47 CFR 1.1623 - Probability calculation.
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a) All calculations shall be...
Collective probabilities algorithm for surface hopping calculations
International Nuclear Information System (INIS)
Bastida, Adolfo; Cruz, Carlos; Zuniga, Jose; Requena, Alberto
2003-01-01
General equations that transition probabilities of the hopping algorithms in surface hopping calculations must obey to assure the equality between the average quantum and classical populations are derived. These equations are solved for two particular cases. In the first it is assumed that probabilities are the same for all trajectories and that the number of hops is kept to a minimum. These assumptions specify the collective probabilities (CP) algorithm, for which the transition probabilities depend on the average populations for all trajectories. In the second case, the probabilities for each trajectory are supposed to be completely independent of the results from the other trajectories. There is, then, a unique solution of the general equations assuring that the transition probabilities are equal to the quantum population of the target state, which is referred to as the independent probabilities (IP) algorithm. The fewest switches (FS) algorithm developed by Tully is accordingly understood as an approximate hopping algorithm which takes elements from the accurate CP and IP solutions. A numerical test of all these hopping algorithms is carried out for a one-dimensional two-state problem with two avoiding crossings which shows the accuracy and computational efficiency of the collective probabilities algorithm proposed, the limitations of the FS algorithm and the similarity between the results offered by the IP algorithm and those obtained with the Ehrenfest method
Calculating Cumulative Binomial-Distribution Probabilities
Scheuer, Ernest M.; Bowerman, Paul N.
1989-01-01
Cumulative-binomial computer program, CUMBIN, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), used independently of one another. Reliabilities and availabilities of k-out-of-n systems analyzed. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Used for calculations of reliability and availability. Program written in C.
Monte Carlo methods to calculate impact probabilities
Rickman, H.; Wiśniowski, T.; Wajer, P.; Gabryszewski, R.; Valsecchi, G. B.
2014-09-01
Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429). Aims: We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods: We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results: We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward
[Biometric bases: basic concepts of probability calculation].
Dinya, E
1998-04-26
The author gives or outline of the basic concepts of probability theory. The bases of the event algebra, definition of the probability, the classical probability model and the random variable are presented.
Pade approximant calculations for neutron escape probability
International Nuclear Information System (INIS)
El Wakil, S.A.; Saad, E.A.; Hendi, A.A.
1984-07-01
The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)
Probability calculations for three-part mineral resource assessments
Ellefsen, Karl J.
2017-06-27
Three-part mineral resource assessment is a methodology for predicting, in a specified geographic region, both the number of undiscovered mineral deposits and the amount of mineral resources in those deposits. These predictions are based on probability calculations that are performed with computer software that is newly implemented. Compared to the previous implementation, the new implementation includes new features for the probability calculations themselves and for checks of those calculations. The development of the new implementation lead to a new understanding of the probability calculations, namely the assumptions inherent in the probability calculations. Several assumptions strongly affect the mineral resource predictions, so it is crucial that they are checked during an assessment. The evaluation of the new implementation leads to new findings about the probability calculations,namely findings regarding the precision of the computations,the computation time, and the sensitivity of the calculation results to the input.
Calculating the albedo characteristics by the method of transmission probabilities
International Nuclear Information System (INIS)
Lukhvich, A.A.; Rakhno, I.L.; Rubin, I.E.
1983-01-01
The possibility to use the method of transmission probabilities for calculating the albedo characteristics of homogeneous and heterogeneous zones is studied. The transmission probabilities method is a numerical method for solving the transport equation in the integrated form. All calculations have been conducted as a one-group approximation for the planes and rods with different optical thicknesses and capture-to-scattering ratios. Above calculations for plane and cylindrical geometries have shown the possibility to use the numerical method of transmission probabilities for calculating the albedo characteristics of homogeneous and heterogeneous zones with high accuracy. In this case the computer time consumptions are minimum even with the cylindrical geometry, if the interpolation calculation of characteristics is used for the neutrons of the first path
Calculating the Probability of Returning a Loan with Binary Probability Models
Directory of Open Access Journals (Sweden)
Julian Vasilev
2014-12-01
Full Text Available The purpose of this article is to give a new approach in calculating the probability of returning a loan. A lot of factors affect the value of the probability. In this article by using statistical and econometric models some influencing factors are proved. The main approach is concerned with applying probit and logit models in loan management institutions. A new aspect of the credit risk analysis is given. Calculating the probability of returning a loan is a difficult task. We assume that specific data fields concerning the contract (month of signing, year of signing, given sum and data fields concerning the borrower of the loan (month of birth, year of birth (age, gender, region, where he/she lives may be independent variables in a binary logistics model with a dependent variable “the probability of returning a loan”. It is proved that the month of signing a contract, the year of signing a contract, the gender and the age of the loan owner do not affect the probability of returning a loan. It is proved that the probability of returning a loan depends on the sum of contract, the remoteness of the loan owner and the month of birth. The probability of returning a loan increases with the increase of the given sum, decreases with the proximity of the customer, increases for people born in the beginning of the year and decreases for people born at the end of the year.
Thermal disadvantage factor calculation by the multiregion collision probability method
International Nuclear Information System (INIS)
Ozgener, B.; Ozgener, H.A.
2004-01-01
A multi-region collision probability formulation that is capable of applying white boundary condition directly is presented and applied to thermal neutron transport problems. The disadvantage factors computed are compared with their counterparts calculated by S N methods with both direct and indirect application of white boundary condition. The results of the ABH and collision probability method with indirect application of white boundary condition are also considered and comparisons with benchmark Monte Carlo results are carried out. The studies show that the proposed formulation is capable of calculating thermal disadvantage factor with sufficient accuracy without resorting to the fictitious scattering outer shell approximation associated with the indirect application of the white boundary condition in collision probability solutions
Fostering Positive Attitude in Probability Learning Using Graphing Calculator
Tan, Choo-Kim; Harji, Madhubala Bava; Lau, Siong-Hoe
2011-01-01
Although a plethora of research evidence highlights positive and significant outcomes of the incorporation of the Graphing Calculator (GC) in mathematics education, its use in the teaching and learning process appears to be limited. The obvious need to revisit the teaching and learning of Probability has resulted in this study, i.e. to incorporate…
Research advances in probability of causation calculation of radiogenic neoplasms
International Nuclear Information System (INIS)
Ning Jing; Yuan Yong; Xie Xiangdong; Yang Guoshan
2009-01-01
Probability of causation (PC) was used to facilitate the adjudication of compensation claims for cancers diagnosed following exposure to ionizing radiation. In this article, the excess cancer risk assessment models used for PC calculation are reviewed. Cancer risk transfer models between different populations, dependence of cancer risk on dose and dose rate, modification by epidemiological risk factors and application of PC are also discussed in brief. (authors)
Calculation of cranial nerve complication probability for acoustic neuroma radiosurgery
International Nuclear Information System (INIS)
Meeks, Sanford L.; Buatti, John M.; Foote, Kelly D.; Friedman, William A.; Bova, Francis J.
2000-01-01
Purpose: Estimations of complications from stereotactic radiosurgery usually rely simply on dose-volume or dose-diameter isoeffect curves. Due to the sparse clinical data available, these curves have typically not considered the target location in the brain, target histology, or treatment plan conformality as parameters in the calculation. In this study, a predictive model was generated to estimate the probability of cranial neuropathies as a result of acoustic schwannoma radiosurgery. Methods and Materials: The dose-volume histogram reduction scheme was used to calculate the normal tissue complication probability (NTCP) from brainstem dose-volume histograms. The model's fitting parameters were optimized to provide the best fit to the observed complication data for acoustic neuroma patients treated with stereotactic radiosurgery at the University of Florida. The calculation was then applied to the remainder of the patients in the database. Results: The best fit to our clinical data was obtained using n = 0.04, m = 0.15, and no. alphano. /no. betano. = 2.1 Gy -1 . Although the fitting parameter m is relatively consistent with ranges found in the literature, both the volume parameter, n, and no. alphano. /no. betano. are much smaller than the values quoted in the literature. The fit to our clinical data indicates that brainstem, or possibly a specific portion of the brainstem, is more radiosensitive than the parameters in the literature indicate, and that there is very little volume effect; in other words, irradiation of a small fraction of the brainstem yields NTCPs that are nearly as high as those calculated for entire volume irradiation. These new fitting parameters are specific to acoustic neuroma radiosurgery, and the small volume effect that we observe may be an artifact of the fixed relationship of acoustic tumors to specific regions of the brainstem. Applying the model to our patient database, we calculate an average NTCP of 7.2% for patients who had no
On calculating the probability of a set of orthologous sequences
Directory of Open Access Journals (Sweden)
Junfeng Liu
2009-02-01
Full Text Available Junfeng Liu1,2, Liang Chen3, Hongyu Zhao4, Dirk F Moore1,2, Yong Lin1,2, Weichung Joe Shih1,21Biometrics Division, The Cancer, Institute of New Jersey, New Brunswick, NJ, USA; 2Department of Biostatistics, School of Public Health, University of Medicine and Dentistry of New Jersey, Piscataway, NJ, USA; 3Department of Biological Sciences, University of Southern California, Los Angeles, CA, USA; 4Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT, USAAbstract: Probabilistic DNA sequence models have been intensively applied to genome research. Within the evolutionary biology framework, this article investigates the feasibility for rigorously estimating the probability of a set of orthologous DNA sequences which evolve from a common progenitor. We propose Monte Carlo integration algorithms to sample the unknown ancestral and/or root sequences a posteriori conditional on a reference sequence and apply pairwise Needleman–Wunsch alignment between the sampled and nonreference species sequences to estimate the probability. We test our algorithms on both simulated and real sequences and compare calculated probabilities from Monte Carlo integration to those induced by single multiple alignment.Keywords: evolution, Jukes–Cantor model, Monte Carlo integration, Needleman–Wunsch alignment, orthologous
Jet identification based on probability calculations using Bayes' theorem
International Nuclear Information System (INIS)
Jacobsson, C.; Joensson, L.; Lindgren, G.; Nyberg-Werther, M.
1994-11-01
The problem of identifying jets at LEP and HERA has been studied. Identification using jet energies and fragmentation properties was treated separately in order to investigate the degree of quark-gluon separation that can be achieved by either of these approaches. In the case of the fragmentation-based identification, a neural network was used, and a test of the dependence on the jet production process and the fragmentation model was done. Instead of working with the separation variables directly, these have been used to calculate probabilities of having a specific type of jet, according to Bayes' theorem. This offers a direct interpretation of the performance of the jet identification and provides a simple means of combining the results of the energy- and fragmentation-based identifications. (orig.)
Probability Density Estimation Using Neural Networks in Monte Carlo Calculations
International Nuclear Information System (INIS)
Shim, Hyung Jin; Cho, Jin Young; Song, Jae Seung; Kim, Chang Hyo
2008-01-01
The Monte Carlo neutronics analysis requires the capability for a tally distribution estimation like an axial power distribution or a flux gradient in a fuel rod, etc. This problem can be regarded as a probability density function estimation from an observation set. We apply the neural network based density estimation method to an observation and sampling weight set produced by the Monte Carlo calculations. The neural network method is compared with the histogram and the functional expansion tally method for estimating a non-smooth density, a fission source distribution, and an absorption rate's gradient in a burnable absorber rod. The application results shows that the neural network method can approximate a tally distribution quite well. (authors)
Problems involved in calculating the probability of rare occurrences
International Nuclear Information System (INIS)
Tittes, E.
1986-01-01
Also with regard to the characteristics such as occurrence probability or occurrence rate, there are limits which have to be observed, or else probability data and thus the concept of determinable risk itself will lose its practical value. The mathematical models applied for probability assessment are based on data supplied by the insurance companies, reliability experts in the automobile industry, or by planning experts in the field of traffic or information supply. (DG) [de
Flipping Out: Calculating Probability with a Coin Game
Degner, Kate
2015-01-01
In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…
Method to Calculate Accurate Top Event Probability in a Seismic PSA
Energy Technology Data Exchange (ETDEWEB)
Jung, Woo Sik [Sejong Univ., Seoul (Korea, Republic of)
2014-05-15
ACUBE(Advanced Cutset Upper Bound Estimator) calculates the top event probability and importance measures from cutsets by dividing cutsets into major and minor groups depending on the cutset probability, where the cutsets that have higher cutset probability are included in the major group and the others in minor cutsets, converting major cutsets into a Binary Decision Diagram (BDD). By applying the ACUBE algorithm to the seismic PSA cutsets, the accuracy of a top event probability and importance measures can be significantly improved. ACUBE works by dividing the cutsets into two groups (higher and lower cutset probability groups), calculating the top event probability and importance measures in each group, and combining the two results from the two groups. Here, ACUBE calculates the top event probability and importance measures of the higher cutset probability group exactly. On the other hand, ACUBE calculates these measures of the lower cutset probability group with an approximation such as MCUB. The ACUBE algorithm is useful for decreasing the conservatism that is caused by approximating the top event probability and importance measure calculations with given cutsets. By applying the ACUBE algorithm to the seismic PSA cutsets, the accuracy of a top event probability and importance measures can be significantly improved. This study shows that careful attention should be paid and an appropriate method be provided in order to avoid the significant overestimation of the top event probability calculation. Due to the strength of ACUBE that is explained in this study, the ACUBE became a vital tool for calculating more accurate CDF of the seismic PSA cutsets than the conventional probability calculation method.
Shiryaev, A N
1996-01-01
This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter Many examples are discussed in detail, and there are a large number of exercises The book is accessible to advanced undergraduates and can be used as a text for self-study This new edition contains substantial revisions and updated references The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures Proofs for a number of some important results which were merely stated in the first edition have been added The author included new material on the probability of large deviations, and on the central limit theorem for sums of dependent random variables
Calculation of transition probabilities using the multiconfiguration Dirac-Fock method
International Nuclear Information System (INIS)
Kim, Yong Ki; Desclaux, Jean Paul; Indelicato, Paul
1998-01-01
The performance of the multiconfiguration Dirac-Fock (MCDF) method in calculating transition probabilities of atoms is reviewed. In general, the MCDF wave functions will lead to transition probabilities accurate to ∼ 10% or better for strong, electric-dipole allowed transitions for small atoms. However, it is more difficult to get reliable transition probabilities for weak transitions. Also, some MCDF wave functions for a specific J quantum number may not reduce to the appropriate L and S quantum numbers in the nonrelativistic limit. Transition probabilities calculated from such MCDF wave functions for nonrelativistically forbidden transitions are unreliable. Remedies for such cases are discussed
International Nuclear Information System (INIS)
Wasastjerna, F.; Lux, I.
