the release of components with inherent design faults (e.g. use of `shortcuts' that only work most of the time). In addition, the components might be more complex than needed and, hence, potentially have more design faults than simpler components. However, given economic constraints and the ability to cope with some of the problems using fault-evasion and fault-tolerance, only for a small percentage of systems can one justify not using COTS components. Distributed systems built from current COTS components are asynchronous systems in the sense that there exists no a priori known bound on the transmission delay of messages or the execution time of processes. When designing a distributed algorithm, one would like to make sure (e.g. by testing or verification) that it is correct, i.e. satisfies its specification. Many distributed algorithms make use of consensus (eventually all non-crashed processes have to agree on a value), leader election (a crashed leader is eventually replaced by a new leader, but at any time there is at most one leader) or a group membership detection service (a crashed process is eventually suspected to have crashed but only crashed processes are suspected). From a theoretical point of view, the service specifications given for such services are not implementable in asynchronous systems. In particular, for each implementation one can derive a counter example in which the service violates its specification. From a practical point of view, the consensus, the leader election, and the membership detection problem are solvable in asynchronous distributed systems. In this special section, Raynal and Tronel show how to bridge this difference by showing how to implement the group membership detection problem with a negligible probability [1] to fail in an asynchronous system. The group membership detection problem is specified by a liveness condition (L) and a safety property (S): (L) if a process p crashes, then eventually every non-crashed process q has to suspect that p has crashed; and (S) if a process q suspects p, then p has indeed crashed. One can show that either (L) or (S) is implementable, but one cannot implement both (L) and (S) at the same time in an asynchronous system. In practice, one only needs to implement (L) and (S) such that the probability that (L) or (S) is violated becomes negligible. Raynal and Tronel propose and analyse a protocol that implements (L) with certainty and that can be tuned such that the probability that (S) is violated becomes negligible. Designing and implementing distributed fault-tolerant protocols for asynchronous systems is a difficult but not an impossible task. A fault-tolerant protocol has to detect and mask certain failure classes, e.g. crash failures and message omission failures. There is a trade-off between the performance of a fault-tolerant protocol and the failure classes the protocol can tolerate. One wants to tolerate as many failure classes as needed to satisfy the stochastic requirements of the protocol [1] while still maintaining a sufficient performance. Since clients of a protocol have different requirements with respect to the performance/fault-tolerance trade-off, one would like to be able to customize protocols such that one can select an appropriate performance/fault-tolerance trade-off. In this special section Hiltunen et al describe how one can compose protocols from micro-protocols in their Cactus system. They show how a group RPC system can be tailored to the needs of a client. In particular, they show how considering additional failure classes affects the performance of a group RPC system. References [1] Cristian F 1991 Understanding fault-tolerant distributed systems Communications of ACM 34 (2) 56-78 [2] Heimerdinger W L and Weinstock C B 1992 A conceptual framework for system fault tolerance Technical Report 92-TR-33, CMU/SEI [3] Laprie J C (ed) 1992 Dependability: Basic Concepts and Terminology (Vienna: Springer)

Theoretical cratering rates on Ida, Mathilde, Eros and Gaspra

NASA Astrophysics Data System (ADS)

Jeffers, S. V.; Asher, D. J.; Bailey, M. E.

2002-11-01

We investigate the main influences on crater size distributions, by deriving results for the four example target objects, (951) Gaspra, (243) Ida, (253) Mathilde and (433) Eros. The dynamical history of each of these asteroids is modelled using the MERCURY (Chambers 1999) numerical integrator. The use of an efficient, Öpik-type, collision code enables the calculation of a velocity histogram and the probability of impact. This when combined with a crater scaling law and an impactor size distribution, through a Monte Carlo method, results in a crater size distribution. The resulting crater probability distributions are in good agreement with observed crater distributions on these asteroids.

The Probability Distribution for a Biased Spinner

ERIC Educational Resources Information Center

Foster, Colin

2012-01-01

This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)

A mathematical model for generating bipartite graphs and its application to protein networks

NASA Astrophysics Data System (ADS)

Nacher, J. C.; Ochiai, T.; Hayashida, M.; Akutsu, T.

2009-12-01

Complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology. Most of these systems can be organized into networks composed of nodes and interacting edges. Here, we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes. We then use this model to investigate protein-domain networks. A protein can be composed of up to hundreds of domains. Each domain represents a conserved sequence segment with specific functional tasks. We analyze the distribution of domains in Homo sapiens and Arabidopsis thaliana organisms and the statistical analysis shows that while (a) the number of domain types shared by k proteins exhibits a power-law distribution, (b) the number of proteins composed of k types of domains decays as an exponential distribution. The proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of (a) power-law and (b) exponential distributions. Our theoretical and computational results show that this model requires (1) growth process and (2) copy mechanism.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

A probable probability distribution of a series nonequilibrium states in a simple system out of equilibrium

NASA Astrophysics Data System (ADS)

Gao, Haixia; Li, Ting; Xiao, Changming

2016-05-01

When a simple system is in its nonequilibrium state, it will shift to its equilibrium state. Obviously, in this process, there are a series of nonequilibrium states. With the assistance of Bayesian statistics and hyperensemble, a probable probability distribution of these nonequilibrium states can be determined by maximizing the hyperensemble entropy. It is known that the largest probability is the equilibrium state, and the far a nonequilibrium state is away from the equilibrium one, the smaller the probability will be, and the same conclusion can also be obtained in the multi-state space. Furthermore, if the probability stands for the relative time the corresponding nonequilibrium state can stay, then the velocity of a nonequilibrium state returning back to its equilibrium can also be determined through the reciprocal of the derivative of this probability. It tells us that the far away the state from the equilibrium is, the faster the returning velocity will be; if the system is near to its equilibrium state, the velocity will tend to be smaller and smaller, and finally tends to 0 when it gets the equilibrium state.

Study on probability distributions for evolution in modified extremal optimization

NASA Astrophysics Data System (ADS)

Zeng, Guo-Qiang; Lu, Yong-Zai; Mao, Wei-Jie; Chu, Jian

2010-05-01

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.

Site specific passive acoustic detection and densities of humpback whale calls off the coast of California

NASA Astrophysics Data System (ADS)

Helble, Tyler Adam

Passive acoustic monitoring of marine mammal calls is an increasingly important method for assessing population numbers, distribution, and behavior. Automated methods are needed to aid in the analyses of the recorded data. When a mammal vocalizes in the marine environment, the received signal is a filtered version of the original waveform emitted by the marine mammal. The waveform is reduced in amplitude and distorted due to propagation effects that are influenced by the bathymetry and environment. It is important to account for these effects to determine a site-specific probability of detection for marine mammal calls in a given study area. A knowledge of that probability function over a range of environmental and ocean noise conditions allows vocalization statistics from recordings of single, fixed, omnidirectional sensors to be compared across sensors and at the same sensor over time with less bias and uncertainty in the results than direct comparison of the raw statistics. This dissertation focuses on both the development of new tools needed to automatically detect humpback whale vocalizations from single-fixed omnidirectional sensors as well as the determination of the site-specific probability of detection for monitoring sites off the coast of California. Using these tools, detected humpback calls are "calibrated" for environmental properties using the site-specific probability of detection values, and presented as call densities (calls per square kilometer per time). A two-year monitoring effort using these calibrated call densities reveals important biological and ecological information on migrating humpback whales off the coast of California. Call density trends are compared between the monitoring sites and at the same monitoring site over time. Call densities also are compared to several natural and human-influenced variables including season, time of day, lunar illumination, and ocean noise. The results reveal substantial differences in call densities between the two sites which were not noticeable using uncorrected (raw) call counts. Additionally, a Lombard effect was observed for humpback whale vocalizations in response to increasing ocean noise. The results presented in this thesis develop techniques to accurately measure marine mammal abundances from passive acoustic sensors.

