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.

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 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.

Optimum space shuttle launch times relative to natural environment

NASA Technical Reports Server (NTRS)

King, R. L.

1977-01-01

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

Optimum space shuttle launch times relative to natural environment

NASA Technical Reports Server (NTRS)

King, R. L.

1977-01-01

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

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

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)

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.

Sampling--how big a sample?

PubMed

Aitken, C G

1999-07-01

It is thought that, in a consignment of discrete units, a certain proportion of the units contain illegal material. A sample of the consignment is to be inspected. Various methods for the determination of the sample size are compared. The consignment will be considered as a random sample from some super-population of units, a certain proportion of which contain drugs. For large consignments, a probability distribution, known as the beta distribution, for the proportion of the consignment which contains illegal material is obtained. This distribution is based on prior beliefs about the proportion. Under certain specific conditions the beta distribution gives the same numerical results as an approach based on the binomial distribution. The binomial distribution provides a probability for the number of units in a sample which contain illegal material, conditional on knowing the proportion of the consignment which contains illegal material. This is in contrast to the beta distribution which provides probabilities for the proportion of a consignment which contains illegal material, conditional on knowing the number of units in the sample which contain illegal material. The interpretation when the beta distribution is used is much more intuitively satisfactory. It is also much more flexible in its ability to cater for prior beliefs which may vary given the different circumstances of different crimes. For small consignments, a distribution, known as the beta-binomial distribution, for the number of units in the consignment which are found to contain illegal material, is obtained, based on prior beliefs about the number of units in the consignment which are thought to contain illegal material. As with the beta and binomial distributions for large samples, it is shown that, in certain specific conditions, the beta-binomial and hypergeometric distributions give the same numerical results. However, the beta-binomial distribution, as with the beta distribution, has a more intuitively satisfactory interpretation and greater flexibility. The beta and the beta-binomial distributions provide methods for the determination of the minimum sample size to be taken from a consignment in order to satisfy a certain criterion. The criterion requires the specification of a proportion and a probability.

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.

Experimental investigation of the intensity fluctuation joint probability and conditional distributions of the twin-beam quantum state.

PubMed

Zhang, Yun; Kasai, Katsuyuki; Watanabe, Masayoshi

2003-01-13

We give the intensity fluctuation joint probability of the twin-beam quantum state, which was generated with an optical parametric oscillator operating above threshold. Then we present what to our knowledge is the first measurement of the intensity fluctuation conditional probability distributions of twin beams. The measured inference variance of twin beams 0.62+/-0.02, which is less than the standard quantum limit of unity, indicates inference with a precision better than that of separable states. The measured photocurrent variance exhibits a quantum correlation of as much as -4.9+/-0.2 dB between the signal and the idler.

Conditional probability distribution function of "energy transfer rate" (PDF(ɛ|PVI)) as compared with its counterpart of temperature (PDF(T|PVI)) at the same condition of fluctuation

NASA Astrophysics Data System (ADS)

He, Jiansen; Wang, Yin; Pei, Zhongtian; Zhang, Lei; Tu, Chuanyi

2017-04-01

Energy transfer rate of turbulence is not uniform everywhere but suggested to follow a certain distribution, e.g., lognormal distribution (Kolmogorov 1962). The inhomogeneous transfer rate leads to emergence of intermittency, which may be identified with some parameter, e.g., normalized partial variance increments (PVI) (Greco et al., 2009). Large PVI of magnetic field fluctuations are found to have a temperature distribution with the median and mean values higher than that for small PVI level (Osman et al., 2012). However, there is a large proportion of overlap between temperature distributions associated with the smaller and larger PVIs. So it is recognized that only PVI cannot fully determine the temperature, since the one-to-one mapping relationship does not exist. One may be curious about the reason responsible for the considerable overlap of conditional temperature distribution for different levels of PVI. Usually the hotter plasma with higher temperature is speculated to be heated more with more dissipation of turbulence energy corresponding to more energy cascading rate, if the temperature fluctuation of the eigen wave mode is not taken into account. To explore the statistical relationship between turbulence cascading and plasma thermal state, we aim to study and reveal, for the first time, the conditional probability function of "energy transfer rate" under different levels of PVI condition (PDF(ɛ|PVI)), and compare it with the conditional probability function of temperature. The conditional probability distribution function, PDF(ɛ|PVI), is derived from PDF(PVI|ɛ)·PDF(ɛ)/PDF(PVI) according to the Bayesian theorem. PDF(PVI) can be obtained directly from the data. PDF(ɛ) is derived from the conjugate-gradient inversion of PDF(PVI) by assuming reasonably that PDF(δB|σ) is a Gaussian distribution, where PVI=|δB|/ σ and σ ( ɛι)1/3. PDF(ɛ) can also be acquired from fitting PDF(δB) with an integral function ∫PDF(δB|σ)PDF(σ)d σ. As a result, PDF(ɛ|PVI) is found to shift to higher median value of ɛ with increasing PVI but with a significant overlap of PDFs for different PVIs. Therefore, PDF(ɛ|PVI) is similar to PDF(T|PVI) in the sense of slow migration along with increasing PVI. The detailed comparison between these two conditional PDFs are also performed.

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.

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

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.

Estimation of transition probabilities of credit ratings

NASA Astrophysics Data System (ADS)

Peng, Gan Chew; Hin, Pooi Ah

2015-12-01

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

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.

Conditional Probabilities and Collapse in Quantum Measurements

NASA Astrophysics Data System (ADS)

Laura, Roberto; Vanni, Leonardo

2008-09-01

We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a measurement with a given result, which gives the probability distribution for all possible consecutive measurements on the system. This statistical operator, representing the state of the system after the first measurement, is in general not the same that would be obtained using the postulate of collapse.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

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.

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.

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.

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.

Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Schwartz, Robert N.; Wang, Kang L.

2016-03-01

The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.

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

ERIC Educational Resources Information Center

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…

Simulation of precipitation by weather pattern and frontal analysis

NASA Astrophysics Data System (ADS)

Wilby, Robert

1995-12-01

Daily rainfall from two sites in central and southern England was stratified according to the presence or absence of weather fronts and then cross-tabulated with the prevailing Lamb Weather Type (LWT). A semi-Markov chain model was developed for simulating daily sequences of LWTs from matrices of transition probabilities between weather types for the British Isles 1970-1990. Daily and annual rainfall distributions were then simulated from the prevailing LWTs using historic conditional probabilities for precipitation occurrence and frontal frequencies. When compared with a conventional rainfall generator the frontal model produced improved estimates of the overall size distribution of daily rainfall amounts and in particular the incidence of low-frequency high-magnitude totals. Further research is required to establish the contribution of individual frontal sub-classes to daily rainfall totals and of long-term fluctuations in frontal frequencies to conditional probabilities.

The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process

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

Korhonen, Marko; Lee, Eunghyun

2014-01-15

We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A 31, 6057–6071 (1998)] or the q-totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle'smore » position at time t. To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.« less

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

Chang, Shih-Jung

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

A smooth mixture of Tobits model for healthcare expenditure.

PubMed

Keane, Michael; Stavrunova, Olena

2011-09-01

This paper develops a smooth mixture of Tobits (SMTobit) model for healthcare expenditure. The model is a generalization of the smoothly mixing regressions framework of Geweke and Keane (J Econometrics 2007; 138: 257-290) to the case of a Tobit-type limited dependent variable. A Markov chain Monte Carlo algorithm with data augmentation is developed to obtain the posterior distribution of model parameters. The model is applied to the US Medicare Current Beneficiary Survey data on total medical expenditure. The results suggest that the model can capture the overall shape of the expenditure distribution very well, and also provide a good fit to a number of characteristics of the conditional (on covariates) distribution of expenditure, such as the conditional mean, variance and probability of extreme outcomes, as well as the 50th, 90th, and 95th, percentiles. We find that healthier individuals face an expenditure distribution with lower mean, variance and probability of extreme outcomes, compared with their counterparts in a worse state of health. Males have an expenditure distribution with higher mean, variance and probability of an extreme outcome, compared with their female counterparts. The results also suggest that heart and cardiovascular diseases affect the expenditure of males more than that of females. Copyright © 2011 John Wiley & Sons, Ltd.

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.

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.

Method for localizing and isolating an errant process step

DOEpatents

Tobin, Jr., Kenneth W.; Karnowski, Thomas P.; Ferrell, Regina K.

2003-01-01

A method for localizing and isolating an errant process includes the steps of retrieving from a defect image database a selection of images each image having image content similar to image content extracted from a query image depicting a defect, each image in the selection having corresponding defect characterization data. A conditional probability distribution of the defect having occurred in a particular process step is derived from the defect characterization data. A process step as a highest probable source of the defect according to the derived conditional probability distribution is then identified. A method for process step defect identification includes the steps of characterizing anomalies in a product, the anomalies detected by an imaging system. A query image of a product defect is then acquired. A particular characterized anomaly is then correlated with the query image. An errant process step is then associated with the correlated image.

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.

Volume-weighted measure for eternal inflation

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

Winitzki, Sergei

2008-08-15

I propose a new volume-weighted probability measure for cosmological 'multiverse' scenarios involving eternal inflation. The 'reheating-volume (RV) cutoff' calculates the distribution of observable quantities on a portion of the reheating hypersurface that is conditioned to be finite. The RV measure is gauge-invariant, does not suffer from the 'youngness paradox', and is independent of initial conditions at the beginning of inflation. In slow-roll inflationary models with a scalar inflaton, the RV-regulated probability distributions can be obtained by solving nonlinear diffusion equations. I discuss possible applications of the new measure to 'landscape' scenarios with bubble nucleation. As an illustration, I compute themore » predictions of the RV measure in a simple toy landscape.« less

Low Probability of Intercept Waveforms via Intersymbol Dither Performance Under Multiple Conditions

DTIC Science & Technology

2009-03-01

United States Air Force, Department of Defense, or the United States Government . AFIT/GE/ENG/09-23 Low Probability of Intercept Waveforms via...21 D random variable governing the distribution of dither values 21 p (ct) D (t) probability density function of the...potential performance loss of a non-cooperative receiver compared to a cooperative receiver designed to account for ISI and multipath. 1.3 Thesis

Low Probability of Intercept Waveforms via Intersymbol Dither Performance Under Multipath Conditions

DTIC Science & Technology

2009-03-01

United States Air Force, Department of Defense, or the United States Government . AFIT/GE/ENG/09-23 Low Probability of Intercept Waveforms via...21 D random variable governing the distribution of dither values 21 p (ct) D (t) probability density function of the...potential performance loss of a non-cooperative receiver compared to a cooperative receiver designed to account for ISI and multipath. 1.3 Thesis

CProb: a computational tool for conducting conditional probability analysis.

PubMed

Hollister, Jeffrey W; Walker, Henry A; Paul, John F

2008-01-01

Conditional probability is the probability of observing one event given that another event has occurred. In an environmental context, conditional probability helps to assess the association between an environmental contaminant (i.e., the stressor) and the ecological condition of a resource (i.e., the response). These analyses, when combined with controlled experiments and other methodologies, show great promise in evaluating ecological conditions from observational data and in defining water quality and other environmental criteria. Current applications of conditional probability analysis (CPA) are largely done via scripts or cumbersome spreadsheet routines, which may prove daunting to end-users and do not provide access to the underlying scripts. Combining spreadsheets with scripts eases computation through a familiar interface (i.e., Microsoft Excel) and creates a transparent process through full accessibility to the scripts. With this in mind, we developed a software application, CProb, as an Add-in for Microsoft Excel with R, R(D)com Server, and Visual Basic for Applications. CProb calculates and plots scatterplots, empirical cumulative distribution functions, and conditional probability. In this short communication, we describe CPA, our motivation for developing a CPA tool, and our implementation of CPA as a Microsoft Excel Add-in. Further, we illustrate the use of our software with two examples: a water quality example and a landscape example. CProb is freely available for download at http://www.epa.gov/emap/nca/html/regions/cprob.

Modeling stream fish distributions using interval-censored detection times.

PubMed

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

2016-08-01

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

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.

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.

Cost of Crashes Related to Road Conditions, United States, 2006

PubMed Central

Zaloshnja, Eduard; Miller, Ted R.

2009-01-01

This is the first study to estimate the cost of crashes related to road conditions in the U.S. To model the probability that road conditions contributed to the involvement of a vehicle in the crash, we used 2000–03 Large Truck Crash Causation Study (LTCCS) data, the only dataset that provides detailed information whether road conditions contributed to crash occurrence. We applied the logistic regression results to a costed national crash dataset in order to calculate the probability that road conditions contributed to the involvement of a vehicle in each crash. In crashes where someone was moderately to seriously injured (AIS-2-6) in a vehicle that harmfully impacted a large tree or medium or large non-breakaway pole, or if the first harmful event was collision with a bridge, we changed the calculated probability of being road-related to 1. We used the state distribution of costs of fatal crashes where road conditions contributed to crash occurrence or severity to estimate the respective state distribution of non-fatal crash costs. The estimated comprehensive cost of traffic crashes where road conditions contributed to crash occurrence or severity was $217.5 billion in 2006. This represented 43.6% of the total comprehensive crash cost. The large share of crash costs related to road design and conditions underlines the importance of these factors in highway safety. Road conditions are largely controllable. Road maintenance and upgrading can prevent crashes and reduce injury severity. PMID:20184840

Chronology of Postglacial Eruptive Activity and Calculation of Eruption Probabilities for Medicine Lake Volcano, Northern California

USGS Publications Warehouse

Nathenson, Manuel; Donnelly-Nolan, Julie M.; Champion, Duane E.; Lowenstern, Jacob B.

2007-01-01

Medicine Lake volcano has had 4 eruptive episodes in its postglacial history (since 13,000 years ago) comprising 16 eruptions. Time intervals between events within the episodes are relatively short, whereas time intervals between the episodes are much longer. An updated radiocarbon chronology for these eruptions is presented that uses paleomagnetic data to constrain the choice of calibrated ages. This chronology is used with exponential, Weibull, and mixed-exponential probability distributions to model the data for time intervals between eruptions. The mixed exponential distribution is the best match to the data and provides estimates for the conditional probability of a future eruption given the time since the last eruption. The probability of an eruption at Medicine Lake volcano in the next year from today is 0.00028.

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.

On defense strategies for system of systems using aggregated correlations

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

Rao, Nageswara S.; Imam, Neena; Ma, Chris Y. T.

2017-04-01

We consider a System of Systems (SoS) wherein each system Si, i = 1; 2; ... ;N, is composed of discrete cyber and physical components which can be attacked and reinforced. We characterize the disruptions using aggregate failure correlation functions given by the conditional failure probability of SoS given the failure of an individual system. We formulate the problem of ensuring the survival of SoS as a game between an attacker and a provider, each with a utility function composed of asurvival probability term and a cost term, both expressed in terms of the number of components attacked and reinforced.more » The survival probabilities of systems satisfy simple product-form, first-order differential conditions, which simplify the Nash Equilibrium (NE) conditions. We derive the sensitivity functions that highlight the dependence of SoS survival probability at NE on cost terms, correlation functions, and individual system survival probabilities.We apply these results to a simplified model of distributed cloud computing infrastructure.« less

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

USGS Publications Warehouse

Gilliom, Robert J.; Helsel, Dennis R.

1986-01-01

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

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

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

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

1986-02-01

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

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

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

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

1984-01-01

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

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.

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

Prediction of future asset prices

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Comparison of Aperture Averaging and Receiver Diversity Techniques for Free Space Optical Links in Presence of Turbulence and Various Weather Conditions

NASA Astrophysics Data System (ADS)

Kaur, Prabhmandeep; Jain, Virander Kumar; Kar, Subrat

2014-12-01

In this paper, we investigate the performance of a Free Space Optic (FSO) link considering the impairments caused by the presence of various weather conditions such as very clear air, drizzle, haze, fog, etc., and turbulence in the atmosphere. Analytic expression for the outage probability is derived using the gamma-gamma distribution for turbulence and accounting the effect of weather conditions using the Beer-Lambert's law. The effect of receiver diversity schemes using aperture averaging and array receivers on the outage probability is studied and compared. As the aperture diameter is increased, the outage probability decreases irrespective of the turbulence strength (weak, moderate and strong) and weather conditions. Similar effects are observed when the number of direct detection receivers in the array are increased. However, it is seen that as the desired level of performance in terms of the outage probability decreases, array receiver becomes the preferred choice as compared to the receiver with aperture averaging.

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

Forecasting of future earthquakes in the northeast region of India considering energy released concept

NASA Astrophysics Data System (ADS)

Zarola, Amit; Sil, Arjun

2018-04-01

This study presents the forecasting of time and magnitude size of the next earthquake in the northeast India, using four probability distribution models (Gamma, Lognormal, Weibull and Log-logistic) considering updated earthquake catalog of magnitude Mw ≥ 6.0 that occurred from year 1737-2015 in the study area. On the basis of past seismicity of the region, two types of conditional probabilities have been estimated using their best fit model and respective model parameters. The first conditional probability is the probability of seismic energy (e × 1020 ergs), which is expected to release in the future earthquake, exceeding a certain level of seismic energy (E × 1020 ergs). And the second conditional probability is the probability of seismic energy (a × 1020 ergs/year), which is expected to release per year, exceeding a certain level of seismic energy per year (A × 1020 ergs/year). The logarithm likelihood functions (ln L) were also estimated for all four probability distribution models. A higher value of ln L suggests a better model and a lower value shows a worse model. The time of the future earthquake is forecasted by dividing the total seismic energy expected to release in the future earthquake with the total seismic energy expected to release per year. The epicentre of recently occurred 4 January 2016 Manipur earthquake (M 6.7), 13 April 2016 Myanmar earthquake (M 6.9) and the 24 August 2016 Myanmar earthquake (M 6.8) are located in zone Z.12, zone Z.16 and zone Z.15, respectively and that are the identified seismic source zones in the study area which show that the proposed techniques and models yield good forecasting accuracy.

Probabilistic sensitivity analysis for decision trees with multiple branches: use of the Dirichlet distribution in a Bayesian framework.

PubMed

Briggs, Andrew H; Ades, A E; Price, Martin J

2003-01-01

In structuring decision models of medical interventions, it is commonly recommended that only 2 branches be used for each chance node to avoid logical inconsistencies that can arise during sensitivity analyses if the branching probabilities do not sum to 1. However, information may be naturally available in an unconditional form, and structuring a tree in conditional form may complicate rather than simplify the sensitivity analysis of the unconditional probabilities. Current guidance emphasizes using probabilistic sensitivity analysis, and a method is required to provide probabilistic probabilities over multiple branches that appropriately represents uncertainty while satisfying the requirement that mutually exclusive event probabilities should sum to 1. The authors argue that the Dirichlet distribution, the multivariate equivalent of the beta distribution, is appropriate for this purpose and illustrate its use for generating a fully probabilistic transition matrix for a Markov model. Furthermore, they demonstrate that by adopting a Bayesian approach, the problem of observing zero counts for transitions of interest can be overcome.

The Generalized Quantum Episodic Memory Model.

PubMed

Trueblood, Jennifer S; Hemmer, Pernille

2017-11-01

Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory. Copyright © 2016 Cognitive Science Society, Inc.

Comonotonic bounds on the survival probabilities in the Lee-Carter model for mortality projection

NASA Astrophysics Data System (ADS)

Denuit, Michel; Dhaene, Jan

2007-06-01

In the Lee-Carter framework, future survival probabilities are random variables with an intricate distribution function. In large homogeneous portfolios of life annuities, value-at-risk or conditional tail expectation of the total yearly payout of the company are approximately equal to the corresponding quantities involving random survival probabilities. This paper aims to derive some bounds in the increasing convex (or stop-loss) sense on these random survival probabilities. These bounds are obtained with the help of comonotonic upper and lower bounds on sums of correlated random variables.

Maritime Search and Rescue via Multiple Coordinated UAS

DTIC Science & Technology

2016-01-01

partitioning method uses the underlying probability distribution assumptions to place that probability near the geometric center of the partitions. There...During partitioning the known locations are accommodated, but the unaccounted for objects are placed into geometrically unfavorable conditions. The...Zeitlin, A.D.: UAS Sence and Avoid Develop- ment - the Challenges of Technology, Standards, and Certification. Aerospace Sciences Meeting including

Timescales of isotropic and anisotropic cluster collapse

NASA Astrophysics Data System (ADS)

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

1993-12-01

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

Computing exact bundle compliance control charts via probability generating functions.

PubMed

Chen, Binchao; Matis, Timothy; Benneyan, James

2016-06-01

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

Short-term capture of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-06-01

In this paper, the short-term capture (STC) of an asteroid in the Earth-Moon system is proposed and investigated. First, the space condition of STC is analysed and five subsets of the feasible region are defined and discussed. Then, the time condition of STC is studied by parameter scanning in the Sun-Earth-Moon-asteroid restricted four-body problem. Numerical results indicate that there is a clear association between the distributions of the time probability of STC and the five subsets. Next, the influence of the Jacobi constant on STC is examined using the space and time probabilities of STC. Combining the space and time probabilities of STC, we propose a STC index to evaluate the probability of STC comprehensively. Finally, three potential STC asteroids are found and analysed.

Modeling Women's Menstrual Cycles using PICI Gates in Bayesian Network.

PubMed

Zagorecki, Adam; Łupińska-Dubicka, Anna; Voortman, Mark; Druzdzel, Marek J

2016-03-01

A major difficulty in building Bayesian network (BN) models is the size of conditional probability tables, which grow exponentially in the number of parents. One way of dealing with this problem is through parametric conditional probability distributions that usually require only a number of parameters that is linear in the number of parents. In this paper, we introduce a new class of parametric models, the Probabilistic Independence of Causal Influences (PICI) models, that aim at lowering the number of parameters required to specify local probability distributions, but are still capable of efficiently modeling a variety of interactions. A subset of PICI models is decomposable and this leads to significantly faster inference as compared to models that cannot be decomposed. We present an application of the proposed method to learning dynamic BNs for modeling a woman's menstrual cycle. We show that PICI models are especially useful for parameter learning from small data sets and lead to higher parameter accuracy than when learning CPTs.

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

The extraction and integration framework: a two-process account of statistical learning.

PubMed

Thiessen, Erik D; Kronstein, Alexandra T; Hufnagle, Daniel G

2013-07-01

The term statistical learning in infancy research originally referred to sensitivity to transitional probabilities. Subsequent research has demonstrated that statistical learning contributes to infant development in a wide array of domains. The range of statistical learning phenomena necessitates a broader view of the processes underlying statistical learning. Learners are sensitive to a much wider range of statistical information than the conditional relations indexed by transitional probabilities, including distributional and cue-based statistics. We propose a novel framework that unifies learning about all of these kinds of statistical structure. From our perspective, learning about conditional relations outputs discrete representations (such as words). Integration across these discrete representations yields sensitivity to cues and distributional information. To achieve sensitivity to all of these kinds of statistical structure, our framework combines processes that extract segments of the input with processes that compare across these extracted items. In this framework, the items extracted from the input serve as exemplars in long-term memory. The similarity structure of those exemplars in long-term memory leads to the discovery of cues and categorical structure, which guides subsequent extraction. The extraction and integration framework provides a way to explain sensitivity to both conditional statistical structure (such as transitional probabilities) and distributional statistical structure (such as item frequency and variability), and also a framework for thinking about how these different aspects of statistical learning influence each other. 2013 APA, all rights reserved

On the issues of probability distribution of GPS carrier phase observations

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Winter movement dynamics of Black Brant

USGS Publications Warehouse

Lindberg, Mark S.; Ward, David H.; Tibbitts, T. Lee; Roser, John

2007-01-01

Although North American geese are managed based on their breeding distributions, the dynamics of those breeding populations may be affected by events that occur during the winter. Birth rates of capital breeding geese may be influenced by wintering conditions, mortality may be influenced by timing of migration and wintering distribution, and immigration and emigration among breeding populations may depend on winter movement and timing of pair formation. We examined factors affecting movements of black brant (Branta bernicla nigricans) among their primary wintering sites in Mexico and southern California, USA, (Mar 1998-Mar 2000) using capture-recapture models. Although brant exhibited high probability (>0.85) of monthly and annual fidelity to the wintering sites we sampled, we observed movements among all wintering sites. Movement probabilities both within and among winters were negatively related to distance between sites. We observed a higher probability both of southward movement between winters (Mar to Dec) and northward movement between months within winters. Between-winter movements were probably most strongly affected by spatial and temporal variation in habitat quality as we saw movement patterns consistent with contrasting environmental conditions (e.g., La Niña and El Niño southern oscillation cycles). Month-to-month movements were related to migration patterns and may also have been affected by differences in habitat conditions among sites. Patterns of winter movements indicate that a network of wintering sites may be necessary for effective conservation of brant.

Winter movement dynamics of black brant

USGS Publications Warehouse

Lindberg, Mark S.; Ward, David H.; Tibbitts, T. Lee; Roser, John

2007-01-01

Although North American geese are managed based on their breeding distributions, the dynamics of those breeding populations may be affected by events that occur during the winter. Birth rates of capital breeding geese may be influenced by wintering conditions, mortality may be influenced by timing of migration and wintering distribution, and immigration and emigration among breeding populations may depend on winter movement and timing of pair formation. We examined factors affecting movements of black brant (Branta bernicla nigricans) among their primary wintering sites in Mexico and southern California, USA, (Mar 1998–Mar 2000) using capture–recapture models. Although brant exhibited high probability (>0.85) of monthly and annual fidelity to the wintering sites we sampled, we observed movements among all wintering sites. Movement probabilities both within and among winters were negatively related to distance between sites. We observed a higher probability both of southward movement between winters (Mar to Dec) and northward movement between months within winters. Between-winter movements were probably most strongly affected by spatial and temporal variation in habitat quality as we saw movement patterns consistent with contrasting environmental conditions (e.g., La Niña and El Niño southern oscillation cycles). Month-to-month movements were related to migration patterns and may also have been affected by differences in habitat conditions among sites. Patterns of winter movements indicate that a network of wintering sites may be necessary for effective conservation of brant.

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

NASA Astrophysics Data System (ADS)

Imoto, Masajiro

2003-02-01

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

Quantum Teleportation and Grover's Algorithm Without the Wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2017-02-01

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.

Change Point Problems in Regression

DTIC Science & Technology

1988-06-01

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

Game-Theoretic strategies for systems of components using product-form utilities

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

Rao, Nageswara S; Ma, Cheng-Yu; Hausken, K.

Many critical infrastructures are composed of multiple systems of components which are correlated so that disruptions to one may propagate to others. We consider such infrastructures with correlations characterized in two ways: (i) an aggregate failure correlation function specifies the conditional failure probability of the infrastructure given the failure of an individual system, and (ii) a pairwise correlation function between two systems specifies the failure probability of one system given the failure of the other. We formulate a game for ensuring the resilience of the infrastructure, wherein the utility functions of the provider and attacker are products of an infrastructuremore » survival probability term and a cost term, both expressed in terms of the numbers of system components attacked and reinforced. The survival probabilities of individual systems satisfy first-order differential conditions that lead to simple Nash Equilibrium conditions. We then derive sensitivity functions that highlight the dependence of infrastructure resilience on the cost terms, correlation functions, and individual system survival probabilities. We apply these results to simplified models of distributed cloud computing and energy grid infrastructures.« less

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.

Most recent common ancestor probability distributions in gene genealogies under selection.

PubMed

Slade, P F

2000-12-01

A computational study is made of the conditional probability distribution for the allelic type of the most recent common ancestor in genealogies of samples of n genes drawn from a population under selection, given the initial sample configuration. Comparisons with the corresponding unconditional cases are presented. Such unconditional distributions differ from samples drawn from the unique stationary distribution of population allelic frequencies, known as Wright's formula, and are quantified. Biallelic haploid and diploid models are considered. A simplified structure for the ancestral selection graph of S. M. Krone and C. Neuhauser (1997, Theor. Popul. Biol. 51, 210-237) is enhanced further, reducing the effective branching rate in the graph. This improves efficiency of such a nonneutral analogue of the coalescent for use with computational likelihood-inference techniques.

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

USGS Publications Warehouse

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

2011-01-01

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

CADDIS Volume 4. Data Analysis: Exploratory Data Analysis

EPA Pesticide Factsheets

Intro to exploratory data analysis. Overview of variable distributions, scatter plots, correlation analysis, GIS datasets. Use of conditional probability to examine stressor levels and impairment. Exploring correlations among multiple stressors.

Distribution of chirality in the quantum walk: Markov process and entanglement

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

Romanelli, Alejandro

The asymptotic behavior of the quantum walk on the line is investigated, focusing on the probability distribution of chirality independently of position. It is shown analytically that this distribution has a longtime limit that is stationary and depends on the initial conditions. This result is unexpected in the context of the unitary evolution of the quantum walk as it is usually linked to a Markovian process. The asymptotic value of the entanglement between the coin and the position is determined by the chirality distribution. For given asymptotic values of both the entanglement and the chirality distribution, it is possible tomore » find the corresponding initial conditions within a particular class of spatially extended Gaussian distributions.« less

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.

Statistics of velocity gradients in two-dimensional Navier-Stokes and ocean turbulence.

PubMed

Schorghofer, Norbert; Gille, Sarah T

2002-02-01

Probability density functions and conditional averages of velocity gradients derived from upper ocean observations are compared with results from forced simulations of the two-dimensional Navier-Stokes equations. Ocean data are derived from TOPEX satellite altimeter measurements. The simulations use rapid forcing on large scales, characteristic of surface winds. The probability distributions of transverse velocity derivatives from the ocean observations agree with the forced simulations, although they differ from unforced simulations reported elsewhere. The distribution and cross correlation of velocity derivatives provide clear evidence that large coherent eddies play only a minor role in generating the observed statistics.

Simulation of Stochastic Processes by Coupled ODE-PDE

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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.

Activated recombinative desorption: A potential component in mechanisms of spacecraft glow

NASA Technical Reports Server (NTRS)

Cross, J. B.

1985-01-01

The concept of activated recombination of atomic species on surfaces can explain the production of vibrationally and translationally excited desorbed molecular species. Equilibrium statistical mechanics predicts that the molecular quantum state distributions of desorbing molecules is a function of surface temperature only when the adsorption probability is unity and independent of initial collision conditions. In most cases, the adsorption probability is dependent upon initial conditions such as collision energy or internal quantum state distribution of impinging molecules. From detailed balance, such dynamical behavior is reflected in the internal quantum state distribution of the desorbing molecule. This concept, activated recombinative desorption, may offer a common thread in proposed mechanisms of spacecraft glow. Using molecular beam techniques and equipment available at Los Alamos, which includes a high translational energy 0-atom beam source, mass spectrometric detection of desorbed species, chemiluminescence/laser induced fluorescence detection of electronic and vibrationally excited reaction products, and Auger detection of surface adsorbed reaction products, a fundamental study of the gas surface chemistry underlying the glow process is proposed.

Adaptive Conditioning of Multiple-Point Geostatistical Facies Simulation to Flow Data with Facies Probability Maps

NASA Astrophysics Data System (ADS)

Khodabakhshi, M.; Jafarpour, B.

2013-12-01

Characterization of complex geologic patterns that create preferential flow paths in certain reservoir systems requires higher-order geostatistical modeling techniques. Multipoint statistics (MPS) provides a flexible grid-based approach for simulating such complex geologic patterns from a conceptual prior model known as a training image (TI). In this approach, a stationary TI that encodes the higher-order spatial statistics of the expected geologic patterns is used to represent the shape and connectivity of the underlying lithofacies. While MPS is quite powerful for describing complex geologic facies connectivity, the nonlinear and complex relation between the flow data and facies distribution makes flow data conditioning quite challenging. We propose an adaptive technique for conditioning facies simulation from a prior TI to nonlinear flow data. Non-adaptive strategies for conditioning facies simulation to flow data can involves many forward flow model solutions that can be computationally very demanding. To improve the conditioning efficiency, we develop an adaptive sampling approach through a data feedback mechanism based on the sampling history. In this approach, after a short period of sampling burn-in time where unconditional samples are generated and passed through an acceptance/rejection test, an ensemble of accepted samples is identified and used to generate a facies probability map. This facies probability map contains the common features of the accepted samples and provides conditioning information about facies occurrence in each grid block, which is used to guide the conditional facies simulation process. As the sampling progresses, the initial probability map is updated according to the collective information about the facies distribution in the chain of accepted samples to increase the acceptance rate and efficiency of the conditioning. This conditioning process can be viewed as an optimization approach where each new sample is proposed based on the sampling history to improve the data mismatch objective function. We extend the application of this adaptive conditioning approach to the case where multiple training images are proposed to describe the geologic scenario in a given formation. We discuss the advantages and limitations of the proposed adaptive conditioning scheme and use numerical experiments from fluvial channel formations to demonstrate its applicability and performance compared to non-adaptive conditioning techniques.

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-03-01

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

Confined active Brownian particles: theoretical description of propulsion-induced accumulation

NASA Astrophysics Data System (ADS)

Das, Shibananda; Gompper, Gerhard; Winkler, Roland G.

2018-01-01

The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.

Dose-volume histogram prediction using density estimation.

PubMed

Skarpman Munter, Johanna; Sjölund, Jens

2015-09-07

Knowledge of what dose-volume histograms can be expected for a previously unseen patient could increase consistency and quality in radiotherapy treatment planning. We propose a machine learning method that uses previous treatment plans to predict such dose-volume histograms. The key to the approach is the framing of dose-volume histograms in a probabilistic setting.The training consists of estimating, from the patients in the training set, the joint probability distribution of some predictive features and the dose. The joint distribution immediately provides an estimate of the conditional probability of the dose given the values of the predictive features. The prediction consists of estimating, from the new patient, the distribution of the predictive features and marginalizing the conditional probability from the training over this. Integrating the resulting probability distribution for the dose yields an estimate of the dose-volume histogram.To illustrate how the proposed method relates to previously proposed methods, we use the signed distance to the target boundary as a single predictive feature. As a proof-of-concept, we predicted dose-volume histograms for the brainstems of 22 acoustic schwannoma patients treated with stereotactic radiosurgery, and for the lungs of 9 lung cancer patients treated with stereotactic body radiation therapy. Comparing with two previous attempts at dose-volume histogram prediction we find that, given the same input data, the predictions are similar.In summary, we propose a method for dose-volume histogram prediction that exploits the intrinsic probabilistic properties of dose-volume histograms. We argue that the proposed method makes up for some deficiencies in previously proposed methods, thereby potentially increasing ease of use, flexibility and ability to perform well with small amounts of training data.

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.

Meteorological conditions affecting the Freeman Lake (Idaho) fire

Treesearch

George M. Jemison

1932-01-01

Measurements of meteorological conditions prevailing during the rapid spread of forest fires are greatly needed so that when their recurrence seems probable, fire-weather forecasters may issue warnings of the danger. Such determinations also can be used by forest protective agencies which operate meteorological stations to guide their own action in the distribution of...

Meaner king uses biased bases

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

Reimpell, Michael; Werner, Reinhard F.

2007-06-15

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

Meaner king uses biased bases

NASA Astrophysics Data System (ADS)

Reimpell, Michael; Werner, Reinhard F.