1980-03-01
A transmission probability method implemented in the program TPHEX is described. This program was developed for the calculation of neutron flux distributions in hexagonal light water reactor fuel assemblies. The accuracy appears to be superior to diffusion theory, and the computation time is shorter than that of the collision probability method. (author)
Sloma, Michael F.; Mathews, David H.
2016-01-01
RNA secondary structure prediction is widely used to analyze RNA sequences. In an RNA partition function calculation, free energy nearest neighbor parameters are used in a dynamic programming algorithm to estimate statistical properties of the secondary structure ensemble. Previously, partition functions have largely been used to estimate the probability that a given pair of nucleotides form a base pair, the conditional stacking probability, the accessibility to binding of a continuous stretch of nucleotides, or a representative sample of RNA structures. Here it is demonstrated that an RNA partition function can also be used to calculate the exact probability of formation of hairpin loops, internal loops, bulge loops, or multibranch loops at a given position. This calculation can also be used to estimate the probability of formation of specific helices. Benchmarking on a set of RNA sequences with known secondary structures indicated that loops that were calculated to be more probable were more likely to be present in the known structure than less probable loops. Furthermore, highly probable loops are more likely to be in the known structure than the set of loops predicted in the lowest free energy structures. PMID:27852924
The risk of major nuclear accident: calculation and perception of probabilities
International Nuclear Information System (INIS)
Leveque, Francois
2013-01-01
Whereas before the Fukushima accident, already eight major accidents occurred in nuclear power plants, a number which is higher than that expected by experts and rather close to that corresponding of people perception of risk, the author discusses how to understand these differences and reconcile observations, objective probability of accidents and subjective assessment of risks, why experts have been over-optimistic, whether public opinion is irrational regarding nuclear risk, and how to measure risk and its perception. Thus, he addresses and discusses the following issues: risk calculation (cost, calculated frequency of major accident, bias between the number of observed accidents and model predictions), perceived probabilities and aversion for disasters (perception biases of probability, perception biases unfavourable to nuclear), the Bayes contribution and its application (Bayes-Laplace law, statistics, choice of an a priori probability, prediction of the next event, probability of a core fusion tomorrow)
Calculation of magnetization curves and probability distribution for monoclinic and uniaxial systems
International Nuclear Information System (INIS)
Sobh, Hala A.; Aly, Samy H.; Yehia, Sherif
2013-01-01
We present the application of a simple classical statistical mechanics-based model to selected monoclinic and hexagonal model systems. In this model, we treat the magnetization as a classical vector whose angular orientation is dictated by the laws of equilibrium classical statistical mechanics. We calculate for these anisotropic systems, the magnetization curves, energy landscapes and probability distribution for different sets of relevant parameters and magnetic fields of different strengths and directions. Our results demonstrate a correlation between the most probable orientation of the magnetization vector, the system's parameters, and the external magnetic field. -- Highlights: ► We calculate magnetization curves and probability angular distribution of the magnetization. ► The magnetization curves are consistent with probability results for the studied systems. ► Monoclinic and hexagonal systems behave differently due to their different anisotropies
'PRIZE': A program for calculating collision probabilities in R-Z geometry
International Nuclear Information System (INIS)
Pitcher, H.H.W.
1964-10-01
PRIZE is an IBM7090 program which computes collision probabilities for systems with axial symmetry and outputs them on cards in suitable format for the PIP1 program. Its method of working, data requirements, output, running time and accuracy are described. The program has been used to compute non-escape (self-collision) probabilities of finite circular cylinders, and a table is given by which non-escape probabilities of slabs, finite and infinite circular cylinders, infinite square cylinders, cubes, spheres and hemispheres may quickly be calculated to 1/2% or better. (author)
'PRIZE': A program for calculating collision probabilities in R-Z geometry
Energy Technology Data Exchange (ETDEWEB)
Pitcher, H.H.W. [General Reactor Physics Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)
1964-10-15
PRIZE is an IBM7090 program which computes collision probabilities for systems with axial symmetry and outputs them on cards in suitable format for the PIP1 program. Its method of working, data requirements, output, running time and accuracy are described. The program has been used to compute non-escape (self-collision) probabilities of finite circular cylinders, and a table is given by which non-escape probabilities of slabs, finite and infinite circular cylinders, infinite square cylinders, cubes, spheres and hemispheres may quickly be calculated to 1/2% or better. (author)
Calculation of the exit probability of a particle from a cylinder of matter
International Nuclear Information System (INIS)
Ertaud, A.; Mercier, C.
1949-02-01
In the elementary calculation of the ε coefficient and of the slowing down length inside a nuclear pile made of a network of cylindrical rods, it is necessary to know the exit probability of a neutron initially located inside a cylinder filled up with a given substance. This probability is the ratio between the number of output neutrons and the number of neutrons produced inside the surface of the cylinder. This report makes the resolution of this probabilistic equation (integral calculation) both for the cylindrical case and for the spherical case. (J.S.)
International Nuclear Information System (INIS)
Ozgener, B.; Ozgener, H.A.
2005-01-01
A multiregion, multigroup collision probability method with white boundary condition is developed for thermalization calculations of light water moderated reactors. Hydrogen scatterings are treated by Nelkin's kernel while scatterings from other nuclei are assumed to obey the free-gas scattering kernel. The isotropic return (white) boundary condition is applied directly by using the appropriate collision probabilities. Comparisons with alternate numerical methods show the validity of the present formulation. Comparisons with some experimental results indicate that the present formulation is capable of calculating disadvantage factors which are closer to the experimental results than alternative methods
International Nuclear Information System (INIS)
Shang Yanlong; Cai Qi; Chen Lisheng; Zhang Yangwei
2012-01-01
In this paper, the combined method of response surface and importance sampling was applied for calculation of parameter failure probability of the thermodynamic system. The mathematics model was present for the parameter failure of physics process in the thermodynamic system, by which the combination arithmetic model of response surface and importance sampling was established, then the performance degradation model of the components and the simulation process of parameter failure in the physics process of thermodynamic system were also present. The parameter failure probability of the purification water system in nuclear reactor was obtained by the combination method. The results show that the combination method is an effective method for the calculation of the parameter failure probability of the thermodynamic system with high dimensionality and non-linear characteristics, because of the satisfactory precision with less computing time than the direct sampling method and the drawbacks of response surface method. (authors)
A semi-mechanistic approach to calculate the probability of fuel defects
International Nuclear Information System (INIS)
Tayal, M.; Millen, E.; Sejnoha, R.
1992-10-01
In this paper the authors describe the status of a semi-mechanistic approach to the calculation of the probability of fuel defects. This approach expresses the defect probability in terms of fundamental parameters such as local stresses, local strains, and fission product concentration. The calculations of defect probability continue to reflect the influences of the conventional parameters like power ramp, burnup and CANLUB. In addition, the new approach provides a mechanism to account for the impacts of additional factors involving detailed fuel design and reactor operation, for example pellet density, pellet shape and size, sheath diameter and thickness, pellet/sheath clearance, and coolant temperature and pressure. The approach has been validated against a previous empirical correlation. AN illustrative example shows how the defect thresholds are influenced by changes in the internal design of the element and in the coolant pressure. (Author) (7 figs., tab., 12 refs.)
Failure Probability Calculation Method Using Kriging Metamodel-based Importance Sampling Method
Energy Technology Data Exchange (ETDEWEB)
Lee, Seunggyu [Korea Aerospace Research Institue, Daejeon (Korea, Republic of); Kim, Jae Hoon [Chungnam Nat’l Univ., Daejeon (Korea, Republic of)
2017-05-15
The kernel density was determined based on sampling points obtained in a Markov chain simulation and was assumed to be an important sampling function. A Kriging metamodel was constructed in more detail in the vicinity of a limit state. The failure probability was calculated based on importance sampling, which was performed for the Kriging metamodel. A pre-existing method was modified to obtain more sampling points for a kernel density in the vicinity of a limit state. A stable numerical method was proposed to find a parameter of the kernel density. To assess the completeness of the Kriging metamodel, the possibility of changes in the calculated failure probability due to the uncertainty of the Kriging metamodel was calculated.
Cognitive-psychology expertise and the calculation of the probability of a wrongful conviction.
Rouder, Jeffrey N; Wixted, John T; Christenfeld, Nicholas J S
2018-05-08
Cognitive psychologists are familiar with how their expertise in understanding human perception, memory, and decision-making is applicable to the justice system. They may be less familiar with how their expertise in statistical decision-making and their comfort working in noisy real-world environments is just as applicable. Here we show how this expertise in ideal-observer models may be leveraged to calculate the probability of guilt of Gary Leiterman, a man convicted of murder on the basis of DNA evidence. We show by common probability theory that Leiterman is likely a victim of a tragic contamination event rather than a murderer. Making any calculation of the probability of guilt necessarily relies on subjective assumptions. The conclusion about Leiterman's innocence is not overly sensitive to the assumptions-the probability of innocence remains high for a wide range of reasonable assumptions. We note that cognitive psychologists may be well suited to make these calculations because as working scientists they may be comfortable with the role a reasonable degree of subjectivity plays in analysis.
International Nuclear Information System (INIS)
Humbert, Ph.
2005-01-01
In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)
Calculating failure probabilities for TRISO-coated fuel particles using an integral formulation
International Nuclear Information System (INIS)
Miller, Gregory K.; Maki, John T.; Knudson, Darrell L.; Petti, David A.
2010-01-01
The fundamental design for a gas-cooled reactor relies on the safe behavior of the coated particle fuel. The coating layers surrounding the fuel kernels in these spherical particles, termed the TRISO coating, act as a pressure vessel that retains fission products. The quality of the fuel is reflected in the number of particle failures that occur during reactor operation, where failed particles become a source for fission products that can then diffuse through the fuel element. The failure probability for any batch of particles, which has traditionally been calculated using the Monte Carlo method, depends on statistical variations in design parameters and on variations in the strengths of coating layers among particles in the batch. An alternative approach to calculating failure probabilities is developed herein that uses direct numerical integration of a failure probability integral. Because this is a multiple integral where the statistically varying parameters become integration variables, a fast numerical integration approach is also developed. In sample cases analyzed involving multiple failure mechanisms, results from the integration methods agree closely with Monte Carlo results. Additionally, the fast integration approach, particularly, is shown to significantly improve efficiency of failure probability calculations. These integration methods have been implemented in the PARFUME fuel performance code along with the Monte Carlo method, where each serves to verify accuracy of the others.
Using the probability method for multigroup calculations of reactor cells in a thermal energy range
International Nuclear Information System (INIS)
Rubin, I.E.; Pustoshilova, V.S.
1984-01-01
The possibility of using the transmission probability method with performance inerpolation for determining spatial-energy neutron flux distribution in cells of thermal heterogeneous reactors is considered. The results of multigroup calculations of several uranium-water plane and cylindrical cells with different fuel enrichment in a thermal energy range are given. A high accuracy of results is obtained with low computer time consumption. The use of the transmission probability method is particularly reasonable in algorithms of the programmes compiled computer with significant reserve of internal memory
Calculation of the tunneling time using the extended probability of the quantum histories approach
International Nuclear Information System (INIS)
Rewrujirek, Jiravatt; Hutem, Artit; Boonchui, Sutee
2014-01-01
The dwell time of quantum tunneling has been derived by Steinberg (1995) [7] as a function of the relation between transmission and reflection times τ t and τ r , weighted by the transmissivity and the reflectivity. In this paper, we reexamine the dwell time using the extended probability approach. The dwell time is calculated as the weighted average of three mutually exclusive events. We consider also the scattering process due to a resonance potential in the long-time limit. The results show that the dwell time can be expressed as the weighted sum of transmission, reflection and internal probabilities.
International Nuclear Information System (INIS)
Kang, Dae Il; Han, Sang Hoon
2006-01-01
RG 1.177 requires that the conditional risk (incremental conditional core damage probability and incremental conditional large early release probability: ICCDP and ICLERP), given that a specific component is out of service (OOS), be quantified for a permanent change of the allowed outage time (AOT) of a safety system. An AOT is the length of time that a particular component or system is permitted to be OOS while the plant is operating. The ICCDP is defined as: ICCDP = [(conditional CDF with the subject equipment OOS)- (baseline CDF with nominal expected equipment unavailabilities)] [duration of the single AOT under consideration]. Any event enabling the component OOS can initiate the time clock for the limiting condition of operation for a nuclear power plant. Thus, the largest ICCDP among the ICCDPs estimated from any occurrence of the basic events for the component fault tree should be selected for determining whether the AOT can be extended or not. If the component is under a preventive maintenance, the conditional risk can be straightforwardly calculated without changing the CCF probability. The main concern is the estimations of the CCF probability because there are the possibilities of the failures of other similar components due to the same root causes. The quantifications of the risk, given that a subject equipment is in a failed state, are performed by setting the identified event of subject equipment to TRUE. The CCF probabilities are also changed according to the identified failure cause. In the previous studies, however, the ICCDP was quantified with the consideration of the possibility of a simultaneous occurrence of two CCF events. Based on the above, we derived the formulas of the CCF probabilities for the cases where a specific component is in a failed state and we presented sample calculation results of the ICCDP for the low pressure safety injection system (LPSIS) of Ulchin Unit 3
The use of collision probabilities in calculations for light water reactors
International Nuclear Information System (INIS)
Janse van Rensburg, J.
1984-01-01
A procedure is developed to prepare representative two-group neutron data for fuel elements of pressurized water reactors. This procedure is based on the method of collision probabilities and this theory is completely derived and implemented. The computer code, CLUPCO, which is developed for this purpose, is briefly discussed. The accuracy of the method is compared with other established calculational methods by means of experimental results. 30 figs., 29 tabs., 71 refs
Energy Technology Data Exchange (ETDEWEB)
Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ebeida, Mohamed Salah [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Romero, Vicente J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Swiler, Laura Painton [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rushdi, Ahmad A. [Univ. of Texas, Austin, TX (United States); Abdelkader, Ahmad [Univ. of Maryland, College Park, MD (United States)
2015-09-01
This SAND report summarizes our work on the Sandia National Laboratory LDRD project titled "Efficient Probability of Failure Calculations for QMU using Computational Geometry" which was project #165617 and proposal #13-0144. This report merely summarizes our work. Those interested in the technical details are encouraged to read the full published results, and contact the report authors for the status of the software and follow-on projects.