Role of the repartition of wetland breeding sites on the spatial distribution of Anopheles and Culex, human disease vectors in southern France.

PubMed

Cailly, Priscilla; Balenghien, Thomas; Ezanno, Pauline; Fontenille, Didier; Toty, Céline; Tran, Annelise

2011-05-06

In this study, carried out in the Camargue region (France), we combined entomological data with geomatic and modelling tools to assess whether the location of breeding sites may explain the spatial distribution of adult mosquitoes. The species studied are important and competent disease vectors in Europe: Culex modestus Ficalbi and Cx. pipiens Linnaeus (West Nile virus), Anopheles atroparvus Van Thiel, a former Plasmodium vector, and An. melanoon Hackett, competent to transmit Plasmodium.Using a logistic regression model, we first evaluated which land cover variables determined the presence of Culex and Anopheles larva. The resulting probability map of larval presence then was used to project the average probability of finding adults in a buffer area. This was compared to the actual number of adults collected, providing a quantitative assessment of adult dispersal ability for each species. The distribution of Cx. modestus and An. melanoon is mainly driven by the repartition of irrigated farm fields and reed beds, their specific breeding habitats. The presence of breeding sites explained the distribution of adults of both species. The buffer size, reflecting the adult dispersal ability, was 700 m for Cx. modestus and 1000 m for An. melanoon. The comparatively stronger correlation observed for Cx. modestus suggested that other factors may affect the distribution of adult An. melanoon. We did not find any association between Cx. pipiens larval presence and the biotope due to the species' ubiquist character. By applying the same method to different species, we highlighted different strengths of association between land cover (irrigated farm fields and reed beds), larval presence and adult population distribution.This paper demonstrates the power of geomatic tools to quantify the spatial organization of mosquito populations, and allows a better understanding of links between landcover, breeding habitats, presence of immature mosquito populations and adult distributions for different species.

Role of the repartition of wetland breeding sites on the spatial distribution of Anopheles and Culex, human disease vectors in Southern France

PubMed Central

2011-01-01

Background In this study, carried out in the Camargue region (France), we combined entomological data with geomatic and modelling tools to assess whether the location of breeding sites may explain the spatial distribution of adult mosquitoes. The species studied are important and competent disease vectors in Europe: Culex modestus Ficalbi and Cx. pipiens Linnaeus (West Nile virus), Anopheles atroparvus Van Thiel, a former Plasmodium vector, and An. melanoon Hackett, competent to transmit Plasmodium. Using a logistic regression model, we first evaluated which land cover variables determined the presence of Culex and Anopheles larva. The resulting probability map of larval presence then was used to project the average probability of finding adults in a buffer area. This was compared to the actual number of adults collected, providing a quantitative assessment of adult dispersal ability for each species. Results The distribution of Cx. modestus and An. melanoon is mainly driven by the repartition of irrigated farm fields and reed beds, their specific breeding habitats. The presence of breeding sites explained the distribution of adults of both species. The buffer size, reflecting the adult dispersal ability, was 700 m for Cx. modestus and 1000 m for An. melanoon. The comparatively stronger correlation observed for Cx. modestus suggested that other factors may affect the distribution of adult An. melanoon. We did not find any association between Cx. pipiens larval presence and the biotope due to the species' ubiquist character. Conclusion By applying the same method to different species, we highlighted different strengths of association between land cover (irrigated farm fields and reed beds), larval presence and adult population distribution. This paper demonstrates the power of geomatic tools to quantify the spatial organization of mosquito populations, and allows a better understanding of links between landcover, breeding habitats, presence of immature mosquito populations and adult distributions for different species. PMID:21548912

Rapidly assessing the probability of exceptionally high natural hazard losses

NASA Astrophysics Data System (ADS)

Gollini, Isabella; Rougier, Jonathan

2014-05-01

One of the objectives in catastrophe modeling is to assess the probability distribution of losses for a specified period, such as a year. From the point of view of an insurance company, the whole of the loss distribution is interesting, and valuable in determining insurance premiums. But the shape of the righthand tail is critical, because it impinges on the solvency of the company. A simple measure of the risk of insolvency is the probability that the annual loss will exceed the company's current operating capital. Imposing an upper limit on this probability is one of the objectives of the EU Solvency II directive. If a probabilistic model is supplied for the loss process, then this tail probability can be computed, either directly, or by simulation. This can be a lengthy calculation for complex losses. Given the inevitably subjective nature of quantifying loss distributions, computational resources might be better used in a sensitivity analysis. This requires either a quick approximation to the tail probability or an upper bound on the probability, ideally a tight one. We present several different bounds, all of which can be computed nearly instantly from a very general event loss table. We provide a numerical illustration, and discuss the conditions under which the bound is tight. Although we consider the perspective of insurance and reinsurance companies, exactly the same issues concern the risk manager, who is typically very sensitive to large losses.

Variation in the standard deviation of the lure rating distribution: Implications for estimates of recollection probability.

PubMed

Dopkins, Stephen; Varner, Kaitlin; Hoyer, Darin

2017-10-01

In word recognition semantic priming of test words increased the false-alarm rate and the mean of confidence ratings to lures. Such priming also increased the standard deviation of confidence ratings to lures and the slope of the z-ROC function, suggesting that the priming increased the standard deviation of the lure evidence distribution. The Unequal Variance Signal Detection (UVSD) model interpreted the priming as increasing the standard deviation of the lure evidence distribution. Without additional parameters the Dual Process Signal Detection (DPSD) model could only accommodate the results by fitting the data for related and unrelated primes separately, interpreting the priming, implausibly, as decreasing the probability of target recollection (DPSD). With an additional parameter, for the probability of false (lure) recollection the model could fit the data for related and unrelated primes together, interpreting the priming as increasing the probability of false recollection. These results suggest that DPSD estimates of target recollection probability will decrease with increases in the lure confidence/evidence standard deviation unless a parameter is included for false recollection. Unfortunately the size of a given lure confidence/evidence standard deviation relative to other possible lure confidence/evidence standard deviations is often unspecified by context. Hence the model often has no way of estimating false recollection probability and thereby correcting its estimates of target recollection probability.