2007-06-01

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

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

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

Fan, Linlin; Wang, Hongrui; Wang, Cheng

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

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

DOE PAGES

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

2017-05-16

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

The influence of surface properties on the plasma dynamics in radio-frequency driven oxygen plasmas: Measurements and simulations

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

Greb, Arthur; Niemi, Kari; O'Connell, Deborah

2013-12-09

Plasma parameters and dynamics in capacitively coupled oxygen plasmas are investigated for different surface conditions. Metastable species concentration, electronegativity, spatial distribution of particle densities as well as the ionization dynamics are significantly influenced by the surface loss probability of metastable singlet delta oxygen (SDO). Simulated surface conditions are compared to experiments in the plasma-surface interface region using phase resolved optical emission spectroscopy. It is demonstrated how in-situ measurements of excitation features can be used to determine SDO surface loss probabilities for different surface materials.

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

NASA Astrophysics Data System (ADS)

Donovan, J.; Jordan, T. H.

2012-12-01

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

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

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

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

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

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

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 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.

Lost in search: (Mal-)adaptation to probabilistic decision environments in children and adults.

PubMed

Betsch, Tilmann; Lehmann, Anne; Lindow, Stefanie; Lang, Anna; Schoemann, Martin

2016-02-01

Adaptive decision making in probabilistic environments requires individuals to use probabilities as weights in predecisional information searches and/or when making subsequent choices. Within a child-friendly computerized environment (Mousekids), we tracked 205 children's (105 children 5-6 years of age and 100 children 9-10 years of age) and 103 adults' (age range: 21-22 years) search behaviors and decisions under different probability dispersions (.17; .33, .83 vs. .50, .67, .83) and constraint conditions (instructions to limit search: yes vs. no). All age groups limited their depth of search when instructed to do so and when probability dispersion was high (range: .17-.83). Unlike adults, children failed to use probabilities as weights for their searches, which were largely not systematic. When examining choices, however, elementary school children (unlike preschoolers) systematically used probabilities as weights in their decisions. This suggests that an intuitive understanding of probabilities and the capacity to use them as weights during integration is not a sufficient condition for applying simple selective search strategies that place one's focus on weight distributions. PsycINFO Database Record (c) 2016 APA, all rights reserved.

Probability, geometry, and dynamics in the toss of a thick coin

NASA Astrophysics Data System (ADS)

Yong, Ee Hou; Mahadevan, L.

2011-12-01

When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a function of its dimensions and the distribution of its initial conditions. Our theory yields a simple expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads or tails compared to sides, which we validate using data from the results of tossing coins of different aspect ratios.

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.

Quantum probability assignment limited by relativistic causality.

PubMed

Han, Yeong Deok; Choi, Taeseung

2016-03-14

Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species.

PubMed

Wang, Xueying; Walton, Jay R; Parshad, Rana D

2016-01-01

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.

Statistical Maps of Ground Magnetic Disturbance Derived from Global Geospace Models

NASA Astrophysics Data System (ADS)

Rigler, E. J.; Wiltberger, M. J.; Love, J. J.

2017-12-01

Electric currents in space are the principal driver of magnetic variations measured at Earth's surface. These in turn induce geoelectric fields that present a natural hazard for technological systems like high-voltage power distribution networks. Modern global geospace models can reasonably simulate large-scale geomagnetic response to solar wind variations, but they are less successful at deterministic predictions of intense localized geomagnetic activity that most impacts technological systems on the ground. Still, recent studies have shown that these models can accurately reproduce the spatial statistical distributions of geomagnetic activity, suggesting that their physics are largely correct. Since the magnetosphere is a largely externally driven system, most model-measurement discrepancies probably arise from uncertain boundary conditions. So, with realistic distributions of solar wind parameters to establish its boundary conditions, we use the Lyon-Fedder-Mobarry (LFM) geospace model to build a synthetic multivariate statistical model of gridded ground magnetic disturbance. From this, we analyze the spatial modes of geomagnetic response, regress on available measurements to fill in unsampled locations on the grid, and estimate the global probability distribution of extreme magnetic disturbance. The latter offers a prototype geomagnetic "hazard map", similar to those used to characterize better-known geophysical hazards like earthquakes and floods.

Moments of catchment storm area

NASA Technical Reports Server (NTRS)

Eagleson, P. S.; Wang, Q.

1985-01-01

The portion of a catchment covered by a stationary rainstorm is modeled by the common area of two overlapping circles. Given that rain occurs within the catchment and conditioned by fixed storm and catchment sizes, the first two moments of the distribution of the common area are derived from purely geometrical considerations. The variance of the wetted fraction is shown to peak when the catchment size is equal to the size of the predominant storm. The conditioning on storm size is removed by assuming a probability distribution based upon the observed fractal behavior of cloud and rainstorm areas.

Measurement of the Errors of Service Altimeter Installations During Landing-Approach and Take-Off Operations

NASA Technical Reports Server (NTRS)

Gracey, William; Jewel, Joseph W., Jr.; Carpenter, Gene T.

1960-01-01

The overall errors of the service altimeter installations of a variety of civil transport, military, and general-aviation airplanes have been experimentally determined during normal landing-approach and take-off operations. The average height above the runway at which the data were obtained was about 280 feet for the landings and about 440 feet for the take-offs. An analysis of the data obtained from 196 airplanes during 415 landing approaches and from 70 airplanes during 152 take-offs showed that: 1. The overall error of the altimeter installations in the landing- approach condition had a probable value (50 percent probability) of +/- 36 feet and a maximum probable value (99.7 percent probability) of +/- 159 feet with a bias of +10 feet. 2. The overall error in the take-off condition had a probable value of +/- 47 feet and a maximum probable value of +/- 207 feet with a bias of -33 feet. 3. The overall errors of the military airplanes were generally larger than those of the civil transports in both the landing-approach and take-off conditions. In the landing-approach condition the probable error and the maximum probable error of the military airplanes were +/- 43 and +/- 189 feet, respectively, with a bias of +15 feet, whereas those for the civil transports were +/- 22 and +/- 96 feet, respectively, with a bias of +1 foot. 4. The bias values of the error distributions (+10 feet for the landings and -33 feet for the take-offs) appear to represent a measure of the hysteresis characteristics (after effect and recovery) and friction of the instrument and the pressure lag of the tubing-instrument system.

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.

Inference for the Bivariate and Multivariate Hidden Truncated Pareto(type II) and Pareto(type IV) Distribution and Some Measures of Divergence Related to Incompatibility of Probability Distribution

ERIC Educational Resources Information Center

Ghosh, Indranil

2011-01-01

Consider a discrete bivariate random variable (X, Y) with possible values x[subscript 1], x[subscript 2],..., x[subscript I] for X and y[subscript 1], y[subscript 2],..., y[subscript J] for Y. Further suppose that the corresponding families of conditional distributions, for X given values of Y and of Y for given values of X are available. We…

Simulated big sagebrush regeneration supports predicted changes at the trailing and leading edges of distribution shifts

USGS Publications Warehouse

Schlaepfer, Daniel R.; Taylor, Kyle A.; Pennington, Victoria E.; Nelson, Kellen N.; Martin, Trace E.; Rottler, Caitlin M.; Lauenroth, William K.; Bradford, John B.

2015-01-01

Many semi-arid plant communities in western North America are dominated by big sagebrush. These ecosystems are being reduced in extent and quality due to economic development, invasive species, and climate change. These pervasive modifications have generated concern about the long-term viability of sagebrush habitat and sagebrush-obligate wildlife species (notably greater sage-grouse), highlighting the need for better understanding of the future big sagebrush distribution, particularly at the species' range margins. These leading and trailing edges of potential climate-driven sagebrush distribution shifts are likely to be areas most sensitive to climate change. We used a process-based regeneration model for big sagebrush, which simulates potential germination and seedling survival in response to climatic and edaphic conditions and tested expectations about current and future regeneration responses at trailing and leading edges that were previously identified using traditional species distribution models. Our results confirmed expectations of increased probability of regeneration at the leading edge and decreased probability of regeneration at the trailing edge below current levels. Our simulations indicated that soil water dynamics at the leading edge became more similar to the typical seasonal ecohydrological conditions observed within the current range of big sagebrush ecosystems. At the trailing edge, an increased winter and spring dryness represented a departure from conditions typically supportive of big sagebrush. Our results highlighted that minimum and maximum daily temperatures as well as soil water recharge and summer dry periods are important constraints for big sagebrush regeneration. Overall, our results confirmed previous predictions, i.e., we see consistent changes in areas identified as trailing and leading edges; however, we also identified potential local refugia within the trailing edge, mostly at sites at higher elevation. Decreasing regeneration probability at the trailing edge underscores the Schlaepfer et al. Future regeneration potential of big sagebrush potential futility of efforts to preserve and/or restore big sagebrush in these areas. Conversely, increasing regeneration probability at the leading edge suggest a growing potential for conflicts in management goals between maintaining existing grasslands by preventing sagebrush expansion versus accepting a shift in plant community composition to sagebrush dominance.

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.

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

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

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

USGS Publications Warehouse

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

2016-01-01

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

Questioning the Relevance of Model-Based Probability Statements on Extreme Weather and Future Climate

NASA Astrophysics Data System (ADS)

Smith, L. A.

2007-12-01

We question the relevance of climate-model based Bayesian (or other) probability statements for decision support and impact assessment on spatial scales less than continental and temporal averages less than seasonal. Scientific assessment of higher resolution space and time scale information is urgently needed, given the commercial availability of "products" at high spatiotemporal resolution, their provision by nationally funded agencies for use both in industry decision making and governmental policy support, and their presentation to the public as matters of fact. Specifically we seek to establish necessary conditions for probability forecasts (projections conditioned on a model structure and a forcing scenario) to be taken seriously as reflecting the probability of future real-world events. We illustrate how risk management can profitably employ imperfect models of complicated chaotic systems, following NASA's study of near-Earth PHOs (Potentially Hazardous Objects). Our climate models will never be perfect, nevertheless the space and time scales on which they provide decision- support relevant information is expected to improve with the models themselves. Our aim is to establish a set of baselines of internal consistency; these are merely necessary conditions (not sufficient conditions) that physics based state-of-the-art models are expected to pass if their output is to be judged decision support relevant. Probabilistic Similarity is proposed as one goal which can be obtained even when our models are not empirically adequate. In short, probabilistic similarity requires that, given inputs similar to today's empirical observations and observational uncertainties, we expect future models to produce similar forecast distributions. Expert opinion on the space and time scales on which we might reasonably expect probabilistic similarity may prove of much greater utility than expert elicitation of uncertainty in parameter values in a model that is not empirically adequate; this may help to explain the reluctance of experts to provide information on "parameter uncertainty." Probability statements about the real world are always conditioned on some information set; they may well be conditioned on "False" making them of little value to a rational decision maker. In other instances, they may be conditioned on physical assumptions not held by any of the modellers whose model output is being cast as a probability distribution. Our models will improve a great deal in the next decades, and our insight into the likely climate fifty years hence will improve: maintaining the credibility of the science and the coherence of science based decision support, as our models improve, require a clear statement of our current limitations. What evidence do we have that today's state-of-the-art models provide decision-relevant probability forecasts? What space and time scales do we currently have quantitative, decision-relevant information on for 2050? 2080?

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

PubMed

Allen, Jeff; Ghattas, Andrew

2016-06-01

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

Effect of Individual Component Life Distribution on Engine Life Prediction

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Probabilistic structural analysis methods and applications

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Wu, Y.-T.; Dias, B.; Rajagopal, K. R.

1988-01-01

An advanced algorithm for simulating the probabilistic distribution of structural responses due to statistical uncertainties in loads, geometry, material properties, and boundary conditions is reported. The method effectively combines an advanced algorithm for calculating probability levels for multivariate problems (fast probability integration) together with a general-purpose finite-element code for stress, vibration, and buckling analysis. Application is made to a space propulsion system turbine blade for which the geometry and material properties are treated as random variables.

Application of a multipurpose unequal probability stream survey in the Mid-Atlantic Coastal Plain

USGS Publications Warehouse

Ator, S.W.; Olsen, A.R.; Pitchford, A.M.; Denver, J.M.

2003-01-01

A stratified, spatially balanced sample with unequal probability selection was used to design a multipurpose survey of headwater streams in the Mid-Atlantic Coastal Plain. Objectives for the survey include unbiased estimates of regional stream conditions, and adequate coverage of unusual but significant environmental settings to support empirical modeling of the factors affecting those conditions. The design and field application of the survey are discussed in light of these multiple objectives. A probability (random) sample of 175 first-order nontidal streams was selected for synoptic sampling of water chemistry and benthic and riparian ecology during late winter and spring 2000. Twenty-five streams were selected within each of seven hydrogeologic subregions (strata) that were delineated on the basis of physiography and surficial geology. In each subregion, unequal inclusion probabilities were used to provide an approximately even distribution of streams along a gradient of forested to developed (agricultural or urban) land in the contributing watershed. Alternate streams were also selected. Alternates were included in groups of five in each subregion when field reconnaissance demonstrated that primary streams were inaccessible or otherwise unusable. Despite the rejection and replacement of a considerable number of primary streams during reconnaissance (up to 40 percent in one subregion), the desired land use distribution was maintained within each hydrogeologic subregion without sacrificing the probabilistic design.

United States Geological Survey fire science: fire danger monitoring and forecasting

USGS Publications Warehouse

Eidenshink, Jeff C.; Howard, Stephen M.

2012-01-01

Each day, the U.S. Geological Survey produces 7-day forecasts for all Federal lands of the distributions of number of ignitions, number of fires above a given size, and conditional probabilities of fires growing larger than a specified size. The large fire probability map is an estimate of the likelihood that ignitions will become large fires. The large fire forecast map is a probability estimate of the number of fires on federal lands exceeding 100 acres in the forthcoming week. The ignition forecast map is a probability estimate of the number of fires on Federal land greater than 1 acre in the forthcoming week. The extreme event forecast is the probability estimate of the number of fires on Federal land that may exceed 5,000 acres in the forthcoming week.

Modeling Spatial Dependence of Rainfall Extremes Across Multiple Durations

NASA Astrophysics Data System (ADS)

Le, Phuong Dong; Leonard, Michael; Westra, Seth

2018-03-01

Determining the probability of a flood event in a catchment given that another flood has occurred in a nearby catchment is useful in the design of infrastructure such as road networks that have multiple river crossings. These conditional flood probabilities can be estimated by calculating conditional probabilities of extreme rainfall and then transforming rainfall to runoff through a hydrologic model. Each catchment's hydrological response times are unlikely to be the same, so in order to estimate these conditional probabilities one must consider the dependence of extreme rainfall both across space and across critical storm durations. To represent these types of dependence, this study proposes a new approach for combining extreme rainfall across different durations within a spatial extreme value model using max-stable process theory. This is achieved in a stepwise manner. The first step defines a set of common parameters for the marginal distributions across multiple durations. The parameters are then spatially interpolated to develop a spatial field. Storm-level dependence is represented through the max-stable process for rainfall extremes across different durations. The dependence model shows a reasonable fit between the observed pairwise extremal coefficients and the theoretical pairwise extremal coefficient function across all durations. The study demonstrates how the approach can be applied to develop conditional maps of the return period and return level across different durations.

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

PubMed

Zhang, Xiang; Woodall, William H

2015-11-10

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

Extreme river flow dependence in Northern Scotland

NASA Astrophysics Data System (ADS)

Villoria, M. Franco; Scott, M.; Hoey, T.; Fischbacher-Smith, D.

2012-04-01

Various methods for the spatial analysis of hydrologic data have been developed recently. Here we present results using the conditional probability approach proposed by Keef et al. [Appl. Stat. (2009): 58,601-18] to investigate spatial interdependence in extreme river flows in Scotland. This approach does not require the specification of a correlation function, being mostly suitable for relatively small geographical areas. The work is motivated by the Flood Risk Management Act (Scotland (2009)) which requires maps of flood risk that take account of spatial dependence in extreme river flow. The method is based on two conditional measures of spatial flood risk: firstly the conditional probability PC(p) that a set of sites Y = (Y 1,...,Y d) within a region C of interest exceed a flow threshold Qp at time t (or any lag of t), given that in the specified conditioning site X > Qp; and, secondly the expected number of sites within C that will exceed a flow Qp on average (given that X > Qp). The conditional probabilities are estimated using the conditional distribution of Y |X = x (for large x), which can be modeled using a semi-parametric approach (Heffernan and Tawn [Roy. Statist. Soc. Ser. B (2004): 66,497-546]). Once the model is fitted, pseudo-samples can be generated to estimate functionals of the joint tails of the distribution of (Y,X). Conditional return level plots were directly compared to traditional return level plots thus improving our understanding of the dependence structure of extreme river flow events. Confidence intervals were calculated using block bootstrapping methods (100 replicates). We report results from applying this approach to a set of four rivers (Dulnain, Lossie, Ewe and Ness) in Northern Scotland. These sites were chosen based on data quality, spatial location and catchment characteristics. The river Ness, being the largest (catchment size 1839.1km2) was chosen as the conditioning river. Both the Ewe (441.1km2) and Ness catchments have predominantly impermeable bedrock, with the Ewe's one being very wet. The Lossie(216km2) and Dulnain (272.2km2) both contain significant areas of glacial deposits. River flow in the Dulnain is usually affected by snowmelt. In all cases, the conditional probability of each of the three rivers (Dulnain, Lossie, Ewe) decreases as the event in the conditioning river (Ness) becomes more extreme. The Ewe, despite being the furthest of the three sites from the Ness shows the strongest dependence, with relatively high (>0.4) conditional probabilities even for very extreme events (>0.995). Although the Lossie is closer geographically to the Ness than the Ewe, it shows relatively low conditional probabilities and can be considered independent of the Ness for very extreme events (> 0.990). The conditional probabilities seem to reflect the different catchment characteristics and dominant precipitation generating events, with the Ewe being more similar to the Ness than the other two rivers. This interpretation suggests that the conditional method may yield improved estimates of extreme events, but the approach is time consuming. An alternative model that is easier to implement, using a spatial quantile regression, is currently being investigated, which would also allow the introduction of further covariates, essential as the effects of climate change are incorporated into estimation procedures.

Paleoseismic event dating and the conditional probability of large earthquakes on the southern San Andreas fault, California

USGS Publications Warehouse

Biasi, G.P.; Weldon, R.J.; Fumal, T.E.; Seitz, G.G.

2002-01-01

We introduce a quantitative approach to paleoearthquake dating and apply it to paleoseismic data from the Wrightwood and Pallett Creek sites on the southern San Andreas fault. We illustrate how stratigraphic ordering, sedimentological, and historical data can be used quantitatively in the process of estimating earthquake ages. Calibrated radiocarbon age distributions are used directly from layer dating through recurrence intervals and recurrence probability estimation. The method does not eliminate subjective judgements in event dating, but it does provide a means of systematically and objectively approaching the dating process. Date distributions for the most recent 14 events at Wrightwood are based on sample and contextual evidence in Fumal et al. (2002) and site context and slip history in Weldon et al. (2002). Pallett Creek event and dating descriptions are from published sources. For the five most recent events at Wrightwood, our results are consistent with previously published estimates, with generally comparable or narrower uncertainties. For Pallett Creek, our earthquake date estimates generally overlap with previous results but typically have broader uncertainties. Some event date estimates are very sensitive to details of data interpretation. The historical earthquake in 1857 ruptured the ground at both sites but is not constrained by radiocarbon data. Radiocarbon ages, peat accumulation rates, and historical constraints at Pallett Creek for event X yield a date estimate in the earliest 1800s and preclude a date in the late 1600s. This event is almost certainly the historical 1812 earthquake, as previously concluded by Sieh et al. (1989). This earthquake also produced ground deformation at Wrightwood. All events at Pallett Creek, except for event T, about A.D. 1360, and possibly event I, about A.D. 960, have corresponding events at Wrightwood with some overlap in age ranges. Event T falls during a period of low sedimentation at Wrightwood when conditions were not favorable for recording earthquake evidence. Previously proposed correlations of Pallett Creek X with Wrightwood W3 in the 1690s and Pallett Creek event V with W5 around 1480 (Fumal et al., 1993) appear unlikely after our dating reevaluation. Apparent internal inconsistencies among event, layer, and dating relationships around events R and V identify them as candidates for further investigation at the site. Conditional probabilities of earthquake recurrence were estimated using Poisson, lognormal, and empirical models. The presence of 12 or 13 events at Wrightwood during the same interval that 10 events are reported at Pallett Creek is reflected in mean recurrence intervals of 105 and 135 years, respectively. Average Poisson model 30-year conditional probabilities are about 20% at Pallett Creek and 25% at Wrightwood. The lognormal model conditional probabilities are somewhat higher, about 25% for Pallett Creek and 34% for Wrightwood. Lognormal variance ??ln estimates of 0.76 and 0.70, respectively, imply only weak time predictability. Conditional probabilities of 29% and 46%, respectively, were estimated for an empirical distribution derived from the data alone. Conditional probability uncertainties are dominated by the brevity of the event series; dating uncertainty contributes only secondarily. Wrightwood and Pallett Creek event chronologies both suggest variations in recurrence interval with time, hinting that some form of recurrence rate modulation may be at work, but formal testing shows that neither series is more ordered than might be produced by a Poisson process.

Design and development of a ceramic radial turbine for the AGT101

NASA Technical Reports Server (NTRS)

Finger, D. G.; Gupta, S. K.

1982-01-01

An acceptable and feasible ceramic turbine wheel design has been achieved, and the relevant temperature, stress, and success probability analyses are discussed. The design is described, the materials selection presented, and the engine cycle conditions analysis parameters shown. Measured MOR four-point strengths are indicated for room and elevated temperatures, and engine conditions are analyzed for various cycle states, materials, power states, turbine inlet temperatures, and speeds. An advanced gas turbine ceramic turbine rotor thermal and stress model is developed, and cumulative probability of survival is shown for first and third-year properties of SiC and Si3N4 rotors under different operating conditions, computed for both blade and hub regions. Temperature and stress distributions for steady-state and worst-case shutdown transients are depicted.

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.

Non-linear relationship of cell hit and transformation probabilities in a low dose of inhaled radon progenies.

PubMed

Balásházy, Imre; Farkas, Arpád; Madas, Balázs Gergely; Hofmann, Werner

2009-06-01

Cellular hit probabilities of alpha particles emitted by inhaled radon progenies in sensitive bronchial epithelial cell nuclei were simulated at low exposure levels to obtain useful data for the rejection or support of the linear-non-threshold (LNT) hypothesis. In this study, local distributions of deposited inhaled radon progenies in airway bifurcation models were computed at exposure conditions characteristic of homes and uranium mines. Then, maximum local deposition enhancement factors at bronchial airway bifurcations, expressed as the ratio of local to average deposition densities, were determined to characterise the inhomogeneity of deposition and to elucidate their effect on resulting hit probabilities. The results obtained suggest that in the vicinity of the carinal regions of the central airways the probability of multiple hits can be quite high, even at low average doses. Assuming a uniform distribution of activity there are practically no multiple hits and the hit probability as a function of dose exhibits a linear shape in the low dose range. The results are quite the opposite in the case of hot spots revealed by realistic deposition calculations, where practically all cells receive multiple hits and the hit probability as a function of dose is non-linear in the average dose range of 10-100 mGy.

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

NASA Astrophysics Data System (ADS)

Sallah, M.

2014-03-01

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

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

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

Statistical analysis of landing contact conditions for three lifting body research vehicles

NASA Technical Reports Server (NTRS)

Larson, R. R.

1972-01-01

The landing contact conditions for the HL-10, M2-F2/F3, and the X-24A lifting body vehicles are analyzed statistically for 81 landings. The landing contact parameters analyzed are true airspeed, peak normal acceleration at the center of gravity, roll angle, and roll velocity. Ground measurement parameters analyzed are lateral and longitudinal distance from intended touchdown, lateral distance from touchdown to full stop, and rollout distance. The results are presented in the form of histograms for frequency distributions and cumulative frequency distribution probability curves with a Pearson Type 3 curve fit for extrapolation purposes.

Face Recognition for Access Control Systems Combining Image-Difference Features Based on a Probabilistic Model

NASA Astrophysics Data System (ADS)

Miwa, Shotaro; Kage, Hiroshi; Hirai, Takashi; Sumi, Kazuhiko

We propose a probabilistic face recognition algorithm for Access Control System(ACS)s. Comparing with existing ACSs using low cost IC-cards, face recognition has advantages in usability and security that it doesn't require people to hold cards over scanners and doesn't accept imposters with authorized cards. Therefore face recognition attracts more interests in security markets than IC-cards. But in security markets where low cost ACSs exist, price competition is important, and there is a limitation on the quality of available cameras and image control. Therefore ACSs using face recognition are required to handle much lower quality images, such as defocused and poor gain-controlled images than high security systems, such as immigration control. To tackle with such image quality problems we developed a face recognition algorithm based on a probabilistic model which combines a variety of image-difference features trained by Real AdaBoost with their prior probability distributions. It enables to evaluate and utilize only reliable features among trained ones during each authentication, and achieve high recognition performance rates. The field evaluation using a pseudo Access Control System installed in our office shows that the proposed system achieves a constant high recognition performance rate independent on face image qualities, that is about four times lower EER (Equal Error Rate) under a variety of image conditions than one without any prior probability distributions. On the other hand using image difference features without any prior probabilities are sensitive to image qualities. We also evaluated PCA, and it has worse, but constant performance rates because of its general optimization on overall data. Comparing with PCA, Real AdaBoost without any prior distribution performs twice better under good image conditions, but degrades to a performance as good as PCA under poor image conditions.

GENERAL A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

NASA Astrophysics Data System (ADS)

Gerd, Niestegge

2010-12-01

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

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

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

Fan, J; Fan, J; Hu, W

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

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

Naive Probability: Model-Based Estimates of Unique Events.

PubMed

Khemlani, Sangeet S; Lotstein, Max; Johnson-Laird, Philip N

2015-08-01

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning. © 2014 Cognitive Science Society, Inc.

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

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

Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu

In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, P ∼ 10{sup −3}.

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.

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 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.

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

Ecological niche models reveal the importance of climate variability for the biogeography of protosteloid amoebae

PubMed Central

Aguilar, María; Lado, Carlos

2012-01-01

Habitat availability and environmental preferences of species are among the most important factors in determining the success of dispersal processes and therefore in shaping the distribution of protists. We explored the differences in fundamental niches and potential distributions of an ecological guild of slime moulds—protosteloid amoebae—in the Iberian Peninsula. A large set of samples collected in a north-east to south-west transect of approximately 1000 km along the peninsula was used to test the hypothesis that, together with the existence of suitable microhabitats, climate conditions may determine the probability of survival of species. Although protosteloid amoebae share similar morphologies and life history strategies, canonical correspondence analyses showed that they have varied ecological optima, and that climate conditions have an important effect in niche differentiation. Maxent environmental niche models provided consistent predictions of the probability of presence of the species based on climate data, and they were used to generate maps of potential distribution in an ‘everything is everywhere' scenario. The most important climatic factors were, in both analyses, variables that measure changes in conditions throughout the year, confirming that the alternation of fruiting bodies, cysts and amoeboid stages in the life cycles of protosteloid amoebae constitutes an advantage for surviving in a changing environment. Microhabitat affinity seems to be influenced by climatic conditions, which suggests that the micro-environment may vary at a local scale and change together with the external climate at a larger scale. PMID:22402402

Ecological niche models reveal the importance of climate variability for the biogeography of protosteloid amoebae.

PubMed

Aguilar, María; Lado, Carlos

2012-08-01

Habitat availability and environmental preferences of species are among the most important factors in determining the success of dispersal processes and therefore in shaping the distribution of protists. We explored the differences in fundamental niches and potential distributions of an ecological guild of slime moulds-protosteloid amoebae-in the Iberian Peninsula. A large set of samples collected in a north-east to south-west transect of approximately 1000 km along the peninsula was used to test the hypothesis that, together with the existence of suitable microhabitats, climate conditions may determine the probability of survival of species. Although protosteloid amoebae share similar morphologies and life history strategies, canonical correspondence analyses showed that they have varied ecological optima, and that climate conditions have an important effect in niche differentiation. Maxent environmental niche models provided consistent predictions of the probability of presence of the species based on climate data, and they were used to generate maps of potential distribution in an 'everything is everywhere' scenario. The most important climatic factors were, in both analyses, variables that measure changes in conditions throughout the year, confirming that the alternation of fruiting bodies, cysts and amoeboid stages in the life cycles of protosteloid amoebae constitutes an advantage for surviving in a changing environment. Microhabitat affinity seems to be influenced by climatic conditions, which suggests that the micro-environment may vary at a local scale and change together with the external climate at a larger scale.

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).

The Geothermal Probabilistic Cost Model with an Application to a Geothermal Reservoir at Heber, California

NASA Technical Reports Server (NTRS)

Orren, L. H.; Ziman, G. M.; Jones, S. C.

1981-01-01

A financial accounting model that incorporates physical and institutional uncertainties was developed for geothermal projects. Among the uncertainties it can handle are well depth, flow rate, fluid temperature, and permit and construction times. The outputs of the model are cumulative probability distributions of financial measures such as capital cost, levelized cost, and profit. These outputs are well suited for use in an investment decision incorporating risk. The model has the powerful feature that conditional probability distribution can be used to account for correlations among any of the input variables. The model has been applied to a geothermal reservoir at Heber, California, for a 45-MW binary electric plant. Under the assumptions made, the reservoir appears to be economically viable.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Estimated Accuracy of Three Common Trajectory Statistical Methods

NASA Technical Reports Server (NTRS)

Kabashnikov, Vitaliy P.; Chaikovsky, Anatoli P.; Kucsera, Tom L.; Metelskaya, Natalia S.

2011-01-01

Three well-known trajectory statistical methods (TSMs), namely concentration field (CF), concentration weighted trajectory (CWT), and potential source contribution function (PSCF) methods were tested using known sources and artificially generated data sets to determine the ability of TSMs to reproduce spatial distribution of the sources. In the works by other authors, the accuracy of the trajectory statistical methods was estimated for particular species and at specified receptor locations. We have obtained a more general statistical estimation of the accuracy of source reconstruction and have found optimum conditions to reconstruct source distributions of atmospheric trace substances. Only virtual pollutants of the primary type were considered. In real world experiments, TSMs are intended for application to a priori unknown sources. Therefore, the accuracy of TSMs has to be tested with all possible spatial distributions of sources. An ensemble of geographical distributions of virtual sources was generated. Spearman s rank order correlation coefficient between spatial distributions of the known virtual and the reconstructed sources was taken to be a quantitative measure of the accuracy. Statistical estimates of the mean correlation coefficient and a range of the most probable values of correlation coefficients were obtained. All the TSMs that were considered here showed similar close results. The maximum of the ratio of the mean correlation to the width of the correlation interval containing the most probable correlation values determines the optimum conditions for reconstruction. An optimal geographical domain roughly coincides with the area supplying most of the substance to the receptor. The optimal domain s size is dependent on the substance decay time. Under optimum reconstruction conditions, the mean correlation coefficients can reach 0.70 0.75. The boundaries of the interval with the most probable correlation values are 0.6 0.9 for the decay time of 240 h and 0.5 0.95 for the decay time of 12 h. The best results of source reconstruction can be expected for the trace substances with a decay time on the order of several days. Although the methods considered in this paper do not guarantee high accuracy they are computationally simple and fast. Using the TSMs in optimum conditions and taking into account the range of uncertainties, one can obtain a first hint on potential source areas.

Transient queue-size distribution in a finite-capacity queueing system with server breakdowns and Bernoulli feedback

NASA Astrophysics Data System (ADS)

Kempa, Wojciech M.

2017-12-01

A finite-capacity queueing system with server breakdowns is investigated, in which successive exponentially distributed failure-free times are followed by repair periods. After the processing a customer may either rejoin the queue (feedback) with probability q, or definitely leave the system with probability 1 - q. The system of integral equations for transient queue-size distribution, conditioned by the initial level of buffer saturation, is build. The solution of the corresponding system written for Laplace transforms is found using the linear algebraic approach. The considered queueing system can be successfully used in modelling production lines with machine failures, in which the parameter q may be considered as a typical fraction of items demanding corrections. Morever, this queueing model can be applied in the analysis of real TCP/IP performance, where q stands for the fraction of packets requiring retransmission.

Empirical models of transitions between coral reef states: effects of region, protection, and environmental change.

PubMed

Lowe, Phillip K; Bruno, John F; Selig, Elizabeth R; Spencer, Matthew

2011-01-01

There has been substantial recent change in coral reef communities. To date, most analyses have focussed on static patterns or changes in single variables such as coral cover. However, little is known about how community-level changes occur at large spatial scales. Here, we develop Markov models of annual changes in coral and macroalgal cover in the Caribbean and Great Barrier Reef (GBR) regions. We analyzed reef surveys from the Caribbean and GBR (1996-2006). We defined a set of reef states distinguished by coral and macroalgal cover, and obtained Bayesian estimates of the annual probabilities of transitions between these states. The Caribbean and GBR had different transition probabilities, and therefore different rates of change in reef condition. This could be due to differences in species composition, management or the nature and extent of disturbances between these regions. We then estimated equilibrium probability distributions for reef states, and coral and macroalgal cover under constant environmental conditions. In both regions, the current distributions are close to equilibrium. In the Caribbean, coral cover is much lower and macroalgal cover is higher at equilibrium than in the GBR. We found no evidence for differences in transition probabilities between the first and second halves of our survey period, or between Caribbean reefs inside and outside marine protected areas. However, our power to detect such differences may have been low. We also examined the effects of altering transition probabilities on the community state equilibrium, along a continuum from unfavourable (e.g., increased sea surface temperature) to favourable (e.g., improved management) conditions. Both regions showed similar qualitative responses, but different patterns of uncertainty. In the Caribbean, uncertainty was greatest about effects of favourable changes, while in the GBR, we are most uncertain about effects of unfavourable changes. Our approach could be extended to provide risk analysis for management decisions.

The stochastic distribution of available coefficient of friction for human locomotion of five different floor surfaces.

PubMed

Chang, Wen-Ruey; Matz, Simon; Chang, Chien-Chi

2014-05-01

The maximum coefficient of friction that can be supported at the shoe and floor interface without a slip is usually called the available coefficient of friction (ACOF) for human locomotion. The probability of a slip could be estimated using a statistical model by comparing the ACOF with the required coefficient of friction (RCOF), assuming that both coefficients have stochastic distributions. An investigation of the stochastic distributions of the ACOF of five different floor surfaces under dry, water and glycerol conditions is presented in this paper. One hundred friction measurements were performed on each floor surface under each surface condition. The Kolmogorov-Smirnov goodness-of-fit test was used to determine if the distribution of the ACOF was a good fit with the normal, log-normal and Weibull distributions. The results indicated that the ACOF distributions had a slightly better match with the normal and log-normal distributions than with the Weibull in only three out of 15 cases with a statistical significance. The results are far more complex than what had heretofore been published and different scenarios could emerge. Since the ACOF is compared with the RCOF for the estimate of slip probability, the distribution of the ACOF in seven cases could be considered a constant for this purpose when the ACOF is much lower or higher than the RCOF. A few cases could be represented by a normal distribution for practical reasons based on their skewness and kurtosis values without a statistical significance. No representation could be found in three cases out of 15. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.

The role of probabilities in physics.