SILENE and TDT: A code for collision probability calculations in XY geometries
International Nuclear Information System (INIS)
Sanchez, R.; Stankovski, Z.
1993-01-01
Collision probability methods are routinely used for cell and assembly multigroup transport calculations in core design tasks. Collision probability methods use a specialized tracking routine to compute neutron trajectories within a given geometric object. These trajectories are then used to generate the appropriate collision matrices in as many groups as required. Traditional tracking routines are based on open-quotes globalclose quotes geometric descriptions (such as regular meshes) and are not able to cope with the geometric detail required in actual core calculations. Therefore, users have to modify their geometry in order to match the geometric model accepted by the tracking routine, introducing thus a modeling error whose evaluation requires the use of a open-quotes referenceclose quotes method. Recently, an effort has been made to develop more flexible tracking routines either by directly adopting tracking Monte Carlo techniques or by coding of complicated geometries. Among these, the SILENE and TDT package is being developed at the Commissariat a l' Energie Atomique to provide routine as well as reference calculations in arbitrarily shaped XY geometries. This package combines a direct graphical acquisition system (SILENE) together with a node-based collision probability code for XY geometries (TDT)
International Nuclear Information System (INIS)
Calabrese, C.R.; Grant, C.R.
1990-01-01
This work presents comparisons between measured fluxes obtained by activation of Manganese foils in the light water, enriched uranium research pool reactor RA-2 MTR (Materials Testing Reactors) fuel element) and fluxes calculated by the finite element method FEM using DELFIN code, and describes the heterogeneus finite elements by a set of solutions of the transport equations for several different configurations obtained using the collision probability code HUEMUL. The agreement between calculated and measured fluxes is good, and the advantage of using FEM is showed because to obtain the flux distribution with same detail using an usual diffusion calculation it would be necessary 12000 mesh points against the 2000 points that FEM uses, hence the processing time is reduced in a factor ten. An interesting alternative to use in MTR fuel management is presented. (Author) [es
[CALCULATION OF THE PROBABILITY OF METALS INPUT INTO AN ORGANISM WITH DRINKING POTABLE WATERS].
Tunakova, Yu A; Fayzullin, R I; Valiev, V S
2015-01-01
The work was performed in framework of the State program for the improvement of the competitiveness of Kazan (Volga) Federal University among the world's leading research and education centers and subsidies unveiled to Kazan Federal University to perform public tasks in the field of scientific research. In the current methodological recommendations "Guide for assessing the risk to public health under the influence of chemicals that pollute the environment," P 2.1.10.1920-04 there is regulated the determination of quantitative and/or qualitative characteristics of the harmful effects to human health from exposure to environmental factors. We proposed to complement the methodological approaches presented in P 2.1.10.1920-04, with the estimation of the probability of pollutants input in the body with drinking water which is the greater, the higher the order of the excess of the actual concentrations of the substances in comparison with background concentrations. In the paper there is proposed a method of calculation of the probability of exceeding the actual concentrations of metal cations above the background in samples of drinking water consumed by the population, which were selected at the end points of consumption in houses and apartments, to accommodate the passage of secondary pollution ofwater pipelines and distributing paths. Research was performed on the example of Kazan, divided into zones. The calculation of probabilities was made with the use of Bayes' theorem.
Computing Moment-Based Probability Tables for Self-Shielding Calculations in Lattice Codes
International Nuclear Information System (INIS)
Hebert, Alain; Coste, Mireille
2002-01-01
As part of the self-shielding model used in the APOLLO2 lattice code, probability tables are required to compute self-shielded cross sections for coarse energy groups (typically with 99 or 172 groups). This paper describes the replacement of the multiband tables (typically with 51 subgroups) with moment-based tables in release 2.5 of APOLLO2. An improved Ribon method is proposed to compute moment-based probability tables, allowing important savings in CPU resources while maintaining the accuracy of the self-shielding algorithm. Finally, a validation is presented where the absorption rates obtained with each of these techniques are compared with exact values obtained using a fine-group elastic slowing-down calculation in the resolved energy domain. Other results, relative to the Rowland's benchmark and to three assembly production cases, are also presented
Calculation of ruin probabilities for a dense class of heavy tailed distributions
DEFF Research Database (Denmark)
Bladt, Mogens; Nielsen, Bo Friis; Samorodnitsky, Gennady
2015-01-01
In this paper, we propose a class of infinite-dimensional phase-type distributions with finitely many parameters as models for heavy tailed distributions. The class of finite-dimensional phase-type distributions is dense in the class of distributions on the positive reals and may hence approximate...... any such distribution. We prove that formulas from renewal theory, and with a particular attention to ruin probabilities, which are true for common phase-type distributions also hold true for the infinite-dimensional case. We provide algorithms for calculating functionals of interest...... such as the renewal density and the ruin probability. It might be of interest to approximate a given heavy tailed distribution of some other type by a distribution from the class of infinite-dimensional phase-type distributions and to this end we provide a calibration procedure which works for the approximation...
International Nuclear Information System (INIS)
Bosevski, T.
1986-01-01
An improved collision probability method for thermal-neutron-flux calculation in a cylindrical reactor cell has been developed. Expanding the neutron flux and source into a series of even powers of the radius, one' gets a convenient method for integration of the one-energy group integral transport equation. It is shown that it is possible to perform an analytical integration in the x-y plane in one variable and to use the effective Gaussian integration over another one. Choosing a convenient distribution of space points in fuel and moderator the transport matrix calculation and cell reaction rate integration were condensed. On the basis of the proposed method, the computer program DISKRET for the ZUSE-Z 23 K computer has been written. The suitability of the proposed method for the calculation of the thermal-neutron-flux distribution in a reactor cell can be seen from the test results obtained. Compared with the other collision probability methods, the proposed treatment excels with a mathematical simplicity and a faster convergence. (author)
Failures probability calculation of the energy supply of the Angra-1 reactor rods assembly
International Nuclear Information System (INIS)
Borba, P.R.
1978-01-01
This work analyses the electric power system of the Angra I PWR plant. It is demonstrated that this system is closely coupled with the safety engineering features, which are the equipments provided to prevent, limit, or mitigate the release of radioactive material and to permit the safe reactor shutdown. Event trees are used to analyse the operation of those systems which can lead to the release of radioactivity following a specified initial event. The fault trees technique is used to calculate the failure probability of the on-site electric power system [pt
Energy Technology Data Exchange (ETDEWEB)
Wampler, William R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Myers, Samuel M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Modine, Normand A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-09-01
The energy-dependent probability density of tunneled carrier states for arbitrarily specified longitudinal potential-energy profiles in planar bipolar devices is numerically computed using the scattering method. Results agree accurately with a previous treatment based on solution of the localized eigenvalue problem, where computation times are much greater. These developments enable quantitative treatment of tunneling-assisted recombination in irradiated heterojunction bipolar transistors, where band offsets may enhance the tunneling effect by orders of magnitude. The calculations also reveal the density of non-tunneled carrier states in spatially varying potentials, and thereby test the common approximation of uniform- bulk values for such densities.
Cheng, Chih-Wen; Hua, Jian; Hwang, Daw-Shang
2017-10-01
An important marine pollution issue identified by the International Maritime Organization (IMO) is NO x emissions; however, the stipulated method for determining the NO x certification value does not reflect the actual high emission factors of slow-speed two-stroke diesel engines over long-term slow steaming. In this study, an accurate method is presented for calculating the NO x emission factors and total amount of NO x emissions by using the actual power probabilities of the diesel engines in four types of bulk carriers. The proposed method is suitable for all types and purposes of diesel engines, is not restricted to any operating modes, and is highly accurate. Moreover, it is recommended that the IMO-stipulated certification value calculation method be modified accordingly to genuinely reduce the amount of NO x emissions. The successful achievement of this level of reduction will help improve the air quality, especially in coastal and port areas, and the health of local residents. As per the IMO, the NO x emission certification value of marine diesel engines having a rated power over 130 kW must be obtained using specified weighting factor (WF)-based calculation. However, this calculation fails to represent the current actual situation. Effective emission reductions of 6.91% (at sea) and 31.9% (in ports) were achieved using a mathematical model of power probability functions. Thus, we strongly recommend amending the certification value of NO x Technical Code 2008 (NTC 2008) by removing the WF constraints, such that the NO x emissions of diesel engines is lower than the Tier-limits at any load level to obtain genuine NO x emission reductions.
Calculating Absolute Transition Probabilities for Deformed Nuclei in the Rare-Earth Region
Stratman, Anne; Casarella, Clark; Aprahamian, Ani
2017-09-01
Absolute transition probabilities are the cornerstone of understanding nuclear structure physics in comparison to nuclear models. We have developed a code to calculate absolute transition probabilities from measured lifetimes, using a Python script and a Mathematica notebook. Both of these methods take pertinent quantities such as the lifetime of a given state, the energy and intensity of the emitted gamma ray, and the multipolarities of the transitions to calculate the appropriate B(E1), B(E2), B(M1) or in general, any B(σλ) values. The program allows for the inclusion of mixing ratios of different multipolarities and the electron conversion of gamma-rays to correct for their intensities, and yields results in absolute units or results normalized to Weisskopf units. The code has been tested against available data in a wide range of nuclei from the rare earth region (28 in total), including 146-154Sm, 154-160Gd, 158-164Dy, 162-170Er, 168-176Yb, and 174-182Hf. It will be available from the Notre Dame Nuclear Science Laboratory webpage for use by the community. This work was supported by the University of Notre Dame College of Science, and by the National Science Foundation, under Contract PHY-1419765.
International Nuclear Information System (INIS)
Watterson, Ian G.
2007-01-01
Full text: he IPCC Fourth Assessment Report (Meehl ef al. 2007) presents multi-model means of the CMIP3 simulations as projections of the global climate change over the 21st century under several SRES emission scenarios. To assess the possible range of change for Australia based on the CMIP3 ensemble, we can follow Whetton etal. (2005) and use the 'pattern scaling' approach, which separates the uncertainty in the global mean warming from that in the local change per degree of warming. This study presents several ways of representing these two factors as probability density functions (PDFs). The beta distribution, a smooth, bounded, function allowing skewness, is found to provide a useful representation of the range of CMIP3 results. A weighting of models based on their skill in simulating seasonal means in the present climate over Australia is included. Dessai ef al. (2005) and others have used Monte-Carlo sampling to recombine such global warming and scaled change factors into values of net change. Here, we use a direct integration of the product across the joint probability space defined by the two PDFs. The result is a cumulative distribution function (CDF) for change, for each variable, location, and season. The median of this distribution provides a best estimate of change, while the 10th and 90th percentiles represent a likely range. The probability of exceeding a specified threshold can also be extracted from the CDF. The presentation focuses on changes in Australian temperature and precipitation at 2070 under the A1B scenario. However, the assumption of linearity behind pattern scaling allows results for different scenarios and times to be simply obtained. In the case of precipitation, which must remain non-negative, a simple modification of the calculations (based on decreases being exponential with warming) is used to avoid unrealistic results. These approaches are currently being used for the new CSIRO/ Bureau of Meteorology climate projections
No shortcut solution to the problem of Y-STR match probability calculation.
Caliebe, Amke; Jochens, Arne; Willuweit, Sascha; Roewer, Lutz; Krawczak, Michael
2015-03-01
Match probability calculation is deemed much more intricate for lineage genetic markers, including Y-chromosomal short tandem repeats (Y-STRs), than for autosomal markers. This is because, owing to the lack of recombination, strong interdependence between markers is likely, which implies that haplotype frequency estimates cannot simply be obtained through the multiplication of allele frequency estimates. As yet, however, the practical relevance of this problem has not been studied in much detail using real data. In fact, such scrutiny appears well warranted because the high mutation rates of Y-STRs and the possibility of backward mutation should have worked against the statistical association of Y-STRs. We examined haplotype data of 21 markers included in the PowerPlex(®)Y23 set (PPY23, Promega Corporation, Madison, WI) originating from six different populations (four European and two Asian). Assessing the conditional entropies of the markers, given different subsets of markers from the same panel, we demonstrate that the PowerPlex(®)Y23 set cannot be decomposed into smaller marker subsets that would be (conditionally) independent. Nevertheless, in all six populations, >94% of the joint entropy of the 21 markers is explained by the seven most rapidly mutating markers. Although this result might render a reduction in marker number a sensible option for practical casework, the partial haplotypes would still be almost as diverse as the full haplotypes. Therefore, match probability calculation remains difficult and calls for the improvement of currently available methods of haplotype frequency estimation. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
New results to BDD truncation method for efficient top event probability calculation
International Nuclear Information System (INIS)
Mo, Yuchang; Zhong, Farong; Zhao, Xiangfu; Yang, Quansheng; Cui, Gang
2012-01-01
A Binary Decision Diagram (BDD) is a graph-based data structure that calculates an exact top event probability (TEP). It has been a very difficult task to develop an efficient BDD algorithm that can solve a large problem since its memory consumption is very high. Recently, in order to solve a large reliability problem within limited computational resources, Jung presented an efficient method to maintain a small BDD size by a BDD truncation during a BDD calculation. In this paper, it is first identified that Jung's BDD truncation algorithm can be improved for a more practical use. Then, a more efficient truncation algorithm is proposed in this paper, which can generate truncated BDD with smaller size and approximate TEP with smaller truncation error. Empirical results showed this new algorithm uses slightly less running time and slightly more storage usage than Jung's algorithm. It was also found, that designing a truncation algorithm with ideal features for every possible fault tree is very difficult, if not impossible. The so-called ideal features of this paper would be that with the decrease of truncation limits, the size of truncated BDD converges to the size of exact BDD, but should never be larger than exact BDD.
Energy Technology Data Exchange (ETDEWEB)
Mooney, L. G.