Statistical properties of two sine waves in Gaussian noise.

NASA Technical Reports Server (NTRS)

Esposito, R.; Wilson, L. R.

1973-01-01

A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).

Structural Health Monitoring System Trade Space Analysis Tool with Consideration for Crack Growth, Sensor Degradation and a Variable Detection Threshold

DTIC Science & Technology

2014-09-18

Erdogan , 1963). 26 Paris’s Law Under a fatigue stress regime Paris’s Law relates sub-critical crack growth to stress intensity factor. The basic...Paris and Erdogan , 1963). After takeoff, the model generates a probability distribution for the crack length in that specific sortie based on the...Law is one of the most widely used fatigue crack growth models and was used in this research effort (Paris and Erdogan , 1963). Paris’s Law Under a

Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers.

PubMed

Hammani, Kamal; Finot, Christophe; Dudley, John M; Millot, Guy

2008-10-13

We report experimental observation and characterization of rogue wave-like extreme value statistics arising from pump-signal noise transfer in a fiber Raman amplifier. Specifically, by exploiting Raman amplification with an incoherent pump, the amplified signal is shown to develop a series of temporal intensity spikes whose peak power follows a power-law probability distribution. The results are interpreted using a numerical model of the Raman gain process using coupled nonlinear Schrödinger equations, and the numerical model predicts results in good agreement with experiment.

Malate dehydrogenase isozymes in the longnose dace, Rhinichthys cataractae.

PubMed

Starzyk, R M; Merritt, R B

1980-08-01

The interspecies homology of dace supernatant (A2,AB,B2) and mitochondrial (C2) malate dehydrogenase isozymes has been established through cell fractionation and tissue distribution studies. Isolated supernatant malate dehydrogenase (s-MDH) isozymes show significant differences in Michaelis constants for oxaloacetate and in pH optima. Shifts in s-MDH isozyme pH optima with temperature may result in immediate compensation for increase in ectotherm body pH with decrease in temperature, but duplicate s-MDH isozymes are probably maintained through selection for tissue specific regulation of metabolism.

Potential Sources of Polarized Light from a Plant Canopy

NASA Technical Reports Server (NTRS)

Vanderbilt, Vern; Daughtry, Craig; Dahlgren, Robert

2016-01-01

Field measurements have demonstrated that sunlight polarized during a first surface reflection by shiny leaves dominates the optical polarization of the light reflected by shiny-leafed plant canopies having approximately spherical leaf angle probability density functions ("Leaf Angle Distributions" - LAD). Yet for other canopies - specifically those without shiny leaves and/or spherical LADs - potential sources of optically polarized light may not always be obvious. Here we identify possible sources of polarized light within those other canopies and speculate on the ecologically important information polarization measurements of those sources might contain.

Bayesian analysis of multimodal data and brain imaging

NASA Astrophysics Data System (ADS)

Assadi, Amir H.; Eghbalnia, Hamid; Backonja, Miroslav; Wakai, Ronald T.; Rutecki, Paul; Haughton, Victor

2000-06-01

It is often the case that information about a process can be obtained using a variety of methods. Each method is employed because of specific advantages over the competing alternatives. An example in medical neuro-imaging is the choice between fMRI and MEG modes where fMRI can provide high spatial resolution in comparison to the superior temporal resolution of MEG. The combination of data from varying modes provides the opportunity to infer results that may not be possible by means of any one mode alone. We discuss a Bayesian and learning theoretic framework for enhanced feature extraction that is particularly suited to multi-modal investigations of massive data sets from multiple experiments. In the following Bayesian approach, acquired knowledge (information) regarding various aspects of the process are all directly incorporated into the formulation. This information can come from a variety of sources. In our case, it represents statistical information obtained from other modes of data collection. The information is used to train a learning machine to estimate a probability distribution, which is used in turn by a second machine as a prior, in order to produce a more refined estimation of the distribution of events. The computational demand of the algorithm is handled by proposing a distributed parallel implementation on a cluster of workstations that can be scaled to address real-time needs if required. We provide a simulation of these methods on a set of synthetically generated MEG and EEG data. We show how spatial and temporal resolutions improve by using prior distributions. The method on fMRI signals permits one to construct the probability distribution of the non-linear hemodynamics of the human brain (real data). These computational results are in agreement with biologically based measurements of other labs, as reported to us by researchers from UK. We also provide preliminary analysis involving multi-electrode cortical recording that accompanies behavioral data in pain experiments on freely moving mice subjected to moderate heat delivered by an electric bulb. Summary of new or breakthrough ideas: (1) A new method to estimate probability distribution for measurement of nonlinear hemodynamics of brain from a multi- modal neuronal data. This is the first time that such an idea is tried, to our knowledge. (2) Breakthrough in improvement of time resolution of fMRI signals using (1) above.

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.

Application of wildfire spread and behavior models to assess fire probability and severity in the Mediterranean region

NASA Astrophysics Data System (ADS)

Salis, Michele; Arca, Bachisio; Bacciu, Valentina; Spano, Donatella; Duce, Pierpaolo; Santoni, Paul; Ager, Alan; Finney, Mark

2010-05-01

Characterizing the spatial pattern of large fire occurrence and severity is an important feature of the fire management planning in the Mediterranean region. The spatial characterization of fire probabilities, fire behavior distributions and value changes are key components for quantitative risk assessment and for prioritizing fire suppression resources, fuel treatments and law enforcement. Because of the growing wildfire severity and frequency in recent years (e.g.: Portugal, 2003 and 2005; Italy and Greece, 2007 and 2009), there is an increasing demand for models and tools that can aid in wildfire prediction and prevention. Newer wildfire simulation systems offer promise in this regard, and allow for fine scale modeling of wildfire severity and probability. Several new applications has resulted from the development of a minimum travel time (MTT) fire spread algorithm (Finney, 2002), that models the fire growth searching for the minimum time for fire to travel among nodes in a 2D network. The MTT approach makes computationally feasible to simulate thousands of fires and generate burn probability and fire severity maps over large areas. The MTT algorithm is imbedded in a number of research and fire modeling applications. High performance computers are typically used for MTT simulations, although the algorithm is also implemented in the FlamMap program (www.fire.org). In this work, we described the application of the MTT algorithm to estimate spatial patterns of burn probability and to analyze wildfire severity in three fire prone areas of the Mediterranean Basin, specifically Sardinia (Italy), Sicily (Italy) and Corsica (France) islands. We assembled fuels and topographic data for the simulations in 500 x 500 m grids for the study areas. The simulations were run using 100,000 ignitions under weather conditions that replicated severe and moderate weather conditions (97th and 70th percentile, July and August weather, 1995-2007). We used both random ignition locations and ignition probability grids (1000 x 1000 m) built from historical fire data (1995-2007). The simulation outputs were then examined to understand relationships between burn probability and specific vegetation types and ignition sources. Wildfire threats to specific values of human interest were quantified to map landscape patterns of wildfire risk. The simulation outputs also allowed us to differentiate between areas of the landscape that were progenitors of fires versus "victims" of large fires. The results provided spatially explicit data on wildfire likelihood and intensity that can be used in a variety of strategic and tactical planning forums to mitigate wildfire threats to human and other values in the Mediterranean Basin.