PubMed

Le Bellac, Michel

2012-09-01

Although modern physics was born in the XVIIth century as a fully deterministic theory in the form of Newtonian mechanics, the use of probabilistic arguments turned out later on to be unavoidable. Three main situations can be distinguished. (1) When the number of degrees of freedom is very large, on the order of Avogadro's number, a detailed dynamical description is not possible, and in fact not useful: we do not care about the velocity of a particular molecule in a gas, all we need is the probability distribution of the velocities. This statistical description introduced by Maxwell and Boltzmann allows us to recover equilibrium thermodynamics, gives a microscopic interpretation of entropy and underlies our understanding of irreversibility. (2) Even when the number of degrees of freedom is small (but larger than three) sensitivity to initial conditions of chaotic dynamics makes determinism irrelevant in practice, because we cannot control the initial conditions with infinite accuracy. Although die tossing is in principle predictable, the approach to chaotic dynamics in some limit implies that our ignorance of initial conditions is translated into a probabilistic description: each face comes up with probability 1/6. (3) As is well-known, quantum mechanics is incompatible with determinism. However, quantum probabilities differ in an essential way from the probabilities introduced previously: it has been shown from the work of John Bell that quantum probabilities are intrinsic and cannot be given an ignorance interpretation based on a hypothetical deeper level of description. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

NASA Technical Reports Server (NTRS)

Solakiewiz, Richard; Koshak, William

2008-01-01

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

Influence of item distribution pattern and abundance on efficiency of benthic core sampling

USGS Publications Warehouse

Behney, Adam C.; O'Shaughnessy, Ryan; Eichholz, Michael W.; Stafford, Joshua D.

2014-01-01

ore sampling is a commonly used method to estimate benthic item density, but little information exists about factors influencing the accuracy and time-efficiency of this method. We simulated core sampling in a Geographic Information System framework by generating points (benthic items) and polygons (core samplers) to assess how sample size (number of core samples), core sampler size (cm2), distribution of benthic items, and item density affected the bias and precision of estimates of density, the detection probability of items, and the time-costs. When items were distributed randomly versus clumped, bias decreased and precision increased with increasing sample size and increased slightly with increasing core sampler size. Bias and precision were only affected by benthic item density at very low values (500–1,000 items/m2). Detection probability (the probability of capturing ≥ 1 item in a core sample if it is available for sampling) was substantially greater when items were distributed randomly as opposed to clumped. Taking more small diameter core samples was always more time-efficient than taking fewer large diameter samples. We are unable to present a single, optimal sample size, but provide information for researchers and managers to derive optimal sample sizes dependent on their research goals and environmental conditions.

Stochastic Analysis of Wind Energy for Wind Pump Irrigation in Coastal Andhra Pradesh, India

NASA Astrophysics Data System (ADS)

Raju, M. M.; Kumar, A.; Bisht, D.; Rao, D. B.

2014-09-01

The rapid escalation in the prices of oil and gas as well as increasing demand for energy has attracted the attention of scientists and researchers to explore the possibility of generating and utilizing the alternative and renewable sources of wind energy in the long coastal belt of India with considerable wind energy resources. A detailed analysis of wind potential is a prerequisite to harvest the wind energy resources efficiently. Keeping this in view, the present study was undertaken to analyze the wind energy potential to assess feasibility of the wind-pump operated irrigation system in the coastal region of Andhra Pradesh, India, where high ground water table conditions are available. The stochastic analysis of wind speed data were tested to fit a probability distribution, which describes the wind energy potential in the region. The normal and Weibull probability distributions were tested; and on the basis of Chi square test, the Weibull distribution gave better results. Hence, it was concluded that the Weibull probability distribution may be used to stochastically describe the annual wind speed data of coastal Andhra Pradesh with better accuracy. The size as well as the complete irrigation system with mass curve analysis was determined to satisfy various daily irrigation demands at different risk levels.

Computing under-ice discharge: A proof-of-concept using hydroacoustics and the Probability Concept

NASA Astrophysics Data System (ADS)

Fulton, John W.; Henneberg, Mark F.; Mills, Taylor J.; Kohn, Michael S.; Epstein, Brian; Hittle, Elizabeth A.; Damschen, William C.; Laveau, Christopher D.; Lambrecht, Jason M.; Farmer, William H.

2018-07-01

Under-ice discharge is estimated using open-water reference hydrographs; however, the ratings for ice-affected sites are generally qualified as poor. The U.S. Geological Survey (USGS), in collaboration with the Colorado Water Conservation Board, conducted a proof-of-concept to develop an alternative method for computing under-ice discharge using hydroacoustics and the Probability Concept. The study site was located south of Minturn, Colorado (CO), USA, and was selected because of (1) its proximity to the existing USGS streamgage 09064600 Eagle River near Minturn, CO, and (2) its ease-of-access to verify discharge using a variety of conventional methods. From late September 2014 to early March 2015, hydraulic conditions varied from open water to under ice. These temporal changes led to variations in water depth and velocity. Hydroacoustics (tethered and uplooking acoustic Doppler current profilers and acoustic Doppler velocimeters) were deployed to measure the vertical-velocity profile at a singularly important vertical of the channel-cross section. Because the velocity profile was non-standard and cannot be characterized using a Power Law or Log Law, velocity data were analyzed using the Probability Concept, which is a probabilistic formulation of the velocity distribution. The Probability Concept-derived discharge was compared to conventional methods including stage-discharge and index-velocity ratings and concurrent field measurements; each is complicated by the dynamics of ice formation, pressure influences on stage measurements, and variations in cross-sectional area due to ice formation. No particular discharge method was assigned as truth. Rather one statistical metric (Kolmogorov-Smirnov; KS), agreement plots, and concurrent measurements provided a measure of comparability between various methods. Regardless of the method employed, comparisons between each method revealed encouraging results depending on the flow conditions and the absence or presence of ice cover. For example, during lower discharges dominated by under-ice and transition (intermittent open-water and under-ice) conditions, the KS metric suggests there is not sufficient information to reject the null hypothesis and implies that the Probability Concept and index-velocity rating represent similar distributions. During high-flow, open-water conditions, the comparisons are less definitive; therefore, it is important that the appropriate analytical method and instrumentation be selected. Six conventional discharge measurements were collected concurrently with Probability Concept-derived discharges with percent differences (%) of -9.0%, -21%, -8.6%, 17.8%, 3.6%, and -2.3%. This proof-of-concept demonstrates that riverine discharges can be computed using the Probability Concept for a range of hydraulic extremes (variations in discharge, open-water and under-ice conditions) immediately after the siting phase is complete, which typically requires one day. Computing real-time discharges is particularly important at sites, where (1) new streamgages are planned, (2) river hydraulics are complex, and (3) shifts in the stage-discharge rating are needed to correct the streamflow record. Use of the Probability Concept does not preclude the need to maintain a stage-area relation. Both the Probability Concept and index-velocity rating offer water-resource managers and decision makers alternatives for computing real-time discharge for open-water and under-ice conditions.

Computing under-ice discharge: A proof-of-concept using hydroacoustics and the Probability Concept

USGS Publications Warehouse

Fulton, John W.; Henneberg, Mark F.; Mills, Taylor J.; Kohn, Michael S.; Epstein, Brian; Hittle, Elizabeth A.; Damschen, William C.; Laveau, Christopher D.; Lambrecht, Jason M.; Farmer, William H.

2018-01-01

Under-ice discharge is estimated using open-water reference hydrographs; however, the ratings for ice-affected sites are generally qualified as poor. The U.S. Geological Survey (USGS), in collaboration with the Colorado Water Conservation Board, conducted a proof-of-concept to develop an alternative method for computing under-ice discharge using hydroacoustics and the Probability Concept.The study site was located south of Minturn, Colorado (CO), USA, and was selected because of (1) its proximity to the existing USGS streamgage 09064600 Eagle River near Minturn, CO, and (2) its ease-of-access to verify discharge using a variety of conventional methods. From late September 2014 to early March 2015, hydraulic conditions varied from open water to under ice. These temporal changes led to variations in water depth and velocity. Hydroacoustics (tethered and uplooking acoustic Doppler current profilers and acoustic Doppler velocimeters) were deployed to measure the vertical-velocity profile at a singularly important vertical of the channel-cross section. Because the velocity profile was non-standard and cannot be characterized using a Power Law or Log Law, velocity data were analyzed using the Probability Concept, which is a probabilistic formulation of the velocity distribution. The Probability Concept-derived discharge was compared to conventional methods including stage-discharge and index-velocity ratings and concurrent field measurements; each is complicated by the dynamics of ice formation, pressure influences on stage measurements, and variations in cross-sectional area due to ice formation.No particular discharge method was assigned as truth. Rather one statistical metric (Kolmogorov-Smirnov; KS), agreement plots, and concurrent measurements provided a measure of comparability between various methods. Regardless of the method employed, comparisons between each method revealed encouraging results depending on the flow conditions and the absence or presence of ice cover.For example, during lower discharges dominated by under-ice and transition (intermittent open-water and under-ice) conditions, the KS metric suggests there is not sufficient information to reject the null hypothesis and implies that the Probability Concept and index-velocity rating represent similar distributions. During high-flow, open-water conditions, the comparisons are less definitive; therefore, it is important that the appropriate analytical method and instrumentation be selected. Six conventional discharge measurements were collected concurrently with Probability Concept-derived discharges with percent differences (%) of −9.0%, −21%, −8.6%, 17.8%, 3.6%, and −2.3%.This proof-of-concept demonstrates that riverine discharges can be computed using the Probability Concept for a range of hydraulic extremes (variations in discharge, open-water and under-ice conditions) immediately after the siting phase is complete, which typically requires one day. Computing real-time discharges is particularly important at sites, where (1) new streamgages are planned, (2) river hydraulics are complex, and (3) shifts in the stage-discharge rating are needed to correct the streamflow record. Use of the Probability Concept does not preclude the need to maintain a stage-area relation. Both the Probability Concept and index-velocity rating offer water-resource managers and decision makers alternatives for computing real-time discharge for open-water and under-ice conditions.

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

PubMed

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

2013-02-01

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Human instrumental performance in ratio and interval contingencies: A challenge for associative theory.

PubMed

Pérez, Omar D; Aitken, Michael R F; Zhukovsky, Peter; Soto, Fabián A; Urcelay, Gonzalo P; Dickinson, Anthony

2016-12-15

Associative learning theories regard the probability of reinforcement as the critical factor determining responding. However, the role of this factor in instrumental conditioning is not completely clear. In fact, free-operant experiments show that participants respond at a higher rate on variable ratio than on variable interval schedules even though the reinforcement probability is matched between the schedules. This difference has been attributed to the differential reinforcement of long inter-response times (IRTs) by interval schedules, which acts to slow responding. In the present study, we used a novel experimental design to investigate human responding under random ratio (RR) and regulated probability interval (RPI) schedules, a type of interval schedule that sets a reinforcement probability independently of the IRT duration. Participants responded on each type of schedule before a final choice test in which they distributed responding between two schedules similar to those experienced during training. Although response rates did not differ during training, the participants responded at a lower rate on the RPI schedule than on the matched RR schedule during the choice test. This preference cannot be attributed to a higher probability of reinforcement for long IRTs and questions the idea that similar associative processes underlie classical and instrumental conditioning.

Unbiased multi-fidelity estimate of failure probability of a free plane jet

NASA Astrophysics Data System (ADS)

Marques, Alexandre; Kramer, Boris; Willcox, Karen; Peherstorfer, Benjamin

2017-11-01

Estimating failure probability related to fluid flows is a challenge because it requires a large number of evaluations of expensive models. We address this challenge by leveraging multiple low fidelity models of the flow dynamics to create an optimal unbiased estimator. In particular, we investigate the effects of uncertain inlet conditions in the width of a free plane jet. We classify a condition as failure when the corresponding jet width is below a small threshold, such that failure is a rare event (failure probability is smaller than 0.001). We estimate failure probability by combining the frameworks of multi-fidelity importance sampling and optimal fusion of estimators. Multi-fidelity importance sampling uses a low fidelity model to explore the parameter space and create a biasing distribution. An unbiased estimate is then computed with a relatively small number of evaluations of the high fidelity model. In the presence of multiple low fidelity models, this framework offers multiple competing estimators. Optimal fusion combines all competing estimators into a single estimator with minimal variance. We show that this combined framework can significantly reduce the cost of estimating failure probabilities, and thus can have a large impact in fluid flow applications. This work was funded by DARPA.

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.

Potential distribution dataset of honeybees in Indian Ocean Islands: Case study of Zanzibar Island.

PubMed

Mwalusepo, Sizah; Muli, Eliud; Nkoba, Kiatoko; Nguku, Everlyn; Kilonzo, Joseph; Abdel-Rahman, Elfatih M; Landmann, Tobias; Fakih, Asha; Raina, Suresh

2017-10-01

Honeybees ( Apis mellifera ) are principal insect pollinators, whose worldwide distribution and abundance is known to largely depend on climatic conditions. However, the presence records dataset on potential distribution of honeybees in Indian Ocean Islands remain less documented. Presence records in shape format and probability of occurrence of honeybees with different temperature change scenarios is provided in this article across Zanzibar Island. Maximum entropy (Maxent) package was used to analyse the potential distribution of honeybees. The dataset provides information on the current and future distribution of the honey bees in Zanzibar Island. The dataset is of great importance for improving stakeholders understanding of the role of temperature change on the spatial distribution of honeybees.

Interference experiment with asymmetric double slit by using 1.2-MV field emission transmission electron microscope.

PubMed

Harada, Ken; Akashi, Tetsuya; Niitsu, Kodai; Shimada, Keiko; Ono, Yoshimasa A; Shindo, Daisuke; Shinada, Hiroyuki; Mori, Shigeo

2018-01-17

Advanced electron microscopy technologies have made it possible to perform precise double-slit interference experiments. We used a 1.2-MV field emission electron microscope providing coherent electron waves and a direct detection camera system enabling single-electron detections at a sub-second exposure time. We developed a method to perform the interference experiment by using an asymmetric double-slit fabricated by a focused ion beam instrument and by operating the microscope under a "pre-Fraunhofer" condition, different from the Fraunhofer condition of conventional double-slit experiments. Here, pre-Fraunhofer condition means that each single-slit observation was performed under the Fraunhofer condition, while the double-slit observations were performed under the Fresnel condition. The interference experiments with each single slit and with the asymmetric double slit were carried out under two different electron dose conditions: high-dose for calculation of electron probability distribution and low-dose for each single electron distribution. Finally, we exemplified the distribution of single electrons by color-coding according to the above three types of experiments as a composite image.

Time-dependent earthquake probabilities

USGS Publications Warehouse

Gomberg, J.; Belardinelli, M.E.; Cocco, M.; Reasenberg, P.

2005-01-01

We have attempted to provide a careful examination of a class of approaches for estimating the conditional probability of failure of a single large earthquake, particularly approaches that account for static stress perturbations to tectonic loading as in the approaches of Stein et al. (1997) and Hardebeck (2004). We have loading as in the framework based on a simple, generalized rate change formulation and applied it to these two approaches to show how they relate to one another. We also have attempted to show the connection between models of seismicity rate changes applied to (1) populations of independent faults as in background and aftershock seismicity and (2) changes in estimates of the conditional probability of failures of different members of a the notion of failure rate corresponds to successive failures of different members of a population of faults. The latter application requires specification of some probability distribution (density function of PDF) that describes some population of potential recurrence times. This PDF may reflect our imperfect knowledge of when past earthquakes have occurred on a fault (epistemic uncertainty), the true natural variability in failure times, or some combination of both. We suggest two end-member conceptual single-fault models that may explain natural variability in recurrence times and suggest how they might be distinguished observationally. When viewed deterministically, these single-fault patch models differ significantly in their physical attributes, and when faults are immature, they differ in their responses to stress perturbations. Estimates of conditional failure probabilities effectively integrate over a range of possible deterministic fault models, usually with ranges that correspond to mature faults. Thus conditional failure probability estimates usually should not differ significantly for these models. Copyright 2005 by the American Geophysical Union.

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.

Probability of detecting perchlorate under natural conditions in deep groundwater in California and the Southwestern United States

USGS Publications Warehouse

Fram, Miranda S.; Belitz, Kenneth

2011-01-01

We use data from 1626 groundwater samples collected in California, primarily from public drinking water supply wells, to investigate the distribution of perchlorate in deep groundwater under natural conditions. The wells were sampled for the California Groundwater Ambient Monitoring and Assessment Priority Basin Project. We develop a logistic regression model for predicting probabilities of detecting perchlorate at concentrations greater than multiple threshold concentrations as a function of climate (represented by an aridity index) and potential anthropogenic contributions of perchlorate (quantified as an anthropogenic score, AS). AS is a composite categorical variable including terms for nitrate, pesticides, and volatile organic compounds. Incorporating water-quality parameters in AS permits identification of perturbation of natural occurrence patterns by flushing of natural perchlorate salts from unsaturated zones by irrigation recharge as well as addition of perchlorate from industrial and agricultural sources. The data and model results indicate low concentrations (0.1-0.5 μg/L) of perchlorate occur under natural conditions in groundwater across a wide range of climates, beyond the arid to semiarid climates in which they mostly have been previously reported. The probability of detecting perchlorate at concentrations greater than 0.1 μg/L under natural conditions ranges from 50-70% in semiarid to arid regions of California and the Southwestern United States to 5-15% in the wettest regions sampled (the Northern California coast). The probability of concentrations above 1 μg/L under natural conditions is low (generally <3%).

Design and application of air-conditioning suit based on eddy current cooling principle for distribution network working with power uninterrupted

NASA Astrophysics Data System (ADS)

Xu, Li; Liu, Lanlan; Niu, Jie; Tang, Li; Li, Jinliang; Zhou, Zhanfan; Long, Chenhai; Yang, Qi; Yi, Ziqi; Guo, Hao; Long, Yang; Fu, Yanyi

2017-05-01

As social requirement of power supply reliability keeps rising, distribution network working with power uninterrupted has been widely carried out, while the high - temperature operating environment in summer can easily lead to physical discomfort for the operators, and then lead to safety incidents. Aiming at above problem, air-conditioning suit for distribution network working with power uninterrupted has been putted forward in this paper, and the structure composition and cooling principle of which has been explained, and it has been ultimately put to on-site application. The results showed that, cooling effect of air-conditioning suits was remarkable, and improved the working environment for the operators effectively, which is of great significance to improve Chinese level of working with power uninterrupted, reduce the probability of accidents and enhance the reliability of power supply.

Effects of life-history requirements on the distribution of a threatened reptile.

PubMed

Thompson, Denise M; Ligon, Day B; Patton, Jason C; Papeş, Monica

2017-04-01

Survival and reproduction are the two primary life-history traits essential for species' persistence; however, the environmental conditions that support each of these traits may not be the same. Despite this, reproductive requirements are seldom considered when estimating species' potential distributions. We sought to examine potentially limiting environmental factors influencing the distribution of an oviparous reptile of conservation concern with respect to the species' survival and reproduction and to assess the implications of the species' predicted climatic constraints on current conservation practices. We used ecological niche modeling to predict the probability of environmental suitability for the alligator snapping turtle (Macrochelys temminckii). We built an annual climate model to examine survival and a nesting climate model to examine reproduction. We combined incubation temperature requirements, products of modeled soil temperature data, and our estimated distributions to determine whether embryonic development constrained the northern distribution of the species. Low annual precipitation constrained the western distribution of alligator snapping turtles, whereas the northern distribution was constrained by thermal requirements during embryonic development. Only a portion of the geographic range predicted to have a high probability of suitability for alligator snapping turtle survival was estimated to be capable of supporting successful embryonic development. Historic occurrence records suggest adult alligator snapping turtles can survive in regions with colder climes than those associated with consistent and successful production of offspring. Estimated egg-incubation requirements indicated that current reintroductions at the northern edge of the species' range are within reproductively viable environmental conditions. Our results highlight the importance of considering survival and reproduction when estimating species' ecological niches, implicating conservation plans, and benefits of incorporating physiological data when evaluating species' distributions. © 2016 Society for Conservation Biology.

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.

A Deterministic Annealing Approach to Clustering AIRS Data

NASA Technical Reports Server (NTRS)

Guillaume, Alexandre; Braverman, Amy; Ruzmaikin, Alexander

2012-01-01

We will examine the validity of means and standard deviations as a basis for climate data products. We will explore the conditions under which these two simple statistics are inadequate summaries of the underlying empirical probability distributions by contrasting them with a nonparametric, method called Deterministic Annealing technique

Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

NASA Astrophysics Data System (ADS)

Abe, Sumiyoshi

2014-11-01

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.

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.

Game-theoretic strategies for asymmetric networked systems

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

Rao, Nageswara S.; Ma, Chris Y. T.; Hausken, Kjell

Abstract—We consider an infrastructure consisting of a network of systems each composed of discrete components that can be reinforced at a certain cost to guard against attacks. The network provides the vital connectivity between systems, and hence plays a critical, asymmetric role in the infrastructure operations. We characterize the system-level correlations using the aggregate failure correlation function that specifies the infrastructure failure probability given the failure of an individual system or network. The survival probabilities of systems and network satisfy first-order differential conditions that capture the component-level correlations. We formulate the problem of ensuring the infrastructure survival as a gamemore » between anattacker and a provider, using the sum-form and product-form utility functions, each composed of a survival probability term and a cost term. We derive Nash Equilibrium conditions which provide expressions for individual system survival probabilities, and also the expected capacity specified by the total number of operational components. These expressions differ only in a single term for the sum-form and product-form utilities, despite their significant differences.We apply these results to simplified models of distributed cloud computing infrastructures.« less

Bayesian network models for error detection in radiotherapy plans

NASA Astrophysics Data System (ADS)

Kalet, Alan M.; Gennari, John H.; Ford, Eric C.; Phillips, Mark H.

2015-04-01

The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network’s conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.

Scaling and clustering effects of extreme precipitation distributions

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Zhou, Yu; Singh, Vijay P.; Li, Jianfeng

2012-08-01

SummaryOne of the impacts of climate change and human activities on the hydrological cycle is the change in the precipitation structure. Closely related to the precipitation structure are two characteristics: the volume (m) of wet periods (WPs) and the time interval between WPs or waiting time (t). Using daily precipitation data for a period of 1960-2005 from 590 rain gauge stations in China, these two characteristics are analyzed, involving scaling and clustering of precipitation episodes. Our findings indicate that m and t follow similar probability distribution curves, implying that precipitation processes are controlled by similar underlying thermo-dynamics. Analysis of conditional probability distributions shows a significant dependence of m and t on their previous values of similar volumes, and the dependence tends to be stronger when m is larger or t is longer. It indicates that a higher probability can be expected when high-intensity precipitation is followed by precipitation episodes with similar precipitation intensity and longer waiting time between WPs is followed by the waiting time of similar duration. This result indicates the clustering of extreme precipitation episodes and severe droughts or floods are apt to occur in groups.

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.

An estimation method of the direct benefit of a waterlogging control project applicable to the changing environment

NASA Astrophysics Data System (ADS)

Zengmei, L.; Guanghua, Q.; Zishen, C.

2015-05-01

The direct benefit of a waterlogging control project is reflected by the reduction or avoidance of waterlogging loss. Before and after the construction of a waterlogging control project, the disaster-inducing environment in the waterlogging-prone zone is generally different. In addition, the category, quantity and spatial distribution of the disaster-bearing bodies are also changed more or less. Therefore, under the changing environment, the direct benefit of a waterlogging control project should be the reduction of waterlogging losses compared to conditions with no control project. Moreover, the waterlogging losses with or without the project should be the mathematical expectations of the waterlogging losses when rainstorms of all frequencies meet various water levels in the drainage-accepting zone. So an estimation model of the direct benefit of waterlogging control is proposed. Firstly, on the basis of a Copula function, the joint distribution of the rainstorms and the water levels are established, so as to obtain their joint probability density function. Secondly, according to the two-dimensional joint probability density distribution, the dimensional domain of integration is determined, which is then divided into small domains so as to calculate the probability for each of the small domains and the difference between the average waterlogging loss with and without a waterlogging control project, called the regional benefit of waterlogging control project, under the condition that rainstorms in the waterlogging-prone zone meet the water level in the drainage-accepting zone. Finally, it calculates the weighted mean of the project benefit of all small domains, with probability as the weight, and gets the benefit of the waterlogging control project. Taking the estimation of benefit of a waterlogging control project in Yangshan County, Guangdong Province, as an example, the paper briefly explains the procedures in waterlogging control project benefit estimation. The results show that the waterlogging control benefit estimation model constructed is applicable to the changing conditions that occur in both the disaster-inducing environment of the waterlogging-prone zone and disaster-bearing bodies, considering all conditions when rainstorms of all frequencies meet different water levels in the drainage-accepting zone. Thus, the estimation method of waterlogging control benefit can reflect the actual situation more objectively, and offer a scientific basis for rational decision-making for waterlogging control projects.

New approach in bivariate drought duration and severity analysis

NASA Astrophysics Data System (ADS)

Montaseri, Majid; Amirataee, Babak; Rezaie, Hossein

2018-04-01

The copula functions have been widely applied as an advance technique to create joint probability distribution of drought duration and severity. The approach of data collection as well as the amount of data and dispersion of data series can last a significant impact on creating such joint probability distribution using copulas. Usually, such traditional analyses have shed an Unconnected Drought Runs (UDR) approach towards droughts. In other word, droughts with different durations would be independent of each other. Emphasis on such data collection method causes the omission of actual potentials of short-term extreme droughts located within a long-term UDR. Meanwhile, traditional method is often faced with significant gap in drought data series. However, a long-term UDR can be approached as a combination of short-term Connected Drought Runs (CDR). Therefore this study aims to evaluate systematically two UDR and CDR procedures in joint probability of drought duration and severity investigations. For this purpose, rainfall data (1971-2013) from 24 rain gauges in Lake Urmia basin, Iran were applied. Also, seven common univariate marginal distributions and seven types of bivariate copulas were examined. Compared to traditional approach, the results demonstrated a significant comparative advantage of the new approach. Such comparative advantages led to determine the correct copula function, more accurate estimation of copula parameter, more realistic estimation of joint/conditional probabilities of drought duration and severity and significant reduction in uncertainty for modeling.

A Dynamic Bayesian Network Model for the Production and Inventory Control

NASA Astrophysics Data System (ADS)

Shin, Ji-Sun; Takazaki, Noriyuki; Lee, Tae-Hong; Kim, Jin-Il; Lee, Hee-Hyol

In general, the production quantities and delivered goods are changed randomly and then the total stock is also changed randomly. This paper deals with the production and inventory control using the Dynamic Bayesian Network. Bayesian Network is a probabilistic model which represents the qualitative dependence between two or more random variables by the graph structure, and indicates the quantitative relations between individual variables by the conditional probability. The probabilistic distribution of the total stock is calculated through the propagation of the probability on the network. Moreover, an adjusting rule of the production quantities to maintain the probability of a lower limit and a ceiling of the total stock to certain values is shown.

Some properties of a 5-parameter bivariate probability distribution

NASA Technical Reports Server (NTRS)

Tubbs, J. D.; Brewer, D. W.; Smith, O. E.

1983-01-01

A five-parameter bivariate gamma distribution having two shape parameters, two location parameters and a correlation parameter was developed. This more general bivariate gamma distribution reduces to the known four-parameter distribution. The five-parameter distribution gives a better fit to the gust data. The statistical properties of this general bivariate gamma distribution and a hypothesis test were investigated. Although these developments have come too late in the Shuttle program to be used directly as design criteria for ascent wind gust loads, the new wind gust model has helped to explain the wind profile conditions which cause large dynamic loads. Other potential applications of the newly developed five-parameter bivariate gamma distribution are in the areas of reliability theory, signal noise, and vibration mechanics.

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).

Product plots.

PubMed

Wickham, Hadley; Hofmann, Heike

2011-12-01

We propose a new framework for visualising tables of counts, proportions and probabilities. We call our framework product plots, alluding to the computation of area as a product of height and width, and the statistical concept of generating a joint distribution from the product of conditional and marginal distributions. The framework, with extensions, is sufficient to encompass over 20 visualisations previously described in fields of statistical graphics and infovis, including bar charts, mosaic plots, treemaps, equal area plots and fluctuation diagrams. © 2011 IEEE

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

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

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

Probability density function formalism for optical coherence tomography signal analysis: a controlled phantom study.

PubMed

Weatherbee, Andrew; Sugita, Mitsuro; Bizheva, Kostadinka; Popov, Ivan; Vitkin, Alex

2016-06-15

The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications.

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

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

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

Bayesian model averaging using particle filtering and Gaussian mixture modeling: Theory, concepts, and simulation experiments

NASA Astrophysics Data System (ADS)

Rings, Joerg; Vrugt, Jasper A.; Schoups, Gerrit; Huisman, Johan A.; Vereecken, Harry

2012-05-01

Bayesian model averaging (BMA) is a standard method for combining predictive distributions from different models. In recent years, this method has enjoyed widespread application and use in many fields of study to improve the spread-skill relationship of forecast ensembles. The BMA predictive probability density function (pdf) of any quantity of interest is a weighted average of pdfs centered around the individual (possibly bias-corrected) forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts, and reflect the individual models skill over a training (calibration) period. The original BMA approach presented by Raftery et al. (2005) assumes that the conditional pdf of each individual model is adequately described with a rather standard Gaussian or Gamma statistical distribution, possibly with a heteroscedastic variance. Here we analyze the advantages of using BMA with a flexible representation of the conditional pdf. A joint particle filtering and Gaussian mixture modeling framework is presented to derive analytically, as closely and consistently as possible, the evolving forecast density (conditional pdf) of each constituent ensemble member. The median forecasts and evolving conditional pdfs of the constituent models are subsequently combined using BMA to derive one overall predictive distribution. This paper introduces the theory and concepts of this new ensemble postprocessing method, and demonstrates its usefulness and applicability by numerical simulation of the rainfall-runoff transformation using discharge data from three different catchments in the contiguous United States. The revised BMA method receives significantly lower-prediction errors than the original default BMA method (due to filtering) with predictive uncertainty intervals that are substantially smaller but still statistically coherent (due to the use of a time-variant conditional pdf).

Global Pyrogeography: the Current and Future Distribution of Wildfire

PubMed Central

Krawchuk, Meg A.; Moritz, Max A.; Parisien, Marc-André; Van Dorn, Jeff; Hayhoe, Katharine

2009-01-01

Climate change is expected to alter the geographic distribution of wildfire, a complex abiotic process that responds to a variety of spatial and environmental gradients. How future climate change may alter global wildfire activity, however, is still largely unknown. As a first step to quantifying potential change in global wildfire, we present a multivariate quantification of environmental drivers for the observed, current distribution of vegetation fires using statistical models of the relationship between fire activity and resources to burn, climate conditions, human influence, and lightning flash rates at a coarse spatiotemporal resolution (100 km, over one decade). We then demonstrate how these statistical models can be used to project future changes in global fire patterns, highlighting regional hotspots of change in fire probabilities under future climate conditions as simulated by a global climate model. Based on current conditions, our results illustrate how the availability of resources to burn and climate conditions conducive to combustion jointly determine why some parts of the world are fire-prone and others are fire-free. In contrast to any expectation that global warming should necessarily result in more fire, we find that regional increases in fire probabilities may be counter-balanced by decreases at other locations, due to the interplay of temperature and precipitation variables. Despite this net balance, our models predict substantial invasion and retreat of fire across large portions of the globe. These changes could have important effects on terrestrial ecosystems since alteration in fire activity may occur quite rapidly, generating ever more complex environmental challenges for species dispersing and adjusting to new climate conditions. Our findings highlight the potential for widespread impacts of climate change on wildfire, suggesting severely altered fire regimes and the need for more explicit inclusion of fire in research on global vegetation-climate change dynamics and conservation planning. PMID:19352494

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.

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

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.

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.

Survival curve estimation with dependent left truncated data using Cox's model.

PubMed

Mackenzie, Todd

2012-10-19

The Kaplan-Meier and closely related Lynden-Bell estimators are used to provide nonparametric estimation of the distribution of a left-truncated random variable. These estimators assume that the left-truncation variable is independent of the time-to-event. This paper proposes a semiparametric method for estimating the marginal distribution of the time-to-event that does not require independence. It models the conditional distribution of the time-to-event given the truncation variable using Cox's model for left truncated data, and uses inverse probability weighting. We report the results of simulations and illustrate the method using a survival study.

Statistical prescission point model of fission fragment angular distributions

NASA Astrophysics Data System (ADS)

John, Bency; Kataria, S. K.

1998-03-01

In light of recent developments in fission studies such as slow saddle to scission motion and spin equilibration near the scission point, the theory of fission fragment angular distribution is examined and a new statistical prescission point model is developed. The conditional equilibrium of the collective angular bearing modes at the prescission point, which is guided mainly by their relaxation times and population probabilities, is taken into account in the present model. The present model gives a consistent description of the fragment angular and spin distributions for a wide variety of heavy and light ion induced fission reactions.

Review of probabilistic analysis of dynamic response of systems with random parameters

NASA Technical Reports Server (NTRS)

Kozin, F.; Klosner, J. M.

1989-01-01

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

The Dynamics of Conditioning and Extinction

PubMed Central

Killeen, Peter R.; Sanabria, Federico; Dolgov, Igor

2009-01-01

Pigeons responded to intermittently reinforced classical conditioning trials with erratic bouts of responding to the CS. Responding depended on whether the prior trial contained a peck, food, or both. A linear-persistence/learning model moved animals into and out of a response state, and a Weibull distribution for number of within-trial responses governed in-state pecking. Variations of trial and inter-trial durations caused correlated changes in rate and probability of responding, and model parameters. A novel prediction—in the protracted absence of food, response rates can plateau above zero—was validated. The model predicted smooth acquisition functions when instantiated with the probability of food, but a more accurate jagged learning curve when instantiated with trial-to-trial records of reinforcement. The Skinnerian parameter was dominant only when food could be accelerated or delayed by pecking. These experiments provide a framework for trial-by-trial accounts of conditioning and extinction that increases the information available from the data, permitting them to comment more definitively on complex contemporary models of momentum and conditioning. PMID:19839699

Size distribution of submarine landslides along the U.S. Atlantic margin

USGS Publications Warehouse

Chaytor, J.D.; ten Brink, Uri S.; Solow, A.R.; Andrews, B.D.

2009-01-01

Assessment of the probability for destructive landslide-generated tsunamis depends on the knowledge of the number, size, and frequency of large submarine landslides. This paper investigates the size distribution of submarine landslides along the U.S. Atlantic continental slope and rise using the size of the landslide source regions (landslide failure scars). Landslide scars along the margin identified in a detailed bathymetric Digital Elevation Model (DEM) have areas that range between 0.89??km2 and 2410??km2 and volumes between 0.002??km3 and 179??km3. The area to volume relationship of these failure scars is almost linear (inverse power-law exponent close to 1), suggesting a fairly uniform failure thickness of a few 10s of meters in each event, with only rare, deep excavating landslides. The cumulative volume distribution of the failure scars is very well described by a log-normal distribution rather than by an inverse power-law, the most commonly used distribution for both subaerial and submarine landslides. A log-normal distribution centered on a volume of 0.86??km3 may indicate that landslides preferentially mobilize a moderate amount of material (on the order of 1??km3), rather than large landslides or very small ones. Alternatively, the log-normal distribution may reflect an inverse power law distribution modified by a size-dependent probability of observing landslide scars in the bathymetry data. If the latter is the case, an inverse power-law distribution with an exponent of 1.3 ?? 0.3, modified by a size-dependent conditional probability of identifying more failure scars with increasing landslide size, fits the observed size distribution. This exponent value is similar to the predicted exponent of 1.2 ?? 0.3 for subaerial landslides in unconsolidated material. Both the log-normal and modified inverse power-law distributions of the observed failure scar volumes suggest that large landslides, which have the greatest potential to generate damaging tsunamis, occur infrequently along the margin. ?? 2008 Elsevier B.V.

One hundred years of return period: Strengths and limitations

NASA Astrophysics Data System (ADS)

Volpi, E.; Fiori, A.; Grimaldi, S.; Lombardo, F.; Koutsoyiannis, D.