1963-06-15
Calculations of neutron penetration probabilities were performed to evaluate the Monte Carlo Multilayer Slab Penetration Procedure. A 9-in. polyethylene alab was chosen for the calculations and results were compared with experimental data. The calculated and measured dose rates agree within 20% for all exit polar angles. The calculations indicate that incident neutrons with energies less than 2.5 Mev do not contribute significantly to the transmitted dose rate. (auth)
Risk, probability and uncertainty in the calculations of gas cooled reactor of PBMR type. Part 2
International Nuclear Information System (INIS)
Serbanescu, Dan
2004-01-01
The paper presents the main conclusions of the insights to a cooled gas reactor from the perspective of the following notions: probability, uncertainty, entropy and risk. Some results of the on-going comparison between the insights obtained from three models and approaches are presented. The approaches consider the Pebble Bed Module Reactor (PBMR) NPP as a thermodynamic installation and as hierarchical system with or without considering the information exchange between its various levels. The existing model was a basis for a PRA going on in phases for PBMR. In the first part of this paper results from phase II of this PRA were presented. Further activities going on in the preparation for phase II PRA and for the development of a specific application of using PRA during the design phases for PBMR are undergoing with some preliminary results and conclusions. However, for the purposes of this paper and the comparative review of various models in the part two one presents the risk model (model B) based on the assumption and ideas laid down at the basis of the future inter-comparison of this model with other plant models. The assumptions concern: the uncertainties for the quantification of frequencies; list of initiated events; interfaces with the deterministic calculation; integrated evaluation of all the plant states; risk of the release of radionuclide; the balance between the number and function of the active systems and the passive systems; systems interdependencies in PBMR PRA; use of PRA for the evaluation of the impact of various design changes on plant risk. The model B allows basically evaluating the level of risk of the plant by calculating it as a result of acceptance challenge to the plant. By using this model the departure from a reference state is given by the variation in the risk metrics adopted for the study. The paper present also the synergetic model (model C). The evaluation of risk in the model C is considering also the information process. The
International Nuclear Information System (INIS)
Tercariol, Cesar Augusto Sangaletti; Kiipper, Felipe de Moura; Martinez, Alexandre Souto
2007-01-01
Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability P (d,N) m,n that an arbitrary point is the mth nearest neighbour to its own nth nearest neighbour (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we propose a simpler derivation of Cox probabilities, where we stress the role played by the system dimensionality d. In the limit d → ∞, the distances between pair of points become independent (random link model) and closed analytical forms for the neighbourhood probabilities are obtained both for the thermodynamic limit and finite-size system. Breaking the distance symmetry constraint drives us to the random map model, for which the Cox probabilities are obtained for two cases: whether a point is its own nearest neighbour or not
International Nuclear Information System (INIS)
Begnozzi, L.; Gentile, F.P.; Di Nallo, A.M.; Chiatti, L.; Zicari, C.; Consorti, R.; Benassi, M.
1994-01-01
Since volumetric dose distributions are available with 3-dimensional radiotherapy treatment planning they can be used in statistical evaluation of response to radiation. This report presents a method to calculate the influence of dose inhomogeneity and fractionation in normal tissue complication probability evaluation. The mathematical expression for the calculation of normal tissue complication probability has been derived combining the Lyman model with the histogram reduction method of Kutcher et al. and using the normalized total dose (NTD) instead of the total dose. The fitting of published tolerance data, in case of homogeneous or partial brain irradiation, has been considered. For the same total or partial volume homogeneous irradiation of the brain, curves of normal tissue complication probability have been calculated with fraction size of 1.5 Gy and of 3 Gy instead of 2 Gy, to show the influence of fraction size. The influence of dose distribution inhomogeneity and α/β value has also been simulated: Considering α/β=1.6 Gy or α/β=4.1 Gy for kidney clinical nephritis, the calculated curves of normal tissue complication probability are shown. Combining NTD calculations and histogram reduction techniques, normal tissue complication probability can be estimated taking into account the most relevant contributing factors, including the volume effect. (orig.) [de
The risk of a major nuclear accident: calculation and perception of probabilities
International Nuclear Information System (INIS)
Leveque, Francois
2013-07-01
The accident at Fukushima Daiichi, Japan, occurred on 11 March 2011. This nuclear disaster, the third on such a scale, left a lasting mark in the minds of hundreds of millions of people. Much as Three Mile Island or Chernobyl, yet another place will be permanently associated with a nuclear power plant which went out of control. Fukushima Daiichi revived the issue of the hazards of civil nuclear power, stirring up all the associated passion and emotion. The whole of this paper is devoted to the risk of a major nuclear accident. By this we mean a failure initiating core meltdown, a situation in which the fuel rods melt and mix with the metal in their cladding. Such accidents are classified as at least level 5 on the International Nuclear Event Scale. The Three Mile Island accident, which occurred in 1979 in the United States, reached this level of severity. The explosion of reactor 4 at the Chernobyl plant in Ukraine in 1986 and the recent accident in Japan were classified as class 7, the highest grade on this logarithmic scale. The main difference between the top two levels and level 5 relates to a significant or major release of radioactive material to the environment. In the event of a level-5 accident, damage is restricted to the inside of the plant, whereas, in the case of level-7 accidents, huge areas of land, above or below the surface, and/or sea may be contaminated. Before the meltdown of reactors 1, 2 and 3 at Fukushima Daiichi, eight major accidents affecting nuclear power plants had occurred worldwide. This is a high figure compared with the one calculated by the experts. Observations in the field do not appear to fit the results of the probabilistic models of nuclear accidents produced since the 1970's. Oddly enough the number of major accidents is closer to the risk as perceived by the general public. In general we tend to overestimate any risk relating to rare, fearsome accidents. What are we to make of this divergence? How are we to reconcile
The new MPN Calculator is an easy-to-use stand alone Windows application built by Avineon, Inc. for the EPA. The calculator was built using Microsoft .NET (dot NET) version 3.5 SP1 (C#) and Windows Presentation Foundation technologies. The new calculator not only combines the mai...
Mielke, Steven L.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
Improved techniques and well-optimized basis sets are presented for application of the outgoing wave variational principle to calculate converged quantum mechanical reaction probabilities. They are illustrated with calculations for the reactions D + H2 yields HD + H with total angular momentum J = 3 and F + H2 yields HF + H with J = 0 and 3. The optimization involves the choice of distortion potential, the grid for calculating half-integrated Green's functions, the placement, width, and number of primitive distributed Gaussians, and the computationally most efficient partition between dynamically adapted and primitive basis functions. Benchmark calculations with 224-1064 channels are presented.
International Nuclear Information System (INIS)
Vargin, A.N.; Ganina, N.A.; Konyukhov, V.K.; Selyakov, V.I.
1975-01-01
The problem of calculation of collisional probabilities of rotational transitions (CPRT) in molecule-molecule and molecule-atom interactions in a three-dimensional space has been solved in this paper. A quasiclassical approach was used. The calculation of collisional probabilities of rotational transitions trajectory was carried out in the following way. The particle motion trajectory was calculated by a classical method and the time dependence of the perturbation operator was obtained, its averaging over wave functions of initial and finite states produced CPRT. The classical calculation of the molecule motion trajectory was justified by triviality of the de Broglie wavelength, compared with characteristic atomic distances, and by triviality of a transfered rotational quantum compared with the energy of translational motion of particles. The results of calculation depend on the chosen interaction potential of collisional particles. It follows from the Messy criterion that the region of nonadiabaticity of interaction may be compared with internuclear distances of a molecule. Therefore, for the description of the interaction a short-range potential is required. Analytical expressions were obtained appropriate for practical calculations for one- and two-quantum rotational transitions of diatomic molecules. The CPRT was averaged over the Maxwell distribution over velocities and analytical dependences on a gas temperature were obtained. The results of the numerical calculation of probabilities for the HCl-HCl, HCl-He, CO-CO interactions are presented to illustrate the method
International Nuclear Information System (INIS)
Elicson, Tom; Harwood, Bentley; Lucek, Heather; Bouchard, Jim
2011-01-01
Over a 12 month period, a fire PRA was developed for a DOE facility using the NUREG/CR-6850 EPRI/NRC fire PRA methodology. The fire PRA modeling included calculation of fire severity factors (SFs) and fire non-suppression probabilities (PNS) for each safe shutdown (SSD) component considered in the fire PRA model. The SFs were developed by performing detailed fire modeling through a combination of CFAST fire zone model calculations and Latin Hypercube Sampling (LHS). Component damage times and automatic fire suppression system actuation times calculated in the CFAST LHS analyses were then input to a time-dependent model of fire non-suppression probability. The fire non-suppression probability model is based on the modeling approach outlined in NUREG/CR-6850 and is supplemented with plant specific data. This paper presents the methodology used in the DOE facility fire PRA for modeling fire-induced SSD component failures and includes discussions of modeling techniques for: Development of time-dependent fire heat release rate profiles (required as input to CFAST), Calculation of fire severity factors based on CFAST detailed fire modeling, and Calculation of fire non-suppression probabilities.
International Nuclear Information System (INIS)
Caldarola, L.
1976-01-01
A method is proposed for the analytical evaluation of the cumulative failure probability distribution of complex repairable systems. The method is based on a set of integral equations each one referring to a specific minimal cut set of the system. Each integral equation links the unavailability of a minimal cut set to its failure probability density distribution and to the probability that the minimal cut set is down at the time t under the condition that it was down at time t'(t'<=t). The limitations for the applicability of the method are also discussed. It has been concluded that the method is applicable if the process describing the failure of a minimal cut set is a 'delayed semi-regenerative process'. (Auth.)
ELIPGRID-PC: A PC program for calculating hot spot probabilities
International Nuclear Information System (INIS)
Davidson, J.R.
1994-10-01
ELIPGRID-PC, a new personal computer program has been developed to provide easy access to Singer's 1972 ELIPGRID algorithm for hot-spot detection probabilities. Three features of the program are the ability to determine: (1) the grid size required for specified conditions, (2) the smallest hot spot that can be sampled with a given probability, and (3) the approximate grid size resulting from specified conditions and sampling cost. ELIPGRID-PC also provides probability of hit versus cost data for graphing with spread-sheets or graphics software. The program has been successfully tested using Singer's published ELIPGRID results. An apparent error in the original ELIPGRID code has been uncovered and an appropriate modification incorporated into the new program
International Nuclear Information System (INIS)
Queiroz Bogado Leite, S. de.
1989-10-01
A widely used but otherwise physically incorrect assumption in unit-cell calculations by the method of interface currents in cylindrical or spherical geometries, is that of that of isotropic fluxes at the surfaces of the cell annular regions, when computing transmission probabilities. In this work, new interface-current relations are developed without making use of this assumption and the effects on calculated integral parameters are shown for an idealized unit-cell example. (author) [pt
International Nuclear Information System (INIS)
Costa, A M; Martins, M C; Santos, J P; Indelicato, P; Parente, F
2006-01-01
Energies and transition probabilities of Kβ hypersatellite lines are computed using the Dirac-Fock model for several values of Z throughout the periodic table. The influence of the Breit interaction on the energy shifts from the corresponding diagram lines and on the Kβ h 1 /Kβ h 3 intensity ratio is evaluated. The widths of the double-K hole levels are calculated for Al and Sc. The results are compared to experiment and to other theoretical calculations
Calculating method on human error probabilities considering influence of management and organization
International Nuclear Information System (INIS)
Gao Jia; Huang Xiangrui; Shen Zupei
1996-01-01
This paper is concerned with how management and organizational influences can be factored into quantifying human error probabilities on risk assessments, using a three-level Influence Diagram (ID) which is originally only as a tool for construction and representation of models of decision-making trees or event trees. An analytical model of human errors causation has been set up with three influence levels, introducing a method for quantification assessments (of the ID), which can be applied into quantifying probabilities) of human errors on risk assessments, especially into the quantification of complex event trees (system) as engineering decision-making analysis. A numerical case study is provided to illustrate the approach
International Nuclear Information System (INIS)
Tikhonirov, V.V.
1993-01-01
The results of calculations of the intensity and polarization of radiation from channeled and unchanneled e +- are presented. The Fourier transformation (FT) is used to calculate numerous matrix elements. The calculations for channeled e + showed fast approach of spectral intensity to its value calculated in the approximation of self-consistent field (ASCF) with growing photon energy. In the case of 150 GeV unchanneled e - in Ge at T=293 K the ASCF gives a significantly higher value as compared to the FT. 4 refs., 3 figs
The calculation of average error probability in a digital fibre optical communication system
Rugemalira, R. A. M.
1980-03-01
This paper deals with the problem of determining the average error probability in a digital fibre optical communication system, in the presence of message dependent inhomogeneous non-stationary shot noise, additive Gaussian noise and intersymbol interference. A zero-forcing equalization receiver filter is considered. Three techniques for error rate evaluation are compared. The Chernoff bound and the Gram-Charlier series expansion methods are compared to the characteristic function technique. The latter predicts a higher receiver sensitivity
Monte Carlo calculation of the total probability for gamma-Ray interaction in toluene
International Nuclear Information System (INIS)
Grau Malonda, A.; Garcia-Torano, E.
1983-01-01
Interaction and absorption probabilities for gamma-rays with energies between 1 and 1000 KeV have been computed and tabulated. Toluene based scintillator solution has been assumed in the computation. Both, point sources and homogeneously dispersed radioactive material have been assumed. These tables may be applied to cylinders with radii between 1.25 cm and 0.25 cm and heights between 4.07 cm and 0.20 cm. (Author) 26 refs
International Nuclear Information System (INIS)
Jowzani-Moghaddam, A.
1981-01-01
An integral transport method of calculating the geometrical shadowing factor in multiregion annular cells for infinite closely packed lattices in cylindrical geometry is developed. This analytical method has been programmed in the TPGS code. This method is based upon a consideration of the properties of the integral transport method for a nonuniform body, which together with Bonalumi's approximations allows the determination of the approximate multiregion collision probability matrix for infinite closely packed lattices with sufficient accuracy. The multiregion geometrical shadowing factors have been calculated for variations in fuel pin annular segment rings in a geometry of annular cells. These shadowing factors can then be used in the calculation of neutron transport from one annulus to another in an infinite lattice. The result of this new geometrical shadowing and collision probability matrix are compared with the Dancoff-Ginsburg correction and the probability matrix using constant shadowing on Yankee fuel elements in an infinite lattice. In these cases the Dancoff-Ginsburg correction factor and collision probability matrix using constant shadowing are in difference by at most 6.2% and 6%, respectively
International Nuclear Information System (INIS)
Bouhelal, O.K.A.