Application of a time probabilistic approach to seismic landslide hazard estimates in Iran

NASA Astrophysics Data System (ADS)

Rajabi, A. M.; Del Gaudio, V.; Capolongo, D.; Khamehchiyan, M.; Mahdavifar, M. R.

2009-04-01

Iran is a country located in a tectonic active belt and is prone to earthquake and related phenomena. In the recent years, several earthquakes caused many fatalities and damages to facilities, e.g. the Manjil (1990), Avaj (2002), Bam (2003) and Firuzabad-e-Kojur (2004) earthquakes. These earthquakes generated many landslides. For instance, catastrophic landslides triggered by the Manjil Earthquake (Ms = 7.7) in 1990 buried the village of Fatalak, killed more than 130 peoples and cut many important road and other lifelines, resulting in major economic disruption. In general, earthquakes in Iran have been concentrated in two major zones with different seismicity characteristics: one is the region of Alborz and Central Iran and the other is the Zagros Orogenic Belt. Understanding where seismically induced landslides are most likely to occur is crucial in reducing property damage and loss of life in future earthquakes. For this purpose a time probabilistic approach for earthquake-induced landslide hazard at regional scale, proposed by Del Gaudio et al. (2003), has been applied to the whole Iranian territory to provide the basis of hazard estimates. This method consists in evaluating the recurrence of seismically induced slope failure conditions inferred from the Newmark's model. First, by adopting Arias Intensity to quantify seismic shaking and using different Arias attenuation relations for Alborz - Central Iran and Zagros regions, well-established methods of seismic hazard assessment, based on the Cornell (1968) method, were employed to obtain the occurrence probabilities for different levels of seismic shaking in a time interval of interest (50 year). Then, following Jibson (1998), empirical formulae specifically developed for Alborz - Central Iran and Zagros, were used to represent, according to the Newmark's model, the relation linking Newmark's displacement Dn to Arias intensity Ia and to slope critical acceleration ac. These formulae were employed to evaluate the slope critical acceleration (Ac)x for which a prefixed probability exists that seismic shaking would result in a Dn value equal to a threshold x whose exceedence would cause landslide triggering. The obtained ac values represent the minimum slope resistance required to keep the probability of seismic-landslide triggering within the prefixed value. In particular we calculated the spatial distribution of (Ac)x for x thresholds of 10 and 2 cm in order to represent triggering conditions for coherent slides (e.g., slumps, block slides, slow earth flows) and disrupted slides (e.g., rock falls, rock slides, rock avalanches), respectively. Then we produced a probabilistic national map that shows the spatial distribution of (Ac)10 and (Ac)2, for a 10% probability of exceedence in 50 year, which is a significant level of hazard equal to that commonly used for building codes. The spatial distribution of the calculated (Ac)xvalues can be compared with the in situ actual ac values of specific slopes to estimate whether these slopes have a significant probability of failing under seismic action in the future. As example of possible application of this kind of time probabilistic map to hazard estimates, we compared the values obtained for the Manjil region with a GIS map providing spatial distribution of estimated ac values in the same region. The spatial distribution of slopes characterized by ac < (Ac)10 was then compared with the spatial distribution of the major landslides of coherent type triggered by the Manjil earthquake. This comparison provides indications on potential, problems and limits of the experimented approach for the study area. References Cornell, C.A., 1968: Engineering seismic risk analysis, Bull. Seism. Soc. Am., 58, 1583-1606. Del Gaudio V., Wasowski J., & Pierri P., 2003: An approach to time probabilistic evaluation of seismically-induced landslide hazard. Bull Seism. Soc. Am., 93, 557-569. Jibson, R.W., E.L. Harp and J.A. Michael, 1998: A method for producing digital probabilistic seismic landslide hazard maps: an example from the Los Angeles, California, area, U.S. Geological Survey Open-File Report 98-113, Golden, Colorado, 17 pp.

Digital simulation of an arbitrary stationary stochastic process by spectral representation.

PubMed

Yura, Harold T; Hanson, Steen G

2011-04-01

In this paper we present a straightforward, efficient, and computationally fast method for creating a large number of discrete samples with an arbitrary given probability density function and a specified spectral content. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In contrast to previous work, where the analyses were limited to auto regressive and or iterative techniques to obtain satisfactory results, we find that a single application of the inverse transform method yields satisfactory results for a wide class of arbitrary probability distributions. Although a single application of the inverse transform technique does not conserve the power spectra exactly, it yields highly accurate numerical results for a wide range of probability distributions and target power spectra that are sufficient for system simulation purposes and can thus be regarded as an accurate engineering approximation, which can be used for wide range of practical applications. A sufficiency condition is presented regarding the range of parameter values where a single application of the inverse transform method yields satisfactory agreement between the simulated and target power spectra, and a series of examples relevant for the optics community are presented and discussed. Outside this parameter range the agreement gracefully degrades but does not distort in shape. Although we demonstrate the method here focusing on stationary random processes, we see no reason why the method could not be extended to simulate non-stationary random processes. © 2011 Optical Society of America

Estimating alarm thresholds and the number of components in mixture distributions

NASA Astrophysics Data System (ADS)

Burr, Tom; Hamada, Michael S.

2012-09-01

Mixtures of probability distributions arise in many nuclear assay and forensic applications, including nuclear weapon detection, neutron multiplicity counting, and in solution monitoring (SM) for nuclear safeguards. SM data is increasingly used to enhance nuclear safeguards in aqueous reprocessing facilities having plutonium in solution form in many tanks. This paper provides background for mixture probability distributions and then focuses on mixtures arising in SM data. SM data can be analyzed by evaluating transfer-mode residuals defined as tank-to-tank transfer differences, and wait-mode residuals defined as changes during non-transfer modes. A previous paper investigated impacts on transfer-mode and wait-mode residuals of event marking errors which arise when the estimated start and/or stop times of tank events such as transfers are somewhat different from the true start and/or stop times. Event marking errors contribute to non-Gaussian behavior and larger variation than predicted on the basis of individual tank calibration studies. This paper illustrates evidence for mixture probability distributions arising from such event marking errors and from effects such as condensation or evaporation during non-transfer modes, and pump carryover during transfer modes. A quantitative assessment of the sample size required to adequately characterize a mixture probability distribution arising in any context is included.

Construction and identification of a D-Vine model applied to the probability distribution of modal parameters in structural dynamics

NASA Astrophysics Data System (ADS)

Dubreuil, S.; Salaün, M.; Rodriguez, E.; Petitjean, F.