2015-10-01

One hundred years from its original definition by Fuller, the probabilistic concept of return period is widely used in hydrology as well as in other disciplines of geosciences to give an indication on critical event rareness. This concept gains its popularity, especially in engineering practice for design and risk assessment, due to its ease of use and understanding; however, return period relies on some basic assumptions that should be satisfied for a correct application of this statistical tool. Indeed, conventional frequency analysis in hydrology is performed by assuming as necessary conditions that extreme events arise from a stationary distribution and are independent of one another. The main objective of this paper is to investigate the properties of return period when the independence condition is omitted; hence, we explore how the different definitions of return period available in literature affect results of frequency analysis for processes correlated in time. We demonstrate that, for stationary processes, the independence condition is not necessary in order to apply the classical equation of return period (i.e., the inverse of exceedance probability). On the other hand, we show that the time-correlation structure of hydrological processes modifies the shape of the distribution function of which the return period represents the first moment. This implies that, in the context of time-dependent processes, the return period might not represent an exhaustive measure of the probability of failure, and that its blind application could lead to misleading results. To overcome this problem, we introduce the concept of Equivalent Return Period, which controls the probability of failure still preserving the virtue of effectively communicating the event rareness.

Surveillance of industrial processes with correlated parameters

DOEpatents

White, Andrew M.; Gross, Kenny C.; Kubic, William L.; Wigeland, Roald A.

1996-01-01

A system and method for surveillance of an industrial process. The system and method includes a plurality of sensors monitoring industrial process parameters, devices to convert the sensed data to computer compatible information and a computer which executes computer software directed to analyzing the sensor data to discern statistically reliable alarm conditions. The computer software is executed to remove serial correlation information and then calculate Mahalanobis distribution data to carry out a probability ratio test to determine alarm conditions.

Unified Description of Scattering and Propagation FY15 Annual Report

DTIC Science & Technology

2015-09-30

the Texas coast. For both cases a conditional posterior probability distribution ( PPD ) is formed for a parameter space that includes both geoacoustic...for this second application of ME. For each application of ME it is important to note that a new likelihood function and thus PPD is computed. One...the 50-700 Hz band. These data offered a means by which the results of using the ship radiated noise could be partially validated. The conditional PPD

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

NASA Technical Reports Server (NTRS)

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

1998-01-01

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

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

NASA Astrophysics Data System (ADS)

Iacobellis, Vito; Fiorentino, Mauro

2000-02-01

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

Aggregate and individual replication probability within an explicit model of the research process.

PubMed

Miller, Jeff; Schwarz, Wolf

2011-09-01

We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by obtaining either a statistically significant result in the same direction or any effect in that direction. We analyze both the probability of successfully replicating a particular experimental effect (i.e., the individual replication probability) and the average probability of successful replication across different studies within some research context (i.e., the aggregate replication probability), and we identify the conditions under which the latter can be approximated using the formulas of Killeen (2005a, 2007). We show how both of these probabilities depend on parameters of the research context that would rarely be known in practice. In addition, we show that the statistical uncertainty associated with the size of an initial observed effect would often prevent accurate estimation of the desired individual replication probability even if these research context parameters were known exactly. We conclude that accurate estimates of replication probability are generally unattainable.

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

PubMed

Boitard, Simon; Loisel, Patrice

2007-05-01

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

Transport of chromium and selenium in the suboxic zone of a shallow aquifer: Influence of redox and adsorption reactions

USGS Publications Warehouse

Kent, D.B.; Davis, J.A.; Anderson, L.C.D.; Rea, B.A.; Waite, T.D.

1994-01-01

Breakthrough of Cr(VI) (chromate), Se(VI) (selenate), and O2 (dissolved oxygen) was observed in tracer tests conducted in a shallow, sand and gravel aquifer with mildly reducing conditions. Loss of Cr, probably due to reduction of Cr(VI) to Cr(III) and irreversible sorption of Cr(III), occurred along with slight retardation of Cr(VI), owing to reversible sorption. Reduction of Se(VI) and O2 was thermodynamically feasible but did not occur, indicating conditions, were unfavorable to microbial reduction. Cr(VI) reduction by constituents of aquifer sediments did not achieve local equilibrium during transport. The reduction rate was probably limited by incomplete contact between Cr(VI) transported along predominant flow paths and reductants located in regions within aquifer sediments of comparatively low permeability. Scatter in the amount of Cr reduction calculated from individual breakthrough curves at identical distances downgradient probably resulted from heterogeneities in the distribution of reductants in the sediments. Predictive modeling of the transport and fate of redox-sensitive solutes cannot be based strictly on thermodynamic considerations; knowledge of reaction rates is critical. Potentially important mass transfer rate limitations between solutes and reactants in sediments as well as heterogeneities in the distribution of redox properties in aquifers complicate determination of limiting rates for use in predictive simulations of the transport of redox-sensitive contaminants in groundwater.

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

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

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

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

Shipping and natural environmental conditions determine the distribution of the invasive non-indigenous round goby Neogobius melanostomus in a regional sea

NASA Astrophysics Data System (ADS)

Kotta, Jonne; Nurkse, Kristiina; Puntila, Riikka; Ojaveer, Henn

2016-02-01

Introductions of non-indigenous species (NIS) are considered a major threat to aquatic ecosystems worldwide. While it is valuable to know the distributions and ranges of NIS, predictive spatial models along different environmental gradients are more useful for management of these species. In this study we modelled how external drivers and local environmental conditions contribute to the spatial distribution of an invasive species using the distribution of the round goby Neogobius melanostomus in the Baltic Sea as an example. Using the collected distribution data, an updated map on the species distribution and its invasion progress in the Baltic Sea was produced. The current range of the round goby observations is extensive, covering all major sub-basins of the Baltic Sea. The most recent observations appeared in the northern regions (Northern Baltic Proper, the Gulf of Bothnia and the Gulf of Finland) and on the eastern and western coasts of southern Sweden. Modelling results show that the distribution of the round goby is primarily related to local abiotic hydrological conditions (wave exposure). Furthermore, the probability of round goby occurrence was very high in areas in close proximity to large cargo ports. This links patterns of the round goby distribution in the Baltic Sea to shipping traffic and suggests that human factors together with natural environmental conditions are responsible for the spread of NIS at a regional sea scale.

Spatial estimation from remotely sensed data via empirical Bayes models

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

Approaches to quantifying long-term continental shelf sediment transport with an example from the Northern California STRESS mid-shelf site

NASA Astrophysics Data System (ADS)

Harris, Courtney K.; Wiberg, Patricia L.

1997-09-01

Modeling shelf sediment transport rates and bed reworking depths is problematic when the wave and current forcing conditions are not precisely known, as is usually the case when long-term sedimentation patterns are of interest. Two approaches to modeling sediment transport under such circumstances are considered. The first relies on measured or simulated time series of flow conditions to drive model calculations. The second approach uses as model input probability distribution functions of bottom boundary layer flow conditions developed from wave and current measurements. Sediment transport rates, frequency of bed resuspension by waves and currents, and bed reworking calculated using the two methods are compared at the mid-shelf STRESS (Sediment TRansport on Shelves and Slopes) site on the northern California continental shelf. Current, wave and resuspension measurements at the site are used to generate model inputs and test model results. An 11-year record of bottom wave orbital velocity, calculated from surface wave spectra measured by the National Data Buoy Center (NDBC) Buoy 46013 and verified against bottom tripod measurements, is used to characterize the frequency and duration of wave-driven transport events and to estimate the joint probability distribution of wave orbital velocity and period. A 109-day record of hourly current measurements 10 m above bottom is used to estimate the probability distribution of bottom boundary layer current velocity at this site and to develop an auto-regressive model to simulate current velocities for times when direct measurements of currents are not available. Frequency of transport, the maximum volume of suspended sediment, and average flux calculated using measured wave and simulated current time series agree well with values calculated using measured time series. A probabilistic approach is more amenable to calculations over time scales longer than existing wave records, but it tends to underestimate net transport because it does not capture the episodic nature of transport events. Both methods enable estimates to be made of the uncertainty in transport quantities that arise from an incomplete knowledge of the specific timing of wave and current conditions. 1997 Elsevier Science Ltd

Bankruptcy risk model and empirical tests

PubMed Central

Podobnik, Boris; Horvatic, Davor; Petersen, Alexander M.; Urošević, Branko; Stanley, H. Eugene

2010-01-01

We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor—the debt-to-asset ratio R—in order to study the stability of the Zipf distribution of R over time. We find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, we employ Bayes’s theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value. For 2,737 bankrupt firms, we demonstrate size dependence in assets change during the bankruptcy proceedings. Prepetition firm assets and petition firm assets follow Zipf distributions but with different exponents, meaning that firms with smaller assets adjust their assets more than firms with larger assets during the bankruptcy process. We compare bankrupt firms with nonbankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 New York Stock Exchange (NYSE) members. We find that both assets and liabilities follow a Pareto distribution. The finding is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees—although the market capitalization of Nasdaq stocks follows a Pareto distribution, the same distribution does not describe NYSE stocks. We propose a coupled Simon model that simultaneously evolves both assets and debt with the possibility of bankruptcy, and we also consider the possibility of firm mergers. PMID:20937903

Predictive models attribute effects on fish assemblages to toxicity and habitat alteration.

PubMed

de Zwart, Dick; Dyer, Scott D; Posthuma, Leo; Hawkins, Charles P

2006-08-01

Biological assessments should both estimate the condition of a biological resource (magnitude of alteration) and provide environmental managers with a diagnosis of the potential causes of impairment. Although methods of quantifying condition are well developed, identifying and proportionately attributing impairment to probable causes remain problematic. Furthermore, analyses of both condition and cause have often been difficult to communicate. We developed an approach that (1) links fish, habitat, and chemistry data collected from hundreds of sites in Ohio (USA) streams, (2) assesses the biological condition at each site, (3) attributes impairment to multiple probable causes, and (4) provides the results of the analyses in simple-to-interpret pie charts. The data set was managed using a geographic information system. Biological condition was assessed using a RIVPACS (river invertebrate prediction and classification system)-like predictive model. The model provided probabilities of capture for 117 fish species based on the geographic location of sites and local habitat descriptors. Impaired biological condition was defined as the proportion of those native species predicted to occur at a site that were observed. The potential toxic effects of exposure to mixtures of contaminants were estimated using species sensitivity distributions and mixture toxicity principles. Generalized linear regression models described species abundance as a function of habitat characteristics. Statistically linking biological condition, habitat characteristics including mixture risks, and species abundance allowed us to evaluate the losses of species with environmental conditions. Results were mapped as simple effect and probable-cause pie charts (EPC pie diagrams), with pie sizes corresponding to magnitude of local impairment, and slice sizes to the relative probable contributions of different stressors. The types of models we used have been successfully applied in ecology and ecotoxicology, but they have not previously been used in concert to quantify impairment and its likely causes. Although data limitations constrained our ability to examine complex interactions between stressors and species, the direct relationships we detected likely represent conservative estimates of stressor contributions to local impairment. Future refinements of the general approach and specific methods described here should yield even more promising results.

Endogenous modulation of low frequency oscillations by temporal expectations

PubMed Central

Cravo, Andre M.; Rohenkohl, Gustavo; Wyart, Valentin

2011-01-01

Recent studies have associated increasing temporal expectations with synchronization of higher frequency oscillations and suppression of lower frequencies. In this experiment, we explore a proposal that low-frequency oscillations provide a mechanism for regulating temporal expectations. We used a speeded Go/No-go task and manipulated temporal expectations by changing the probability of target presentation after certain intervals. Across two conditions, the temporal conditional probability of target events differed substantially at the first of three possible intervals. We found that reactions times differed significantly at this first interval across conditions, decreasing with higher temporal expectations. Interestingly, the power of theta activity (4–8 Hz), distributed over central midline sites, also differed significantly across conditions at this first interval. Furthermore, we found a transient coupling between theta phase and beta power after the first interval in the condition with high temporal expectation for targets at this time point. Our results suggest that the adjustments in theta power and the phase-power coupling between theta and beta contribute to a central mechanism for controlling neural excitability according to temporal expectations. PMID:21900508

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

NASA Technical Reports Server (NTRS)

Nitsche, Ludwig C.; Nitsche, Johannes M.; Brenner, Howard

1988-01-01

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Prediction of Malaysian monthly GDP

NASA Astrophysics Data System (ADS)

Hin, Pooi Ah; Ching, Soo Huei; Yeing, Pan Wei

2015-12-01

The paper attempts to use a method based on multivariate power-normal distribution to predict the Malaysian Gross Domestic Product next month. Letting r(t) be the vector consisting of the month-t values on m selected macroeconomic variables, and GDP, we model the month-(t+1) GDP to be dependent on the present and l-1 past values r(t), r(t-1),…,r(t-l+1) via a conditional distribution which is derived from a [(m+1)l+1]-dimensional power-normal distribution. The 100(α/2)% and 100(1-α/2)% points of the conditional distribution may be used to form an out-of sample prediction interval. This interval together with the mean of the conditional distribution may be used to predict the month-(t+1) GDP. The mean absolute percentage error (MAPE), estimated coverage probability and average length of the prediction interval are used as the criterions for selecting the suitable lag value l-1 and the subset from a pool of 17 macroeconomic variables. It is found that the relatively better models would be those of which 2 ≤ l ≤ 3, and involving one or two of the macroeconomic variables given by Market Indicative Yield, Oil Prices, Exchange Rate and Import Trade.

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

PubMed

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

2016-06-01

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

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

PubMed Central

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

2015-01-01

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

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-01-01

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

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.

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

Distribution of injected power fluctuations in electroconvection.

PubMed

Tóth-Katona, Tibor; Gleeson, J T

2003-12-31

We report on the distribution spectra of the fluctations in the amount of power injected into a liquid crystal undergoing electroconvective flow. The probability distribution functions (PDFs) of the fluc-tuations as well as the magnitude of the fluctuations have been determined in a wide range of imposed stress both for unconfined and confined flow geometries. These spectra are compared to those found in other systems held far from equilibrium, and find that in certain conditions we obtain the universal PDF form reported by Phys. Rev. Lett. 84, 3744 (2000)]. Moreover, the PDF approaches this universal form via an interesting mechanism whereby the distribution's negative tail evolves towards form in a different manner than the positive tail.

A brief introduction to probability.

PubMed

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

2018-02-01

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

The risk of Vibrio parahaemolyticus infections associated with consumption of raw oysters as affected by processing and distribution conditions in Taiwan

USDA-ARS?s Scientific Manuscript database

The steadily increased consumption of raw oysters in Taiwan warrants an assessment of the risk (probability of illness) of raw oyster consumption attributed by Vibrio parahaemolyticus. The aim of this study was to estimate the risk of V. parahaemolyticus infection associated with raw oyster consumpt...

Analysis of high-resolution foreign exchange data of USD-JPY for 13 years

NASA Astrophysics Data System (ADS)

Mizuno, Takayuki; Kurihara, Shoko; Takayasu, Misako; Takayasu, Hideki

2003-06-01

We analyze high-resolution foreign exchange data consisting of 20 million data points of USD-JPY for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations. A conditional probability density analysis clearly shows the existence of trend-following movements at time scale of 8-ticks, about 1 min.

Development of a European Ensemble System for Seasonal Prediction: Application to crop yield

NASA Astrophysics Data System (ADS)

Terres, J. M.; Cantelaube, P.

2003-04-01

Western European agriculture is highly intensive and the weather is the main source of uncertainty for crop yield assessment and for crop management. In the current system, at the time when a crop yield forecast is issued, the weather conditions leading up to harvest time are unknown and are therefore a major source of uncertainty. The use of seasonal weather forecast would bring additional information for the remaining crop season and has valuable benefit for improving the management of agricultural markets and environmentally sustainable farm practices. An innovative method for supplying seasonal forecast information to crop simulation models has been developed in the frame of the EU funded research project DEMETER. It consists in running a crop model on each individual member of the seasonal hindcasts to derive a probability distribution of crop yield. Preliminary results of cumulative probability function of wheat yield provides information on both the yield anomaly and the reliability of the forecast. Based on the spread of the probability distribution, the end-user can directly quantify the benefits and risks of taking weather-sensitive decisions.

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

NASA Astrophysics Data System (ADS)

Wable, Pawan S.; Jha, Madan K.

2018-02-01

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

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

PubMed Central

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

2016-01-01

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

Probability theory versus simulation of petroleum potential in play analysis

USGS Publications Warehouse

Crovelli, R.A.

1987-01-01

An analytic probabilistic methodology for resource appraisal of undiscovered oil and gas resources in play analysis is presented. This play-analysis methodology is a geostochastic system for petroleum resource appraisal in explored as well as frontier areas. An objective was to replace an existing Monte Carlo simulation method in order to increase the efficiency of the appraisal process. Underlying the two methods is a single geologic model which considers both the uncertainty of the presence of the assessed hydrocarbon and its amount if present. The results of the model are resource estimates of crude oil, nonassociated gas, dissolved gas, and gas for a geologic play in terms of probability distributions. The analytic method is based upon conditional probability theory and a closed form solution of all means and standard deviations, along with the probabilities of occurrence. ?? 1987 J.C. Baltzer A.G., Scientific Publishing Company.

The effect of kerosene injection on ignition probability of local ignition in a scramjet combustor

NASA Astrophysics Data System (ADS)

Bao, Heng; Zhou, Jin; Pan, Yu

2017-03-01

The spark ignition of kerosene is investigated in a scramjet combustor with a flight condition of Ma 4, 17 km. Based plentiful of experimental data, the ignition probabilities of the local ignition have been acquired for different injection setups. The ignition probability distributions show that the injection pressure and injection location have a distinct effect on spark ignition. The injection pressure has both upper and lower limit for local ignition. Generally, the larger mass flow rate will reduce the ignition probability. The ignition position also affects the ignition near the lower pressure limit. The reason is supposed to be the cavity swallow effect on upstream jet spray near the leading edge, which will make the cavity fuel rich. The corner recirculation zone near the front wall of the cavity plays a significant role in the stabilization of local flame.

Surveillance of industrial processes with correlated parameters

DOEpatents

White, A.M.; Gross, K.C.; Kubic, W.L.; Wigeland, R.A.

1996-12-17

A system and method for surveillance of an industrial process are disclosed. The system and method includes a plurality of sensors monitoring industrial process parameters, devices to convert the sensed data to computer compatible information and a computer which executes computer software directed to analyzing the sensor data to discern statistically reliable alarm conditions. The computer software is executed to remove serial correlation information and then calculate Mahalanobis distribution data to carry out a probability ratio test to determine alarm conditions. 10 figs.

Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

PubMed

Sulis, William H

2017-10-01

Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

ZERODUR: deterministic approach for strength design

NASA Astrophysics Data System (ADS)

Hartmann, Peter

2012-12-01

There is an increasing request for zero expansion glass ceramic ZERODUR substrates being capable of enduring higher operational static loads or accelerations. The integrity of structures such as optical or mechanical elements for satellites surviving rocket launches, filigree lightweight mirrors, wobbling mirrors, and reticle and wafer stages in microlithography must be guaranteed with low failure probability. Their design requires statistically relevant strength data. The traditional approach using the statistical two-parameter Weibull distribution suffered from two problems. The data sets were too small to obtain distribution parameters with sufficient accuracy and also too small to decide on the validity of the model. This holds especially for the low failure probability levels that are required for reliable applications. Extrapolation to 0.1% failure probability and below led to design strengths so low that higher load applications seemed to be not feasible. New data have been collected with numbers per set large enough to enable tests on the applicability of the three-parameter Weibull distribution. This distribution revealed to provide much better fitting of the data. Moreover it delivers a lower threshold value, which means a minimum value for breakage stress, allowing of removing statistical uncertainty by introducing a deterministic method to calculate design strength. Considerations taken from the theory of fracture mechanics as have been proven to be reliable with proof test qualifications of delicate structures made from brittle materials enable including fatigue due to stress corrosion in a straight forward way. With the formulae derived, either lifetime can be calculated from given stress or allowable stress from minimum required lifetime. The data, distributions, and design strength calculations for several practically relevant surface conditions of ZERODUR are given. The values obtained are significantly higher than those resulting from the two-parameter Weibull distribution approach and no longer subject to statistical uncertainty.

Modeling and mapping the probability of occurrence of invasive wild pigs across the contiguous United States.

PubMed

McClure, Meredith L; Burdett, Christopher L; Farnsworth, Matthew L; Lutman, Mark W; Theobald, David M; Riggs, Philip D; Grear, Daniel A; Miller, Ryan S

2015-01-01

Wild pigs (Sus scrofa), also known as wild swine, feral pigs, or feral hogs, are one of the most widespread and successful invasive species around the world. Wild pigs have been linked to extensive and costly agricultural damage and present a serious threat to plant and animal communities due to their rooting behavior and omnivorous diet. We modeled the current distribution of wild pigs in the United States to better understand the physiological and ecological factors that may determine their invasive potential and to guide future study and eradication efforts. Using national-scale wild pig occurrence data reported between 1982 and 2012 by wildlife management professionals, we estimated the probability of wild pig occurrence across the United States using a logistic discrimination function and environmental covariates hypothesized to influence the distribution of the species. Our results suggest the distribution of wild pigs in the U.S. was most strongly limited by cold temperatures and availability of water, and that they were most likely to occur where potential home ranges had higher habitat heterogeneity, providing access to multiple key resources including water, forage, and cover. High probability of occurrence was also associated with frequent high temperatures, up to a high threshold. However, this pattern is driven by pigs' historic distribution in warm climates of the southern U.S. Further study of pigs' ability to persist in cold northern climates is needed to better understand whether low temperatures actually limit their distribution. Our model highlights areas at risk of invasion as those with habitat conditions similar to those found in pigs' current range that are also near current populations. This study provides a macro-scale approach to generalist species distribution modeling that is applicable to other generalist and invasive species.

Stochastic optimal operation of reservoirs based on copula functions

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Invariance in the recurrence of large returns and the validation of models of price dynamics

NASA Astrophysics Data System (ADS)

Chang, Lo-Bin; Geman, Stuart; Hsieh, Fushing; Hwang, Chii-Ruey

2013-08-01

Starting from a robust, nonparametric definition of large returns (“excursions”), we study the statistics of their occurrences, focusing on the recurrence process. The empirical waiting-time distribution between excursions is remarkably invariant to year, stock, and scale (return interval). This invariance is related to self-similarity of the marginal distributions of returns, but the excursion waiting-time distribution is a function of the entire return process and not just its univariate probabilities. Generalized autoregressive conditional heteroskedasticity (GARCH) models, market-time transformations based on volume or trades, and generalized (Lévy) random-walk models all fail to fit the statistical structure of excursions.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

Lian, Shizhong; Chen, Jiangping; Luo, Minghai

2016-06-01

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

Econophysics: Two-phase behaviour of financial markets

NASA Astrophysics Data System (ADS)

Plerou, Vasiliki; Gopikrishnan, Parameswaran; Stanley, H. Eugene

2003-01-01

Buying and selling in financial markets is driven by demand, which can be quantified by the imbalance in the number of shares transacted by buyers and sellers over a given time interval. Here we analyse the probability distribution of demand, conditioned on its local noise intensity Σ, and discover the surprising existence of a critical threshold, Σc. For Σ < Σc, the most probable value of demand is roughly zero; we interpret this as an equilibrium phase in which neither buying nor selling predominates. For Σ > Σc, two most probable values emerge that are symmetrical around zero demand, corresponding to excess demand and excess supply; we interpret this as an out-of-equilibrium phase in which the market behaviour is mainly buying for half of the time, and mainly selling for the other half.

Detailed Analysis of the Interoccurrence Time Statistics in Seismic Activity

NASA Astrophysics Data System (ADS)

Tanaka, Hiroki; Aizawa, Yoji

2017-02-01

The interoccurrence time statistics of seismiciry is studied theoretically as well as numerically by taking into account the conditional probability and the correlations among many earthquakes in different magnitude levels. It is known so far that the interoccurrence time statistics is well approximated by the Weibull distribution, but the more detailed information about the interoccurrence times can be obtained from the analysis of the conditional probability. Firstly, we propose the Embedding Equation Theory (EET), where the conditional probability is described by two kinds of correlation coefficients; one is the magnitude correlation and the other is the inter-event time correlation. Furthermore, the scaling law of each correlation coefficient is clearly determined from the numerical data-analysis carrying out with the Preliminary Determination of Epicenter (PDE) Catalog and the Japan Meteorological Agency (JMA) Catalog. Secondly, the EET is examined to derive the magnitude dependence of the interoccurrence time statistics and the multi-fractal relation is successfully formulated. Theoretically we cannot prove the universality of the multi-fractal relation in seismic activity; nevertheless, the theoretical results well reproduce all numerical data in our analysis, where several common features or the invariant aspects are clearly observed. Especially in the case of stationary ensembles the multi-fractal relation seems to obey an invariant curve, furthermore in the case of non-stationary (moving time) ensembles for the aftershock regime the multi-fractal relation seems to satisfy a certain invariant curve at any moving times. It is emphasized that the multi-fractal relation plays an important role to unify the statistical laws of seismicity: actually the Gutenberg-Richter law and the Weibull distribution are unified in the multi-fractal relation, and some universality conjectures regarding the seismicity are briefly discussed.

Process, System, Causality, and Quantum Mechanics: A Psychoanalysis of Animal Faith

NASA Astrophysics Data System (ADS)

Etter, Tom; Noyes, H. Pierre

We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantum mechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantum mechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantum mechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.

Future probabilities of coastal floods in Finland

NASA Astrophysics Data System (ADS)

Pellikka, Havu; Leijala, Ulpu; Johansson, Milla M.; Leinonen, Katri; Kahma, Kimmo K.

2018-04-01

Coastal planning requires detailed knowledge of future flooding risks, and effective planning must consider both short-term sea level variations and the long-term trend. We calculate distributions that combine short- and long-term effects to provide estimates of flood probabilities in 2050 and 2100 on the Finnish coast in the Baltic Sea. Our distributions of short-term sea level variations are based on 46 years (1971-2016) of observations from the 13 Finnish tide gauges. The long-term scenarios of mean sea level combine postglacial land uplift, regionally adjusted scenarios of global sea level rise, and the effect of changes in the wind climate. The results predict that flooding risks will clearly increase by 2100 in the Gulf of Finland and the Bothnian Sea, while only a small increase or no change compared to present-day conditions is expected in the Bothnian Bay, where the land uplift is stronger.

Parsimonious nonstationary flood frequency analysis

NASA Astrophysics Data System (ADS)

Serago, Jake M.; Vogel, Richard M.

2018-02-01

There is now widespread awareness of the impact of anthropogenic influences on extreme floods (and droughts) and thus an increasing need for methods to account for such influences when estimating a frequency distribution. We introduce a parsimonious approach to nonstationary flood frequency analysis (NFFA) based on a bivariate regression equation which describes the relationship between annual maximum floods, x, and an exogenous variable which may explain the nonstationary behavior of x. The conditional mean, variance and skewness of both x and y = ln (x) are derived, and combined with numerous common probability distributions including the lognormal, generalized extreme value and log Pearson type III models, resulting in a very simple and general approach to NFFA. Our approach offers several advantages over existing approaches including: parsimony, ease of use, graphical display, prediction intervals, and opportunities for uncertainty analysis. We introduce nonstationary probability plots and document how such plots can be used to assess the improved goodness of fit associated with a NFFA.

Generalized monogamy of contextual inequalities from the no-disturbance principle.

PubMed

Ramanathan, Ravishankar; Soeda, Akihito; Kurzyński, Paweł; Kaszlikowski, Dagomir

2012-08-03

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.

Distributions and fate of chlorinated pesticides, biomarkers and polycyclic aromatic hydrocarbons in sediments along a contamination gradient from a point-source in San Francisco Bay, California

USGS Publications Warehouse

Pereira, W.E.; Hostettler, F.D.; Rapp, J.B.

1996-01-01

The distribution and fate of chlorinated pesticides, biomarkers, and polycyclic aromatic hydrocarbons (PAHs) in surficial sediments along a contamination gradient in the Lauritzen Canal and Richmond Harbor in San Francisco Bay was investigated. Compounds were identified and quantified using gas chromatography-ion trap mass spectrometry. Biomarkers and PAHs were derived primarily from weathered petroleum. DDT was reductively dechlorinated under anoxic conditions to DDD and several minor degradation products, DDMU, DDMS, and DDNU. Under aerobic conditions, DDT was dehydrochlorinated to DDE and DBP. Aerobic degradation of DDT was diminished or inhibited in zones of high concentration, and increased significantly in zones of lower concentration: Other chlorinated pesticides identified in sediment included dieldrin and chlordane isomers. Multivariate analysis of the distributions of the DDTs suggested that there are probably two sources of DDD. In addition, DDE and DDMU are probably formed by similar mechanisms, i.e. dehydrochlorination. A steep concentration gradient existed from the Canal to the Outer Richmond Harbor, but higher levels of DDD than those found in the remainder of the Bay indicated that these contaminants are transported on particulates and colloidal organic matter from this source into San Francisco Bay. Chlorinated pesticides and PAHs may pose a potential problem to biota in San Francisco Bay.

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

Versino, Daniele; Bronkhorst, Curt Allan

The computational formulation of a micro-mechanical material model for the dynamic failure of ductile metals is presented in this paper. The statistical nature of porosity initiation is accounted for by introducing an arbitrary probability density function which describes the pores nucleation pressures. Each micropore within the representative volume element is modeled as a thick spherical shell made of plastically incompressible material. The treatment of porosity by a distribution of thick-walled spheres also allows for the inclusion of micro-inertia effects under conditions of shock and dynamic loading. The second order ordinary differential equation governing the microscopic porosity evolution is solved withmore » a robust implicit procedure. A new Chebyshev collocation method is employed to approximate the porosity distribution and remapping is used to optimize memory usage. The adaptive approximation of the porosity distribution leads to a reduction of computational time and memory usage of up to two orders of magnitude. Moreover, the proposed model affords consistent performance: changing the nucleation pressure probability density function and/or the applied strain rate does not reduce accuracy or computational efficiency of the material model. The numerical performance of the model and algorithms presented is tested against three problems for high density tantalum: single void, one-dimensional uniaxial strain, and two-dimensional plate impact. Here, the results using the integration and algorithmic advances suggest a significant improvement in computational efficiency and accuracy over previous treatments for dynamic loading conditions.« less

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

PubMed

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

2010-12-01

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

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.

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.

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.

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

Stewart, Gordon M.; Robertson, Amy; Jonkman, Jason

A database of meteorological and ocean conditions is presented for use in offshore wind energy research and design. The original data are from 23 ocean sites around the USA and were obtained from the National Data Buoy Center run by the National Oceanic and Atmospheric Administration. The data are presented in a processed form that includes the variables of interest for offshore wind energy design: wind speed, significant wave height, wave peak-spectral period, wind direction and wave direction. For each site, a binning process is conducted to create conditional probability functions for each of these variables. The sites are thenmore » grouped according to geographic location and combined to create three representative sites, including a West Coast site, an East Coast site and a Gulf of Mexico site. Both the processed data and the probability distribution parameters for the individual and representative sites are being hosted on a publicly available domain by the National Renewable Energy Laboratory, with the intent of providing a standard basis of comparison for meteorological and ocean conditions for offshore wind energy research worldwide.« less

Space Station laboratory module power loading analysis

NASA Astrophysics Data System (ADS)

Fu, S. J.

1994-07-01

The electrical power system of Space Station Freedom is an isolated electrical power generation and distribution network designed to meet the demands of a large number of electrical loads. An algorithm is developed to determine the power bus loading status under normal operating conditions to ensure the supply meets demand. The probabilities of power availability for payload operations (experiments) are also derived.

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.

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.

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

PubMed

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

2017-02-15

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

Statistical thermodynamics of clustered populations.

PubMed

Matsoukas, Themis

2014-08-01

We present a thermodynamic theory for a generic population of M individuals distributed into N groups (clusters). We construct the ensemble of all distributions with fixed M and N, introduce a selection functional that embodies the physics that governs the population, and obtain the distribution that emerges in the scaling limit as the most probable among all distributions consistent with the given physics. We develop the thermodynamics of the ensemble and establish a rigorous mapping to regular thermodynamics. We treat the emergence of a so-called giant component as a formal phase transition and show that the criteria for its emergence are entirely analogous to the equilibrium conditions in molecular systems. We demonstrate the theory by an analytic model and confirm the predictions by Monte Carlo simulation.

Radar prediction of absolute rain fade distributions for earth-satellite paths and general methods for extrapolation of fade statistics to other locations

NASA Technical Reports Server (NTRS)

Goldhirsh, J.

1982-01-01

The first absolute rain fade distribution method described establishes absolute fade statistics at a given site by means of a sampled radar data base. The second method extrapolates absolute fade statistics from one location to another, given simultaneously measured fade and rain rate statistics at the former. Both methods employ similar conditional fade statistic concepts and long term rain rate distributions. Probability deviations in the 2-19% range, with an 11% average, were obtained upon comparison of measured and predicted levels at given attenuations. The extrapolation of fade distributions to other locations at 28 GHz showed very good agreement with measured data at three sites located in the continental temperate region.

Forecasting distributions of large federal-lands fires utilizing satellite and gridded weather information

USGS Publications Warehouse

Preisler, H.K.; Burgan, R.E.; Eidenshink, J.C.; Klaver, Jacqueline M.; Klaver, R.W.

2009-01-01

The current study presents a statistical model for assessing the skill of fire danger indices and for forecasting the distribution of the expected numbers of large fires over a given region and for the upcoming week. The procedure permits development of daily maps that forecast, for the forthcoming week and within federal lands, percentiles of the distributions of (i) number of ignitions; (ii) number of fires above a given size; (iii) conditional probabilities of fires greater than a specified size, given ignition. As an illustration, we used the methods to study the skill of the Fire Potential Index an index that incorporates satellite and surface observations to map fire potential at a national scale in forecasting distributions of large fires. ?? 2009 IAWF.

Characterization of intermittency in renewal processes: Application to earthquakes

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

Akimoto, Takuma; Hasumi, Tomohiro; Aizawa, Yoji

2010-03-15

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a framework to understand a unified characterization of intermittency and also present the Lyapunov exponent for renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency and the National Earthquake Information Center catalog. By analyzing the return map of interevent times, we find that interevent times are not independent and identically distributed random variablesmore » but that the conditional probability distribution functions in the tail obey the Weibull distribution.« less

Unstable density distribution associated with equatorial plasma bubble

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

Kherani, E. A., E-mail: esfhan.kherani@inpe.br; Meneses, F. Carlos de; Bharuthram, R.