1990-01-01
The exact determination of the effective multigroup cross sections imposes the numerical solution of the slowing down equation on a very fine energy mesh. Given the complexity of these calculations, different approximation methods have been developed but without a satisfactory treatment of the slowing-down effect. The usual methods are essentially based on interpolations using precalculated tables. The models that use the probability tables allow to reduce the amount of data and the computational effort. A variety of methods proposed by Soviets, then by Americans, and finally the French method, based on the ''moments of a probability distribution'' are incontestably valid within the framework of the statistical hypothesis. This stipulates that the collision densities do not depend on cross section and there is no ambiguity in the effective cross section calculation. The objective of our work is to show that the non statistical phenomena, such as the slowing-down effect which is taken into account, can be described by probability tables which are able to represent the neutronic values and collision densities. The formalism involved in the statistical hypothesis, is based on the Gauss quadrature of the cross sections moments. In the non-statistical hypothesis we introduce the crossed probability tables using the quadratures of double integrals of cross sections, comments. Moreover, a mathematical formalism allowing to establish a relationship between the crossed probability tables and the collision densities was developed. This method was applied on uranium-238 in the range of resolved resonances where the slowing down effect is significant. Validity of the method and the analysis of the obtained results are studied through a reference calculation based on a solution of a discretized slowing down equation using a very fine mesh in which each microgroup can be correctly defined via the statistical probability tables. 42 figs., 32 tabs., 49 refs. (author)
ZUT, Resonance Integrals in Resolved Region at Various Temperature, Escape Probability Calculation
International Nuclear Information System (INIS)
Kuncir, G.F.
1984-01-01
1 - Nature of physical problem solved: ZUT computes resonance integrals from resonance parameters for a wide variety of temperatures, compositions, and geometries for the resolved resonances. 2 - Method of solution: The form used permits specification of escape probability as a function of the lump dimension and the mean free path. The absorber term may be treated by the integral method, the narrow resonance or the infinite mass approximation. Moderator terms may be represented either by the full integral method (IM) or the asymptotic (NR) form
[Probabilities cannot be calculated retrospectively--not even in the courtroom].
van Gijn, J
2005-12-24
Chance events are part of everyday life, but coincidence of diseases often raises suspicions about hidden causes, for example when power lines are blamed for the geographical clustering of cancer. Recently, criminal procedures in the Netherlands have revolved around the question of whether statistical 'predictions' are a valid reason to hold a hospital nurse accountable for the occurrence of excess deaths during her duty hours, or a kindergarten employee for unexplained respiratory problems in several infants. In both cases, the appeals court judges did not accept the statistical 'argument' in the absence of other evidence. In the UK, however, Sally Clark's initial life sentence for the double murder of her 2 babies was largely based on 'probabilities in retrospect', put forward by the paediatrician Sir Roy Meadow as an expert witness. 4 years later she was acquitted, whereas Meadow was struck off the medical register on a charge of professional misconduct. There is no Bayesian or other mathematical solution to the problem of chance events. Only the detection of causal factors that are plausible and supported by new evidence can help to reinterpret coincidences as relationships. Scrupulous reasoning about probabilities is required, not only of physicians but also of judges and politicians.
Directory of Open Access Journals (Sweden)
Michael J. Markham
2011-07-01
Full Text Available Some problems occurring in Expert Systems can be resolved by employing a causal (Bayesian network and methodologies exist for this purpose. These require data in a specific form and make assumptions about the independence relationships involved. Methodologies using Maximum Entropy (ME are free from these conditions and have the potential to be used in a wider context including systems consisting of given sets of linear and independence constraints, subject to consistency and convergence. ME can also be used to validate results from the causal network methodologies. Three ME methods for determining the prior probability distribution of causal network systems are considered. The first method is Sequential Maximum Entropy in which the computation of a progression of local distributions leads to the over-all distribution. This is followed by development of the Method of Tribus. The development takes the form of an algorithm that includes the handling of explicit independence constraints. These fall into two groups those relating parents of vertices, and those deduced from triangulation of the remaining graph. The third method involves a variation in the part of that algorithm which handles independence constraints. Evidence is presented that this adaptation only requires the linear constraints and the parental independence constraints to emulate the second method in a substantial class of examples.
ERF/ERFC, Calculation of Error Function, Complementary Error Function, Probability Integrals
International Nuclear Information System (INIS)
Vogel, J.E.
1983-01-01
1 - Description of problem or function: ERF and ERFC are used to compute values of the error function and complementary error function for any real number. They may be used to compute other related functions such as the normal probability integrals. 4. Method of solution: The error function and complementary error function are approximated by rational functions. Three such rational approximations are used depending on whether - x .GE.4.0. In the first region the error function is computed directly and the complementary error function is computed via the identity erfc(x)=1.0-erf(x). In the other two regions the complementary error function is computed directly and the error function is computed from the identity erf(x)=1.0-erfc(x). The error function and complementary error function are real-valued functions of any real argument. The range of the error function is (-1,1). The range of the complementary error function is (0,2). 5. Restrictions on the complexity of the problem: The user is cautioned against using ERF to compute the complementary error function by using the identity erfc(x)=1.0-erf(x). This subtraction may cause partial or total loss of significance for certain values of x
Calculation of complication probability of pion treatment at PSI using dose-volume histograms
International Nuclear Information System (INIS)
Nakagawa, Keiichi; Akanuma, Atsuo; Aoki, Yukimasa
1991-01-01
In the conformation technique a target volume is irradiated uniformly as in conventional radiations, whereas surrounding tissue and organs are nonuniformly irradiated. Clinical data on radiation injuries that accumulate with conventional radiation are not applicable without appropriate compensation. Recently a putative solution of this problem was proposed by Lyman using dose-volume histograms. This histogram reduction method reduces a given dose-volume histogram of an organ to a single step which corresponds to the equivalent complication probability by interpolation. As a result it converts nonuniform radiation into a unique dose to the whole organ which has the equivalent likelihood of radiation injury. This method is based on low LET radiation with conventional fractionation schedules. When it is applied to high LET radiation such as negative pion treatment, a high LET dose should be converted to an equivalent photon dose using an appropriate value of RBE. In the present study the histogram reduction method was applied to actual patients treated by the negative pion conformation technique at the Paul Scherrer Institute. Out of evaluable 90 cases of pelvic tumors, 16 developed grade III-IV bladder injury, and 7 developed grade III-IV rectal injury. The 90 cases were divided into roughly equal groups according to the equivalent doses to the entire bladder and rectum. Complication rates and equivalent doses to the full organs in these groups could be represented by a sigmoid dose-effect relation. When RBE from a pion dose to a photon dose is assumed to be 2.1 for bladder injury, the rates of bladder complications fit best to the theoretical complication curve. When the RBE value was 2.3, the rates of rectal injury fit the theoretical curve best. These values are close to the conversion factor of 2.0 that is used in clinical practice at PSI. This agreement suggests the clinical feasibility of the histogram reduction method in conformation radiotherapy. (author)
Nanjo, K. Z.; Sakai, S.; Kato, A.; Tsuruoka, H.; Hirata, N.
2013-05-01
Seismicity in southern Kanto activated with the 2011 March 11 Tohoku earthquake of magnitude M9.0, but does this cause a significant difference in the probability of more earthquakes at the present or in the To? future answer this question, we examine the effect of a change in the seismicity rate on the probability of earthquakes. Our data set is from the Japan Meteorological Agency earthquake catalogue, downloaded on 2012 May 30. Our approach is based on time-dependent earthquake probabilistic calculations, often used for aftershock hazard assessment, and are based on two statistical laws: the Gutenberg-Richter (GR) frequency-magnitude law and the Omori-Utsu (OU) aftershock-decay law. We first confirm that the seismicity following a quake of M4 or larger is well modelled by the GR law with b ˜ 1. Then, there is good agreement with the OU law with p ˜ 0.5, which indicates that the slow decay was notably significant. Based on these results, we then calculate the most probable estimates of future M6-7-class events for various periods, all with a starting date of 2012 May 30. The estimates are higher than pre-quake levels if we consider a period of 3-yr duration or shorter. However, for statistics-based forecasting such as this, errors that arise from parameter estimation must be considered. Taking into account the contribution of these errors to the probability calculations, we conclude that any increase in the probability of earthquakes is insignificant. Although we try to avoid overstating the change in probability, our observations combined with results from previous studies support the likelihood that afterslip (fault creep) in southern Kanto will slowly relax a stress step caused by the Tohoku earthquake. This afterslip in turn reminds us of the potential for stress redistribution to the surrounding regions. We note the importance of varying hazards not only in time but also in space to improve the probabilistic seismic hazard assessment for southern Kanto.
International Nuclear Information System (INIS)
Difilippo, F.C.
1982-01-01
Calculations of the resonance integrals of particular isotopes in a mixture of isotopes show that the overlapping of the resonances of one isotope by resonances of other isotopes affects the final values of effective cross sections. The same effect might adversely influence those nondestructive techniques which assay fissile materials on the basis of resonance effects. Of relevance for these applications is the knowledge of the probability of overlapping resonances of a family of nuclear levels (class 1) with resonances of an independent family (class 2). For the sequence of class 1 resonances we calculate the probability distribution, p(delta), to find a class 2, first-neighbor resonance at distance (in energy) delta from a class 1 resonance; integration of p(delta) over the average finite width of the resonances would give the aforementioned probability of overlapping. Because a class 1 resonance can have a class 1 or a class 2 resonance as a first neighbor, the resultant p(delta) is not given by the distribution of spacings of the composite family
International Nuclear Information System (INIS)
Klasen, M.; Kramer, G.
2009-08-01
We perform next-to-leading order calculations of the single-diffractive and non-diffractive cross sections for dijet production in proton-antiproton collisions at the Tevatron. By comparing their ratio to the data published by the CDF collaboration for two different center-of-mass energies, we deduce the rapidity-gap survival probability as a function of the momentum fraction of the parton in the antiproton. Assuming Regge factorization, this probability can be interpreted as a suppression factor for the diffractive structure function measured in deep-inelastic scattering at HERA. In contrast to the observations for photoproduction, the suppression factor in protonantiproton collisions depends on the momentum fraction of the parton in the Pomeron even at next-to-leading order. (orig.)
International Nuclear Information System (INIS)
Stankovski, Z.
1995-01-01
The collision probability method in neutron transport, as applied to 2D geometries, consume a great amount of computer time, for a typical 2D assembly calculation about 90% of the computing time is consumed in the collision probability evaluations. Consequently RZ or 3D calculations became prohibitive. In this paper the author presents a simple but efficient parallel algorithm based on the message passing host/node programmation model. Parallelization was applied to the energy group treatment. Such approach permits parallelization of the existing code, requiring only limited modifications. Sequential/parallel computer portability is preserved, which is a necessary condition for a industrial code. Sequential performances are also preserved. The algorithm is implemented on a CRAY 90 coupled to a 128 processor T3D computer, a 16 processor IBM SPI and a network of workstations, using the Public Domain PVM library. The tests were executed for a 2D geometry with the standard 99-group library. All results were very satisfactory, the best ones with IBM SPI. Because of heterogeneity of the workstation network, the author did not ask high performances for this architecture. The same source code was used for all computers. A more impressive advantage of this algorithm will appear in the calculations of the SAPHYR project (with the future fine multigroup library of about 8000 groups) with a massively parallel computer, using several hundreds of processors
International Nuclear Information System (INIS)
Schilstra, C.; Meertens, H.
2001-01-01
Purpose: Usually, models that predict normal tissue complication probability (NTCP) are fitted to clinical data with the maximum likelihood (ML) method. This method inevitably causes a loss of information contained in the data. In this study, an alternative method is investigated that calculates the parameter probability distribution (PD), and, thus, conserves all information. The PD method also allows the calculation of the uncertainty in the NTCP, which is an (often-neglected) prerequisite for the intercomparison of both treatment plans and NTCP models. The PD and ML methods are applied to parotid gland data, and the results are compared. Methods and Materials: The drop in salivary flow due to radiotherapy was measured in 25 parotid glands of 15 patients. Together with the parotid gland dose-volume histograms (DVH), this enabled the calculation of the parameter PDs for three different NTCP models (Lyman, relative seriality, and critical volume). From these PDs, the NTCP and its uncertainty could be calculated for arbitrary parotid gland DVHs. ML parameters and resulting NTCP values were calculated also. Results: All models fitted equally well. The parameter PDs turned out to have nonnormal shapes and long tails. The NTCP predictions of the ML and PD method usually differed considerably, depending on the NTCP model and the nature of irradiation. NTCP curves and ML parameters suggested a highly parallel organization of the parotid gland. Conclusions: Considering the substantial differences between the NTCP predictions of the ML and PD method, the use of the PD method is preferred, because this is the only method that takes all information contained in the clinical data into account. Furthermore, PD method gives a true measure of the uncertainty in the NTCP
International Nuclear Information System (INIS)
Tsuchihashi, Keichiro
1985-03-01
A series of formulations to evaluate collision probability for multi-region cells expressed by either of three one-dimensional coordinate systems (plane, sphere and cylinder) or by the general two-dimensional cylindrical coordinate system is presented. They are expressed in a suitable form to have a common numerical process named ''Ray-Trace'' method. Applications of the collision probability method to two optional treatments for the resonance absorption are presented. One is a modified table-look-up method based on the intermediate resonance approximation, and the other is a rigorous method to calculate the resonance absorption in a multi-region cell in which nearly continuous energy spectra of the resonance neutron range can be solved and interaction effect between different resonance nuclides can be evaluated. Two works on resonance absorption in a doubly heterogeneous system with grain structure are presented. First, the effect of a random distribution of particles embedded in graphite diluent on the resonance integral is studied. Next, the ''Accretion'' method proposed by Leslie and Jonsson to define the collision probability in a doubly heterogeneous system is applied to evaluate the resonance absorption in coated particles dispersed in fuel pellet of the HTGR. Several optional models are proposed to define the collision rates in the medium with the microscopic heterogeneity. By making use of the collision probability method developed by the present study, the JAERI thermal reactor standard nuclear design code system SRAC has been developed. Results of several benchmark tests for the SRAC are presented. The analyses of critical experiments of the SHE, DCA, and FNR show good agreement of critical masses with their experimental values. (J.P.N.)