2018-01-01

This study investigates the construction and identification of the probability distribution of random modal parameters (natural frequencies and effective parameters) in structural dynamics. As these parameters present various types of dependence structures, the retained approach is based on pair copula construction (PCC). A literature review leads us to choose a D-Vine model for the construction of modal parameters probability distributions. Identification of this model is based on likelihood maximization which makes it sensitive to the dimension of the distribution, namely the number of considered modes in our context. To this respect, a mode selection preprocessing step is proposed. It allows the selection of the relevant random modes for a given transfer function. The second point, addressed in this study, concerns the choice of the D-Vine model. Indeed, D-Vine model is not uniquely defined. Two strategies are proposed and compared. The first one is based on the context of the study whereas the second one is purely based on statistical considerations. Finally, the proposed approaches are numerically studied and compared with respect to their capabilities, first in the identification of the probability distribution of random modal parameters and second in the estimation of the 99 % quantiles of some transfer functions.

Probability distribution functions in turbulent convection

NASA Technical Reports Server (NTRS)

Balachandar, S.; Sirovich, L.

1991-01-01

Results of an extensive investigation of probability distribution functions (pdfs) for Rayleigh-Benard convection, in hard turbulence regime, are presented. It is shown that the pdfs exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to the universality is presented.

KINETICS OF LOW SOURCE REACTOR STARTUPS. PART II

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

hurwitz, H. Jr.; MacMillan, D.B.; Smith, J.H.

1962-06-01

A computational technique is described for computation of the probability distribution of power level for a low source reactor startup. The technique uses a mathematical model, for the time-dependent probability distribution of neutron and precursor concentration, having finite neutron lifetime, one group of delayed neutron precursors, and no spatial dependence. Results obtained by the technique are given. (auth)

Generating an Empirical Probability Distribution for the Andrews-Pregibon Statistic.

ERIC Educational Resources Information Center

Jarrell, Michele G.

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

Animating Statistics: A New Kind of Applet for Exploring Probability Distributions

ERIC Educational Resources Information Center

Kahle, David

2014-01-01

In this article, I introduce a novel applet ("module") for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive…

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

Modeling and impacts of the latent heat of phase change and specific heat for phase change materials

NASA Astrophysics Data System (ADS)

Scoggin, J.; Khan, R. S.; Silva, H.; Gokirmak, A.

2018-05-01

We model the latent heats of crystallization and fusion in phase change materials with a unified latent heat of phase change, ensuring energy conservation by coupling the heat of phase change with amorphous and crystalline specific heats. We demonstrate the model with 2-D finite element simulations of Ge2Sb2Te5 and find that the heat of phase change increases local temperature up to 180 K in 300 nm × 300 nm structures during crystallization, significantly impacting grain distributions. We also show in electrothermal simulations of 45 nm confined and 10 nm mushroom cells that the higher amorphous specific heat predicted by this model increases nucleation probability at the end of reset operations. These nuclei can decrease set time, leading to variability, as demonstrated for the mushroom cell.

A hierarchical two-phase framework for selecting genes in cancer datasets with a neuro-fuzzy system.

PubMed

Lim, Jongwoo; Wang, Bohyun; Lim, Joon S

2016-04-29

Finding the minimum number of appropriate biomarkers for specific targets such as a lung cancer has been a challenging issue in bioinformatics. We propose a hierarchical two-phase framework for selecting appropriate biomarkers that extracts candidate biomarkers from the cancer microarray datasets and then selects the minimum number of appropriate biomarkers from the extracted candidate biomarkers datasets with a specific neuro-fuzzy algorithm, which is called a neural network with weighted fuzzy membership function (NEWFM). In this context, as the first phase, the proposed framework is to extract candidate biomarkers by using a Bhattacharyya distance method that measures the similarity of two discrete probability distributions. Finally, the proposed framework is able to reduce the cost of finding biomarkers by not receiving medical supplements and improve the accuracy of the biomarkers in specific cancer target datasets.

Neural correlates of the divergence of instrumental probability distributions.

PubMed

Liljeholm, Mimi; Wang, Shuo; Zhang, June; O'Doherty, John P

2013-07-24

Flexible action selection requires knowledge about how alternative actions impact the environment: a "cognitive map" of instrumental contingencies. Reinforcement learning theories formalize this map as a set of stochastic relationships between actions and states, such that for any given action considered in a current state, a probability distribution is specified over possible outcome states. Here, we show that activity in the human inferior parietal lobule correlates with the divergence of such outcome distributions-a measure that reflects whether discrimination between alternative actions increases the controllability of the future-and, further, that this effect is dissociable from those of other information theoretic and motivational variables, such as outcome entropy, action values, and outcome utilities. Our results suggest that, although ultimately combined with reward estimates to generate action values, outcome probability distributions associated with alternative actions may be contrasted independently of valence computations, to narrow the scope of the action selection problem.

Qualitative fusion technique based on information poor system and its application to factor analysis for vibration of rolling bearings

NASA Astrophysics Data System (ADS)

Xia, Xintao; Wang, Zhongyu

2008-10-01

For some methods of stability analysis of a system using statistics, it is difficult to resolve the problems of unknown probability distribution and small sample. Therefore, a novel method is proposed in this paper to resolve these problems. This method is independent of probability distribution, and is useful for small sample systems. After rearrangement of the original data series, the order difference and two polynomial membership functions are introduced to estimate the true value, the lower bound and the supper bound of the system using fuzzy-set theory. Then empirical distribution function is investigated to ensure confidence level above 95%, and the degree of similarity is presented to evaluate stability of the system. Cases of computer simulation investigate stable systems with various probability distribution, unstable systems with linear systematic errors and periodic systematic errors and some mixed systems. The method of analysis for systematic stability is approved.

A double hit model for the distribution of time to AIDS onset

NASA Astrophysics Data System (ADS)

Chillale, Nagaraja Rao

2013-09-01

Incubation time is a key epidemiologic descriptor of an infectious disease. In the case of HIV infection this is a random variable and is probably the longest one. The probability distribution of incubation time is the major determinant of the relation between the incidences of HIV infection and its manifestation to Aids. This is also one of the key factors used for accurate estimation of AIDS incidence in a region. The present article i) briefly reviews the work done, points out uncertainties in estimation of AIDS onset time and stresses the need for its precise estimation, ii) highlights some of the modelling features of onset distribution including immune failure mechanism, and iii) proposes a 'Double Hit' model for the distribution of time to AIDS onset in the cases of (a) independent and (b) dependent time variables of the two markers and examined the applicability of a few standard probability models.

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

NASA Astrophysics Data System (ADS)

Ghosh, Surya K.; Cherstvy, Andrey G.; Grebenkov, Denis S.; Metzler, Ralf

2016-01-01

A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.

On Replacing "Quantum Thinking" with Counterfactual Reasoning

NASA Astrophysics Data System (ADS)

Narens, Louis

The probability theory used in quantum mechanics is currently being employed by psychologists to model the impact of context on decision. Its event space consists of closed subspaces of a Hilbert space, and its probability function sometimes violate the law of the finite additivity of probabilities. Results from the quantum mechanics literature indicate that such a "Hilbert space probability theory" cannot be extended in a useful way to standard, finitely additive, probability theory by the addition of new events with specific probabilities. This chapter presents a new kind of probability theory that shares many fundamental algebraic characteristics with Hilbert space probability theory but does extend to standard probability theory by adjoining new events with specific probabilities. The new probability theory arises from considerations about how psychological experiments are related through counterfactual reasoning.