2016-04-15

In this work, we present a simulation study of equatorial plasma bubble (EPB) in the evening time ionosphere. The fluid simulation is performed with a high grid resolution, enabling us to probe the steepened updrafting density structures inside EPB. Inside the density depletion that eventually evolves as EPB, both density and updraft are functions of space from which the density as implicit function of updraft velocity or the density distribution function is constructed. In the present study, this distribution function and the corresponding probability distribution function are found to evolve from Maxwellian to non-Maxwellian as the initial small depletion growsmore » to EPB. This non-Maxwellian distribution is of a gentle-bump type, in confirmation with the recently reported distribution within EPB from space-borne measurements that offer favorable condition for small scale kinetic instabilities.« less

Bayesian network representing system dynamics in risk analysis of nuclear systems

NASA Astrophysics Data System (ADS)

Varuttamaseni, Athi

2011-12-01

A dynamic Bayesian network (DBN) model is used in conjunction with the alternating conditional expectation (ACE) regression method to analyze the risk associated with the loss of feedwater accident coupled with a subsequent initiation of the feed and bleed operation in the Zion-1 nuclear power plant. The use of the DBN allows the joint probability distribution to be factorized, enabling the analysis to be done on many simpler network structures rather than on one complicated structure. The construction of the DBN model assumes conditional independence relations among certain key reactor parameters. The choice of parameter to model is based on considerations of the macroscopic balance statements governing the behavior of the reactor under a quasi-static assumption. The DBN is used to relate the peak clad temperature to a set of independent variables that are known to be important in determining the success of the feed and bleed operation. A simple linear relationship is then used to relate the clad temperature to the core damage probability. To obtain a quantitative relationship among different nodes in the DBN, surrogates of the RELAP5 reactor transient analysis code are used. These surrogates are generated by applying the ACE algorithm to output data obtained from about 50 RELAP5 cases covering a wide range of the selected independent variables. These surrogates allow important safety parameters such as the fuel clad temperature to be expressed as a function of key reactor parameters such as the coolant temperature and pressure together with important independent variables such as the scram delay time. The time-dependent core damage probability is calculated by sampling the independent variables from their probability distributions and propagate the information up through the Bayesian network to give the clad temperature. With the knowledge of the clad temperature and the assumption that the core damage probability has a one-to-one relationship to it, we have calculated the core damage probably as a function of transient time. The use of the DBN model in combination with ACE allows risk analysis to be performed with much less effort than if the analysis were done using the standard techniques.

Incorporating Skew into RMS Surface Roughness Probability Distribution

NASA Technical Reports Server (NTRS)

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

2013-01-01

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

FASP, an analytic resource appraisal program for petroleum play analysis

USGS Publications Warehouse

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

1986-01-01

An analytic probabilistic methodology for resource appraisal of undiscovered oil and gas resources in play analysis is presented in a FORTRAN program termed FASP. This play-analysis methodology is a geostochastic system for petroleum resource appraisal in explored as well as frontier areas. An established geologic model considers both the uncertainty of the presence of the assessed hydrocarbon and its amount if present. The program FASP produces resource estimates of crude oil, nonassociated gas, dissolved gas, and gas for a geologic play in terms of probability distributions. The analytic method is based upon conditional probability theory and many laws of expectation and variance. ?? 1986.

Probability density of aperture-averaged irradiance fluctuations for long range free space optical communication links.

PubMed

Lyke, Stephen D; Voelz, David G; Roggemann, Michael C

2009-11-20

The probability density function (PDF) of aperture-averaged irradiance fluctuations is calculated from wave-optics simulations of a laser after propagating through atmospheric turbulence to investigate the evolution of the distribution as the aperture diameter is increased. The simulation data distribution is compared to theoretical gamma-gamma and lognormal PDF models under a variety of scintillation regimes from weak to strong. Results show that under weak scintillation conditions both the gamma-gamma and lognormal PDF models provide a good fit to the simulation data for all aperture sizes studied. Our results indicate that in moderate scintillation the gamma-gamma PDF provides a better fit to the simulation data than the lognormal PDF for all aperture sizes studied. In the strong scintillation regime, the simulation data distribution is gamma gamma for aperture sizes much smaller than the coherence radius rho0 and lognormal for aperture sizes on the order of rho0 and larger. Examples of how these results affect the bit-error rate of an on-off keyed free space optical communication link are presented.

Drilling High Precision Holes in Ti6Al4V Using Rotary Ultrasonic Machining and Uncertainties Underlying Cutting Force, Tool Wear, and Production Inaccuracies.

PubMed

Chowdhury, M A K; Sharif Ullah, A M M; Anwar, Saqib

2017-09-12

Ti6Al4V alloys are difficult-to-cut materials that have extensive applications in the automotive and aerospace industry. A great deal of effort has been made to develop and improve the machining operations of Ti6Al4V alloys. This paper presents an experimental study that systematically analyzes the effects of the machining conditions (ultrasonic power, feed rate, spindle speed, and tool diameter) on the performance parameters (cutting force, tool wear, overcut error, and cylindricity error), while drilling high precision holes on the workpiece made of Ti6Al4V alloys using rotary ultrasonic machining (RUM). Numerical results were obtained by conducting experiments following the design of an experiment procedure. The effects of the machining conditions on each performance parameter have been determined by constructing a set of possibility distributions (i.e., trapezoidal fuzzy numbers) from the experimental data. A possibility distribution is a probability-distribution-neural representation of uncertainty, and is effective in quantifying the uncertainty underlying physical quantities when there is a limited number of data points which is the case here. Lastly, the optimal machining conditions have been identified using these possibility distributions.

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.

Distributed fault detection over sensor networks with Markovian switching topologies

NASA Astrophysics Data System (ADS)

Ge, Xiaohua; Han, Qing-Long

2014-05-01

This paper deals with the distributed fault detection for discrete-time Markov jump linear systems over sensor networks with Markovian switching topologies. The sensors are scatteredly deployed in the sensor field and the fault detectors are physically distributed via a communication network. The system dynamics changes and sensing topology variations are modeled by a discrete-time Markov chain with incomplete mode transition probabilities. Each of these sensor nodes firstly collects measurement outputs from its all underlying neighboring nodes, processes these data in accordance with the Markovian switching topologies, and then transmits the processed data to the remote fault detector node. Network-induced delays and accumulated data packet dropouts are incorporated in the data transmission between the sensor nodes and the distributed fault detector nodes through the communication network. To generate localized residual signals, mode-independent distributed fault detection filters are proposed. By means of the stochastic Lyapunov functional approach, the residual system performance analysis is carried out such that the overall residual system is stochastically stable and the error between each residual signal and the fault signal is made as small as possible. Furthermore, a sufficient condition on the existence of the mode-independent distributed fault detection filters is derived in the simultaneous presence of incomplete mode transition probabilities, Markovian switching topologies, network-induced delays, and accumulated data packed dropouts. Finally, a stirred-tank reactor system is given to show the effectiveness of the developed theoretical results.

A New Approach in Generating Meteorological Forecasts for Ensemble Streamflow Forecasting using Multivariate Functions

NASA Astrophysics Data System (ADS)

Khajehei, S.; Madadgar, S.; Moradkhani, H.

2014-12-01

The reliability and accuracy of hydrological predictions are subject to various sources of uncertainty, including meteorological forcing, initial conditions, model parameters and model structure. To reduce the total uncertainty in hydrological applications, one approach is to reduce the uncertainty in meteorological forcing by using the statistical methods based on the conditional probability density functions (pdf). However, one of the requirements for current methods is to assume the Gaussian distribution for the marginal distribution of the observed and modeled meteorology. Here we propose a Bayesian approach based on Copula functions to develop the conditional distribution of precipitation forecast needed in deriving a hydrologic model for a sub-basin in the Columbia River Basin. Copula functions are introduced as an alternative approach in capturing the uncertainties related to meteorological forcing. Copulas are multivariate joint distribution of univariate marginal distributions, which are capable to model the joint behavior of variables with any level of correlation and dependency. The method is applied to the monthly forecast of CPC with 0.25x0.25 degree resolution to reproduce the PRISM dataset over 1970-2000. Results are compared with Ensemble Pre-Processor approach as a common procedure used by National Weather Service River forecast centers in reproducing observed climatology during a ten-year verification period (2000-2010).

Performance evaluation and bias correction of DBS measurements for a 1290-MHz boundary layer profiler.

PubMed

Liu, Zhao; Zheng, Chaorong; Wu, Yue

2018-02-01

Recently, the government installed a boundary layer profiler (BLP), which is operated under the Doppler beam swinging mode, in a coastal area of China, to acquire useful wind field information in the atmospheric boundary layer for several purposes. And under strong wind conditions, the performance of the BLP is evaluated. It is found that, even though the quality controlled BLP data show good agreement with the balloon observations, a systematic bias can always be found for the BLP data. For the low wind velocities, the BLP data tend to overestimate the atmospheric wind. However, with the increment of wind velocity, the BLP data show a tendency of underestimation. In order to remove the effect of poor quality data on bias correction, the probability distribution function of the differences between the two instruments is discussed, and it is found that the t location scale distribution is the most suitable probability model when compared to other probability models. After the outliers with a large discrepancy, which are outside of 95% confidence interval of the t location scale distribution, are discarded, the systematic bias can be successfully corrected using a first-order polynomial correction function. The methodology of bias correction used in the study not only can be referred for the correction of other wind profiling radars, but also can lay a solid basis for further analysis of the wind profiles.

Performance evaluation and bias correction of DBS measurements for a 1290-MHz boundary layer profiler

NASA Astrophysics Data System (ADS)

Liu, Zhao; Zheng, Chaorong; Wu, Yue

2018-02-01

Recently, the government installed a boundary layer profiler (BLP), which is operated under the Doppler beam swinging mode, in a coastal area of China, to acquire useful wind field information in the atmospheric boundary layer for several purposes. And under strong wind conditions, the performance of the BLP is evaluated. It is found that, even though the quality controlled BLP data show good agreement with the balloon observations, a systematic bias can always be found for the BLP data. For the low wind velocities, the BLP data tend to overestimate the atmospheric wind. However, with the increment of wind velocity, the BLP data show a tendency of underestimation. In order to remove the effect of poor quality data on bias correction, the probability distribution function of the differences between the two instruments is discussed, and it is found that the t location scale distribution is the most suitable probability model when compared to other probability models. After the outliers with a large discrepancy, which are outside of 95% confidence interval of the t location scale distribution, are discarded, the systematic bias can be successfully corrected using a first-order polynomial correction function. The methodology of bias correction used in the study not only can be referred for the correction of other wind profiling radars, but also can lay a solid basis for further analysis of the wind profiles.

Evidence reasoning method for constructing conditional probability tables in a Bayesian network of multimorbidity.

PubMed

Du, Yuanwei; Guo, Yubin

2015-01-01

The intrinsic mechanism of multimorbidity is difficult to recognize and prediction and diagnosis are difficult to carry out accordingly. Bayesian networks can help to diagnose multimorbidity in health care, but it is difficult to obtain the conditional probability table (CPT) because of the lack of clinically statistical data. Today, expert knowledge and experience are increasingly used in training Bayesian networks in order to help predict or diagnose diseases, but the CPT in Bayesian networks is usually irrational or ineffective for ignoring realistic constraints especially in multimorbidity. In order to solve these problems, an evidence reasoning (ER) approach is employed to extract and fuse inference data from experts using a belief distribution and recursive ER algorithm, based on which evidence reasoning method for constructing conditional probability tables in Bayesian network of multimorbidity is presented step by step. A multimorbidity numerical example is used to demonstrate the method and prove its feasibility and application. Bayesian network can be determined as long as the inference assessment is inferred by each expert according to his/her knowledge or experience. Our method is more effective than existing methods for extracting expert inference data accurately and is fused effectively for constructing CPTs in a Bayesian network of multimorbidity.

Survival of Norway spruce remains higher in mixed stands under a dryer and warmer climate.

PubMed

Neuner, Susanne; Albrecht, Axel; Cullmann, Dominik; Engels, Friedrich; Griess, Verena C; Hahn, W Andreas; Hanewinkel, Marc; Härtl, Fabian; Kölling, Christian; Staupendahl, Kai; Knoke, Thomas

2015-02-01

Shifts in tree species distributions caused by climatic change are expected to cause severe losses in the economic value of European forestland. However, this projection disregards potential adaptation options such as tree species conversion, shorter production periods, or establishment of mixed species forests. The effect of tree species mixture has, as yet, not been quantitatively investigated for its potential to mitigate future increases in production risks. For the first time, we use survival time analysis to assess the effects of climate, species mixture and soil condition on survival probabilities for Norway spruce and European beech. Accelerated Failure Time (AFT) models based on an extensive dataset of almost 65,000 trees from the European Forest Damage Survey (FDS)--part of the European-wide Level I monitoring network--predicted a 24% decrease in survival probability for Norway spruce in pure stands at age 120 when unfavorable changes in climate conditions were assumed. Increasing species admixture greatly reduced the negative effects of unfavorable climate conditions, resulting in a decline in survival probabilities of only 7%. We conclude that future studies of forest management under climate change as well as forest policy measures need to take this, as yet unconsidered, strongly advantageous effect of tree species mixture into account. © 2014 John Wiley & Sons Ltd.

Computing Real-time Streamflow Using Emerging Technologies: Non-contact Radars and the Probability Concept

NASA Astrophysics Data System (ADS)

Fulton, J. W.; Bjerklie, D. M.; Jones, J. W.; Minear, J. T.

2015-12-01

Measuring streamflow, developing, and maintaining rating curves at new streamgaging stations is both time-consuming and problematic. Hydro 21 was an initiative by the U.S. Geological Survey to provide vision and leadership to identify and evaluate new technologies and methods that had the potential to change the way in which streamgaging is conducted. Since 2014, additional trials have been conducted to evaluate some of the methods promoted by the Hydro 21 Committee. Emerging technologies such as continuous-wave radars and computationally-efficient methods such as the Probability Concept require significantly less field time, promote real-time velocity and streamflow measurements, and apply to unsteady flow conditions such as looped ratings and unsteady-flood flows. Portable and fixed-mount radars have advanced beyond the development phase, are cost effective, and readily available in the marketplace. The Probability Concept is based on an alternative velocity-distribution equation developed by C.-L. Chiu, who pioneered the concept. By measuring the surface-water velocity and correcting for environmental influences such as wind drift, radars offer a reliable alternative for measuring and computing real-time streamflow for a variety of hydraulic conditions. If successful, these tools may allow us to establish ratings more efficiently, assess unsteady flow conditions, and report real-time streamflow at new streamgaging stations.

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.

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

Cycles till failure of silver-zinc cells with completing failures modes: Preliminary data analysis

NASA Technical Reports Server (NTRS)

Sidik, S. M.; Leibecki, H. F.; Bozek, J. M.

1980-01-01

One hundred and twenty nine cells were run through charge-discharge cycles until failure. The experiment design was a variant of a central composite factorial in five factors. Preliminary data analysis consisted of response surface estimation of life. Batteries fail under two basic modes; a low voltage condition and an internal shorting condition. A competing failure modes analysis using maximum likelihood estimation for the extreme value life distribution was performed. Extensive diagnostics such as residual plotting and probability plotting were employed to verify data quality and choice of model.

Cycles till failure of silver-zinc cells with competing failure modes - Preliminary data analysis

NASA Technical Reports Server (NTRS)

Sidik, S. M.; Leibecki, H. F.; Bozek, J. M.

1980-01-01

The data analysis of cycles to failure of silver-zinc electrochemical cells with competing failure modes is presented. The test ran 129 cells through charge-discharge cycles until failure; preliminary data analysis consisted of response surface estimate of life. Batteries fail through low voltage condition and an internal shorting condition; a competing failure modes analysis was made using maximum likelihood estimation for the extreme value life distribution. Extensive residual plotting and probability plotting were used to verify data quality and selection of model.

A quantum heuristic algorithm for the traveling salesman problem

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

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.

Comparative study of probability distribution distances to define a metric for the stability of multi-source biomedical research data.

PubMed

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

2013-01-01

Research biobanks are often composed by data from multiple sources. In some cases, these different subsets of data may present dissimilarities among their probability density functions (PDF) due to spatial shifts. This, may lead to wrong hypothesis when treating the data as a whole. Also, the overall quality of the data is diminished. With the purpose of developing a generic and comparable metric to assess the stability of multi-source datasets, we have studied the applicability and behaviour of several PDF distances over shifts on different conditions (such as uni- and multivariate, different types of variable, and multi-modality) which may appear in real biomedical data. From the studied distances, we found information-theoretic based and Earth Mover's Distance to be the most practical distances for most conditions. We discuss the properties and usefulness of each distance according to the possible requirements of a general stability metric.

A prototype method for diagnosing high ice water content probability using satellite imager data

NASA Astrophysics Data System (ADS)

Yost, Christopher R.; Bedka, Kristopher M.; Minnis, Patrick; Nguyen, Louis; Strapp, J. Walter; Palikonda, Rabindra; Khlopenkov, Konstantin; Spangenberg, Douglas; Smith, William L., Jr.; Protat, Alain; Delanoe, Julien

2018-03-01

Recent studies have found that ingestion of high mass concentrations of ice particles in regions of deep convective storms, with radar reflectivity considered safe for aircraft penetration, can adversely impact aircraft engine performance. Previous aviation industry studies have used the term high ice water content (HIWC) to define such conditions. Three airborne field campaigns were conducted in 2014 and 2015 to better understand how HIWC is distributed in deep convection, both as a function of altitude and proximity to convective updraft regions, and to facilitate development of new methods for detecting HIWC conditions, in addition to many other research and regulatory goals. This paper describes a prototype method for detecting HIWC conditions using geostationary (GEO) satellite imager data coupled with in situ total water content (TWC) observations collected during the flight campaigns. Three satellite-derived parameters were determined to be most useful for determining HIWC probability: (1) the horizontal proximity of the aircraft to the nearest overshooting convective updraft or textured anvil cloud, (2) tropopause-relative infrared brightness temperature, and (3) daytime-only cloud optical depth. Statistical fits between collocated TWC and GEO satellite parameters were used to determine the membership functions for the fuzzy logic derivation of HIWC probability. The products were demonstrated using data from several campaign flights and validated using a subset of the satellite-aircraft collocation database. The daytime HIWC probability was found to agree quite well with TWC time trends and identified extreme TWC events with high probability. Discrimination of HIWC was more challenging at night with IR-only information. The products show the greatest capability for discriminating TWC ≥ 0.5 g m-3. Product validation remains challenging due to vertical TWC uncertainties and the typically coarse spatio-temporal resolution of the GEO data.

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

Generation of multivariate near shore extreme wave conditions based on an extreme value copula for offshore boundary conditions.

NASA Astrophysics Data System (ADS)

Leyssen, Gert; Mercelis, Peter; De Schoesitter, Philippe; Blanckaert, Joris

2013-04-01

Near shore extreme wave conditions, used as input for numerical wave agitation simulations and for the dimensioning of coastal defense structures, need to be determined at a harbour entrance situated at the French North Sea coast. To obtain significant wave heights, the numerical wave model SWAN has been used. A multivariate approach was used to account for the joint probabilities. Considered variables are: wind velocity and direction, water level and significant offshore wave height and wave period. In a first step a univariate extreme value distribution has been determined for the main variables. By means of a technique based on the mean excess function, an appropriate member of the GPD is selected. An optimal threshold for peak over threshold selection is determined by maximum likelihood optimization. Next, the joint dependency structure for the primary random variables is modeled by an extreme value copula. Eventually the multivariate domain of variables was stratified in different classes, each of which representing a combination of variable quantiles with a joint probability, which are used for model simulation. The main variable is the wind velocity, as in the area of concern extreme wave conditions are wind driven. The analysis is repeated for 9 different wind directions. The secondary variable is water level. In shallow waters extreme waves will be directly affected by water depth. Hence the joint probability of occurrence for water level and wave height is of major importance for design of coastal defense structures. Wind velocity and water levels are only dependent for some wind directions (wind induced setup). Dependent directions are detected using a Kendall and Spearman test and appeared to be those with the longest fetch. For these directions, wind velocity and water level extreme value distributions are multivariately linked through a Gumbel Copula. These distributions are stratified into classes of which the frequency of occurrence can be calculated. For the remaining directions the univariate extreme wind velocity distribution is stratified, each class combined with 5 high water levels. The wave height at the model boundaries was taken into account by a regression with the extreme wind velocity at the offshore location. The regression line and the 95% confidence limits where combined with each class. Eventually the wave period is computed by a new regression with the significant wave height. This way 1103 synthetic events were selected and simulated with the SWAN wave model, each of which a frequency of occurrence is calculated for. Hence near shore significant wave heights are obtained with corresponding frequencies. The statistical distribution of the near shore wave heights is determined by sorting the model results in a descending order and accumulating the corresponding frequencies. This approach allows determination of conditional return periods. For example, for the imposed univariate design return periods of 100 years for significant wave height and 30 years for water level, the joint return period for a simultaneous exceedance of both conditions can be computed as 4000 years. Hence, this methodology allows for a probabilistic design of coastal defense structures.

High monetary reward rates and caloric rewards decrease temporal persistence

PubMed Central

Bode, Stefan; Murawski, Carsten

2017-01-01

Temporal persistence refers to an individual's capacity to wait for future rewards, while forgoing possible alternatives. This requires a trade-off between the potential value of delayed rewards and opportunity costs, and is relevant to many real-world decisions, such as dieting. Theoretical models have previously suggested that high monetary reward rates, or positive energy balance, may result in decreased temporal persistence. In our study, 50 fasted participants engaged in a temporal persistence task, incentivised with monetary rewards. In alternating blocks of this task, rewards were delivered at delays drawn randomly from distributions with either a lower or higher maximum reward rate. During some blocks participants received either a caloric drink or water. We used survival analysis to estimate participants' probability of quitting conditional on the delay distribution and the consumed liquid. Participants had a higher probability of quitting in blocks with the higher reward rate. Furthermore, participants who consumed the caloric drink had a higher probability of quitting than those who consumed water. Our results support the predictions from the theoretical models, and importantly, suggest that both higher monetary reward rates and physiologically relevant rewards can decrease temporal persistence, which is a crucial determinant for survival in many species. PMID:28228517

High monetary reward rates and caloric rewards decrease temporal persistence.

PubMed

Fung, Bowen J; Bode, Stefan; Murawski, Carsten

2017-02-22

Temporal persistence refers to an individual's capacity to wait for future rewards, while forgoing possible alternatives. This requires a trade-off between the potential value of delayed rewards and opportunity costs, and is relevant to many real-world decisions, such as dieting. Theoretical models have previously suggested that high monetary reward rates, or positive energy balance, may result in decreased temporal persistence. In our study, 50 fasted participants engaged in a temporal persistence task, incentivised with monetary rewards. In alternating blocks of this task, rewards were delivered at delays drawn randomly from distributions with either a lower or higher maximum reward rate. During some blocks participants received either a caloric drink or water. We used survival analysis to estimate participants' probability of quitting conditional on the delay distribution and the consumed liquid. Participants had a higher probability of quitting in blocks with the higher reward rate. Furthermore, participants who consumed the caloric drink had a higher probability of quitting than those who consumed water. Our results support the predictions from the theoretical models, and importantly, suggest that both higher monetary reward rates and physiologically relevant rewards can decrease temporal persistence, which is a crucial determinant for survival in many species. © 2017 The Authors.

A New Insight into the Earthquake Recurrence Studies from the Three-parameter Generalized Exponential Distributions

NASA Astrophysics Data System (ADS)

Pasari, S.; Kundu, D.; Dikshit, O.

2012-12-01

Earthquake recurrence interval is one of the important ingredients towards probabilistic seismic hazard assessment (PSHA) for any location. Exponential, gamma, Weibull and lognormal distributions are quite established probability models in this recurrence interval estimation. However, they have certain shortcomings too. Thus, it is imperative to search for some alternative sophisticated distributions. In this paper, we introduce a three-parameter (location, scale and shape) exponentiated exponential distribution and investigate the scope of this distribution as an alternative of the afore-mentioned distributions in earthquake recurrence studies. This distribution is a particular member of the exponentiated Weibull distribution. Despite of its complicated form, it is widely accepted in medical and biological applications. Furthermore, it shares many physical properties with gamma and Weibull family. Unlike gamma distribution, the hazard function of generalized exponential distribution can be easily computed even if the shape parameter is not an integer. To contemplate the plausibility of this model, a complete and homogeneous earthquake catalogue of 20 events (M ≥ 7.0) spanning for the period 1846 to 1995 from North-East Himalayan region (20-32 deg N and 87-100 deg E) has been used. The model parameters are estimated using maximum likelihood estimator (MLE) and method of moment estimator (MOME). No geological or geophysical evidences have been considered in this calculation. The estimated conditional probability reaches quite high after about a decade for an elapsed time of 17 years (i.e. 2012). Moreover, this study shows that the generalized exponential distribution fits the above data events more closely compared to the conventional models and hence it is tentatively concluded that generalized exponential distribution can be effectively considered in earthquake recurrence studies.

A PLUG-AND-PLAY ARCHITECTURE FOR PROBABILISTIC PROGRAMMING

DTIC Science & Technology

2017-04-01

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

Adaptive Decision Making Using Probabilistic Programming and Stochastic Optimization

DTIC Science & Technology

2018-01-01

world optimization problems (and hence 16 Approved for Public Release (PA); Distribution Unlimited Pred. demand (uncertain; discrete ...simplify the setting, we further assume that the demands are discrete , taking on values d1, . . . , dk with probabilities (conditional on x) (pθ)i ≡ p...Tyrrell Rockafellar. Implicit functions and solution mappings. Springer Monogr. Math ., 2009. Anthony V Fiacco and Yo Ishizuka. Sensitivity and stability

The influence of coarse-scale environmental features on current and predicted future distributions of narrow-range endemic crayfish populations

USGS Publications Warehouse

Dyer, Joseph J.; Brewer, Shannon K.; Worthington, Thomas A.; Bergey, Elizabeth A.

2013-01-01

1.A major limitation to effective management of narrow-range crayfish populations is the paucity of information on the spatial distribution of crayfish species and a general understanding of the interacting environmental variables that drive current and future potential distributional patterns. 2.Maximum Entropy Species Distribution Modeling Software (MaxEnt) was used to predict the current and future potential distributions of four endemic crayfish species in the Ouachita Mountains. Current distributions were modelled using climate, geology, soils, land use, landform and flow variables thought to be important to lotic crayfish. Potential changes in the distribution were forecast by using models trained on current conditions and projecting onto the landscape predicted under climate-change scenarios. 3.The modelled distribution of the four species closely resembled the perceived distribution of each species but also predicted populations in streams and catchments where they had not previously been collected. Soils, elevation and winter precipitation and temperature most strongly related to current distributions and represented 6587% of the predictive power of the models. Model accuracy was high for all models, and model predictions of new populations were verified through additional field sampling. 4.Current models created using two spatial resolutions (1 and 4.5km2) showed that fine-resolution data more accurately represented current distributions. For three of the four species, the 1-km2 resolution models resulted in more conservative predictions. However, the modelled distributional extent of Orconectes leptogonopodus was similar regardless of data resolution. Field validations indicated 1-km2 resolution models were more accurate than 4.5-km2 resolution models. 5.Future projected (4.5-km2 resolution models) model distributions indicated three of the four endemic species would have truncated ranges with low occurrence probabilities under the low-emission scenario, whereas two of four species would be severely restricted in range under moderatehigh emissions. Discrepancies in the two emission scenarios probably relate to the exclusion of behavioural adaptations from species-distribution models. 6.These model predictions illustrate possible impacts of climate change on narrow-range endemic crayfish populations. The predictions do not account for biotic interactions, migration, local habitat conditions or species adaptation. However, we identified the constraining landscape features acting on these populations that provide a framework for addressing habitat needs at a fine scale and developing targeted and systematic monitoring programmes.

Ladar range image denoising by a nonlocal probability statistics algorithm

NASA Astrophysics Data System (ADS)

Xia, Zhi-Wei; Li, Qi; Xiong, Zhi-Peng; Wang, Qi

2013-01-01

According to the characteristic of range images of coherent ladar and the basis of nonlocal means (NLM), a nonlocal probability statistics (NLPS) algorithm is proposed in this paper. The difference is that NLM performs denoising using the mean of the conditional probability distribution function (PDF) while NLPS using the maximum of the marginal PDF. In the algorithm, similar blocks are found out by the operation of block matching and form a group. Pixels in the group are analyzed by probability statistics and the gray value with maximum probability is used as the estimated value of the current pixel. The simulated range images of coherent ladar with different carrier-to-noise ratio and real range image of coherent ladar with 8 gray-scales are denoised by this algorithm, and the results are compared with those of median filter, multitemplate order mean filter, NLM, median nonlocal mean filter and its incorporation of anatomical side information, and unsupervised information-theoretic adaptive filter. The range abnormality noise and Gaussian noise in range image of coherent ladar are effectively suppressed by NLPS.

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.

Persistence of exponential bed thickness distributions in the stratigraphic record: Experiments and theory

NASA Astrophysics Data System (ADS)

Straub, K. M.; Ganti, V. K.; Paola, C.; Foufoula-Georgiou, E.

2010-12-01

Stratigraphy preserved in alluvial basins houses the most complete record of information necessary to reconstruct past environmental conditions. Indeed, the character of the sedimentary record is inextricably related to the surface processes that formed it. In this presentation we explore how the signals of surface processes are recorded in stratigraphy through the use of physical and numerical experiments. We focus on linking surface processes to stratigraphy in 1D by quantifying the probability distributions of processes that govern the evolution of depositional systems to the probability distribution of preserved bed thicknesses. In this study we define a bed as a package of sediment bounded above and below by erosional surfaces. In a companion presentation we document heavy-tailed statistics of erosion and deposition from high-resolution temporal elevation data recorded during a controlled physical experiment. However, the heavy tails in the magnitudes of erosional and depositional events are not preserved in the experimental stratigraphy. Similar to many bed thickness distributions reported in field studies we find that an exponential distribution adequately describes the thicknesses of beds preserved in our experiment. We explore the generation of exponential bed thickness distributions from heavy-tailed surface statistics using 1D numerical models. These models indicate that when the full distribution of elevation fluctuations (both erosional and depositional events) is symmetrical, the resulting distribution of bed thicknesses is exponential in form. Finally, we illustrate that a predictable relationship exists between the coefficient of variation of surface elevation fluctuations and the scale-parameter of the resulting exponential distribution of bed thicknesses.

Modelling the Effects of Temperature and Cloud Cover Change on Mountain Permafrost Distribution, Northwest Canada

NASA Astrophysics Data System (ADS)

Bonnaventure, P. P.; Lewkowicz, A. G.

2008-12-01

Spatial models of permafrost probability for three study areas in northwest Canada between 59°N and 61°N were perturbed to investigate climate change impacts. The models are empirical-statistical in nature, based on basal temperature of snow (BTS) measurements in winter, and summer ground-truthing of the presence or absence of frozen ground. Predictions of BTS values are made using independent variables of elevation and potential incoming solar radiation (PISR), both derived from a 30 m DEM. These are then transformed into the probability of the presence or absence of permafrost through logistic regression. Under present climate conditions, permafrost percentages in the study areas are 44% for Haines Summit, British Columbia, 38% for Wolf Creek, Yukon, and 69% for part of the Ruby Range, Yukon (Bonnaventure and Lewkowicz, 2008; Lewkowicz and Bonaventure, 2008). Scenarios of air temperature change from -2K (approximating Neoglacial conditions) to +5K (possible within the next century according to the IPCC) were examined for the three sites. Manipulations were carried out by lowering or raising the terrain within the DEM assuming a mean environmental lapse rate of 6.5K/km. Under a -2K scenario, permafrost extent increased by 22-43% in the three study areas. Under a +5K warming, permafrost essentially disappeared in Haines Summit and Wolf Creek, while in the Ruby Range less than 12% of the area remained perennially frozen. It should be emphasized that these model predictions are for equilibrium conditions which might not be attained for several decades or longer in areas of cold permafrost. Cloud cover changes of -10% to +10% were examined through adjusting the partitioning of direct beam and diffuse radiation in the PISR input field. Changes to permafrost extent were small, ranging from -2% to -4% for greater cloudiness with changes of the opposite magnitude for less cloud. The results show that air temperature change has a much greater potential to affect mountain permafrost distribution in the long-term than the probable range of cloud cover changes. Modelled results for the individual areas respond according to the hypsometry of the terrain and the relative strength of elevation and PISR in the regression models. This study indicates that significant changes to the distribution and extent of mountain permafrost in northwest Canada can be expected in the next few decades. References Bonnaventure, P.P. and Lewkowicz, A.G. (2008). Mountain permafrost probability mapping using the BTS method in two climatically dissimilar locations, northwest Canada. Canadian Journal of Earth Sciences, 45, 443-455. Lewkowicz, A.G. and Bonnaventure, P.P. (2008). Interchangeability of local mountain permafrost probability models, northwest Canada. Permafrost and Periglacial Processes, 19, 49-62.

"Jumping to conclusions" in delusion-prone participants: an experimental economics approach.

PubMed

van der Leer, Leslie; McKay, Ryan

2014-01-01

That delusional and delusion-prone individuals "jump to conclusions" on probabilistic reasoning tasks is a key finding in cognitive neuropsychiatry. Here we focused on a less frequently investigated aspect of "jumping to conclusions" (JTC): certainty judgments. We incorporated rigorous procedures from experimental economics to eliminate potential confounds of miscomprehension and motivation and systematically investigated the effect of incentives on task performance. Low- and high-delusion-prone participants (n = 109) completed a series of computerised trials; on each trial, they were shown a black or a white fish, caught from one of the two lakes containing fish of both colours in complementary ratios. In the betting condition, participants were given £4 to distribute over the two lakes as they wished; in the control condition, participants simply provided an estimate of how probable each lake was. Deviations from Bayesian probabilities were investigated. Whereas high-delusion-prone participants in both the control and betting conditions underestimated the Bayesian probabilities (i.e. were conservative), low-delusion-prone participants in the control condition underestimated but those in the betting condition provided accurate estimates. In the control condition, there was a trend for high-delusion-prone participants to give higher estimates than low-delusion-prone participants, which is consistent with previous reports of "jumping to conclusions" in delusion-prone participants. However, our findings in the betting condition, where high-delusion-prone participants provided lower estimates than low-delusion-prone participants (who were accurate), are inconsistent with the jumping-to-conclusions effect in both a relative and an absolute sense. Our findings highlight the key role of task incentives and underscore the importance of comparing the responses of delusion-prone participants to an objective rational standard as well as to the responses of non-delusion-prone participants.

SUGGEL: A Program Suggesting the Orbital Angular Momentum of a Neutron Resonance from the Magnitude of its Neutron Width

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

Oh, S.Y.

2001-02-02

The SUGGEL computer code has been developed to suggest a value for the orbital angular momentum of a neutron resonance that is consistent with the magnitude of its neutron width. The suggestion is based on the probability that a resonance having a certain value of g{Gamma}{sub n} is an l-wave resonance. The probability is calculated by using Bayes' theorem on the conditional probability. The probability density functions (pdf's) of g{Gamma}{sub n} for up to d-wave (l=2) have been derived from the {chi}{sup 2} distribution of Porter and Thomas. The pdf's take two possible channel spins into account. This code ismore » a tool which evaluators will use to construct resonance parameters and help to assign resonance spin. The use of this tool is expected to reduce time and effort in the evaluation procedure, since the number of repeated runs of the fitting code (e.g., SAMMY) may be reduced.« less

Defense strategies for asymmetric networked systems under composite utilities

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

Rao, Nageswara S.; Ma, Chris Y. T.; Hausken, Kjell

We consider an infrastructure of networked systems with discrete components that can be reinforced at certain costs to guard against attacks. The communications network plays a critical, asymmetric role of providing the vital connectivity between the systems. We characterize the correlations within this infrastructure at two levels using (a) aggregate failure correlation function that specifies the infrastructure failure probability giventhe failure of an individual system or network, and (b) first order differential conditions on system survival probabilities that characterize component-level correlations. We formulate an infrastructure survival game between an attacker and a provider, who attacks and reinforces individual components, respectively.more » They use the composite utility functions composed of a survival probability term and a cost term, and the previously studiedsum-form and product-form utility functions are their special cases. At Nash Equilibrium, we derive expressions for individual system survival probabilities and the expected total number of operational components. We apply and discuss these estimates for a simplified model of distributed cloud computing infrastructure« less

Maximum likelihood density modification by pattern recognition of structural motifs

DOEpatents

Terwilliger, Thomas C.