Shaikh, Nader; Hoberman, Alejandro; Hum, Stephanie W; Alberty, Anastasia; Muniz, Gysella; Kurs-Lasky, Marcia; Landsittel, Douglas; Shope, Timothy
2018-06-01
Accurately estimating the probability of urinary tract infection (UTI) in febrile preverbal children is necessary to appropriately target testing and treatment. To develop and test a calculator (UTICalc) that can first estimate the probability of UTI based on clinical variables and then update that probability based on laboratory results. Review of electronic medical records of febrile children aged 2 to 23 months who were brought to the emergency department of Children's Hospital of Pittsburgh, Pittsburgh, Pennsylvania. An independent training database comprising 1686 patients brought to the emergency department between January 1, 2007, and April 30, 2013, and a validation database of 384 patients were created. Five multivariable logistic regression models for predicting risk of UTI were trained and tested. The clinical model included only clinical variables; the remaining models incorporated laboratory results. Data analysis was performed between June 18, 2013, and January 12, 2018. Documented temperature of 38°C or higher in children aged 2 months to less than 2 years. With the use of culture-confirmed UTI as the main outcome, cutoffs for high and low UTI risk were identified for each model. The resultant models were incorporated into a calculation tool, UTICalc, which was used to evaluate medical records. A total of 2070 children were included in the study. The training database comprised 1686 children, of whom 1216 (72.1%) were female and 1167 (69.2%) white. The validation database comprised 384 children, of whom 291 (75.8%) were female and 200 (52.1%) white. Compared with the American Academy of Pediatrics algorithm, the clinical model in UTICalc reduced testing by 8.1% (95% CI, 4.2%-12.0%) and decreased the number of UTIs that were missed from 3 cases to none. Compared with empirically treating all children with a leukocyte esterase test result of 1+ or higher, the dipstick model in UTICalc would have reduced the number of treatment delays by 10.6% (95% CI
Stage line diagram: an age-conditional reference diagram for tracking development.
van Buuren, Stef; Ooms, Jeroen C L
2009-05-15
This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and disease staging), psychology (stages of cognitive development), human development (pubertal stages) and chronic diseases (stages of dementia). Transition probabilities between successive stages are modeled as smoothly varying functions of age. Age-conditional references are calculated from the modeled probabilities by the mid-P value. It is possible to eliminate the influence of age by calculating standard deviation scores (SDS). The method is applied to the empirical data to produce reference charts on secondary sexual maturation. The mean of the empirical SDS in the reference population is close to zero, whereas the variance depends on age. The stage line diagram provides quick insight into both status (in SDS) and tempo (in SDS/year) of development of an individual child. Other measures (e.g. height SDS, body mass index SDS) from the same child can be added to the chart. Diagrams for sexual maturation are available as a web application at http://vps.stefvanbuuren.nl/puberty. The stage line diagram expresses status and tempo of discrete changes on a continuous scale. Wider application of these measures scores opens up new analytic possibilities. (c) 2009 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Stankovski, Z.
1995-01-01
The collision probability method in neutron transport, as applied to 2D geometries, consume a great amount of computer time, for a typical 2D assembly calculation evaluations. Consequently RZ or 3D calculations became prohibitive. In this paper we present a simple but efficient parallel algorithm based on the message passing host/node programing model. Parallelization was applied to the energy group treatment. Such approach permits parallelization of the existing code, requiring only limited modifications. Sequential/parallel computer portability is preserved, witch is a necessary condition for a industrial code. Sequential performances are also preserved. The algorithm is implemented on a CRAY 90 coupled to a 128 processor T3D computer, a 16 processor IBM SP1 and a network of workstations, using the Public Domain PVM library. The tests were executed for a 2D geometry with the standard 99-group library. All results were very satisfactory, the best ones with IBM SP1. Because of heterogeneity of the workstation network, we did ask high performances for this architecture. The same source code was used for all computers. A more impressive advantage of this algorithm will appear in the calculations of the SAPHYR project (with the future fine multigroup library of about 8000 groups) with a massively parallel computer, using several hundreds of processors. (author). 5 refs., 6 figs., 2 tabs
On the calculation of steady-state loss probabilities in the GI/G/2/0 queue
Directory of Open Access Journals (Sweden)
Igor N. Kovalenko
1994-01-01
Full Text Available This paper considers methods for calculating the steady-state loss probability in the GI/G/2/0 queue. A previous study analyzed this queue in discrete time and this led to an efficient, numerical approximation scheme for continuous-time systems. The primary aim of the present work is to provide an alternative approach by analyzing the GI/ME/2/0 queue; i.e., assuming that the service time can be represented by a matrix-exponential distribution. An efficient computational scheme based on this method is developed and some numerical examples are studied. Some comparisons are made with the discrete-time approach, and the two methods are seen to be complementary.
International Nuclear Information System (INIS)
Hennings, W.
1988-01-01
For calculating the probability of being hit by crashing military aircraft on different buildings, a model was introduced, which has already been used in the conventional fields. In the context of converting the research reactor BER II, this model was also used in the nuclear field. The report introduces this model and shows the application to a vertical cylinder as an example. Compared to the previous model, an exact and also simpler solution of the model attempt for determining the shade surface for different shapes of buildings is derived. The problems of the distribution of crashes given by the previous model is treated via the vertical angle and an attempt to solve these problems is given. (orig./HP) [de
International Nuclear Information System (INIS)
Horacek, L.
1994-12-01
The parameters are summarized for a calculation of the probability of brittle fracture of the WWER-440 reactor pressure vessel (RPV). The parameters were selected for 2 basic approaches, viz., one based on the Monte Carlo method and the other on the FORM and SORM methods (First and Second Order Reliability Methods). The approaches were represented by US computer codes VISA-II and OCA-P and by the German ZERBERUS code. The philosophy of the deterministic and probabilistic aspects of the VISA-II code is outlined, and the differences between the US and Czech PWR's are discussed in this context. Briefly described is the partial approach to the evaluation of the WWER type RPV's based on the assessment of their resistance to brittle fracture by fracture mechanics tools and by using the FORM and SORM methods. Attention is paid to the input data for the WWER modification of the VISA-II code. The data are categorized with respect to randomness, i.e. to the stochastic or deterministic nature of their behavior. 18 tabs., 14 refs
International Nuclear Information System (INIS)
Shafii, M. Ali; Su'ud, Zaki; Waris, Abdul; Kurniasih, Neny; Ariani, Menik; Yulianti, Yanti
2010-01-01
Nuclear reactor design and analysis of next-generation reactors require a comprehensive computing which is better to be executed in a high performance computing. Flat flux (FF) approach is a common approach in solving an integral transport equation with collision probability (CP) method. In fact, the neutron flux distribution is not flat, even though the neutron cross section is assumed to be equal in all regions and the neutron source is uniform throughout the nuclear fuel cell. In non-flat flux (NFF) approach, the distribution of neutrons in each region will be different depending on the desired interpolation model selection. In this study, the linear interpolation using Finite Element Method (FEM) has been carried out to be treated the neutron distribution. The CP method is compatible to solve the neutron transport equation for cylindrical geometry, because the angle integration can be done analytically. Distribution of neutrons in each region of can be explained by the NFF approach with FEM and the calculation results are in a good agreement with the result from the SRAC code. In this study, the effects of the mesh on the k eff and other parameters are investigated.
Ellefsen, Karl J.
2017-06-27
MapMark4 is a software package that implements the probability calculations in three-part mineral resource assessments. Functions within the software package are written in the R statistical programming language. These functions, their documentation, and a copy of this user’s guide are bundled together in R’s unit of shareable code, which is called a “package.” This user’s guide includes step-by-step instructions showing how the functions are used to carry out the probability calculations. The calculations are demonstrated using test data, which are included in the package.
International Nuclear Information System (INIS)
Kruijf, W.J.M. de; Janssen, A.J.
1994-01-01
Very accurate Mote Carlo calculations with Monte Carlo Code have been performed to serve as reference for benchmark calculations on resonance absorption by U 238 in a typical PWR pin-cell geometry. Calculations with the energy-pointwise slowing down code calculates the resonance absorption accurately. Calculations with the multigroup discrete ordinates code XSDRN show that accurate results can only be achieved with a very fine energy mesh. (authors). 9 refs., 5 figs., 2 tabs
Directory of Open Access Journals (Sweden)
Lazăr Cristiana Daniela
2017-01-01
Full Text Available Each organization has among its multiple secondary endpoints subordinated to a centralobjective that one of avoiding the contingencies. The direct procurement is carried out on themarket in SEAP (Electronic System of Public Procurement, and a performing management in apublic institution has as sub-base and risk management. The risks may be investigated byeconometric simulation, which is calculated by the use of calculus of probability and the sample fordetermining the relevance of these probabilities.
Nicholson, Wayne L.
2003-12-01
Thermal inactivation kinetics with extrapolation were used to model the survival probabilities of spores of various Bacillus species over time periods of millions of years at the historical ambient temperatures (25-40 °) encountered within the 250 million-year-old Salado formation, from which the putative ancient spore-forming bacterium Salibacillus marismortui strain 2-9-3 was recovered. The model indicated extremely low-to-moderate survival probabilities for spores of mesophiles, but surprisingly high survival probabilities for thermophilic spores. The significance of the results are discussed in terms of the survival probabilities of (i) terrestrial spores in ancient geologic samples and (ii) spores transported between planets within impact ejecta.
International Nuclear Information System (INIS)
Eisawy, E.A.
2011-01-01
The aim of this paper is to develop a practical method to evaluate the actual step and touch potential distributions in order to determine the risk of failure of the grounding system. The failure probability, indicating the safety level of the grounding system, is related to both applied (stress) and withstand (strength) step or touch potentials. The probability distributions of the applied step and touch potentials as well as the corresponding withstand step and touch potentials which represent the capability of the human body to resist stress potentials are presented. These two distributions are used to evaluate the failure probability of the grounding system which denotes the probability that the applied potential exceeds the withstand potential. The method is accomplished in considering the resistance of the human body, the foot contact resistance and the fault clearing time as an independent random variables, rather than fixed values as treated in the previous analysis in determining the safety requirements for a given grounding system
International Nuclear Information System (INIS)
Tierney, M.S.
1991-11-01
The Waste Isolation Pilot Plant (WIPP), in southeastern New Mexico, is a research and development facility to demonstrate safe disposal of defense-generated transuranic waste. The US Department of Energy will designate WIPP as a disposal facility if it meets the US Environmental Protection Agency's standard for disposal of such waste; the standard includes a requirement that estimates of cumulative releases of radioactivity to the accessible environment be incorporated in an overall probability distribution. The WIPP Project has chosen an approach to calculation of an overall probability distribution that employs the concept of scenarios for release and transport of radioactivity to the accessible environment. This report reviews the use of Monte Carlo methods in the calculation of an overall probability distribution and presents a logical and mathematical foundation for use of the scenario concept in such calculations. The report also draws preliminary conclusions regarding the shape of the probability distribution for the WIPP system; preliminary conclusions are based on the possible occurrence of three events and the presence of one feature: namely, the events ''attempted boreholes over rooms and drifts,'' ''mining alters ground-water regime,'' ''water-withdrawal wells provide alternate pathways,'' and the feature ''brine pocket below room or drift.'' Calculation of the WIPP systems's overall probability distributions for only five of sixteen possible scenario classes that can be obtained by combining the four postulated events or features
International Nuclear Information System (INIS)
Niemierko, Andrzej; Goitein, Michael
1991-01-01
The authors investigate a model of normal tissue complication probability for tissues that may be represented by a critical element architecture. They derive formulas for complication probability that apply to both a partial volume irradiation and to an arbitrary inhomogeneous dose distribution. The dose-volume isoeffect relationship which is a consequence of a critical element architecture is discussed and compared to the empirical power law relationship. A dose-volume histogram reduction scheme for a 'pure' critical element model is derived. In addition, a point-based algorithm which does not require precomputation of a dose-volume histogram is derived. The existing published dose-volume histogram reduction algorithms are analyzed. The authors show that the existing algorithms, developed empirically without an explicit biophysical model, have a close relationship to the critical element model at low levels of complication probability. However, it is also showed that they have aspects which are not compatible with a critical element model and the authors propose a modification to one of them to circumvent its restriction to low complication probabilities. (author). 26 refs.; 7 figs
International Nuclear Information System (INIS)
Heatwole, Eric; Parker, Gary; Holmes, Matt; Dickson, Peter
2015-01-01
Frictional heating of high-melting-point grit particles during oblique impacts of consolidated explosives is considered to be the major source of ignition in accidents involving dropped explosives. It has been shown in other work that the lower temperature melting point of two frictionally interacting surfaces will cap the maximum temperature reached, which provides a simple way to mitigate the danger in facilities by implementing surfaces with melting points below the ignition temperature of the explosive. However, a recent series of skid testing experiments has shown that ignition can occur on low-melting-point surfaces with a high concentration of grit particles, most likely due to a grit–grit collision mechanism. For risk-based safety engineering purposes, the authors present a method to estimate the probability of grit contact and/or grit–grit collision during an oblique impact. These expressions are applied to potentially high-consequence oblique impact scenarios in order to give the probability of striking one or more grit particles (for high-melting-point surfaces), or the probability of one or more grit–grit collisions occurring (for low-melting-point surfaces). The probability is dependent on a variety of factors, many of which can be controlled for mitigation to achieve acceptable risk levels for safe explosives handling operations. - Highlights: • Unexpectedly, grit-mediated ignition of a PBX occurred on low-melting point surfaces. • On high-melting surfaces frictional heating is due to a grit–surface interaction. • For low-melting point surfaces the heating mechanism is grit–grit collisions. • A method for estimating the probability of ignition is presented for both surfaces
Energy Technology Data Exchange (ETDEWEB)
Ertaud, A; Mercier, C
1949-02-01
In the elementary calculation of the {epsilon} coefficient and of the slowing down length inside a nuclear pile made of a network of cylindrical rods, it is necessary to know the exit probability of a neutron initially located inside a cylinder filled up with a given substance. This probability is the ratio between the number of output neutrons and the number of neutrons produced inside the surface of the cylinder. This report makes the resolution of this probabilistic equation (integral calculation) both for the cylindrical case and for the spherical case. (J.S.)