Learning Probabilities From Random Observables in High Dimensions: The Maximum Entropy Distribution and Others

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Cocco, Simona; Monasson, Rémi

2015-11-01

We consider the problem of learning a target probability distribution over a set of N binary variables from the knowledge of the expectation values (with this target distribution) of M observables, drawn uniformly at random. The space of all probability distributions compatible with these M expectation values within some fixed accuracy, called version space, is studied. We introduce a biased measure over the version space, which gives a boost increasing exponentially with the entropy of the distributions and with an arbitrary inverse `temperature' Γ . The choice of Γ allows us to interpolate smoothly between the unbiased measure over all distributions in the version space (Γ =0) and the pointwise measure concentrated at the maximum entropy distribution (Γ → ∞ ). Using the replica method we compute the volume of the version space and other quantities of interest, such as the distance R between the target distribution and the center-of-mass distribution over the version space, as functions of α =(log M)/N and Γ for large N. Phase transitions at critical values of α are found, corresponding to qualitative improvements in the learning of the target distribution and to the decrease of the distance R. However, for fixed α the distance R does not vary with Γ which means that the maximum entropy distribution is not closer to the target distribution than any other distribution compatible with the observable values. Our results are confirmed by Monte Carlo sampling of the version space for small system sizes (N≤ 10).

Statistical Characterization of the Mechanical Parameters of Intact Rock Under Triaxial Compression: An Experimental Proof of the Jinping Marble

NASA Astrophysics Data System (ADS)

Jiang, Quan; Zhong, Shan; Cui, Jie; Feng, Xia-Ting; Song, Leibo

2016-12-01

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress-strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble's probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young's elastic modulus and Poisson's ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering.

Risk Assessment of Bone Fracture During Space Exploration Missions to the Moon and Mars

NASA Technical Reports Server (NTRS)

Lewandowski, Beth E.; Myers, Jerry G.; Nelson, Emily S.; Licatta, Angelo; Griffin, Devon

2007-01-01

The possibility of a traumatic bone fracture in space is a concern due to the observed decrease in astronaut bone mineral density (BMD) during spaceflight and because of the physical demands of the mission. The Bone Fracture Risk Module (BFxRM) was developed to quantify the probability of fracture at the femoral neck and lumbar spine during space exploration missions. The BFxRM is scenario-based, providing predictions for specific activities or events during a particular space mission. The key elements of the BFxRM are the mission parameters, the biomechanical loading models, the bone loss and fracture models and the incidence rate of the activity or event. Uncertainties in the model parameters arise due to variations within the population and unknowns associated with the effects of the space environment. Consequently, parameter distributions were used in Monte Carlo simulations to obtain an estimate of fracture probability under real mission scenarios. The model predicts an increase in the probability of fracture as the mission length increases and fracture is more likely in the higher gravitational field of Mars than on the moon. The resulting probability predictions and sensitivity analyses of the BFxRM can be used as an engineering tool for mission operation and resource planning in order to mitigate the risk of bone fracture in space.

Risk Assessment of Bone Fracture During Space Exploration Missions to the Moon and Mars

NASA Technical Reports Server (NTRS)

Lewandowski, Beth E.; Myers, Jerry G.; Nelson, Emily S.; Griffin, Devon

2008-01-01

The possibility of a traumatic bone fracture in space is a concern due to the observed decrease in astronaut bone mineral density (BMD) during spaceflight and because of the physical demands of the mission. The Bone Fracture Risk Module (BFxRM) was developed to quantify the probability of fracture at the femoral neck and lumbar spine during space exploration missions. The BFxRM is scenario-based, providing predictions for specific activities or events during a particular space mission. The key elements of the BFxRM are the mission parameters, the biomechanical loading models, the bone loss and fracture models and the incidence rate of the activity or event. Uncertainties in the model parameters arise due to variations within the population and unknowns associated with the effects of the space environment. Consequently, parameter distributions were used in Monte Carlo simulations to obtain an estimate of fracture probability under real mission scenarios. The model predicts an increase in the probability of fracture as the mission length increases and fracture is more likely in the higher gravitational field of Mars than on the moon. The resulting probability predictions and sensitivity analyses of the BFxRM can be used as an engineering tool for mission operation and resource planning in order to mitigate the risk of bone fracture in space.

Modeling potential distribution of Oligoryzomys longicaudatus, the Andes virus (Genus: Hantavirus) reservoir, in Argentina.

PubMed

Andreo, Verónica; Glass, Gregory; Shields, Timothy; Provensal, Cecilia; Polop, Jaime

2011-09-01

We constructed a model to predict the potential distribution of Oligoryzomys longicaudatus, the reservoir of Andes virus (Genus: Hantavirus), in Argentina. We developed an extensive database of occurrence records from published studies and our own surveys and compared two methods to model the probability of O. longicaudatus presence; logistic regression and MaxEnt algorithm. The environmental variables used were tree, grass and bare soil cover from MODIS imagery and, altitude and 19 bioclimatic variables from WorldClim database. The models performances were evaluated and compared both by threshold dependent and independent measures. The best models included tree and grass cover, mean diurnal temperature range, and precipitation of the warmest and coldest seasons. The potential distribution maps for O. longicaudatus predicted the highest occurrence probabilities along the Andes range, from 32°S and narrowing southwards. They also predicted high probabilities for the south-central area of Argentina, reaching the Atlantic coast. The Hantavirus Pulmonary Syndrome cases coincided with mean occurrence probabilities of 95 and 77% for logistic and MaxEnt models, respectively. HPS transmission zones in Argentine Patagonia matched the areas with the highest probability of presence. Therefore, colilargos presence probability may provide an approximate risk of transmission and act as an early tool to guide control and prevention plans.

Computation of marginal distributions of peak-heights in electropherograms for analysing single source and mixture STR DNA samples.

PubMed

Cowell, Robert G

2018-05-04

Current models for single source and mixture samples, and probabilistic genotyping software based on them used for analysing STR electropherogram data, assume simple probability distributions, such as the gamma distribution, to model the allelic peak height variability given the initial amount of DNA prior to PCR amplification. Here we illustrate how amplicon number distributions, for a model of the process of sample DNA collection and PCR amplification, may be efficiently computed by evaluating probability generating functions using discrete Fourier transforms. Copyright © 2018 Elsevier B.V. All rights reserved.