2004-04-13

An electron density for a crystallographic structure having protein regions and solvent regions is improved by maximizing the log likelihood of a set of structures factors {F.sub.h } using a local log-likelihood function: (x)+p(.rho.(x).vertline.SOLV)p.sub.SOLV (x)+p(.rho.(x).vertline.H)p.sub.H (x)], where p.sub.PROT (x) is the probability that x is in the protein region, p(.rho.(x).vertline.PROT) is the conditional probability for .rho.(x) given that x is in the protein region, and p.sub.SOLV (x) and p(.rho.(x).vertline.SOLV) are the corresponding quantities for the solvent region, p.sub.H (x) refers to the probability that there is a structural motif at a known location, with a known orientation, in the vicinity of the point x; and p(.rho.(x).vertline.H) is the probability distribution for electron density at this point given that the structural motif actually is present. One appropriate structural motif is a helical structure within the crystallographic structure.

Predictive probability methods for interim monitoring in clinical trials with longitudinal outcomes.

PubMed

Zhou, Ming; Tang, Qi; Lang, Lixin; Xing, Jun; Tatsuoka, Kay

2018-04-17

In clinical research and development, interim monitoring is critical for better decision-making and minimizing the risk of exposing patients to possible ineffective therapies. For interim futility or efficacy monitoring, predictive probability methods are widely adopted in practice. Those methods have been well studied for univariate variables. However, for longitudinal studies, predictive probability methods using univariate information from only completers may not be most efficient, and data from on-going subjects can be utilized to improve efficiency. On the other hand, leveraging information from on-going subjects could allow an interim analysis to be potentially conducted once a sufficient number of subjects reach an earlier time point. For longitudinal outcomes, we derive closed-form formulas for predictive probabilities, including Bayesian predictive probability, predictive power, and conditional power and also give closed-form solutions for predictive probability of success in a future trial and the predictive probability of success of the best dose. When predictive probabilities are used for interim monitoring, we study their distributions and discuss their analytical cutoff values or stopping boundaries that have desired operating characteristics. We show that predictive probabilities utilizing all longitudinal information are more efficient for interim monitoring than that using information from completers only. To illustrate their practical application for longitudinal data, we analyze 2 real data examples from clinical trials. Copyright © 2018 John Wiley & Sons, Ltd.

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

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

Osaki, M.; Ban, M.

2003-08-01

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

Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

NASA Astrophysics Data System (ADS)

Ciaglia, Florio M.; Cosmo, Fabio Di; Felice, Domenico; Mancini, Stefano; Marmo, Giuseppe; Pérez-Pardo, Juan M.

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

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

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.

Experimental Study of the Effect of the Initial Spectrum Width on the Statistics of Random Wave Groups

NASA Astrophysics Data System (ADS)

Shemer, L.; Sergeeva, A.

2009-12-01

The statistics of random water wave field determines the probability of appearance of extremely high (freak) waves. This probability is strongly related to the spectral wave field characteristics. Laboratory investigation of the spatial variation of the random wave-field statistics for various initial conditions is thus of substantial practical importance. Unidirectional nonlinear random wave groups are investigated experimentally in the 300 m long Large Wave Channel (GWK) in Hannover, Germany, which is the biggest facility of its kind in Europe. Numerous realizations of a wave field with the prescribed frequency power spectrum, yet randomly-distributed initial phases of each harmonic, were generated by a computer-controlled piston-type wavemaker. Several initial spectral shapes with identical dominant wave length but different width were considered. For each spectral shape, the total duration of sampling in all realizations was long enough to yield sufficient sample size for reliable statistics. Through all experiments, an effort had been made to retain the characteristic wave height value and thus the degree of nonlinearity of the wave field. Spatial evolution of numerous statistical wave field parameters (skewness, kurtosis and probability distributions) is studied using about 25 wave gauges distributed along the tank. It is found that, depending on the initial spectral shape, the frequency spectrum of the wave field may undergo significant modification in the course of its evolution along the tank; the values of all statistical wave parameters are strongly related to the local spectral width. A sample of the measured wave height probability functions (scaled by the variance of surface elevation) is plotted in Fig. 1 for the initially narrow rectangular spectrum. The results in Fig. 1 resemble findings obtained in [1] for the initial Gaussian spectral shape. The probability of large waves notably surpasses that predicted by the Rayleigh distribution and is the highest at the distance of about 100 m. Acknowledgement This study is carried out in the framework of the EC supported project "Transnational access to large-scale tests in the Large Wave Channel (GWK) of Forschungszentrum Küste (Contract HYDRALAB III - No. 022441). [1] L. Shemer and A. Sergeeva, J. Geophys. Res. Oceans 114, C01015 (2009). Figure 1. Variation along the tank of the measured wave height distribution for rectangular initial spectral shape, the carrier wave period T0=1.5 s.

Tectono-thermal evolution in a region with thin-skinned tectonics: the western nappes in the Cantabrian Zone (Variscan belt of NW Spain)

NASA Astrophysics Data System (ADS)

Bastida, F.; Brime, C.; García-López, S.; Sarmiento, G. N.

The palaeotemperature distribution in the transition from diagenesis to metamorphism in the western nappes of the Cantabrian Zone (Somiedo, La Sobia and Aramo Units) are analysed by conodont colour alteration index (CAI) and illite crystallinity (IC). Structural and stratigraphic control in distribution of CAI and IC values is observed. Both CAI and IC value distributions show that anchizonal conditions are reached in the lower part of the Somiedo Unit. A disruption of the thermal trend by basal thrusts is evidenced by CAI and IC values. There is an apparent discrepancy between the IC and CAI values in Carboniferous rocks of the Aramo Unit; the IC has mainly anchizonal values, whereas the CAI has diagenetic values. Discrepant IC values are explained as a feature inherited from the source area. In the Carboniferous rocks of the La Sobia Unit, both IC and CAI indicate diagenetic conditions. The anchimetamorphism predated completion of emplacement of the major nappes; it probably developed previously and/or during the early stages of motion of the units. Temperature probably decreased when the metamorphosed zones of the sheets rose along ramps and were intensely eroded. In the context of the Iberian Variscan belt, influence of tectonic factors on the metamorphism is greater in the internal parts, where the strain and cleavage are always present, than in the external parts (Cantabrian Zone), where brittle deformation and rock translation are dominant, with an increasing role of the burial on the metamorphism.

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

NASA Technical Reports Server (NTRS)

Chiu, J. Christine; Petty, Grant W.

2005-01-01

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

A computationally efficient ductile damage model accounting for nucleation and micro-inertia at high triaxialities

DOE PAGES

Versino, Daniele; Bronkhorst, Curt Allan

2018-01-31

The computational formulation of a micro-mechanical material model for the dynamic failure of ductile metals is presented in this paper. The statistical nature of porosity initiation is accounted for by introducing an arbitrary probability density function which describes the pores nucleation pressures. Each micropore within the representative volume element is modeled as a thick spherical shell made of plastically incompressible material. The treatment of porosity by a distribution of thick-walled spheres also allows for the inclusion of micro-inertia effects under conditions of shock and dynamic loading. The second order ordinary differential equation governing the microscopic porosity evolution is solved withmore » a robust implicit procedure. A new Chebyshev collocation method is employed to approximate the porosity distribution and remapping is used to optimize memory usage. The adaptive approximation of the porosity distribution leads to a reduction of computational time and memory usage of up to two orders of magnitude. Moreover, the proposed model affords consistent performance: changing the nucleation pressure probability density function and/or the applied strain rate does not reduce accuracy or computational efficiency of the material model. The numerical performance of the model and algorithms presented is tested against three problems for high density tantalum: single void, one-dimensional uniaxial strain, and two-dimensional plate impact. Here, the results using the integration and algorithmic advances suggest a significant improvement in computational efficiency and accuracy over previous treatments for dynamic loading conditions.« less

A Brownian model for recurrent earthquakes

USGS Publications Warehouse

Matthews, M.V.; Ellsworth, W.L.; Reasenberg, P.A.

2002-01-01

We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The load-state process is a Brownian relaxation oscillator. Intervals between events have a Brownian passage-time distribution that may serve as a temporal model for time-dependent, long-term seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t = 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasi-stationary level, in which the conditional probability of an event becomes time independent; and (3) the quasi-stationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than 1/???2 ??? 0.707. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasi-stationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of "interaction" effects due to external perturbations to the state, such as stress-transfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step pertubations occur. Transient effects may be much stronger than would be predicted by the "clock change" method and characteristically decay inversely with elapsed time after the perturbation.

Drought forecasting in Luanhe River basin involving climatic indices

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Use of weather data and remote sensing to predict the geographic and seasonal distribution of Phlebotomus papatasi in southwest Asia.

PubMed

Cross, E R; Newcomb, W W; Tucker, C J

1996-05-01

Sandfly fever and leishmaniasis were major causes of infectious disease morbidity among military personnel deployed to the Middle East during World War II. Recently, leishmaniasis has been reported in the United Nations Multinational Forces and Observers in the Sinai. Despite these indications of endemicity, no cases of sandfly fever and only 31 cases of leishmaniasis have been identified among U.S. veterans of the Persian Gulf War. The distribution in the Persian Gulf of the vector, Phlebotomus papatasi, is thought to be highly dependent on environmental conditions, especially temperature and relative humidity. A computer model was developed using the occurrence of P. papatasi as the dependent variable and weather data as the independent variables. The results of this model indicated that the greatest sand fly activity and thus the highest risk of sandfly fever and leishmania infections occurred during the spring/summer months before U.S. troops were deployed to the Persian Gulf. Because the weather model produced probability of occurrence information for locations of the weather stations only, normalized difference vegetation index (NDVI) levels from remotely sensed Advanced Very High Resolution Radiometer satellites were determined for each weather station. From the results of the frequency of NDVI levels by probability of occurrence, the range of NDVI levels for presence of the vector was determined. The computer then identified all pixels within the NDVI range indicated and produced a computer-generated map of the probable distribution of P. papatasi. The resulting map expanded the analysis to areas where there were no weather stations and from which no information was reported in the literature, identifying these areas as having either a high or low probability of vector occurrence.

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.

Optimal nonlinear filtering using the finite-volume method

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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.

Environmental effects and individual body condition drive seasonal fecundity of rabbits: identifying acute and lagged processes.

PubMed

Wells, Konstans; O'Hara, Robert B; Cooke, Brian D; Mutze, Greg J; Prowse, Thomas A A; Fordham, Damien A

2016-07-01

The reproduction of many species is determined by seasonally-driven resource supply. But it is difficult to quantify whether the fecundity is sensitive to short- or long-term exposure to environmental conditions such as rainfall that drive resource supply. Using 25 years of data on individual fecundity of European female rabbits, Oryctolagus cuniculus, from semiarid Australia, we investigate the role of individual body condition, rainfall and temperature as drivers of seasonal and long-term and population-level changes in fecundity (breeding probability, ovulation rate, embryo survival). We built distributed lag models in a hierarchical Bayesian framework to account for both immediate and time-lagged effects of climate and other environmental drivers, and possible shifts in reproduction over consecutive seasons. We show that rainfall during summer, when rabbits typically breed only rarely, increased breeding probability immediately and with time lags of up to 10 weeks. However, an earlier onset of the yearly breeding period did not result in more overall reproductive output. Better body condition was associated with an earlier onset of breeding and higher embryo survival. Breeding probability in the main breeding season declined with increased breeding activity in the preceding season and only individuals in good body condition were able to breed late in the season. Higher temperatures reduce breeding success across seasons. We conclude that a better understanding of seasonal dynamics and plasticity (and their interplay) in reproduction will provide crucial insights into how lagomorphs are likely to respond and potentially adapt to the influence of future climate and other environmental change.

A Case Series of the Probability Density and Cumulative Distribution of Laryngeal Disease in a Tertiary Care Voice Center.

PubMed

de la Fuente, Jaime; Garrett, C Gaelyn; Ossoff, Robert; Vinson, Kim; Francis, David O; Gelbard, Alexander

2017-11-01

To examine the distribution of clinic and operative pathology in a tertiary care laryngology practice. Probability density and cumulative distribution analyses (Pareto analysis) was used to rank order laryngeal conditions seen in an outpatient tertiary care laryngology practice and those requiring surgical intervention during a 3-year period. Among 3783 new clinic consultations and 1380 operative procedures, voice disorders were the most common primary diagnostic category seen in clinic (n = 3223), followed by airway (n = 374) and swallowing (n = 186) disorders. Within the voice strata, the most common primary ICD-9 code used was dysphonia (41%), followed by unilateral vocal fold paralysis (UVFP) (9%) and cough (7%). Among new voice patients, 45% were found to have a structural abnormality. The most common surgical indications were laryngotracheal stenosis (37%), followed by recurrent respiratory papillomatosis (18%) and UVFP (17%). Nearly 55% of patients presenting to a tertiary referral laryngology practice did not have an identifiable structural abnormality in the larynx on direct or indirect examination. The distribution of ICD-9 codes requiring surgical intervention was disparate from that seen in clinic. Application of the Pareto principle may improve resource allocation in laryngology, but these initial results require confirmation across multiple institutions.

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

Functionally Graded Designer Viscoelastic Materials Tailored to Perform Prescribed Tasks with Probabilistic Failures and Lifetimes

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

Hilton, Harry H.

Protocols are developed for formulating optimal viscoelastic designer functionally graded materials tailored to best respond to prescribed loading and boundary conditions. In essence, an inverse approach is adopted where material properties instead of structures per se are designed and then distributed throughout structural elements. The final measure of viscoelastic material efficacy is expressed in terms of failure probabilities vs. survival time000.

A Simple Probabilistic Combat Model

DTIC Science & Technology

2016-06-13

This page intentionally left blank. 1. INTRODUCTION The Lanchester combat model1 is a simple way to assess the effects of quantity and quality...case model. For the random case, assume R red weapons are allocated to B blue weapons randomly. We are interested in the distribution of weapons...since the initial condition is very close to the break even line. What is more interesting is that the probability density tends to concentrate at

Fall 2014 SEI Research Review Probabilistic Analysis of Time Sensitive Systems

DTIC Science & Technology

2014-10-28

Osmosis SMC Tool Osmosis is a tool for Statistical Model Checking (SMC) with Semantic Importance Sampling. • Input model is written in subset of C...ASSERT() statements in model indicate conditions that must hold. • Input probability distributions defined by the user. • Osmosis returns the...on: – Target relative error, or – Set number of simulations Osmosis Main Algorithm 1 http://dreal.cs.cmu.edu/ (?⃑?): Indicator

Stochastic seismic inversion based on an improved local gradual deformation method

NASA Astrophysics Data System (ADS)

Yang, Xiuwei; Zhu, Peimin

2017-12-01

A new stochastic seismic inversion method based on the local gradual deformation method is proposed, which can incorporate seismic data, well data, geology and their spatial correlations into the inversion process. Geological information, such as sedimentary facies and structures, could provide significant a priori information to constrain an inversion and arrive at reasonable solutions. The local a priori conditional cumulative distributions at each node of model to be inverted are first established by indicator cokriging, which integrates well data as hard data and geological information as soft data. Probability field simulation is used to simulate different realizations consistent with the spatial correlations and local conditional cumulative distributions. The corresponding probability field is generated by the fast Fourier transform moving average method. Then, optimization is performed to match the seismic data via an improved local gradual deformation method. Two improved strategies are proposed to be suitable for seismic inversion. The first strategy is that we select and update local areas of bad fitting between synthetic seismic data and real seismic data. The second one is that we divide each seismic trace into several parts and obtain the optimal parameters for each part individually. The applications to a synthetic example and a real case study demonstrate that our approach can effectively find fine-scale acoustic impedance models and provide uncertainty estimations.

Fundamental niche prediction of the pathogenic yeasts Cryptococcus neoformans and Cryptococcus gattii in Europe.

PubMed

Cogliati, Massimo; Puccianti, Erika; Montagna, Maria T; De Donno, Antonella; Susever, Serdar; Ergin, Cagri; Velegraki, Aristea; Ellabib, Mohamed S; Nardoni, Simona; Macci, Cristina; Trovato, Laura; Dipineto, Ludovico; Rickerts, Volker; Akcaglar, Sevim; Mlinaric-Missoni, Emilija; Bertout, Sebastien; Vencà, Ana C F; Sampaio, Ana C; Criseo, Giuseppe; Ranque, Stéphane; Çerikçioğlu, Nilgün; Marchese, Anna; Vezzulli, Luigi; Ilkit, Macit; Desnos-Ollivier, Marie; Pasquale, Vincenzo; Polacheck, Itzhack; Scopa, Antonio; Meyer, Wieland; Ferreira-Paim, Kennio; Hagen, Ferry; Boekhout, Teun; Dromer, Françoise; Varma, Ashok; Kwon-Chung, Kyung J; Inácio, Joäo; Colom, Maria F

2017-10-01

Fundamental niche prediction of Cryptococcus neoformans and Cryptococcus gattii in Europe is an important tool to understand where these pathogenic yeasts have a high probability to survive in the environment and therefore to identify the areas with high risk of infection. In this study, occurrence data for C. neoformans and C. gattii were compared by MaxEnt software with several bioclimatic conditions as well as with soil characteristics and land use. The results showed that C. gattii distribution can be predicted with high probability along the Mediterranean coast. The analysis of variables showed that its distribution is limited by low temperatures during the coldest season, and by heavy precipitations in the driest season. C. neoformans var. grubii is able to colonize the same areas of C. gattii but is more tolerant to cold winter temperatures and summer precipitations. In contrast, the C. neoformans var. neoformans map was completely different. The best conditions for its survival were displayed in sub-continental areas and not along the Mediterranean coasts. In conclusion, we produced for the first time detailed prediction maps of the species and varieties of the C. neoformans and C. gattii species complex in Europe and Mediterranean area. © 2017 Society for Applied Microbiology and John Wiley & Sons Ltd.

Students' Understanding of Conditional Probability on Entering University

ERIC Educational Resources Information Center

Reaburn, Robyn

2013-01-01

An understanding of conditional probability is essential for students of inferential statistics as it is used in Null Hypothesis Tests. Conditional probability is also used in Bayes' theorem, in the interpretation of medical screening tests and in quality control procedures. This study examines the understanding of conditional probability of…

Local linear estimation of concordance probability with application to covariate effects models on association for bivariate failure-time data.

PubMed

Ding, Aidong Adam; Hsieh, Jin-Jian; Wang, Weijing

2015-01-01

Bivariate survival analysis has wide applications. In the presence of covariates, most literature focuses on studying their effects on the marginal distributions. However covariates can also affect the association between the two variables. In this article we consider the latter issue by proposing a nonstandard local linear estimator for the concordance probability as a function of covariates. Under the Clayton copula, the conditional concordance probability has a simple one-to-one correspondence with the copula parameter for different data structures including those subject to independent or dependent censoring and dependent truncation. The proposed method can be used to study how covariates affect the Clayton association parameter without specifying marginal regression models. Asymptotic properties of the proposed estimators are derived and their finite-sample performances are examined via simulations. Finally, for illustration, we apply the proposed method to analyze a bone marrow transplant data set.

Statistical Inference in Hidden Markov Models Using k-Segment Constraints

PubMed Central

Titsias, Michalis K.; Holmes, Christopher C.; Yau, Christopher

2016-01-01

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online. PMID:27226674

Estimation of the probability of success in petroleum exploration

USGS Publications Warehouse

Davis, J.C.

1977-01-01

A probabilistic model for oil exploration can be developed by assessing the conditional relationship between perceived geologic variables and the subsequent discovery of petroleum. Such a model includes two probabilistic components, the first reflecting the association between a geologic condition (structural closure, for example) and the occurrence of oil, and the second reflecting the uncertainty associated with the estimation of geologic variables in areas of limited control. Estimates of the conditional relationship between geologic variables and subsequent production can be found by analyzing the exploration history of a "training area" judged to be geologically similar to the exploration area. The geologic variables are assessed over the training area using an historical subset of the available data, whose density corresponds to the present control density in the exploration area. The success or failure of wells drilled in the training area subsequent to the time corresponding to the historical subset provides empirical estimates of the probability of success conditional upon geology. Uncertainty in perception of geological conditions may be estimated from the distribution of errors made in geologic assessment using the historical subset of control wells. These errors may be expressed as a linear function of distance from available control. Alternatively, the uncertainty may be found by calculating the semivariogram of the geologic variables used in the analysis: the two procedures will yield approximately equivalent results. The empirical probability functions may then be transferred to the exploration area and used to estimate the likelihood of success of specific exploration plays. These estimates will reflect both the conditional relationship between the geological variables used to guide exploration and the uncertainty resulting from lack of control. The technique is illustrated with case histories from the mid-Continent area of the U.S.A. ?? 1977 Plenum Publishing Corp.

A multi-agent intelligent environment for medical knowledge.

PubMed

Vicari, Rosa M; Flores, Cecilia D; Silvestre, André M; Seixas, Louise J; Ladeira, Marcelo; Coelho, Helder

2003-03-01

AMPLIA is a multi-agent intelligent learning environment designed to support training of diagnostic reasoning and modelling of domains with complex and uncertain knowledge. AMPLIA focuses on the medical area. It is a system that deals with uncertainty under the Bayesian network approach, where learner-modelling tasks will consist of creating a Bayesian network for a problem the system will present. The construction of a network involves qualitative and quantitative aspects. The qualitative part concerns the network topology, that is, causal relations among the domain variables. After it is ready, the quantitative part is specified. It is composed of the distribution of conditional probability of the variables represented. A negotiation process (managed by an intelligent MediatorAgent) will treat the differences of topology and probability distribution between the model the learner built and the one built-in in the system. That negotiation process occurs between the agents that represent the expert knowledge domain (DomainAgent) and the agent that represents the learner knowledge (LearnerAgent).

Distributed decision-making in electric power system transmission maintenance scheduling using multi-agent systems (MAS)

NASA Astrophysics Data System (ADS)

Zhang, Zhong

In this work, motivated by the need to coordinate transmission maintenance scheduling among a multiplicity of self-interested entities in restructured power industry, a distributed decision support framework based on multiagent negotiation systems (MANS) is developed. An innovative risk-based transmission maintenance optimization procedure is introduced. Several models for linking condition monitoring information to the equipment's instantaneous failure probability are presented, which enable quantitative evaluation of the effectiveness of maintenance activities in terms of system cumulative risk reduction. Methodologies of statistical processing, equipment deterioration evaluation and time-dependent failure probability calculation are also described. A novel framework capable of facilitating distributed decision-making through multiagent negotiation is developed. A multiagent negotiation model is developed and illustrated that accounts for uncertainty and enables social rationality. Some issues of multiagent negotiation convergence and scalability are discussed. The relationships between agent-based negotiation and auction systems are also identified. A four-step MAS design methodology for constructing multiagent systems for power system applications is presented. A generic multiagent negotiation system, capable of inter-agent communication and distributed decision support through inter-agent negotiations, is implemented. A multiagent system framework for facilitating the automated integration of condition monitoring information and maintenance scheduling for power transformers is developed. Simulations of multiagent negotiation-based maintenance scheduling among several independent utilities are provided. It is shown to be a viable alternative solution paradigm to the traditional centralized optimization approach in today's deregulated environment. This multiagent system framework not only facilitates the decision-making among competing power system entities, but also provides a tool to use in studying competitive industry relative to monopolistic industry.

Kolmogorov-Smirnov test for spatially correlated data

USGS Publications Warehouse

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

2009-01-01

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

A missing dimension in measures of vaccination impacts

USGS Publications Warehouse

Gomes, M. Gabriela M.; Lipsitch, Marc; Wargo, Andrew R.; Kurath, Gael; Rebelo, Carlota; Medley, Graham F.; Coutinho, Antonio

2013-01-01

Immunological protection, acquired from either natural infection or vaccination, varies among hosts, reflecting underlying biological variation and affecting population-level protection. Owing to the nature of resistance mechanisms, distributions of susceptibility and protection entangle with pathogen dose in a way that can be decoupled by adequately representing the dose dimension. Any infectious processes must depend in some fashion on dose, and empirical evidence exists for an effect of exposure dose on the probability of transmission to mumps-vaccinated hosts [1], the case-fatality ratio of measles [2], and the probability of infection and, given infection, of symptoms in cholera [3]. Extreme distributions of vaccine protection have been termed leaky (partially protects all hosts) and all-or-nothing (totally protects a proportion of hosts) [4]. These distributions can be distinguished in vaccine field trials from the time dependence of infections [5]. Frailty mixing models have also been proposed to estimate the distribution of protection from time to event data [6], [7], although the results are not comparable across regions unless there is explicit control for baseline transmission [8]. Distributions of host susceptibility and acquired protection can be estimated from dose-response data generated under controlled experimental conditions [9]–[11] and natural settings [12], [13]. These distributions can guide research on mechanisms of protection, as well as enable model validity across the entire range of transmission intensities. We argue for a shift to a dose-dimension paradigm in infectious disease science and community health.

Rényi and Tsallis formulations of separability conditions in finite dimensions

NASA Astrophysics Data System (ADS)

Rastegin, Alexey E.

2017-12-01

Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of Rényi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach based on the convolution of discrete probability distributions. Measurements on a total system are constructed of local ones according to the convolution scheme. Separability conditions are derived on the base of uncertainty relations of the Maassen-Uffink type as well as majorization relations. On each of subsystems, we use a pair of sets of subnormalized vectors that form rank-one POVMs. We also obtain entropic separability conditions for local measurements with a special structure, such as mutually unbiased bases and symmetric informationally complete measurements. The relevance of the derived separability conditions is demonstrated with several examples.

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.

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.

Electric Field Simulation of Surge Capacitors with Typical Defects

NASA Astrophysics Data System (ADS)

Zhang, Chenmeng; Mao, Yuxiang; Xie, Shijun; Zhang, Yu

2018-03-01

The electric field of power capacitors with different typical defects in DC working condition and impulse oscillation working condition is studied in this paper. According to the type and location of defects and considering the influence of space charge, two-dimensional models of surge capacitors with different typical defects are simulated based on ANSYS. The distribution of the electric field inside the capacitor is analyzed, and the concentration of electric field and its influence on the insulation performance are obtained. The results show that the type of defects, the location of defects and the space charge all affect the electric field distribution inside the capacitor in varying degrees. Especially the electric field distortion in the local area such as sharp corners and burrs is relatively larger, which increases the probability of partial discharge inside the surge capacitor.

Simulating the component counts of combinatorial structures.

PubMed

Arratia, Richard; Barbour, A D; Ewens, W J; Tavaré, Simon

2018-02-09

This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum. We show how to improve its acceptance rate. We illustrate the method by estimating the probability that a random mapping has no repeated component sizes, and establish the asymptotic distribution of the difference between the number of components and the number of distinct component sizes for a very general class of logarithmic structures. Copyright © 2018. Published by Elsevier Inc.

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

Probabilistic accounting of uncertainty in forecasts of species distributions under climate change

USGS Publications Warehouse

Wenger, Seth J.; Som, Nicholas A.; Dauwalter, Daniel C.; Isaak, Daniel J.; Neville, Helen M.; Luce, Charles H.; Dunham, Jason B.; Young, Michael K.; Fausch, Kurt D.; Rieman, Bruce E.

2013-01-01

Forecasts of species distributions under future climates are inherently uncertain, but there have been few attempts to describe this uncertainty comprehensively in a probabilistic manner. We developed a Monte Carlo approach that accounts for uncertainty within generalized linear regression models (parameter uncertainty and residual error), uncertainty among competing models (model uncertainty), and uncertainty in future climate conditions (climate uncertainty) to produce site-specific frequency distributions of occurrence probabilities across a species’ range. We illustrated the method by forecasting suitable habitat for bull trout (Salvelinus confluentus) in the Interior Columbia River Basin, USA, under recent and projected 2040s and 2080s climate conditions. The 95% interval of total suitable habitat under recent conditions was estimated at 30.1–42.5 thousand km; this was predicted to decline to 0.5–7.9 thousand km by the 2080s. Projections for the 2080s showed that the great majority of stream segments would be unsuitable with high certainty, regardless of the climate data set or bull trout model employed. The largest contributor to uncertainty in total suitable habitat was climate uncertainty, followed by parameter uncertainty and model uncertainty. Our approach makes it possible to calculate a full distribution of possible outcomes for a species, and permits ready graphical display of uncertainty for individual locations and of total habitat.

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.

Defense Strategies for Asymmetric Networked Systems with Discrete Components.

PubMed

Rao, Nageswara S V; Ma, Chris Y T; Hausken, Kjell; He, Fei; Yau, David K Y; Zhuang, Jun

2018-05-03

We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models.

Defense Strategies for Asymmetric Networked Systems with Discrete Components

PubMed Central

Rao, Nageswara S. V.; Ma, Chris Y. T.; Hausken, Kjell; He, Fei; Yau, David K. Y.

2018-01-01

We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models. PMID:29751588

CPROB: A COMPUTATIONAL TOOL FOR CONDUCTING CONDITIONAL PROBABILITY ANALYSIS

EPA Science Inventory

Conditional probability analysis measures the probability of observing one event given that another event has occurred. In an environmental context, conditional probability analysis helps assess the association between an environmental contaminant (i.e. the stressor) and the ec...

The Integrated Medical Model: Statistical Forecasting of Risks to Crew Health and Mission Success

NASA Technical Reports Server (NTRS)

Fitts, M. A.; Kerstman, E.; Butler, D. J.; Walton, M. E.; Minard, C. G.; Saile, L. G.; Toy, S.; Myers, J.

2008-01-01

The Integrated Medical Model (IMM) helps capture and use organizational knowledge across the space medicine, training, operations, engineering, and research domains. The IMM uses this domain knowledge in the context of a mission and crew profile to forecast crew health and mission success risks. The IMM is most helpful in comparing the risk of two or more mission profiles, not as a tool for predicting absolute risk. The process of building the IMM adheres to Probability Risk Assessment (PRA) techniques described in NASA Procedural Requirement (NPR) 8705.5, and uses current evidence-based information to establish a defensible position for making decisions that help ensure crew health and mission success. The IMM quantitatively describes the following input parameters: 1) medical conditions and likelihood, 2) mission duration, 3) vehicle environment, 4) crew attributes (e.g. age, sex), 5) crew activities (e.g. EVA's, Lunar excursions), 6) diagnosis and treatment protocols (e.g. medical equipment, consumables pharmaceuticals), and 7) Crew Medical Officer (CMO) training effectiveness. It is worth reiterating that the IMM uses the data sets above as inputs. Many other risk management efforts stop at determining only likelihood. The IMM is unique in that it models not only likelihood, but risk mitigations, as well as subsequent clinical outcomes based on those mitigations. Once the mathematical relationships among the above parameters are established, the IMM uses a Monte Carlo simulation technique (a random sampling of the inputs as described by their statistical distribution) to determine the probable outcomes. Because the IMM is a stochastic model (i.e. the input parameters are represented by various statistical distributions depending on the data type), when the mission is simulated 10-50,000 times with a given set of medical capabilities (risk mitigations), a prediction of the most probable outcomes can be generated. For each mission, the IMM tracks which conditions occurred and decrements the pharmaceuticals and supplies required to diagnose and treat these medical conditions. If supplies are depleted, then the medical condition goes untreated, and crew and mission risk increase. The IMM currently models approximately 30 medical conditions. By the end of FY2008, the IMM will be modeling over 100 medical conditions, approximately 60 of which have been recorded to have occurred during short and long space missions.

Binocular interactions in random chromatic changes at isoluminance

NASA Astrophysics Data System (ADS)

Medina, José M.

2006-02-01

To examine the type of chromatic interactions at isoluminance in the phenomenon of binocular vision, I have determined simple visual reaction times (VRT) under three observational conditions (monocular left, monocular right, and binocular) for different chromatic stimuli along random color axes at isoluminance (simultaneous L-, M-, and S-cone variations). Upper and lower boundaries of probability summation as well as the binocular capacity coefficient were estimated with observed distributions of reaction times. The results were not consistent with the notion of independent chromatic channels between eyes, suggesting the existence of excitatory and inhibitory binocular interactions at suprathreshold isoluminance conditions.

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…

Study on conditional probability of surface rupture: effect of fault dip and width of seismogenic layer

NASA Astrophysics Data System (ADS)

Inoue, N.

2017-12-01

The conditional probability of surface ruptures is affected by various factors, such as shallow material properties, process of earthquakes, ground motions and so on. Toda (2013) pointed out difference of the conditional probability of strike and reverse fault by considering the fault dip and width of seismogenic layer. This study evaluated conditional probability of surface rupture based on following procedures. Fault geometry was determined from the randomly generated magnitude based on The Headquarters for Earthquake Research Promotion (2017) method. If the defined fault plane was not saturated in the assumed width of the seismogenic layer, the fault plane depth was randomly provided within the seismogenic layer. The logistic analysis was performed to two data sets: surface displacement calculated by dislocation methods (Wang et al., 2003) from the defined source fault, the depth of top of the defined source fault. The estimated conditional probability from surface displacement indicated higher probability of reverse faults than that of strike faults, and this result coincides to previous similar studies (i.e. Kagawa et al., 2004; Kataoka and Kusakabe, 2005). On the contrary, the probability estimated from the depth of the source fault indicated higher probability of thrust faults than that of strike and reverse faults, and this trend is similar to the conditional probability of PFDHA results (Youngs et al., 2003; Moss and Ross, 2011). The probability of combined simulated results of thrust and reverse also shows low probability. The worldwide compiled reverse fault data include low fault dip angle earthquake. On the other hand, in the case of Japanese reverse fault, there is possibility that the conditional probability of reverse faults with less low dip angle earthquake shows low probability and indicates similar probability of strike fault (i.e. Takao et al., 2013). In the future, numerical simulation by considering failure condition of surface by the source fault would be performed in order to examine the amount of the displacement and conditional probability quantitatively.

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.

Future changes in South American biomass distributions, biome distributions and plant trait spectra is dependent on applied atmospheric forcings.

NASA Astrophysics Data System (ADS)

Langan, Liam; Scheiter, Simon; Higgins, Steven

2017-04-01

It remains poorly understood why the position of the forest-savanna biome boundary, in a domain defined by precipitation and temperature, differs in South America, Africa and Australia. Process based Dynamic Global Vegetation Models (DGVMs) are a valuable tool to investigate the determinants of vegetation distributions, however, many DGVMs fail to predict the spatial distribution or indeed presence of the South American savanna biome. Evidence suggests fire plays a significant role in mediating forest-savanna biome boundaries, however, fire alone appear to be insufficient to predict these boundaries in South America. We hypothesize that interactions between precipitation, constraints on tree rooting depth and fire, affect the probability of savanna occurrence and the position of the savanna-forest boundary. We tested our hypotheses at tropical forest and savanna sites in Brazil and Venezuela using a novel DGVM, aDGVM2, which allows plant trait spectra, constrained by trade-offs between traits, to evolve in response to abiotic and biotic conditions. Plant hydraulics is represented by the cohesion-tension theory, this allowed us to explore how soil and plant hydraulics control biome distributions and plant traits. The resulting community trait distributions are emergent properties of model dynamics. We showed that across much of South America the biome state is not determined by climate alone. Interactions between tree rooting depth, fire and precipitation affected the probability of observing a given biome state and the emergent traits of plant communities. Simulations where plant rooting depth varied in space provided the best match to satellite derived biomass estimates and generated biome distributions that reproduced contemporary biome maps well. Future projections showed that biomass distributions, biome distributions and plant trait spectra will change, however, the magnitude of these changes are highly dependent on the applied atmospheric forcings.