International Nuclear Information System (INIS)
Santamarina, C; Schumann, M; Afanasyev, L G; Heim, T
2003-01-01
Chiral perturbation theory predicts the lifetime of pionium, a hydrogen-like π + π - atom, to better than 3% precision. The goal of the DIRAC experiment at CERN is to obtain and check this value experimentally by measuring the break-up probability of pionium in a target. In order to accurately measure the lifetime one needs to know the relationship between the break-up probability and the lifetime to 1% accuracy. We have obtained this dependence by modelling the evolution of pionic atoms in the target using Monte Carlo methods. The model relies on the computation of the pionium-target-atom interaction cross sections. Three different sets of pionium-target cross sections with varying degrees of complexity were used: from the simplest first-order Born approximation involving only the electrostatic interaction to a more advanced approach, taking into account multiphoton exchanges and relativistic effects. We conclude that, in order to obtain the pionium lifetime to 1% accuracy from the break-up probability, the pionium-target cross sections must be known with the same accuracy for the low excited bound states of the pionic atom. This result has been achieved, for low Z targets, with the two most precise cross section sets. For large Z targets only the set accounting for multiphoton exchange satisfies the condition
International Nuclear Information System (INIS)
Zegong, Zhou; Changhong, Liu
1995-01-01
On the basis of the research into original distribution function as the importance function after shifting an appropriate distance, this paper takes the variation of similar ratio of the original function to the importance function as the objective function, the optimum shifting distance obtained by use of an optimization method. The optimum importance function resulting from the optimization method can ensure that the number of Monte Carlo simulations is decreased and at the same time the good estimates of the yearly failure probabilities are obtained
International Nuclear Information System (INIS)
Emery, L.
1993-01-01
A method of determining the deQing requirement of individual cavity higher-order modes (HOM) for a multi-cavity RF system is presented and applied to the APS ring. Since HOM resonator frequency values are to some degree uncertain, the HOM frequencies should be regarded as random variables in predicting the stability of the coupled bunch beam modes. A Monte Carlo simulation provides a histogram of the growth rates from which one obtains an estimate of the probability of instability. The damping of each HOM type is determined such that the damping effort is economized, i.e. no single HOM dominates the specified growth rate histogram
International Nuclear Information System (INIS)
Zheng, S.H.
1994-01-01
It is indispensable to know the fluence on the nuclear reactor pressure vessel. The cross sections and their treatment have an important rule to this problem. In this study, two ''benchmarks'' have been interpreted by the Monte Carlo transport program TRIPOLI to qualify the calculational method and the cross sections used in the calculations. For the treatment of the cross sections, the multigroup method is usually used but it exists some problems such as the difficulty to choose the weighting function and the necessity of a great number of energy to represent well the cross section's fluctuation. In this thesis, we propose a new method called ''Probability Table Method'' to treat the neutron cross sections. For the qualification, a program of the simulation of neutron transport by the Monte Carlo method in one dimension has been written; the comparison of multigroup's results and probability table's results shows the advantages of this new method. The probability table has also been introduced in the TRIPOLI program; the calculational results of the iron deep penetration benchmark has been improved by comparing with the experimental results. So it is interest to use this new method in the shielding and neutronic calculation. (author). 42 refs., 109 figs., 36 tabs
Energy Technology Data Exchange (ETDEWEB)
Mendenhall, Marcus H., E-mail: marcus.h.mendenhall@vanderbilt.edu [Vanderbilt University, Department of Electrical Engineering, P.O. Box 351824B, Nashville, TN 37235 (United States); Weller, Robert A., E-mail: robert.a.weller@vanderbilt.edu [Vanderbilt University, Department of Electrical Engineering, P.O. Box 351824B, Nashville, TN 37235 (United States)
2012-03-01
In Monte Carlo particle transport codes, it is often important to adjust reaction cross-sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analog Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross-section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross-section change. This makes it possible to increase the cross-section of nuclear reactions by factors exceeding 10{sup 4} (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful in problems that involve the computation of particle penetration deep into a target (e.g. atmospheric showers or shielding studies).
International Nuclear Information System (INIS)
Mendenhall, Marcus H.; Weller, Robert A.
2012-01-01
In Monte Carlo particle transport codes, it is often important to adjust reaction cross-sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analog Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross-section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross-section change. This makes it possible to increase the cross-section of nuclear reactions by factors exceeding 10 4 (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful in problems that involve the computation of particle penetration deep into a target (e.g. atmospheric showers or shielding studies).
Mendenhall, Marcus H.; Weller, Robert A.
2011-01-01
In Monte Carlo particle transport codes, it is often important to adjust reaction cross sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analogous Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross section change. This makes it possible t...
Simpson, Matthew J; Baker, Ruth E
2015-09-07
Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard non-growing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.
Bieber, Frederick R; Buckleton, John S; Budowle, Bruce; Butler, John M; Coble, Michael D
2016-08-31
The evaluation and interpretation of forensic DNA mixture evidence faces greater interpretational challenges due to increasingly complex mixture evidence. Such challenges include: casework involving low quantity or degraded evidence leading to allele and locus dropout; allele sharing of contributors leading to allele stacking; and differentiation of PCR stutter artifacts from true alleles. There is variation in statistical approaches used to evaluate the strength of the evidence when inclusion of a specific known individual(s) is determined, and the approaches used must be supportable. There are concerns that methods utilized for interpretation of complex forensic DNA mixtures may not be implemented properly in some casework. Similar questions are being raised in a number of U.S. jurisdictions, leading to some confusion about mixture interpretation for current and previous casework. Key elements necessary for the interpretation and statistical evaluation of forensic DNA mixtures are described. Given the most common method for statistical evaluation of DNA mixtures in many parts of the world, including the USA, is the Combined Probability of Inclusion/Exclusion (CPI/CPE). Exposition and elucidation of this method and a protocol for use is the focus of this article. Formulae and other supporting materials are provided. Guidance and details of a DNA mixture interpretation protocol is provided for application of the CPI/CPE method in the analysis of more complex forensic DNA mixtures. This description, in turn, should help reduce the variability of interpretation with application of this methodology and thereby improve the quality of DNA mixture interpretation throughout the forensic community.
International Nuclear Information System (INIS)
Kase, Yuki; Matsufuji, Naruhiro; Furusawa, Yoshiya; Kanai, Tatsuaki
2007-01-01
In a treatment planning of heavy-ion radiotherapy, it is necessary to estimate the biological effect of the heavy-ion beams. Physical dose should be associated with the relative biological effectiveness (RBE) at each point. Presently, carbon ion radiotherapy has been carried out at the National Institute Radiological Sciences (NIRS) in Japan and the Gesellschaft fuer Schwerionenforschung mbH (GSI) in Germany. Both facilities take individual approach for the calculation of the RBE value. At NIRS, the classical LQ model has been used while the local effect model (LEM) has been incorporated into the treatment planning system at GSI. The first aim of this study is to explain the RBE model of NIRS by the microdosimetric kinetic model (MKM). In addition, the clarification of similarities and differences between the MKM and the LEM was also investigated. (author)
International Nuclear Information System (INIS)
Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.
2013-01-01
The first goal of this paper is to present an exact method able to precisely evaluate very small reactivity effects with a Monte Carlo code (<10 pcm). it has been decided to implement the exact perturbation theory in TRIPOLI-4 and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4 is described. To illustrate the efficiency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the 'direct' estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the 'direct' method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high precision. It offers the possibility to split reactivity contributions on both isotopes and reactions. Other applications of this perturbation method are presented and tested like the calculation of exact kinetic parameters (βeff, Λeff) or sensitivity parameters
Cheng, Chih-Wen; Hua, Jian; Hwang, Daw-Shang
2017-12-07
In this study, the nitrogen oxide (NO x ) emission factors and total NO x emissions of two groups of post-Panamax container ships operating on a long-term slow-steaming basis along Euro-Asian routes were calculated using both the probability density function of engine power levels and the NO x emission function. The main engines of the five sister ships in Group I satisfied the Tier I emission limit stipulated in MARPOL (International Convention for the Prevention of Pollution from Ships) Annex VI, and those in Group II satisfied the Tier II limit. The calculated NO x emission factors of the Group I and Group II ships were 14.73 and 17.85 g/kWhr, respectively. The total NO x emissions of the Group II ships were determined to be 4.4% greater than those of the Group I ships. When the Tier II certification value was used to calculate the average total NO x emissions of Group II engines, the result was lower than the actual value by 21.9%. Although fuel consumption and carbon dioxide (CO 2 ) emissions were increased by 1.76% because of slow steaming, the NO x emissions were markedly reduced by 17.2%. The proposed method is more effective and accurate than the NO x Technical Code 2008. Furthermore, it can be more appropriately applied to determine the NO x emissions of international shipping inventory. The usage of operating power probability density function of diesel engines as the weighting factor and the NO x emission function obtained from test bed for calculating NO x emissions is more accurate and practical. The proposed method is suitable for all types and purposes of diesel engines, irrespective of their operating power level. The method can be used to effectively determine the NO x emissions of international shipping and inventory applications and should be considered in determining the carbon tax to be imposed in the future.
International Nuclear Information System (INIS)
Jasso G, J.; Diaz S, A.; Mendoza G, G.; Sainz M, E.; Garcia de la C, F. M.
2014-10-01
The growth and the cracks propagation by fatigue are a typical degradation mechanism that is presented in the nuclear industry as in the conventional industry; the unstable propagation of a crack can cause the catastrophic failure of a metallic component even with high ductility; for this reason, activities of programmed maintenance have been established in the industry using inspection and visual techniques and/or ultrasound with an established periodicity allowing to follow up to these growths, controlling the undesirable effects; however, these activities increase the operation costs; and in the peculiar case of the nuclear industry, they increase the radiation exposure to the participant personnel. The use of mathematical processes that integrate concepts of uncertainty, material properties and the probability associated to the inspection results, has been constituted as a powerful tool of evaluation of the component reliability, reducing costs and exposure levels. In this work the evaluation of the failure probability by cracks growth preexisting by fatigue is presented, in pipes of a Reactor Core Isolation Cooling system (Rcic) in a nuclear power station. The software WinPRAISE 07 (Piping Reliability Analysis Including Seismic Events) was used supported in the probabilistic fracture mechanics principles. The obtained values of failure probability evidenced a good behavior of the analyzed pipes with a maximum order of 1.0 E-6, therefore is concluded that the performance of the lines of these pipes is reliable even extrapolating the calculations at 10, 20, 30 and 40 years of service. (Author)
International Nuclear Information System (INIS)
Leal, L.C.; de Saussure, G.; Perez, R.B.
1990-01-01
The URR computer code has been developed to calculate cross-section probability tables, Bondarenko self-shielding factors, and self-indication ratios for fertile and fissile isotopes in the unresolved resonance region. Monte Carlo methods are utilized to select appropriate resonance parameters and to compute the cross sections at the desired reference energy. The neutron cross sections are calculated by the single-level Breit-Wigner formalism with s-, p-, and d-wave contributions. The cross-section probability tables are constructed by sampling by Doppler broadened cross-sections. The various self-shielding factors are computer numerically as Lebesgue integrals over the cross-section probability tables
International Nuclear Information System (INIS)
Buffa, Francesca M.
2000-01-01
The aim of this work is to investigate the influence of the statistical fluctuations of Monte Carlo (MC) dose distributions on the dose volume histograms (DVHs) and radiobiological models, in particular the Poisson model for tumour control probability (tcp). The MC matrix is characterized by a mean dose in each scoring voxel, d, and a statistical error on the mean dose, σ d ; whilst the quantities d and σ d depend on many statistical and physical parameters, here we consider only their dependence on the phantom voxel size and the number of histories from the radiation source. Dose distributions from high-energy photon beams have been analysed. It has been found that the DVH broadens when increasing the statistical noise of the dose distribution, and the tcp calculation systematically underestimates the real tumour control value, defined here as the value of tumour control when the statistical error of the dose distribution tends to zero. When increasing the number of energy deposition events, either by increasing the voxel dimensions or increasing the number of histories from the source, the DVH broadening decreases and tcp converges to the 'correct' value. It is shown that the underestimation of the tcp due to the noise in the dose distribution depends on the degree of heterogeneity of the radiobiological parameters over the population; in particular this error decreases with increasing the biological heterogeneity, whereas it becomes significant in the hypothesis of a radiosensitivity assay for single patients, or for subgroups of patients. It has been found, for example, that when the voxel dimension is changed from a cube with sides of 0.5 cm to a cube with sides of 0.25 cm (with a fixed number of histories of 10 8 from the source), the systematic error in the tcp calculation is about 75% in the homogeneous hypothesis, and it decreases to a minimum value of about 15% in a case of high radiobiological heterogeneity. The possibility of using the error on the
International Nuclear Information System (INIS)
Leal, L.C.; de Saussure, G.; Perez, R.B.
1989-01-01
The URR computer code has been developed to calculate cross-section probability tables, Bondarenko self-shielding factors, and self- indication ratios for fertile and fissile isotopes in the unresolved resonance region. Monte Carlo methods are utilized to select appropriate resonance parameters and to compute the cross sections at the desired reference energy. The neutron cross sections are calculated by the single-level Breit-Wigner formalism with s-, p-, and d-wave contributions. The cross-section probability tables are constructed by sampling the Doppler broadened cross-section. The various shelf-shielded factors are computed numerically as Lebesgue integrals over the cross-section probability tables. 6 refs
DEFF Research Database (Denmark)
Asmussen, Søren; Albrecher, Hansjörg
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities......, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially...... updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber–Shiu functions and dependence....
Generalized Probability-Probability Plots
Mushkudiani, N.A.; Einmahl, J.H.J.
2004-01-01
We introduce generalized Probability-Probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real valued data.These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P
Shiryaev, Albert N
2016-01-01
This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for independent study. To accommodate the greatly expanded material in the third edition of Probability, the book is now divided into two volumes. This first volume contains updated references and substantial revisions of the first three chapters of the second edition. In particular, new material has been added on generating functions, the inclusion-exclusion principle, theorems on monotonic classes (relying on a detailed treatment of “π-λ” systems), and the fundamental theorems of mathematical statistics.
Earth Data Analysis Center, University of New Mexico — USFS, State Forestry, BLM, and DOI fire occurrence point locations from 1987 to 2008 were combined and converted into a fire occurrence probability or density grid...
International Nuclear Information System (INIS)
Becker, R.L.; Ford, A.L.; Reading, J.F.
1983-01-01
The distribution of intensities of KL/sup n/ K/sub α/-satellites is nearly binomial, with parameter p/sub L/, the mean L-shell vacancy probability per electron. The chemical environment of an atom produces a shift, δp/sub L/ of p/sub L/ from its value for an isolated target atom. δp/sub L/ tends to increase as p/sub L/ increases, so for greatest chemical sensitivity one wants p/sub L/ as large as possible. p/sub L/ increases with Z/sub p/ but, because it must remain + 9 and even for C + 6
International Nuclear Information System (INIS)
Fraassen, B.C. van
1979-01-01
The interpretation of probabilities in physical theories are considered, whether quantum or classical. The following points are discussed 1) the functions P(μ, Q) in terms of which states and propositions can be represented, are classical (Kolmogoroff) probabilities, formally speaking, 2) these probabilities are generally interpreted as themselves conditional, and the conditions are mutually incompatible where the observables are maximal and 3) testing of the theory typically takes the form of confronting the expectation values of observable Q calculated with probability measures P(μ, Q) for states μ; hence, of comparing the probabilities P(μ, Q)(E) with the frequencies of occurrence of the corresponding events. It seems that even the interpretation of quantum mechanics, in so far as it concerns what the theory says about the empirical (i.e. actual, observable) phenomena, deals with the confrontation of classical probability measures with observable frequencies. This confrontation is studied. (Auth./C.F.)