An Integrated Framework for Model-Based Distributed Diagnosis and Prognosis

DTIC Science & Technology

2012-09-01

0 : t) denotes all measurements observed up to time t. The goal of prognosis is to determine the end of (use- ful) life ( EOL ) of a system, and/or its...remaining useful life (RUL). For a given fault, f , using the fault estimate, p(xf (t),θf (t)|y(0 : t)), a probability distribution of EOL , p(EOLf (tP...is stochas- tic, EOL /RUL are random variables and we represent them by probability distributions. The acceptable behavior of the system is expressed

Reconstruction of far-field tsunami amplitude distributions from earthquake sources

USGS Publications Warehouse

Geist, Eric L.; Parsons, Thomas E.

2016-01-01

The probability distribution of far-field tsunami amplitudes is explained in relation to the distribution of seismic moment at subduction zones. Tsunami amplitude distributions at tide gauge stations follow a similar functional form, well described by a tapered Pareto distribution that is parameterized by a power-law exponent and a corner amplitude. Distribution parameters are first established for eight tide gauge stations in the Pacific, using maximum likelihood estimation. A procedure is then developed to reconstruct the tsunami amplitude distribution that consists of four steps: (1) define the distribution of seismic moment at subduction zones; (2) establish a source-station scaling relation from regression analysis; (3) transform the seismic moment distribution to a tsunami amplitude distribution for each subduction zone; and (4) mix the transformed distribution for all subduction zones to an aggregate tsunami amplitude distribution specific to the tide gauge station. The tsunami amplitude distribution is adequately reconstructed for four tide gauge stations using globally constant seismic moment distribution parameters established in previous studies. In comparisons to empirical tsunami amplitude distributions from maximum likelihood estimation, the reconstructed distributions consistently exhibit higher corner amplitude values, implying that in most cases, the empirical catalogs are too short to include the largest amplitudes. Because the reconstructed distribution is based on a catalog of earthquakes that is much larger than the tsunami catalog, it is less susceptible to the effects of record-breaking events and more indicative of the actual distribution of tsunami amplitudes.

Improving deep convolutional neural networks with mixed maxout units.

PubMed

Zhao, Hui-Zhen; Liu, Fu-Xian; Li, Long-Yue

2017-01-01

Motivated by insights from the maxout-units-based deep Convolutional Neural Network (CNN) that "non-maximal features are unable to deliver" and "feature mapping subspace pooling is insufficient," we present a novel mixed variant of the recently introduced maxout unit called a mixout unit. Specifically, we do so by calculating the exponential probabilities of feature mappings gained by applying different convolutional transformations over the same input and then calculating the expected values according to their exponential probabilities. Moreover, we introduce the Bernoulli distribution to balance the maximum values with the expected values of the feature mappings subspace. Finally, we design a simple model to verify the pooling ability of mixout units and a Mixout-units-based Network-in-Network (NiN) model to analyze the feature learning ability of the mixout models. We argue that our proposed units improve the pooling ability and that mixout models can achieve better feature learning and classification performance.

Stochastic Car-Following Model for Explaining Nonlinear Traffic Phenomena

NASA Astrophysics Data System (ADS)

Meng, Jianping; Song, Tao; Dong, Liyun; Dai, Shiqiang

There is a common time parameter for representing the sensitivity or the lag (response) time of drivers in many car-following models. In the viewpoint of traffic psychology, this parameter could be considered as the perception-response time (PRT). Generally, this parameter is set to be a constant in previous models. However, PRT is actually not a constant but a random variable described by the lognormal distribution. Thus the probability can be naturally introduced into car-following models by recovering the probability of PRT. For demonstrating this idea, a specific stochastic model is constructed based on the optimal velocity model. By conducting simulations under periodic boundary conditions, it is found that some important traffic phenomena, such as the hysteresis and phantom traffic jams phenomena, can be reproduced more realistically. Especially, an interesting experimental feature of traffic jams, i.e., two moving jams propagating in parallel with constant speed stably and sustainably, is successfully captured by the present model.

Solutions of burnt-bridge models for molecular motor transport.

PubMed

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

2007-03-01

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

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

NASA Astrophysics Data System (ADS)

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

2007-03-01

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

Solutions of burnt-bridge models for molecular motor transport

NASA Astrophysics Data System (ADS)

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

2007-03-01

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

A goodness-of-fit test for capture-recapture model M(t) under closure

USGS Publications Warehouse

Stanley, T.R.; Burnham, K.P.

1999-01-01

A new, fully efficient goodness-of-fit test for the time-specific closed-population capture-recapture model M(t) is presented. This test is based on the residual distribution of the capture history data given the maximum likelihood parameter estimates under model M(t), is partitioned into informative components, and is based on chi-square statistics. Comparison of this test with Leslie's test (Leslie, 1958, Journal of Animal Ecology 27, 84- 86) for model M(t), using Monte Carlo simulations, shows the new test generally outperforms Leslie's test. The new test is frequently computable when Leslie's test is not, has Type I error rates that are closer to nominal error rates than Leslie's test, and is sensitive to behavioral variation and heterogeneity in capture probabilities. Leslie's test is not sensitive to behavioral variation in capture probabilities but, when computable, has greater power to detect heterogeneity than the new test.

Survival probability of diffusion with trapping in cellular neurobiology

NASA Astrophysics Data System (ADS)

Holcman, David; Marchewka, Avi; Schuss, Zeev

2005-09-01

The problem of diffusion with absorption and trapping sites arises in the theory of molecular signaling inside and on the membranes of biological cells. In particular, this problem arises in the case of spine-dendrite communication, where the number of calcium ions, modeled as random particles, is regulated across the spine microstructure by pumps, which play the role of killing sites, while the end of the dendritic shaft is an absorbing boundary. We develop a general mathematical framework for diffusion in the presence of absorption and killing sites and apply it to the computation of the time-dependent survival probability of ions. We also compute the ratio of the number of absorbed particles at a specific location to the number of killed particles. We show that the ratio depends on the distribution of killing sites. The biological consequence is that the position of the pumps regulates the fraction of calcium ions that reach the dendrite.

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.

Novel Radiobiological Gamma Index for Evaluation of 3-Dimensional Predicted Dose Distribution

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

Sumida, Iori, E-mail: sumida@radonc.med.osaka-u.ac.jp; Yamaguchi, Hajime; Kizaki, Hisao

2015-07-15

Purpose: To propose a gamma index-based dose evaluation index that integrates the radiobiological parameters of tumor control (TCP) and normal tissue complication probabilities (NTCP). Methods and Materials: Fifteen prostate and head and neck (H&N) cancer patients received intensity modulated radiation therapy. Before treatment, patient-specific quality assurance was conducted via beam-by-beam analysis, and beam-specific dose error distributions were generated. The predicted 3-dimensional (3D) dose distribution was calculated by back-projection of relative dose error distribution per beam. A 3D gamma analysis of different organs (prostate: clinical [CTV] and planned target volumes [PTV], rectum, bladder, femoral heads; H&N: gross tumor volume [GTV], CTV,more » spinal cord, brain stem, both parotids) was performed using predicted and planned dose distributions under 2%/2 mm tolerance and physical gamma passing rate was calculated. TCP and NTCP values were calculated for voxels with physical gamma indices (PGI) >1. We propose a new radiobiological gamma index (RGI) to quantify the radiobiological effects of TCP and NTCP and calculate radiobiological gamma passing rates. Results: The mean RGI gamma passing rates for prostate cases were significantly different compared with those of PGI (P<.03–.001). The mean RGI gamma passing rates for H&N cases (except for GTV) were significantly different compared with those of PGI (P<.001). Differences in gamma passing rates between PGI and RGI were due to dose differences between the planned and predicted dose distributions. Radiobiological gamma distribution was visualized to identify areas where the dose was radiobiologically important. Conclusions: RGI was proposed to integrate radiobiological effects into PGI. This index would assist physicians and medical physicists not only in physical evaluations of treatment delivery accuracy, but also in clinical evaluations of predicted dose distribution.« less

Classic Maximum Entropy Recovery of the Average Joint Distribution of Apparent FRET Efficiency and Fluorescence Photons for Single-molecule Burst Measurements

PubMed Central

DeVore, Matthew S.; Gull, Stephen F.; Johnson, Carey K.