Does probability of occurrence relate to population dynamics?

USGS Publications Warehouse

Thuiller, Wilfried; Münkemüller, Tamara; Schiffers, Katja H.; Georges, Damien; Dullinger, Stefan; Eckhart, Vincent M.; Edwards, Thomas C.; Gravel, Dominique; Kunstler, Georges; Merow, Cory; Moore, Kara; Piedallu, Christian; Vissault, Steve; Zimmermann, Niklaus E.; Zurell, Damaris; Schurr, Frank M.

2014-01-01

Hutchinson defined species' realized niche as the set of environmental conditions in which populations can persist in the presence of competitors. In terms of demography, the realized niche corresponds to the environments where the intrinsic growth rate (r) of populations is positive. Observed species occurrences should reflect the realized niche when additional processes like dispersal and local extinction lags do not have overwhelming effects. Despite the foundational nature of these ideas, quantitative assessments of the relationship between range-wide demographic performance and occurrence probability have not been made. This assessment is needed both to improve our conceptual understanding of species' niches and ranges and to develop reliable mechanistic models of species geographic distributions that incorporate demography and species interactions.The objective of this study is to analyse how demographic parameters (intrinsic growth rate r and carrying capacity K ) and population density (N ) relate to occurrence probability (Pocc ). We hypothesized that these relationships vary with species' competitive ability. Demographic parameters, density, and occurrence probability were estimated for 108 tree species from four temperate forest inventory surveys (Québec, western USA, France and Switzerland). We used published information of shade tolerance as indicators of light competition strategy, assuming that high tolerance denotes high competitive capacity in stable forest environments.Interestingly, relationships between demographic parameters and occurrence probability did not vary substantially across degrees of shade tolerance and regions. Although they were influenced by the uncertainty in the estimation of the demographic parameters, we found that r was generally negatively correlated with Pocc, while N, and for most regions K, was generally positively correlated with Pocc. Thus, in temperate forest trees the regions of highest occurrence probability are those with high densities but slow intrinsic population growth rates. The uncertain relationships between demography and occurrence probability suggests caution when linking species distribution and demographic models.

A numerical 4D Collision Risk Model

NASA Astrophysics Data System (ADS)

Schmitt, Pal; Culloch, Ross; Lieber, Lilian; Kregting, Louise

2017-04-01

With the growing number of marine renewable energy (MRE) devices being installed across the world, some concern has been raised about the possibility of harming mobile, marine fauna by collision. Although physical contact between a MRE device and an organism has not been reported to date, these novel sub-sea structures pose a challenge for accurately estimating collision risks as part of environmental impact assessments. Even if the animal motion is simplified to linear translation, ignoring likely evasive behaviour, the mathematical problem of establishing an impact probability is not trivial. We present a numerical algorithm to obtain such probability distributions using transient, four-dimensional simulations of a novel marine renewable device concept, Deep Green, Minesto's power plant and hereafter referred to as the 'kite' that flies in a figure-of-eight configuration. Simulations were carried out altering several configurations including kite depth, kite speed and kite trajectory while keeping the speed of the moving object constant. Since the kite assembly is defined as two parts in the model, a tether (attached to the seabed) and the kite, collision risk of each part is reported independently. By comparing the number of collisions with the number of collision-free simulations, a probability of impact for each simulated position in the cross- section of the area is considered. Results suggest that close to the bottom, where the tether amplitude is small, the path is always blocked and the impact probability is 100% as expected. However, higher up in the water column, the collision probability is twice as high in the mid line, where the tether passes twice per period than at the extremes of its trajectory. The collision probability distribution is much more complex in the upper end of the water column, where the kite and tether can simultaneously collide with the object. Results demonstrate the viability of such models, which can also incorporate empirical field data for assessing the probability of collision risk of animals with an MRE device under varying operating conditions.

Colonization and extinction in dynamic habitats: an occupancy approach for a Great Plains stream fish assemblage.

PubMed

Falke, Jeffrey A; Bailey, Larissa L; Fausch, Kurt D; Bestgen, Kevin R

2012-04-01

Despite the importance of habitat in determining species distribution and persistence, habitat dynamics are rarely modeled in studies of metapopulations. We used an integrated habitat-occupancy model to simultaneously quantify habitat change, site fidelity, and local colonization and extinction rates for larvae of a suite of Great Plains stream fishes in the Arikaree River, eastern Colorado, USA, across three years. Sites were located along a gradient of flow intermittency and groundwater connectivity. Hydrology varied across years: the first and third being relatively wet and the second dry. Despite hydrologic variation, our results indicated that site suitability was random from one year to the next. Occupancy probabilities were also independent of previous habitat and occupancy state for most species, indicating little site fidelity. Climate and groundwater connectivity were important drivers of local extinction and colonization, but the importance of groundwater differed between periods. Across species, site extinction probabilities were highest during the transition from wet to dry conditions (range: 0.52-0.98), and the effect of groundwater was apparent with higher extinction probabilities for sites not fed by groundwater. Colonization probabilities during this period were relatively low for both previously dry sites (range: 0.02-0.38) and previously wet sites (range: 0.02-0.43). In contrast, no sites dried or remained dry during the transition from dry to wet conditions, yielding lower but still substantial extinction probabilities (range: 0.16-0.63) and higher colonization probabilities (range: 0.06-0.86), with little difference among sites with and without groundwater. This approach of jointly modeling both habitat change and species occupancy will likely be useful to incorporate effects of dynamic habitat on metapopulation processes and to better inform appropriate conservation actions.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

A synopsis of climate change effects on groundwater recharge

NASA Astrophysics Data System (ADS)

Smerdon, Brian D.

2017-12-01

Six review articles published between 2011 and 2016 on groundwater and climate change are briefly summarized. This synopsis focuses on aspects related to predicting changes to groundwater recharge conditions, with several common conclusions between the review articles being noted. The uncertainty of distribution and trend in future precipitation from General Circulation Models (GCMs) results in varying predictions of recharge, so much so that modelling studies are often not able to predict the magnitude and direction (increase or decrease) of future recharge conditions. Evolution of modelling approaches has led to the use of multiple GCMs and hydrologic models to create an envelope of future conditions that reflects the probability distribution. The choice of hydrologic model structure and complexity, and the choice of emissions scenario, has been investigated and somewhat resolved; however, recharge results remain sensitive to downscaling methods. To overcome uncertainty and provide practical use in water management, the research community indicates that modelling at a mesoscale, somewhere between watersheds and continents, is likely ideal. Improvements are also suggested for incorporating groundwater processes within GCMs.

Improving Conceptual Models Using AEM Data and Probability Distributions

NASA Astrophysics Data System (ADS)

Davis, A. C.; Munday, T. J.; Christensen, N. B.

2012-12-01

With emphasis being placed on uncertainty in groundwater modelling and prediction, coupled with questions concerning the value of geophysical methods in hydrogeology, it is important to ask meaningful questions of hydrogeophysical data and inversion results. For example, to characterise aquifers using electromagnetic (EM) data, we ask questions such as "Given that the electrical conductivity of aquifer 'A' is less than x, where is that aquifer elsewhere in the survey area?" The answer may be given by examining inversion models, selecting locations and layers that satisfy the condition 'conductivity <= x', and labelling them as aquifer 'A'. One difficulty with this approach is that the inversion model result often be considered to be the only model for the data. In reality it is just one image of the subsurface that, given the method and the regularisation imposed in the inversion, agrees with measured data within a given error bound. We have no idea whether the final model realised by the inversion satisfies the global minimum error, or whether it is simply in a local minimum. There is a distribution of inversion models that satisfy the error tolerance condition: the final model is not the only one, nor is it necessarily the correct one. AEM inversions are often linearised in the calculation of the parameter sensitivity: we rely on the second derivatives in the Taylor expansion, thus the minimum model has all layer parameters distributed about their mean parameter value with well-defined variance. We investigate the validity of the minimum model, and its uncertainty, by examining the full posterior covariance matrix. We ask questions of the minimum model, and answer them in a probabilistically. The simplest question we can pose is "What is the probability that all layer resistivity values are <= a cut-off value?" We can calculate through use of the erf or the erfc functions. The covariance values of the inversion become marginalised in the integration: only the main diagonal is used. Complications arise when we ask more specific questions, such as "What is the probability that the resistivity of layer 2 <= x, given that layer 1 <= y?" The probability then becomes conditional, calculation includes covariance terms, the integration is taken over many dimensions, and the cross-correlation of parameters becomes important. To illustrate, we examine the inversion results of a Tempest AEM survey over the Uley Basin aquifers in the Eyre Peninsula, South Australia. Key aquifers include the unconfined Bridgewater Formation that overlies the Uley and Wanilla Formations, which contain Tertiary clays and Tertiary sandstone. These Formations overlie weathered basement which define the lower bound of the Uley Basin aquifer systems. By correlating the conductivity of the sub-surface Formation types, we pose questions such as: "What is the probability-depth of the Bridgewater Formation in the Uley South Basin?", "What is the thickness of the Uley Formation?" and "What is the most probable depth to basement?" We use these questions to generate improved conceptual hydrogeological models of the Uley Basin in order to develop better estimates of aquifer extent and the available groundwater resource.

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

NASA Astrophysics Data System (ADS)

Pichl, Lukáš; Kaizoji, Taisei; Yamano, Takuya

2007-08-01

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

Probabilistic Reasoning for Robustness in Automated Planning

NASA Technical Reports Server (NTRS)

Schaffer, Steven; Clement, Bradley; Chien, Steve

2007-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

PubMed

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

2013-11-01

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

Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuating Pressure Excitation

NASA Technical Reports Server (NTRS)

Steinwolf, Alexander; Rizzi, Stephen A.

2003-01-01

The purpose of the study is to investigate properties of the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the exterior of a supersonic transport aircraft. It is shown that fluctuating pressure PDFs differ from the Gaussian distribution even for surface conditions having no significant discontinuities. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations upstream of forward-facing step discontinuities and downstream of aft-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. Various analytical PDF distributions are used and further developed to model this behavior.

Population dynamical behavior of Lotka-Volterra system under regime switching

NASA Astrophysics Data System (ADS)

Li, Xiaoyue; Jiang, Daqing; Mao, Xuerong

2009-10-01

In this paper, we investigate a Lotka-Volterra system under regime switching where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence and extinction. We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Markov chain. The limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients. Finally, the main results are illustrated by several examples.

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

USGS Publications Warehouse

McCammon, R.B.

1977-01-01

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

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.

Statistics of cosmic density profiles from perturbation theory

NASA Astrophysics Data System (ADS)

Bernardeau, Francis; Pichon, Christophe; Codis, Sandrine

2014-11-01

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with Λ -cold dark matter simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope—the density difference between adjacent cells—and its fluctuations is also computed from the two-cell joint PDF; it also compares very well to simulations. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters.

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.

Importance of spatial autocorrelation in modeling bird distributions at a continental scale

USGS Publications Warehouse

Bahn, V.; O'Connor, R.J.; Krohn, W.B.

2006-01-01

Spatial autocorrelation in species' distributions has been recognized as inflating the probability of a type I error in hypotheses tests, causing biases in variable selection, and violating the assumption of independence of error terms in models such as correlation or regression. However, it remains unclear whether these problems occur at all spatial resolutions and extents, and under which conditions spatially explicit modeling techniques are superior. Our goal was to determine whether spatial models were superior at large extents and across many different species. In addition, we investigated the importance of purely spatial effects in distribution patterns relative to the variation that could be explained through environmental conditions. We studied distribution patterns of 108 bird species in the conterminous United States using ten years of data from the Breeding Bird Survey. We compared the performance of spatially explicit regression models with non-spatial regression models using Akaike's information criterion. In addition, we partitioned the variance in species distributions into an environmental, a pure spatial and a shared component. The spatially-explicit conditional autoregressive regression models strongly outperformed the ordinary least squares regression models. In addition, partialling out the spatial component underlying the species' distributions showed that an average of 17% of the explained variation could be attributed to purely spatial effects independent of the spatial autocorrelation induced by the underlying environmental variables. We concluded that location in the range and neighborhood play an important role in the distribution of species. Spatially explicit models are expected to yield better predictions especially for mobile species such as birds, even in coarse-grained models with a large extent. ?? Ecography.

Dynamic heterogeneity and conditional statistics of non-Gaussian temperature fluctuations in turbulent thermal convection

NASA Astrophysics Data System (ADS)

He, Xiaozhou; Wang, Yin; Tong, Penger

2018-05-01

Non-Gaussian fluctuations with an exponential tail in their probability density function (PDF) are often observed in nonequilibrium steady states (NESSs) and one does not understand why they appear so often. Turbulent Rayleigh-Bénard convection (RBC) is an example of such a NESS, in which the measured PDF P (δ T ) of temperature fluctuations δ T in the central region of the flow has a long exponential tail. Here we show that because of the dynamic heterogeneity in RBC, the exponential PDF is generated by a convolution of a set of dynamics modes conditioned on a constant local thermal dissipation rate ɛ . The conditional PDF G (δ T |ɛ ) of δ T under a constant ɛ is found to be of Gaussian form and its variance σT2 for different values of ɛ follows an exponential distribution. The convolution of the two distribution functions gives rise to the exponential PDF P (δ T ) . This work thus provides a physical mechanism of the observed exponential distribution of δ T in RBC and also sheds light on the origin of non-Gaussian fluctuations in other NESSs.

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

Journal of Naval Science. Volume 2, Number 1

DTIC Science & Technology

1976-01-01

has defined a probability distribution function which fits this type of data and forms the basis for statistical analysis of test results (see...Conditions to Assess the Performance of Fire-Resistant Fluids’. Wear, 28 (1974) 29. J.N.S., Vol. 2, No. 1 APPENDIX A Analysis of Fatigue Test Data...used to produce the impulse response and the equipment required for the analysis is relatively simple. The methods that must be used to produce

Technical Report 1205: A Simple Probabilistic Combat Model

DTIC Science & Technology

2016-07-08

This page intentionally left blank. 1. INTRODUCTION The Lanchester combat model1 is a simple way to assess the effects of quantity and quality...model. For the random case, assume R red weapons are allocated to B blue weapons randomly. We are interested in the distribution of weapons assigned...the initial condition is very close to the break even line. What is more interesting is that the probability density tends to concentrate at either a

An evaluation of procedures to estimate monthly precipitation probabilities

NASA Astrophysics Data System (ADS)

Legates, David R.

1991-01-01

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

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

NASA Astrophysics Data System (ADS)

Katz, Yuri A.; Tian, Li

2013-10-01

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

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

USGS Publications Warehouse

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

1979-01-01

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

Univariate Probability Distributions

ERIC Educational Resources Information Center

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

2012-01-01

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

On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type

NASA Astrophysics Data System (ADS)

Onorato, Miguel; Proment, Davide; El, Gennady; Randoux, Stephane; Suret, Pierre

2016-09-01

We study the formation of extreme events in incoherent systems described by the Nonlinear Schrödinger type of equations. We consider an exact identity that relates the evolution of the normalized fourth-order moment of the probability density function of the wave envelope to the rate of change of the width of the Fourier spectrum of the wave field. We show that, given an initial condition characterized by some distribution of the wave envelope, an increase of the spectral bandwidth in the focusing/defocusing regime leads to an increase/decrease of the probability of formation of rogue waves. Extensive numerical simulations in 1D+1 and 2D+1 are also performed to confirm the results.

Outage Analysis of Dual-hop Cognitive Networks with Relay Selection over Nakagami-m Fading Environment

NASA Astrophysics Data System (ADS)

Zhang, Zongsheng; Pi, Xurong

2014-09-01

In this paper, we investigate the outage performance of decode-and-forward cognitive relay networks for Nakagami-m fading channels, with considering both best relay selection and interference constraints. Focusing on the relay selection and making use of the underlay cognitive approach, an exact closed-form outage probability expression is derived in an independent, non-identical distributed Nakagami-m environment. The closed-form outage probability provides an efficient means to evaluate the effects of the maximum allowable interference power, number of cognitive relays, and channel conditions between the primary user and cognitive users. Finally, we present numerical results to validate the theory analysis. Moreover, from the simulation results, we obtain that the system can obtain the full diversity.

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.

Integrated models to support multiobjective ecological restoration decisions.

PubMed

Fraser, Hannah; Rumpff, Libby; Yen, Jian D L; Robinson, Doug; Wintle, Brendan A

2017-12-01

Many objectives motivate ecological restoration, including improving vegetation condition, increasing the range and abundance of threatened species, and improving species richness and diversity. Although models have been used to examine the outcomes of ecological restoration, few researchers have attempted to develop models to account for multiple, potentially competing objectives. We developed a combined state-and-transition, species-distribution model to predict the effects of restoration actions on vegetation condition and extent, bird diversity, and the distribution of several bird species in southeastern Australian woodlands. The actions reflected several management objectives. We then validated the models against an independent data set and investigated how the best management decision might change when objectives were valued differently. We also used model results to identify effective restoration options for vegetation and bird species under a constrained budget. In the examples we evaluated, no one action (improving vegetation condition and extent, increasing bird diversity, or increasing the probability of occurrence for threatened species) provided the best outcome across all objectives. In agricultural lands, the optimal management actions for promoting the occurrence of the Brown Treecreeper (Climacteris picumnus), an iconic threatened species, resulted in little improvement in the extent of the vegetation and a high probability of decreased vegetation condition. This result highlights that the best management action in any situation depends on how much the different objectives are valued. In our example scenario, no management or weed control were most likely to be the best management options to satisfy multiple restoration objectives. Our approach to exploring trade-offs in management outcomes through integrated modeling and structured decision-support approaches has wide application for situations in which trade-offs exist between competing conservation objectives. © 2017 Society for Conservation Biology.

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.

Identification of cloud fields by the nonparametric algorithm of pattern recognition from normalized video data recorded with the AVHRR instrument

NASA Astrophysics Data System (ADS)

Protasov, Konstantin T.; Pushkareva, Tatyana Y.; Artamonov, Evgeny S.

2002-02-01

The problem of cloud field recognition from the NOAA satellite data is urgent for solving not only meteorological problems but also for resource-ecological monitoring of the Earth's underlying surface associated with the detection of thunderstorm clouds, estimation of the liquid water content of clouds and the moisture of the soil, the degree of fire hazard, etc. To solve these problems, we used the AVHRR/NOAA video data that regularly displayed the situation in the territory. The complexity and extremely nonstationary character of problems to be solved call for the use of information of all spectral channels, mathematical apparatus of testing statistical hypotheses, and methods of pattern recognition and identification of the informative parameters. For a class of detection and pattern recognition problems, the average risk functional is a natural criterion for the quality and the information content of the synthesized decision rules. In this case, to solve efficiently the problem of identifying cloud field types, the informative parameters must be determined by minimization of this functional. Since the conditional probability density functions, representing mathematical models of stochastic patterns, are unknown, the problem of nonparametric reconstruction of distributions from the leaning samples arises. To this end, we used nonparametric estimates of distributions with the modified Epanechnikov kernel. The unknown parameters of these distributions were determined by minimization of the risk functional, which for the learning sample was substituted by the empirical risk. After the conditional probability density functions had been reconstructed for the examined hypotheses, a cloudiness type was identified using the Bayes decision rule.

Hydrologic risk analysis in the Yangtze River basin through coupling Gaussian mixtures into copulas

NASA Astrophysics Data System (ADS)

Fan, Y. R.; Huang, W. W.; Huang, G. H.; Li, Y. P.; Huang, K.; Li, Z.

2016-02-01

In this study, a bivariate hydrologic risk framework is proposed through coupling Gaussian mixtures into copulas, leading to a coupled GMM-copula method. In the coupled GMM-Copula method, the marginal distributions of flood peak, volume and duration are quantified through Gaussian mixture models and the joint probability distributions of flood peak-volume, peak-duration and volume-duration are established through copulas. The bivariate hydrologic risk is then derived based on the joint return period of flood variable pairs. The proposed method is applied to the risk analysis for the Yichang station on the main stream of the Yangtze River, China. The results indicate that (i) the bivariate risk for flood peak-volume would keep constant for the flood volume less than 1.0 × 105 m3/s day, but present a significant decreasing trend for the flood volume larger than 1.7 × 105 m3/s day; and (ii) the bivariate risk for flood peak-duration would not change significantly for the flood duration less than 8 days, and then decrease significantly as duration value become larger. The probability density functions (pdfs) of the flood volume and duration conditional on flood peak can also be generated through the fitted copulas. The results indicate that the conditional pdfs of flood volume and duration follow bimodal distributions, with the occurrence frequency of the first vertex decreasing and the latter one increasing as the increase of flood peak. The obtained conclusions from the bivariate hydrologic analysis can provide decision support for flood control and mitigation.

Exact combinatorial approach to finite coagulating systems

NASA Astrophysics Data System (ADS)

Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

2018-02-01

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

Random Walks on Homeo( S 1)

NASA Astrophysics Data System (ADS)

Malicet, Dominique

2017-12-01

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

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.

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

Does prediction error drive one-shot declarative learning?

PubMed

Greve, Andrea; Cooper, Elisa; Kaula, Alexander; Anderson, Michael C; Henson, Richard

2017-06-01

The role of prediction error (PE) in driving learning is well-established in fields such as classical and instrumental conditioning, reward learning and procedural memory; however, its role in human one-shot declarative encoding is less clear. According to one recent hypothesis, PE reflects the divergence between two probability distributions: one reflecting the prior probability (from previous experiences) and the other reflecting the sensory evidence (from the current experience). Assuming unimodal probability distributions, PE can be manipulated in three ways: (1) the distance between the mode of the prior and evidence, (2) the precision of the prior, and (3) the precision of the evidence. We tested these three manipulations across five experiments, in terms of peoples' ability to encode a single presentation of a scene-item pairing as a function of previous exposures to that scene and/or item. Memory was probed by presenting the scene together with three choices for the previously paired item, in which the two foil items were from other pairings within the same condition as the target item. In Experiment 1, we manipulated the evidence to be either consistent or inconsistent with prior expectations, predicting PE to be larger, and hence memory better, when the new pairing was inconsistent. In Experiments 2a-c, we manipulated the precision of the priors, predicting better memory for a new pairing when the (inconsistent) priors were more precise. In Experiment 3, we manipulated both visual noise and prior exposure for unfamiliar faces, before pairing them with scenes, predicting better memory when the sensory evidence was more precise. In all experiments, the PE hypotheses were supported. We discuss alternative explanations of individual experiments, and conclude the Predictive Interactive Multiple Memory Signals (PIMMS) framework provides the most parsimonious account of the full pattern of results.

Predicting future changes in Muskegon River Watershed game fish distributions under future land cover alteration and climate change scenarios

USGS Publications Warehouse

Steen, Paul J.; Wiley, Michael J.; Schaeffer, Jeffrey S.

2010-01-01

Future alterations in land cover and climate are likely to cause substantial changes in the ranges of fish species. Predictive distribution models are an important tool for assessing the probability that these changes will cause increases or decreases in or the extirpation of species. Classification tree models that predict the probability of game fish presence were applied to the streams of the Muskegon River watershed, Michigan. The models were used to study three potential future scenarios: (1) land cover change only, (2) land cover change and a 3°C increase in air temperature by 2100, and (3) land cover change and a 5°C increase in air temperature by 2100. The analysis indicated that the expected change in air temperature and subsequent change in water temperatures would result in the decline of coldwater fish in the Muskegon watershed by the end of the 21st century while cool- and warmwater species would significantly increase their ranges. The greatest decline detected was a 90% reduction in the probability that brook trout Salvelinus fontinalis would occur in Bigelow Creek. The greatest increase was a 276% increase in the probability that northern pike Esox lucius would occur in the Middle Branch River. Changes in land cover are expected to cause large changes in a few fish species, such as walleye Sander vitreus and Chinook salmon Oncorhynchus tshawytscha, but not to drive major changes in species composition. Managers can alter stream environmental conditions to maximize the probability that species will reside in particular stream reaches through application of the classification tree models. Such models represent a good way to predict future changes, as they give quantitative estimates of the n-dimensional niches for particular species.

A multistate dynamic site occupancy model for spatially aggregated sessile communities

USGS Publications Warehouse

Fukaya, Keiichi; Royle, J. Andrew; Okuda, Takehiro; Nakaoka, Masahiro; Noda, Takashi

2017-01-01

Estimation of transition probabilities of sessile communities seems easy in principle but may still be difficult in practice because resampling error (i.e. a failure to resample exactly the same location at fixed points) may cause significant estimation bias. Previous studies have developed novel analytical methods to correct for this estimation bias. However, they did not consider the local structure of community composition induced by the aggregated distribution of organisms that is typically observed in sessile assemblages and is very likely to affect observations.We developed a multistate dynamic site occupancy model to estimate transition probabilities that accounts for resampling errors associated with local community structure. The model applies a nonparametric multivariate kernel smoothing methodology to the latent occupancy component to estimate the local state composition near each observation point, which is assumed to determine the probability distribution of data conditional on the occurrence of resampling error.By using computer simulations, we confirmed that an observation process that depends on local community structure may bias inferences about transition probabilities. By applying the proposed model to a real data set of intertidal sessile communities, we also showed that estimates of transition probabilities and of the properties of community dynamics may differ considerably when spatial dependence is taken into account.Results suggest the importance of accounting for resampling error and local community structure for developing management plans that are based on Markovian models. Our approach provides a solution to this problem that is applicable to broad sessile communities. It can even accommodate an anisotropic spatial correlation of species composition, and may also serve as a basis for inferring complex nonlinear ecological dynamics.

Scaling in the distribution of intertrade durations of Chinese stocks

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Chen, Wei; Zhou, Wei-Xing

2008-10-01

The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis q-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the q-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the q-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.

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...

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

PubMed

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

2016-02-01

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

How Can Histograms Be Useful for Introducing Continuous Probability Distributions?

ERIC Educational Resources Information Center

Derouet, Charlotte; Parzysz, Bernard

2016-01-01

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

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

ERIC Educational Resources Information Center

Moses, Tim; Oh, Hyeonjoo J.

2009-01-01

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

An energy dependent earthquake frequency-magnitude distribution

NASA Astrophysics Data System (ADS)

Spassiani, I.; Marzocchi, W.

2017-12-01

The most popular description of the frequency-magnitude distribution of seismic events is the exponential Gutenberg-Richter (G-R) law, which is widely used in earthquake forecasting and seismic hazard models. Although it has been experimentally well validated in many catalogs worldwide, it is not yet clear at which space-time scales the G-R law still holds. For instance, in a small area where a large earthquake has just happened, the probability that another very large earthquake nucleates in a short time window should diminish because it takes time to recover the same level of elastic energy just released. In short, the frequency-magnitude distribution before and after a large earthquake in a small area should be different because of the different amount of available energy.Our study is then aimed to explore a possible modification of the classical G-R distribution by including the dependence on an energy parameter. In a nutshell, this more general version of the G-R law should be such that a higher release of energy corresponds to a lower probability of strong aftershocks. In addition, this new frequency-magnitude distribution has to satisfy an invariance condition: when integrating over large areas, that is when integrating over infinite energy available, the G-R law must be recovered.Finally we apply a proposed generalization of the G-R law to different seismic catalogs to show how it works and the differences with the classical G-R law.

Analytical performance evaluation of SAR ATR with inaccurate or estimated models

NASA Astrophysics Data System (ADS)

DeVore, Michael D.

2004-09-01

Hypothesis testing algorithms for automatic target recognition (ATR) are often formulated in terms of some assumed distribution family. The parameter values corresponding to a particular target class together with the distribution family constitute a model for the target's signature. In practice such models exhibit inaccuracy because of incorrect assumptions about the distribution family and/or because of errors in the assumed parameter values, which are often determined experimentally. Model inaccuracy can have a significant impact on performance predictions for target recognition systems. Such inaccuracy often causes model-based predictions that ignore the difference between assumed and actual distributions to be overly optimistic. This paper reports on research to quantify the effect of inaccurate models on performance prediction and to estimate the effect using only trained parameters. We demonstrate that for large observation vectors the class-conditional probabilities of error can be expressed as a simple function of the difference between two relative entropies. These relative entropies quantify the discrepancies between the actual and assumed distributions and can be used to express the difference between actual and predicted error rates. Focusing on the problem of ATR from synthetic aperture radar (SAR) imagery, we present estimators of the probabilities of error in both ideal and plug-in tests expressed in terms of the trained model parameters. These estimators are defined in terms of unbiased estimates for the first two moments of the sample statistic. We present an analytical treatment of these results and include demonstrations from simulated radar data.

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.

Experimental observations of Lagrangian sand grain kinematics under bedload transport: statistical description of the step and rest regimes

NASA Astrophysics Data System (ADS)

Guala, M.; Liu, M.

2017-12-01

The kinematics of sediment particles is investigated by non-intrusive imaging methods to provide a statistical description of bedload transport in conditions near the threshold of motion. In particular, we focus on the cyclic transition between motion and rest regimes to quantify the waiting time statistics inferred to be responsible for anomalous diffusion, and so far elusive. Despite obvious limitations in the spatio-temporal domain of the observations, we are able to identify the probability distributions of the particle step time and length, velocity, acceleration, waiting time, and thus distinguish which quantities exhibit well converged mean values, based on the thickness of their respective tails. The experimental results shown here for four different transport conditions highlight the importance of the waiting time distribution and represent a benchmark dataset for the stochastic modeling of bedload transport.

H∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation.

PubMed

Yu, Jimin; Yang, Chenchen; Tang, Xiaoming; Wang, Ping

2018-03-01

This paper investigates the H ∞ control problems for uncertain linear system over networks with random communication data dropout and actuator saturation. The random data dropout process is modeled by a Bernoulli distributed white sequence with a known conditional probability distribution and the actuator saturation is confined in a convex hull by introducing a group of auxiliary matrices. By constructing a quadratic Lyapunov function, effective conditions for the state feedback-based H ∞ controller and the observer-based H ∞ controller are proposed in the form of non-convex matrix inequalities to take the random data dropout and actuator saturation into consideration simultaneously, and the problem of non-convex feasibility is solved by applying cone complementarity linearization (CCL) procedure. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed new design techniques. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear GARCH model and 1 / f noise

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Ruseckas, J.

2015-06-01

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

Velocity and size of droplets in dense region of diesel fuel spray on transient needle opening condition

NASA Astrophysics Data System (ADS)

Ueki, Hironobu; Ishida, Masahiro; Sakaguchi, Daisaku

2005-06-01

In order to investigate the effect of transient needle opening on early stage of spray behavior, simultaneous measurements of velocity and size of droplet were conducted by a newly developed laser 2-focus velocimeter (L2F). The micro-scale probe of the L2F was consisted of two foci with a distance of 36 µm. The tested nozzle had a single hole with a diameter of 0.2 mm. The measurements of injection pressure, needle lift, and crank angle were synchronized with the spray measurement by the L2F at the position 10 mm downstream from the nozzle exit. It has been clearly shown that the velocity and size of droplet increase with needle valve opening and that the probability density distribution of droplet size can be fitted to the Nukiyama-Tanasawa distribution under the transient needle opening condition.

State-space receptive fields of semicircular canal afferent neurons in the bullfrog

NASA Technical Reports Server (NTRS)

Paulin, M. G.; Hoffman, L. F.

2001-01-01

Receptive fields are commonly used to describe spatial characteristics of sensory neuron responses. They can be extended to characterize temporal or dynamical aspects by mapping neural responses in dynamical state spaces. The state-space receptive field of a neuron is the probability distribution of the dynamical state of the stimulus-generating system conditioned upon the occurrence of a spike. We have computed state-space receptive fields for semicircular canal afferent neurons in the bullfrog (Rana catesbeiana). We recorded spike times during broad-band Gaussian noise rotational velocity stimuli, computed the frequency distribution of head states at spike times, and normalized these to obtain conditional pdfs for the state. These state-space receptive fields quantify what the brain can deduce about the dynamical state of the head when a single spike arrives from the periphery. c2001 Elsevier Science B.V. All rights reserved.

A reevaluaion of data on atmospheric turbulence and airplane gust loads for application in spectral calculations

NASA Technical Reports Server (NTRS)

Press, Harry; Meadows, May T; Hadlock, Ivan

1956-01-01

The available information on the spectrum of atmospheric turbulence is first briefly reviewed. On the basis of these results, methods are developed for the conversion of available gust statistics normally given in terms of counts of gusts or acceleration peaks into a form appropriate for use in spectral calculations. The fundamental quantity for this purpose appears to be the probability distribution of the root-mean-square gust velocity. Estimates of this distribution are derived from data for a number of load histories of transport operations; also, estimates of the variation of this distribution with altitude and weather condition are derived from available data and the method of applying these results to the calculation of airplane gust-response histories in operations is also outlined. (author)

Average BER of subcarrier intensity modulated free space optical systems over the exponentiated Weibull fading channels.

PubMed

Wang, Ping; Zhang, Lu; Guo, Lixin; Huang, Feng; Shang, Tao; Wang, Ranran; Yang, Yintang

2014-08-25

The average bit error rate (BER) for binary phase-shift keying (BPSK) modulation in free-space optical (FSO) links over turbulence atmosphere modeled by the exponentiated Weibull (EW) distribution is investigated in detail. The effects of aperture averaging on the average BERs for BPSK modulation under weak-to-strong turbulence conditions are studied. The average BERs of EW distribution are compared with Lognormal (LN) and Gamma-Gamma (GG) distributions in weak and strong turbulence atmosphere, respectively. The outage probability is also obtained for different turbulence strengths and receiver aperture sizes. The analytical results deduced by the generalized Gauss-Laguerre quadrature rule are verified by the Monte Carlo simulation. This work is helpful for the design of receivers for FSO communication systems.

Prompting a consumer behavior for pollution control1

PubMed Central

Geller, E. Scott; Farris, John C.; Post, David S.

1973-01-01

A field application of behavior modification studied the relative effectiveness of different prompting procedures for increasing the probability that customers entering a grocery store would select their soft drinks in returnable rather than nonreturnable containers. Six different 2-hr experimental conditions during which bottle purchases were recorded were (1) No Prompt (i.e., control), (2) one student gave incoming customers a handbill urging the purchase of soft drinks in returnable bottles, (3) distribution of the handbill by one student and public charting of each customer's bottle purchases by another student, (4) handbill distribution and charting by a five-member group, (5) handbills distributed and purchases charted by three females. The variant prompting techniques were equally effective, and in general increased the percentage of returnable-bottle customers by an average of 25%. PMID:16795418

Prompting a consumer behavior for pollution control.

PubMed

Geller, E S; Farris, J C; Post, D S

1973-01-01

A field application of behavior modification studied the relative effectiveness of different prompting procedures for increasing the probability that customers entering a grocery store would select their soft drinks in returnable rather than nonreturnable containers. Six different 2-hr experimental conditions during which bottle purchases were recorded were (1) No Prompt (i.e., control), (2) one student gave incoming customers a handbill urging the purchase of soft drinks in returnable bottles, (3) distribution of the handbill by one student and public charting of each customer's bottle purchases by another student, (4) handbill distribution and charting by a five-member group, (5) handbills distributed and purchases charted by three females. The variant prompting techniques were equally effective, and in general increased the percentage of returnable-bottle customers by an average of 25%.

Data documenting the potential distribution of Aedes aegypti in the center of Veracruz, Mexico.

PubMed

Estrada-Contreras, Israel; Sandoval-Ruiz, César A; Mendoza-Palmero, Fredy S; Ibáñez-Bernal, Sergio; Equihua, Miguel; Benítez, Griselda

2017-02-01

The data presented in this article are related to the research article entitled "Establishment of Aedes aegypti (L.) in mountainous regions in Mexico: Increasing number of population at risk of mosquito-borne disease and future climate conditions" (M. Equihua, S. Ibáñez-Bernal, G. Benítez, I. Estrada-Contreras, C.A. Sandoval-Ruiz, F.S. Mendoza-Palmero, 2016) [1]. This article provides presence records in shapefile format used to generate maps of potential distribution of Aedes aegypti with different climate change scenarios as well as each of the maps obtained in raster format. In addition, tables with values of potential distribution of the vector as well as the average values of probability of presence including data of the mosquito incidence along the altitudinal range.

Laboratory demonstration of lightning strike pattern on different roof tops installed with Franklin Rods

NASA Astrophysics Data System (ADS)

Ullah, Irshad; Baharom, MNR; Ahmed, H.; Luqman, HM.; Zainal, Zainab

2017-11-01

Protection against lightning is always a challenging job for the researcher. The consequences due to lightning on different building shapes needs a comprehensive knowledge in order to provide the information to the common man. This paper is mainly concern with lightning pattern when it strikes on the building with different shape. The work is based on the practical experimental work in high voltage laboratory. Different shapes of the scaled structures have been selected in order to investigate the equal distribution of lightning voltage. The equal distribution of lightning voltage will provide the maximum probability of lightning strike on air terminal of the selected shapes. Building shapes have a very important role in lightning protection. The shapes of the roof tops have different geometry and the Franklin rod installation is also varies with changing the shape of the roof top. According to the ambient weather condition of Malaysia high voltage impulse is applied on the lightning rod installed on different geometrical shape. The equal distribution of high voltage impulse is obtained as the geometry of the scaled structure is identical and the air gap for all the tested object is kept the same. This equal distribution of the lightning voltage also proves that the probability of lightning strike is on the corner and the edges of the building structure.

Improving detection probabilities for pests in stored grain.

PubMed

Elmouttie, David; Kiermeier, Andreas; Hamilton, Grant

2010-12-01

The presence of insects in stored grain is a significant problem for grain farmers, bulk grain handlers and distributors worldwide. Inspection of bulk grain commodities is essential to detect pests and thereby to reduce the risk of their presence in exported goods. It has been well documented that insect pests cluster in response to factors such as microclimatic conditions within bulk grain. Statistical sampling methodologies for grain, however, have typically considered pests and pathogens to be homogeneously distributed throughout grain commodities. In this paper, a sampling methodology is demonstrated that accounts for the heterogeneous distribution of insects in bulk grain. It is shown that failure to account for the heterogeneous distribution of pests may lead to overestimates of the capacity for a sampling programme to detect insects in bulk grain. The results indicate the importance of the proportion of grain that is infested in addition to the density of pests within the infested grain. It is also demonstrated that the probability of detecting pests in bulk grain increases as the number of subsamples increases, even when the total volume or mass of grain sampled remains constant. This study underlines the importance of considering an appropriate biological model when developing sampling methodologies for insect pests. Accounting for a heterogeneous distribution of pests leads to a considerable improvement in the detection of pests over traditional sampling models. Copyright © 2010 Society of Chemical Industry.

Seasonal climate variation and caribou availability: Modeling sequential movement using satellite-relocation data

USGS Publications Warehouse

Nicolson, Craig; Berman, Matthew; West, Colin Thor; Kofinas, Gary P.; Griffith, Brad; Russell, Don; Dugan, Darcy

2013-01-01

Livelihood systems that depend on mobile resources must constantly adapt to change. For people living in permanent settlements, environmental changes that affect the distribution of a migratory species may reduce the availability of a primary food source, with the potential to destabilize the regional social-ecological system. Food security for Arctic indigenous peoples harvesting barren ground caribou (Rangifer tarandus granti) depends on movement patterns of migratory herds. Quantitative assessments of physical, ecological, and social effects on caribou distribution have proven difficult because of the significant interannual variability in seasonal caribou movement patterns. We developed and evaluated a modeling approach for simulating the distribution of a migratory herd throughout its annual cycle over a multiyear period. Beginning with spatial and temporal scales developed in previous studies of the Porcupine Caribou Herd of Canada and Alaska, we used satellite collar locations to compute and analyze season-by-season probabilities of movement of animals between habitat zones under two alternative weather conditions for each season. We then built a set of transition matrices from these movement probabilities, and simulated the sequence of movements across the landscape as a Markov process driven by externally imposed seasonal weather states. Statistical tests showed that the predicted distributions of caribou were consistent with observed distributions, and significantly correlated with subsistence harvest levels for three user communities. Our approach could be applied to other caribou herds and could be adapted for simulating the distribution of other ungulates and species with similarly large interannual variability in the use of their range.

An Alternative Version of Conditional Probabilities and Bayes' Rule: An Application of Probability Logic

ERIC Educational Resources Information Center

Satake, Eiki; Amato, Philip P.

2008-01-01

This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…

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.

Adaptation in pronoun resolution: Evidence from Brazilian and European Portuguese.

PubMed

Fernandes, Eunice G; Luegi, Paula; Correa Soares, Eduardo; de la Fuente, Israel; Hemforth, Barbara

2018-04-26

Previous research accounting for pronoun resolution as a problem of probabilistic inference has not explored the phenomenon of adaptation, whereby the processor constantly tracks and adapts, rationally, to changes in a statistical environment. We investigate whether Brazilian (BP) and European Portuguese (EP) speakers adapt to variations in the probability of occurrence of ambiguous overt and null pronouns, in two experiments assessing resolution toward subject and object referents. For each variety (BP, EP), participants were faced with either the same number of null and overt pronouns (equal distribution), or with an environment with fewer overt (than null) pronouns (unequal distribution). We find that the preference for interpreting overt pronouns as referring back to an object referent (object-biased interpretation) is higher when there are fewer overt pronouns (i.e., in the unequal, relative to the equal distribution condition). This is especially the case for BP, a variety with higher prior frequency and smaller object-biased interpretation of overt pronouns, suggesting that participants adapted incrementally and integrated prior statistical knowledge with the knowledge obtained in the experiment. We hypothesize that comprehenders adapted rationally, with the goal of maintaining, across variations in pronoun probability, the likelihood of subject and object referents. Our findings unify insights from research in pronoun resolution and in adaptation, and add to previous studies in both topics: They provide evidence for the influence of pronoun probability in pronoun resolution, and for an adaptation process whereby the language processor not only tracks statistical information, but uses it to make interpretational inferences. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

A Probabilistic Framework for Quantifying Mixed Uncertainties in Cyber Attacker Payoffs

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

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

Quantification and propagation of uncertainties in cyber attacker payoffs is a key aspect within multiplayer, stochastic security games. These payoffs may represent penalties or rewards associated with player actions and are subject to various sources of uncertainty, including: (1) cyber-system state, (2) attacker type, (3) choice of player actions, and (4) cyber-system state transitions over time. Past research has primarily focused on representing defender beliefs about attacker payoffs as point utility estimates. More recently, within the physical security domain, attacker payoff uncertainties have been represented as Uniform and Gaussian probability distributions, and mathematical intervals. For cyber-systems, probability distributions may helpmore » address statistical (aleatory) uncertainties where the defender may assume inherent variability or randomness in the factors contributing to the attacker payoffs. However, systematic (epistemic) uncertainties may exist, where the defender may not have sufficient knowledge or there is insufficient information about the attacker’s payoff generation mechanism. Such epistemic uncertainties are more suitably represented as generalizations of probability boxes. This paper explores the mathematical treatment of such mixed payoff uncertainties. A conditional probabilistic reasoning approach is adopted to organize the dependencies between a cyber-system’s state, attacker type, player actions, and state transitions. This also enables the application of probabilistic theories to propagate various uncertainties in the attacker payoffs. An example implementation of this probabilistic framework and resulting attacker payoff distributions are discussed. A goal of this paper is also to highlight this uncertainty quantification problem space to the cyber security research community and encourage further advancements in this area.« less

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

Axion excursions of the landscape during inflation

NASA Astrophysics Data System (ADS)

Palma, Gonzalo A.; Riquelme, Walter

2017-07-01

Because of their quantum fluctuations, axion fields had a chance to experience field excursions traversing many minima of their potentials during inflation. We study this situation by analyzing the dynamics of an axion field ψ , present during inflation, with a periodic potential given by v (ψ )=Λ4[1 -cos (ψ /f )]. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say, ψ =0 , we compute every n -point correlation function of ψ up to first order in Λ4 using the in-in formalism. This computation allows us to identify the distribution function describing the probability of measuring ψ at a particular amplitude during inflation. Because ψ is able to tunnel between the barriers of the potential, we find that the probability distribution function consists of a non-Gaussian multimodal distribution such that the probability of measuring ψ at a minimum of v (ψ ) different from ψ =0 increases with time. As a result, at the end of inflation, different patches of the Universe are characterized by different values of the axion field amplitude, leading to important cosmological phenomenology: (a) Isocurvature fluctuations induced by the axion at the end of inflation could be highly non-Gaussian. (b) If the axion defines the strength of standard model couplings, then one is led to a concrete realization of the multiverse. (c) If the axion corresponds to dark matter, one is led to the possibility that, within our observable Universe, dark matter started with a nontrivial initial condition, implying novel signatures for future surveys.

Selective Attention in Pigeon Temporal Discrimination.

PubMed

Subramaniam, Shrinidhi; Kyonka, Elizabeth

2017-07-27

Cues can vary in how informative they are about when specific outcomes, such as food availability, will occur. This study was an experimental investigation of the functional relation between cue informativeness and temporal discrimination in a peak-interval (PI) procedure. Each session consisted of fixed-interval (FI) 2-s and 4-s schedules of food and occasional, 12-s PI trials during which pecks had no programmed consequences. Across conditions, the phi (ϕ) correlation between key light color and FI schedule value was manipulated. Red and green key lights signaled the onset of either or both FI schedules. Different colors were either predictive (ϕ = 1), moderately predictive (ϕ = 0.2-0.8), or not predictive (ϕ = 0) of a specific FI schedule. This study tested the hypothesis that temporal discrimination is a function of the momentary conditional probability of food; that is, pigeons peck the most at either 2 s or 4 s when ϕ = 1 and peck at both intervals when ϕ < 1. Response distributions were bimodal Gaussian curves; distributions from red- and green-key PI trials converged when ϕ ≤ 0.6. Peak times estimated by summed Gaussian functions, averaged across conditions and pigeons, were 1.85 s and 3.87 s, however, pigeons did not always maximize the momentary probability of food. When key light color was highly correlated with FI schedules (ϕ ≥ 0.6), estimates of peak times indicated that temporal discrimination accuracy was reduced at the unlikely interval, but not the likely interval. The mechanism of this reduced temporal discrimination accuracy could be interpreted as an attentional process.

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.

Valid statistical inference methods for a case-control study with missing data.

PubMed

Tian, Guo-Liang; Zhang, Chi; Jiang, Xuejun

2018-04-01

The main objective of this paper is to derive the valid sampling distribution of the observed counts in a case-control study with missing data under the assumption of missing at random by employing the conditional sampling method and the mechanism augmentation method. The proposed sampling distribution, called the case-control sampling distribution, can be used to calculate the standard errors of the maximum likelihood estimates of parameters via the Fisher information matrix and to generate independent samples for constructing small-sample bootstrap confidence intervals. Theoretical comparisons of the new case-control sampling distribution with two existing sampling distributions exhibit a large difference. Simulations are conducted to investigate the influence of the three different sampling distributions on statistical inferences. One finding is that the conclusion by the Wald test for testing independency under the two existing sampling distributions could be completely different (even contradictory) from the Wald test for testing the equality of the success probabilities in control/case groups under the proposed distribution. A real cervical cancer data set is used to illustrate the proposed statistical methods.

What is epistemic value in free energy models of learning and acting? A bounded rationality perspective.

PubMed

Ortega, Pedro A; Braun, Daniel A

2015-01-01

Free energy models of learning and acting do not only care about utility or extrinsic value, but also about intrinsic value, that is, the information value stemming from probability distributions that represent beliefs or strategies. While these intrinsic values can be interpreted as epistemic values or exploration bonuses under certain conditions, the framework of bounded rationality offers a complementary interpretation in terms of information-processing costs that we discuss here.

Physical interrelation between Fokker-Planck and random walk models with application to Coulomb interactions.

NASA Technical Reports Server (NTRS)

Englert, G. W.

1971-01-01

A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.

Gaussian noise and time-reversal symmetry in nonequilibrium Langevin models.

PubMed

Vainstein, M H; Rubí, J M

2007-03-01

We show that in driven systems the Gaussian nature of the fluctuating force and time reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of noninteracting Brownian particles in steady flow.

Characterizing the performance of XOR games and the Shannon capacity of graphs.

PubMed

Ramanathan, Ravishankar; Kay, Alastair; Murta, Gláucia; Horodecki, Paweł

2014-12-12

In this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party XOR game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games that have no quantum advantage for arbitrary input probability distributions, up to certain symmetries. In the future, these might be used in information-theoretic studies on reproducing the set of quantum nonlocal correlations.

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

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Maeda, Nobuo

2014-06-01

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

Feasibility of streamlining an interactive Bayesian-based diagnostic support tool designed for clinical practice

NASA Astrophysics Data System (ADS)

Chen, Po-Hao; Botzolakis, Emmanuel; Mohan, Suyash; Bryan, R. N.; Cook, Tessa

2016-03-01

In radiology, diagnostic errors occur either through the failure of detection or incorrect interpretation. Errors are estimated to occur in 30-35% of all exams and contribute to 40-54% of medical malpractice litigations. In this work, we focus on reducing incorrect interpretation of known imaging features. Existing literature categorizes cognitive bias leading a radiologist to an incorrect diagnosis despite having correctly recognized the abnormal imaging features: anchoring bias, framing effect, availability bias, and premature closure. Computational methods make a unique contribution, as they do not exhibit the same cognitive biases as a human. Bayesian networks formalize the diagnostic process. They modify pre-test diagnostic probabilities using clinical and imaging features, arriving at a post-test probability for each possible diagnosis. To translate Bayesian networks to clinical practice, we implemented an entirely web-based open-source software tool. In this tool, the radiologist first selects a network of choice (e.g. basal ganglia). Then, large, clearly labeled buttons displaying salient imaging features are displayed on the screen serving both as a checklist and for input. As the radiologist inputs the value of an extracted imaging feature, the conditional probabilities of each possible diagnosis are updated. The software presents its level of diagnostic discrimination using a Pareto distribution chart, updated with each additional imaging feature. Active collaboration with the clinical radiologist is a feasible approach to software design and leads to design decisions closely coupling the complex mathematics of conditional probability in Bayesian networks with practice.

A varying-coefficient method for analyzing longitudinal clinical trials data with nonignorable dropout

PubMed Central

Forster, Jeri E.; MaWhinney, Samantha; Ball, Erika L.; Fairclough, Diane

2011-01-01

Dropout is common in longitudinal clinical trials and when the probability of dropout depends on unobserved outcomes even after conditioning on available data, it is considered missing not at random and therefore nonignorable. To address this problem, mixture models can be used to account for the relationship between a longitudinal outcome and dropout. We propose a Natural Spline Varying-coefficient mixture model (NSV), which is a straightforward extension of the parametric Conditional Linear Model (CLM). We assume that the outcome follows a varying-coefficient model conditional on a continuous dropout distribution. Natural cubic B-splines are used to allow the regression coefficients to semiparametrically depend on dropout and inference is therefore more robust. Additionally, this method is computationally stable and relatively simple to implement. We conduct simulation studies to evaluate performance and compare methodologies in settings where the longitudinal trajectories are linear and dropout time is observed for all individuals. Performance is assessed under conditions where model assumptions are both met and violated. In addition, we compare the NSV to the CLM and a standard random-effects model using an HIV/AIDS clinical trial with probable nonignorable dropout. The simulation studies suggest that the NSV is an improvement over the CLM when dropout has a nonlinear dependence on the outcome. PMID:22101223

Fragment size distribution in viscous bag breakup of a drop

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

An Alternative Teaching Method of Conditional Probabilities and Bayes' Rule: An Application of the Truth Table

ERIC Educational Resources Information Center

Satake, Eiki; Vashlishan Murray, Amy

2015-01-01

This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities--especially the ones that involve Bayes' rule--with…

Nuclear risk analysis of the Ulysses mission

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

Fieth, Pascal; Hartmann, Alexander K.

2016-08-01

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

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.

Drivers and uncertainties of forecasted range shifts for warm-water fishes under climate and land cover change

USGS Publications Warehouse

Bouska, Kristen; Whitledge, Gregory W.; Lant, Christopher; Schoof, Justin

2018-01-01

Land cover is an important determinant of aquatic habitat and is projected to shift with climate changes, yet climate-driven land cover changes are rarely factored into climate assessments. To quantify impacts and uncertainty of coupled climate and land cover change on warm-water fish species’ distributions, we used an ensemble model approach to project distributions of 14 species. For each species, current range projections were compared to 27 scenario-based projections and aggregated to visualize uncertainty. Multiple regression and model selection techniques were used to identify drivers of range change. Novel, or no-analogue, climates were assessed to evaluate transferability of models. Changes in total probability of occurrence ranged widely across species, from a 63% increase to a 65% decrease. Distributional gains and losses were largely driven by temperature and flow variables and underscore the importance of habitat heterogeneity and connectivity to facilitate adaptation to changing conditions. Finally, novel climate conditions were driven by mean annual maximum temperature, which stresses the importance of understanding the role of temperature on fish physiology and the role of temperature-mitigating management practices.

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.

Quantum Common Causes and Quantum Causal Models

NASA Astrophysics Data System (ADS)

Allen, John-Mark A.; Barrett, Jonathan; Horsman, Dominic C.; Lee, Ciarán M.; Spekkens, Robert W.

2017-07-01

Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach's principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C , then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models and provide examples of how the formalism works.

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system structural components

NASA Technical Reports Server (NTRS)

Cruse, T. A.

1987-01-01

The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.

Probabilistic Structural Analysis Methods for select space propulsion system structural components (PSAM)

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Burnside, O. H.; Wu, Y.-T.; Polch, E. Z.; Dias, J. B.

1988-01-01

The objective is the development of several modular structural analysis packages capable of predicting the probabilistic response distribution for key structural variables such as maximum stress, natural frequencies, transient response, etc. The structural analysis packages are to include stochastic modeling of loads, material properties, geometry (tolerances), and boundary conditions. The solution is to be in terms of the cumulative probability of exceedance distribution (CDF) and confidence bounds. Two methods of probability modeling are to be included as well as three types of structural models - probabilistic finite-element method (PFEM); probabilistic approximate analysis methods (PAAM); and probabilistic boundary element methods (PBEM). The purpose in doing probabilistic structural analysis is to provide the designer with a more realistic ability to assess the importance of uncertainty in the response of a high performance structure. Probabilistic Structural Analysis Method (PSAM) tools will estimate structural safety and reliability, while providing the engineer with information on the confidence that should be given to the predicted behavior. Perhaps most critically, the PSAM results will directly provide information on the sensitivity of the design response to those variables which are seen to be uncertain.

Determination of the Changes of Drought Occurrence in Turkey Using Regional Climate Modeling

NASA Astrophysics Data System (ADS)

Sibel Saygili, Fatma; Tufan Turp, M.; Kurnaz, M. Levent

2017-04-01

As a consequence of the negative impacts of climate change, Turkey, being a country in the Mediterranean Basin, is under a serious risk of increased drought conditions. In this study, it is aimed to determine and compare the spatial distributions of climatological drought probabilities for Turkey. For this purpose, by making use of Regional Climate Model (RegCM4.4) of the Abdus Salam International Centre for Theoretical Physics (ICTP), the outputs of the MPI-ESM-MR global climate model of the Max Planck Institute for Meteorology are downscaled to 50km for Turkey. To make the future projection over Turkey for the period of 2071-2100 with respect to the reference period of 1986-2005, the worst case emission pathway RCP8.5 is used. The Palmer Drought Severity Index (PDSI) values are computed and classified in accordance with the seven classifications of National Oceanic and Atmospheric Administration (NOAA). Finally, the spatial distribution maps showing the changes in drought probabilities over Turkey are obtained in order to see the impact of climate change on Turkey's drought patterns.

The stochastic model for ternary and quaternary alloys: Application of the Bernoulli relation to the phonon spectra of mixed crystals

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

Marchewka, M., E-mail: marmi@ur.edu.pl; Woźny, M.; Polit, J.

2014-03-21

To understand and interpret the experimental data on the phonon spectra of the solid solutions, it is necessary to describe mathematically the non-regular distribution of atoms in their lattices. It appears that such description is possible in case of the strongly stochastically homogenous distribution which requires a great number of atoms and very carefully mixed alloys. These conditions are generally fulfilled in case of high quality homogenous semiconductor solid solutions of the III–V and II–VI semiconductor compounds. In this case, we can use the Bernoulli relation describing probability of the occurrence of one n equivalent event which can be applied,more » to the probability of finding one from n configurations in the solid solution lattice. The results described in this paper for ternary HgCdTe and GaAsP as well as quaternary ZnCdHgTe can provide an affirmative answer to the question: whether stochastic geometry, e.g., the Bernoulli relation, is enough to describe the observed phonon spectra.« less

Modelling volatility recurrence intervals in the Chinese commodity futures market

NASA Astrophysics Data System (ADS)

Zhou, Weijie; Wang, Zhengxin; Guo, Haiming

2016-09-01

The law of extreme event occurrence attracts much research. The volatility recurrence intervals of Chinese commodity futures market prices are studied: the results show that the probability distributions of the scaled volatility recurrence intervals have a uniform scaling curve for different thresholds q. So we can deduce the probability distribution of extreme events from normal events. The tail of a scaling curve can be well fitted by a Weibull form, which is significance-tested by KS measures. Both short-term and long-term memories are present in the recurrence intervals with different thresholds q, which denotes that the recurrence intervals can be predicted. In addition, similar to volatility, volatility recurrence intervals also have clustering features. Through Monte Carlo simulation, we artificially synthesise ARMA, GARCH-class sequences similar to the original data, and find out the reason behind the clustering. The larger the parameter d of the FIGARCH model, the stronger the clustering effect is. Finally, we use the Fractionally Integrated Autoregressive Conditional Duration model (FIACD) to analyse the recurrence interval characteristics. The results indicated that the FIACD model may provide a method to analyse volatility recurrence intervals.

An analytical model for regular respiratory signals derived from the probability density function of Rayleigh distribution.

PubMed

Li, Xin; Li, Ye

2015-01-01

Regular respiratory signals (RRSs) acquired with physiological sensing systems (e.g., the life-detection radar system) can be used to locate survivors trapped in debris in disaster rescue, or predict the breathing motion to allow beam delivery under free breathing conditions in external beam radiotherapy. Among the existing analytical models for RRSs, the harmonic-based random model (HRM) is shown to be the most accurate, which, however, is found to be subject to considerable error if the RRS has a slowly descending end-of-exhale (EOE) phase. The defect of the HRM motivates us to construct a more accurate analytical model for the RRS. In this paper, we derive a new analytical RRS model from the probability density function of Rayleigh distribution. We evaluate the derived RRS model by using it to fit a real-life RRS in the sense of least squares, and the evaluation result shows that, our presented model exhibits lower error and fits the slowly descending EOE phases of the real-life RRS better than the HRM.

The stochastic model for ternary and quaternary alloys: Application of the Bernoulli relation to the phonon spectra of mixed crystals

NASA Astrophysics Data System (ADS)

Marchewka, M.; Woźny, M.; Polit, J.; Kisiel, A.; Robouch, B. V.; Marcelli, A.; Sheregii, E. M.

2014-03-01

To understand and interpret the experimental data on the phonon spectra of the solid solutions, it is necessary to describe mathematically the non-regular distribution of atoms in their lattices. It appears that such description is possible in case of the strongly stochastically homogenous distribution which requires a great number of atoms and very carefully mixed alloys. These conditions are generally fulfilled in case of high quality homogenous semiconductor solid solutions of the III-V and II-VI semiconductor compounds. In this case, we can use the Bernoulli relation describing probability of the occurrence of one n equivalent event which can be applied, to the probability of finding one from n configurations in the solid solution lattice. The results described in this paper for ternary HgCdTe and GaAsP as well as quaternary ZnCdHgTe can provide an affirmative answer to the question: whether stochastic geometry, e.g., the Bernoulli relation, is enough to describe the observed phonon spectra.

Decadal oscillations and extreme value distribution of river peak flows in the Meuse catchment

NASA Astrophysics Data System (ADS)

De Niel, Jan; Willems, Patrick

2017-04-01

In flood risk management, flood probabilities are often quantified through Generalized Pareto distributions of river peak flows. One of the main underlying assumptions is that all data points need to originate from one single underlying distribution (i.i.d. assumption). However, this hypothesis, although generally assumed to be correct for variables such as river peak flows, remains somehow questionable: flooding might indeed be caused by different hydrological and/or meteorological conditions. This study confirms these findings from previous research by showing a clear indication of the link between atmospheric conditions and flooding for the Meuse river in The Netherlands: decadal oscillations of river peak flows can (at least partially) be attributed to the occurrence of westerly weather types. The study further proposes a method to take this correlation between atmospheric conditions and river peak flows into account when calibrating an extreme value distribution for river peak flows. Rather than calibrating one single distribution to the data and potentially violating the i.i.d. assumption, weather type depending extreme value distributions are derived and composed. The study shows that, for the Meuse river in The Netherlands, such approach results in a more accurate extreme value distribution, especially with regards to extrapolations. Comparison of the proposed method with a traditional extreme value analysis approach and an alternative model-based approach for the same case study shows strong differences in the peak flow extrapolation. The design-flood for a 1,250 year return period is estimated at 4,800 m3s-1 for the proposed method, compared with 3,450 m3s-1 and 3,900 m3s-1 for the traditional method and a previous study. The methods were validated based on instrumental and documentary flood information of the past 500 years.

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

Jager, Yetta; Efroymson, Rebecca Ann; Sublette, K.

Quantitative tools are needed to evaluate the ecological effects of increasing petroleum production. In this article, we describe two stochastic models for simulating the spatial distribution of brine spills on a landscape. One model uses general assumptions about the spatial arrangement of spills and their sizes; the second model distributes spills by siting rectangular well complexes and conditioning spill probabilities on the configuration of pipes. We present maps of landscapes with spills produced by the two methods and compare the ability of the models to reproduce a specified spill area. A strength of the models presented here is their abilitymore » to extrapolate from the existing landscape to simulate landscapes with a higher (or lower) density of oil wells.« less

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.

Investigation of the relation between the return periods of major drought characteristics using copula functions

NASA Astrophysics Data System (ADS)

Hüsami Afşar, Mehdi; Unal Şorman, Ali; Tugrul Yilmaz, Mustafa

2016-04-01

Different drought characteristics (e.g. duration, average severity, and average areal extent) often have monotonic relation that increased magnitude of one often follows a similar increase in the magnitude of the other drought characteristic. Hence it is viable to establish a relationship between different drought characteristics with the goal of predicting one using other ones. Copula functions that relate different variables using their joint and conditional cumulative probability distributions are often used to statistically model the drought characteristics. In this study bivariate and trivariate joint probabilities of these characteristics are obtained over Ankara (Turkey) between 1960 and 2013. Copula-based return period estimation of drought characteristics of duration, average severity, and average areal extent show joint probabilities of these characteristics can be satisfactorily achieved. Among different copula families investigated in this study, elliptical family (i.e. including normal and t-student copula functions) resulted in the lowest root mean square error. "This study was supported by TUBITAK fund #114Y676)."

Infinite capacity multi-server queue with second optional service channel

NASA Astrophysics Data System (ADS)

Ke, Jau-Chuan; Wu, Chia-Huang; Pearn, Wen Lea

2013-02-01

This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with probability (1-θ), or at the completion of the FES may immediately require a SOS with probability θ (0 <= θ <= 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to determine the optimal values of the number of servers and the two service rates, simultaneously, at the minimal total expected cost per unit time. Quasi-Newton method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided in which several system performance measures are calculated based on assumed numerical values of the system parameters.

Dynamic properties of molecular motors in burnt-bridge models

NASA Astrophysics Data System (ADS)

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

2007-08-01

Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic 'burnt-bridge' models. The transport of the particles is viewed as an effective diffusion along one-dimensional lattices with periodically distributed weak links. When an unbiased random walker passes the weak link it can be destroyed ('burned') with probability p, providing a bias in the motion of the molecular motor. We present a theoretical approach that allows one to calculate exactly all dynamic properties of motor proteins, such as velocity and dispersion, under general conditions. It is found that dispersion is a decreasing function of the concentration of bridges, while the dependence of dispersion on the burning probability is more complex. Our calculations also show a gap in dispersion for very low concentrations of weak links or for very low burning probabilities which indicates a dynamic phase transition between unbiased and biased diffusion regimes. Theoretical findings are supported by Monte Carlo computer simulations.

Trace element distributions in the water column near the Deepwater Horizon well blowout.

PubMed

Joung, DongJoo; Shiller, Alan M

2013-03-05

To understand the impact of the Deepwater Horizon well blowout on dissolved trace element concentrations, samples were collected from areas around the oil rig explosion site during four cruises in early and late May 2010, October 2010, and October 2011. In surface waters, Ba, Fe, Cu, Ni, Mn, and Co were relatively well correlated with salinity during all cruises, suggesting mixing with river water was the main influence on metal distributions in these waters. However, in deep oil/gas plumes (1000-1400 m depth), modestly elevated concentrations of Co and Ba were observed in late May, compared with postblowout conditions. Analysis of the oil itself along with leaching experiments confirm the oil as the source of the Co, whereas increased Ba was likely due to drilling mud used in the top kill attempt. Deep plume dissolved Mn largely reflected natural benthic input, though some samples showed slight elevation probably associated with the top kill. Dissolved Fe concentrations were low and also appeared largely topographically controlled and reflective of benthic input. Estimates suggest that microbial Fe demand may have affected the Fe distribution but probably not to the extent of Fe becoming a growth-limiting factor. Experiments showed that the dispersant can have some limited impact on dissolved-particulate metal partitioning.

Probabilistic Analysis of a Composite Crew Module

NASA Technical Reports Server (NTRS)

Mason, Brian H.; Krishnamurthy, Thiagarajan

2011-01-01

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

Event dependence in U.S. executions

PubMed Central

Baumgartner, Frank R.; Box-Steffensmeier, Janet M.

2018-01-01

Since 1976, the United States has seen over 1,400 judicial executions, and these have been highly concentrated in only a few states and counties. The number of executions across counties appears to fit a stretched distribution. These distributions are typically reflective of self-reinforcing processes where the probability of observing an event increases for each previous event. To examine these processes, we employ two-pronged empirical strategy. First, we utilize bootstrapped Kolmogorov-Smirnov tests to determine whether the pattern of executions reflect a stretched distribution, and confirm that they do. Second, we test for event-dependence using the Conditional Frailty Model. Our tests estimate the monthly hazard of an execution in a given county, accounting for the number of previous executions, homicides, poverty, and population demographics. Controlling for other factors, we find that the number of prior executions in a county increases the probability of the next execution and accelerates its timing. Once a jurisdiction goes down a given path, the path becomes self-reinforcing, causing the counties to separate out into those never executing (the vast majority of counties) and those which use the punishment frequently. This finding is of great legal and normative concern, and ultimately, may not be consistent with the equal protection clause of the U.S. Constitution. PMID:29293583

Delay Analysis and Optimization of Bandwidth Request under Unicast Polling in IEEE 802.16e over Gilbert-Elliot Error Channel

NASA Astrophysics Data System (ADS)

Hwang, Eunju; Kim, Kyung Jae; Roijers, Frank; Choi, Bong Dae

In the centralized polling mode in IEEE 802.16e, a base station (BS) polls mobile stations (MSs) for bandwidth reservation in one of three polling modes; unicast, multicast, or broadcast pollings. In unicast polling, the BS polls each individual MS to allow to transmit a bandwidth request packet. This paper presents an analytical model for the unicast polling of bandwidth request in IEEE 802.16e networks over Gilbert-Elliot error channel. We derive the probability distribution for the delay of bandwidth requests due to wireless transmission errors and find the loss probability of request packets due to finite retransmission attempts. By using the delay distribution and the loss probability, we optimize the number of polling slots within a frame and the maximum retransmission number while satisfying QoS on the total loss probability which combines two losses: packet loss due to the excess of maximum retransmission and delay outage loss due to the maximum tolerable delay bound. In addition, we obtain the utilization of polling slots, which is defined as the ratio of the number of polling slots used for the MS's successful transmission to the total number of polling slots used by the MS over a long run time. Analysis results are shown to well match with simulation results. Numerical results give examples of the optimal number of polling slots within a frame and the optimal maximum retransmission number depending on delay bounds, the number of MSs, and the channel conditions.

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.

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

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

A 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.

The Probability Approach to English If-Conditional Sentences

ERIC Educational Resources Information Center

Wu, Mei

2012-01-01

Users of the Probability Approach choose the right one from four basic types of conditional sentences--factual, predictive, hypothetical and counterfactual conditionals, by judging how likely (i.e. the probability) the event in the result-clause will take place when the condition in the if-clause is met. Thirty-three students from the experimental…

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.

Offshore fatigue design turbulence

NASA Astrophysics Data System (ADS)

Larsen, Gunner C.

2001-07-01

Fatigue damage on wind turbines is mainly caused by stochastic loading originating from turbulence. While onshore sites display large differences in terrain topology, and thereby also in turbulence conditions, offshore sites are far more homogeneous, as the majority of them are likely to be associated with shallow water areas. However, despite this fact, specific recommendations on offshore turbulence intensities, applicable for fatigue design purposes, are lacking in the present IEC code. This article presents specific guidelines for such loading. These guidelines are based on the statistical analysis of a large number of wind data originating from two Danish shallow water offshore sites. The turbulence standard deviation depends on the mean wind speed, upstream conditions, measuring height and thermal convection. Defining a population of turbulence standard deviations, at a given measuring position, uniquely by the mean wind speed, variations in upstream conditions and atmospheric stability will appear as variability of the turbulence standard deviation. Distributions of such turbulence standard deviations, conditioned on the mean wind speed, are quantified by fitting the measured data to logarithmic Gaussian distributions. By combining a simple heuristic load model with the parametrized conditional probability density functions of the turbulence standard deviations, an empirical offshore design turbulence intensity is determined. For pure stochastic loading (as associated with standstill situations), the design turbulence intensity yields a fatigue damage equal to the average fatigue damage caused by the distributed turbulence intensity. If the stochastic loading is combined with a periodic deterministic loading (as in the normal operating situation), the proposed design turbulence intensity is shown to be conservative.

PROBABILITY SURVEYS , CONDITIONAL PROBABILITIES AND ECOLOGICAL RISK ASSESSMENT

EPA Science Inventory

We show that probability-based environmental resource monitoring programs, such as the U.S. Environmental Protection Agency's (U.S. EPA) Environmental Monitoring and Assessment Program, and conditional probability analysis can serve as a basis for estimating ecological risk over ...

PROBABILITY SURVEYS, CONDITIONAL PROBABILITIES, AND ECOLOGICAL RISK ASSESSMENT

EPA Science Inventory

We show that probability-based environmental resource monitoring programs, such as U.S. Environmental Protection Agency's (U.S. EPA) Environmental Monitoring and Asscssment Program EMAP) can be analyzed with a conditional probability analysis (CPA) to conduct quantitative probabi...