2012-01-01

We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions. PMID:22338694

The effect of microscopic friction and size distributions on conditional probability distributions in soft particle packings

NASA Astrophysics Data System (ADS)

Saitoh, Kuniyasu; Magnanimo, Vanessa; Luding, Stefan

2017-10-01

Employing two-dimensional molecular dynamics (MD) simulations of soft particles, we study their non-affine responses to quasi-static isotropic compression where the effects of microscopic friction between the particles in contact and particle size distributions are examined. To quantify complicated restructuring of force-chain networks under isotropic compression, we introduce the conditional probability distributions (CPDs) of particle overlaps such that a master equation for distribution of overlaps in the soft particle packings can be constructed. From our MD simulations, we observe that the CPDs are well described by q-Gaussian distributions, where we find that the correlation for the evolution of particle overlaps is suppressed by microscopic friction, while it significantly increases with the increase of poly-dispersity.

Physics of chemoreception.

PubMed Central

Berg, H C; Purcell, E M

1977-01-01

Statistical fluctuations limit the precision with which a microorganism can, in a given time T, determine the concentration of a chemoattractant in the surrounding medium. The best a cell can do is to monitor continually the state of occupation of receptors distributed over its surface. For nearly optimum performance only a small fraction of the surface need be specifically adsorbing. The probability that a molecule that has collided with the cell will find a receptor is Ns/(Ns + pi a), if N receptors, each with a binding site of radius s, are evenly distributed over a cell of radius a. There is ample room for many indenpendent systems of specific receptors. The adsorption rate for molecules of moderate size cannot be significantly enhanced by motion of the cell or by stirring of the medium by the cell. The least fractional error attainable in the determination of a concentration c is approximately (TcaD) - 1/2, where D is diffusion constant of the attractant. The number of specific receptors needed to attain such precision is about a/s. Data on bacteriophage absorption, bacterial chemotaxis, and chemotaxis in a cellular slime mold are evaluated. The chemotactic sensitivity of Escherichia coli approaches that of the cell of optimum design. PMID:911982

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 population model for a long-lived, resprouting chaparral shrub: Adenostoma fasciculatum

USGS Publications Warehouse

Stohlgren, Thomas J.; Rundel, Philip W.

1986-01-01

Extensive stands of Adenostoma fasciculatum H.&A. (chamise) in the chaparral of California are periodically rejuvenated by fire. A population model based on size-specific demographic characteristics (thinning and fire-caused mortality) was developed to generate probable age distributions within size classes and survivorship curves for typical stands. The model was modified to assess the long term effects of different mortality rates on age distributions. Under observed mean mortality rates (28.7%), model output suggests some shrubs can survive more than 23 fires. A 10% increase in mortality rate by size class slightly shortened the survivorship curve, while a 10% decrease in mortality rate by size class greatly elongated the curve. This approach may be applicable to other long-lived plant species with complex life histories.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

Bretthorst, G. Larry

2013-08-01

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.

Effects of pathogen-specific clinical mastitis on probability of conception in Holstein dairy cows.

PubMed

Hertl, J A; Schukken, Y H; Welcome, F L; Tauer, L W; Gröhn, Y T

2014-11-01

The objective of this study was to estimate the effects of pathogen-specific clinical mastitis (CM), occurring in different weekly intervals before or after artificial insemination (AI), on the probability of conception in Holstein cows. Clinical mastitis occurring in weekly intervals from 6 wk before until 6 wk after AI was modeled. The first 4 AI in a cow's lactation were included. The following categories of pathogens were studied: Streptococcus spp. (comprising Streptococcus dysgalactiae, Streptococcus uberis, and other Streptococcus spp.); Staphylococcus aureus; coagulase-negative staphylococci (CNS); Escherichia coli; Klebsiella spp.; cases with CM signs but no bacterial growth (above the level that can be detected from our microbiological procedures) observed in the culture sample and cases with contamination (≥ 3 pathogens in the sample); and other pathogens [including Citrobacter, yeasts, Trueperella pyogenes, gram-negative bacilli (i.e., gram-negative organisms other than E. coli, Klebsiella spp., Enterobacter, and Citrobacter), Corynebacterium bovis, Corynebacterium spp., Pasteurella, Enterococcus, Pseudomonas, Mycoplasma, Prototheca, and others]. Other factors included in the model were parity (1, 2, 3, 4 and higher), season of AI (winter, spring, summer, autumn), day in lactation of first AI, farm, and other non-CM diseases (retained placenta, metritis, ketosis, displaced abomasum). Data from 90,271 AI in 39,361 lactations in 20,328 cows collected from 2003/2004 to 2011 from 5 New York State dairy farms were analyzed in a generalized linear mixed model with a Poisson distribution. The largest reductions in probability of conception were associated with CM occurring in the week before AI or in the 2 wk following AI. Escherichia coli and Klebsiella spp. had the greatest adverse effects on probability of conception. The probability of conception for a cow with any combination of characteristics may be calculated based on the parameter estimates. These findings may be helpful to farmers in assessing reproduction in their dairy cows for more effective cow management. Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Four-dimensional symmetry from a broad viewpoint. II Invariant distribution of quantized field oscillators and questions on infinities

NASA Technical Reports Server (NTRS)

Hsu, J. P.

1983-01-01

The foundation of the quantum field theory is changed by introducing a new universal probability principle into field operators: one single inherent and invariant probability distribution P(/k/) is postulated for boson and fermion field oscillators. This can be accomplished only when one treats the four-dimensional symmetry from a broad viewpoint. Special relativity is too restrictive to allow such a universal probability principle. A radical length, R, appears in physics through the probability distribution P(/k/). The force between two point particles vanishes when their relative distance tends to zero. This appears to be a general property for all forces and resembles the property of asymptotic freedom. The usual infinities in vacuum fluctuations and in local interactions, however complicated they may be, are all removed from quantum field theories. In appendix A a simple finite and unitary theory of unified electroweak interactions is discussed without assuming Higgs scalar bosons.