Waste Package Misload Probability
International Nuclear Information System (INIS)
Knudsen, J.K.
2001-01-01
The objective of this calculation is to calculate the probability of occurrence for fuel assembly (FA) misloads (i.e., Fa placed in the wrong location) and FA damage during FA movements. The scope of this calculation is provided by the information obtained from the Framatome ANP 2001a report. The first step in this calculation is to categorize each fuel-handling events that occurred at nuclear power plants. The different categories are based on FAs being damaged or misloaded. The next step is to determine the total number of FAs involved in the event. Using the information, a probability of occurrence will be calculated for FA misload and FA damage events. This calculation is an expansion of preliminary work performed by Framatome ANP 2001a
Quantum Probabilities as Behavioral Probabilities
Directory of Open Access Journals (Sweden)
Vyacheslav I. Yukalov
2017-03-01
Full Text Available We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans do not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.
DEFF Research Database (Denmark)
Rojas-Nandayapa, Leonardo
Tail probabilities of sums of heavy-tailed random variables are of a major importance in various branches of Applied Probability, such as Risk Theory, Queueing Theory, Financial Management, and are subject to intense research nowadays. To understand their relevance one just needs to think...... analytic expression for the distribution function of a sum of random variables. The presence of heavy-tailed random variables complicates the problem even more. The objective of this dissertation is to provide better approximations by means of sharp asymptotic expressions and Monte Carlo estimators...
International Nuclear Information System (INIS)
Padmanaban, Sriram; Warren, Samantha; Walsh, Anthony; Partridge, Mike; Hawkins, Maria A
2014-01-01
To investigate systematic changes in dose arising when treatment plans optimised using the Anisotropic Analytical Algorithm (AAA) are recalculated using Acuros XB (AXB) in patients treated with definitive chemoradiotherapy (dCRT) for locally advanced oesophageal cancers. We have compared treatment plans created using AAA with those recalculated using AXB. Although the Anisotropic Analytical Algorithm (AAA) is currently more widely used in clinical routine, Acuros XB (AXB) has been shown to more accurately calculate the dose distribution, particularly in heterogeneous regions. Studies to predict clinical outcome should be based on modelling the dose delivered to the patient as accurately as possible. CT datasets from ten patients were selected for this retrospective study. VMAT (Volumetric modulated arc therapy) plans with 2 arcs, collimator rotation ± 5-10° and dose prescription 50 Gy / 25 fractions were created using Varian Eclipse (v10.0). The initial dose calculation was performed with AAA, and AXB plans were created by re-calculating the dose distribution using the same number of monitor units (MU) and multileaf collimator (MLC) files as the original plan. The difference in calculated dose to organs at risk (OAR) was compared using dose-volume histogram (DVH) statistics and p values were calculated using the Wilcoxon signed rank test. The potential clinical effect of dosimetric differences in the gross tumour volume (GTV) was evaluated using three different TCP models from the literature. PTV Median dose was apparently 0.9 Gy lower (range: 0.5 Gy - 1.3 Gy; p < 0.05) for VMAT AAA plans re-calculated with AXB and GTV mean dose was reduced by on average 1.0 Gy (0.3 Gy −1.5 Gy; p < 0.05). An apparent difference in TCP of between 1.2% and 3.1% was found depending on the choice of TCP model. OAR mean dose was lower in the AXB recalculated plan than the AAA plan (on average, dose reduction: lung 1.7%, heart 2.4%). Similar trends were seen for CRT plans
Padmanaban, Sriram; Warren, Samantha; Walsh, Anthony; Partridge, Mike; Hawkins, Maria A
2014-12-23
To investigate systematic changes in dose arising when treatment plans optimised using the Anisotropic Analytical Algorithm (AAA) are recalculated using Acuros XB (AXB) in patients treated with definitive chemoradiotherapy (dCRT) for locally advanced oesophageal cancers. We have compared treatment plans created using AAA with those recalculated using AXB. Although the Anisotropic Analytical Algorithm (AAA) is currently more widely used in clinical routine, Acuros XB (AXB) has been shown to more accurately calculate the dose distribution, particularly in heterogeneous regions. Studies to predict clinical outcome should be based on modelling the dose delivered to the patient as accurately as possible. CT datasets from ten patients were selected for this retrospective study. VMAT (Volumetric modulated arc therapy) plans with 2 arcs, collimator rotation ± 5-10° and dose prescription 50 Gy / 25 fractions were created using Varian Eclipse (v10.0). The initial dose calculation was performed with AAA, and AXB plans were created by re-calculating the dose distribution using the same number of monitor units (MU) and multileaf collimator (MLC) files as the original plan. The difference in calculated dose to organs at risk (OAR) was compared using dose-volume histogram (DVH) statistics and p values were calculated using the Wilcoxon signed rank test. The potential clinical effect of dosimetric differences in the gross tumour volume (GTV) was evaluated using three different TCP models from the literature. PTV Median dose was apparently 0.9 Gy lower (range: 0.5 Gy - 1.3 Gy; p AAA plans re-calculated with AXB and GTV mean dose was reduced by on average 1.0 Gy (0.3 Gy -1.5 Gy; p AAA plan (on average, dose reduction: lung 1.7%, heart 2.4%). Similar trends were seen for CRT plans. Differences in dose distribution are observed with VMAT and CRT plans recalculated with AXB particularly within soft tissue at the tumour/lung interface, where AXB has been shown to more
Grinstead, Charles M; Snell, J Laurie
2011-01-01
This book explores four real-world topics through the lens of probability theory. It can be used to supplement a standard text in probability or statistics. Most elementary textbooks present the basic theory and then illustrate the ideas with some neatly packaged examples. Here the authors assume that the reader has seen, or is learning, the basic theory from another book and concentrate in some depth on the following topics: streaks, the stock market, lotteries, and fingerprints. This extended format allows the authors to present multiple approaches to problems and to pursue promising side discussions in ways that would not be possible in a book constrained to cover a fixed set of topics. To keep the main narrative accessible, the authors have placed the more technical mathematical details in appendices. The appendices can be understood by someone who has taken one or two semesters of calculus.
Dorogovtsev, A Ya; Skorokhod, A V; Silvestrov, D S; Skorokhod, A V
1997-01-01
This book of problems is intended for students in pure and applied mathematics. There are problems in traditional areas of probability theory and problems in the theory of stochastic processes, which has wide applications in the theory of automatic control, queuing and reliability theories, and in many other modern science and engineering fields. Answers to most of the problems are given, and the book provides hints and solutions for more complicated problems.
International Nuclear Information System (INIS)
Kasuya, K.; Funatsu, M.; Saitoh, S.
2001-01-01
The first subject was the development of future ion beam driver with medium-mass ion specie. This may enable us to develop a compromised driver from the point of view of the micro-divergence angle and the cost. We produced nitrogen ion beams, and measured the micro-divergence angle on the anode surface. The measured value was 5-6mrad for the above beam with 300-400keV energy, 300A peak current and 50ns duration. This value was enough small and tolerable for the future energy driver. The corresponding value for the proton beam with higher peak current was 20-30mrad, which was too large. So that, the scale-up experiment with the above kind of medium-mass ion beam must be realized urgently to clarify the beam characteristics in more details. The reactor wall ablation with the implosion X-ray was also calculated as the second subject in this paper. (author)
International Nuclear Information System (INIS)
Rabiti, Arnaldo; Coutsiers, Ernesto; Schivo, Miguel; Mazanttini, Oscar
2003-01-01
This work gives a description of the adjustment process of NUCIRC code to the actual aging conditions of Embalse nuclear power plant. For this adjustment the flow of the fuel channels of the primary heat transport system (PHTS) is calculated using the channel heat balance flow (CHBF) methodology. Then roughness and the localized loss of charge are modified in NUCIRC code for different groups of channels. These adjustments are done in way to fit by regions the channels flows calculated with NUCIRC to the CHBF flows. The fitting results in a discrepancy by regions of less than 0,1% and an average quadratic error of 5% approximately. These values indicate that the code NUCIRC is right adjusted for critical channel power calculations and aging tracking of PHTS. (author)
Energy Technology Data Exchange (ETDEWEB)
Zheng, S H
1994-01-01
It is indispensable to know the fluence on the nuclear reactor pressure vessel. The cross sections and their treatment have an important rule to this problem. In this study, two ``benchmarks`` have been interpreted by the Monte Carlo transport program TRIPOLI to qualify the calculational method and the cross sections used in the calculations. For the treatment of the cross sections, the multigroup method is usually used but it exists some problems such as the difficulty to choose the weighting function and the necessity of a great number of energy to represent well the cross section`s fluctuation. In this thesis, we propose a new method called ``Probability Table Method`` to treat the neutron cross sections. For the qualification, a program of the simulation of neutron transport by the Monte Carlo method in one dimension has been written; the comparison of multigroup`s results and probability table`s results shows the advantages of this new method. The probability table has also been introduced in the TRIPOLI program; the calculational results of the iron deep penetration benchmark has been improved by comparing with the experimental results. So it is interest to use this new method in the shielding and neutronic calculation. (author). 42 refs., 109 figs., 36 tabs.
Statistical probability tables CALENDF program
International Nuclear Information System (INIS)
Ribon, P.
1989-01-01
The purpose of the probability tables is: - to obtain dense data representation - to calculate integrals by quadratures. They are mainly used in the USA for calculations by Monte Carlo and in the USSR and Europe for self-shielding calculations by the sub-group method. The moment probability tables, in addition to providing a more substantial mathematical basis and calculation methods, are adapted for condensation and mixture calculations, which are the crucial operations for reactor physics specialists. However, their extension is limited by the statistical hypothesis they imply. Efforts are being made to remove this obstacle, at the cost, it must be said, of greater complexity
Collision Probability Analysis
DEFF Research Database (Denmark)
Hansen, Peter Friis; Pedersen, Preben Terndrup
1998-01-01
It is the purpose of this report to apply a rational model for prediction of ship-ship collision probabilities as function of the ship and the crew characteristics and the navigational environment for MS Dextra sailing on a route between Cadiz and the Canary Islands.The most important ship and crew...... characteristics are: ship speed, ship manoeuvrability, the layout of the navigational bridge, the radar system, the number and the training of navigators, the presence of a look out etc. The main parameters affecting the navigational environment are ship traffic density, probability distributions of wind speeds...... probability, i.e. a study of the navigator's role in resolving critical situations, a causation factor is derived as a second step.The report documents the first step in a probabilistic collision damage analysis. Future work will inlcude calculation of energy released for crushing of structures giving...
Salah, Faisal Mohammed; Jaya, Ramadhansyah Putra; Mohamed, Azman; Hassan, Norhidayah Abdul; Rosni, Nurul Najihah Mad; Mohamed, Abdullahi Ali; Agussabti
2017-12-01
The influence of styrene butadiene rubber (SBR) on asphaltic concrete properties at different aging conditions was presented in this study. These aging conditions were named as un-aged, short-term, and long-term aging. The conventional asphalt binder of penetration grade 60/70 was used in this work. Four different levels of SBR addition were employed (i.e., 0 %, 1 %, 3 %, and 5 % by binder weight). Asphalt concrete mixes were prepared at selected optimum asphalt content (5 %). The performance was evaluated based on Marshall Stability, resilient modulus, and dynamic creep tests. Results indicated the improving stability and permanent deformation characteristics that the mixes modified with SBR polymer have under aging conditions. The result also showed that the stability, resilient modulus, and dynamic creep tests have the highest rates compared to the short-term aging and un-aged samples. Thus, the use of 5 % SBR can produce more durable asphalt concrete mixtures with better serviceability.
Probability Aggregates in Probability Answer Set Programming
Saad, Emad
2013-01-01
Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of p...
Measurement uncertainty and probability
Willink, Robin
2013-01-01
A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.
Effects of artificial aging conditions on yttria-stabilized zirconia implant abutments.
Basílio, Mariana de Almeida; Cardoso, Kátia Vieira; Antonio, Selma Gutierrez; Rizkalla, Amin Sami; Santos Junior, Gildo Coelho; Arioli Filho, João Neudenir
2016-08-01
Most ceramic abutments are fabricated from yttria-stabilized tetragonal zirconia (Y-TZP). However, Y-TZP undergoes hydrothermal degradation, a process that is not well understood. The purpose of this in vitro study was to assess the effects of artificial aging conditions on the fracture load, phase stability, and surface microstructure of a Y-TZP abutment. Thirty-two prefabricated Y-TZP abutments were screwed and tightened down to external hexagon implants and divided into 4 groups (n = 8): C, control; MC, mechanical cycling (1×10(6) cycles; 10 Hz); AUT, autoclaving (134°C; 5 hours; 0.2 MPa); and TC, thermal cycling (10(4) cycles; 5°/55°C). A single-load-to-fracture test was performed at a crosshead speed of 0.5 mm/min to assess the assembly's resistance to fracture (ISO Norm 14801). X-ray diffraction (XRD) analysis was applied to observe and quantify the tetragonal-monoclinic (t-m) phase transformation. Representative abutments were examined with high-resolution scanning electron microscopy (SEM) to observe the surface characteristics of the abutments. Load-to-fracture test results (N) were compared by ANOVA and Tukey test (α=.05). XRD measurements revealed the monoclinic phase in some abutments after each aging condition. All the aging conditions reduced the fracture load significantly (Paging conditions. Copyright © 2016 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.
The Probability Distribution for a Biased Spinner
Foster, Colin
2012-01-01
This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)
Scaling Qualitative Probability
Burgin, Mark
2017-01-01
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability structures and is more coherent than existing approaches. This setting makes it possible proving that any comparative probability is induced by some probability structure (Theorem 2.1), that classical probability is a probability structure (Theorem 2.2) and that i...
Propensity, Probability, and Quantum Theory
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Briggs, William M.
2012-01-01
The probability leakage of model M with respect to evidence E is defined. Probability leakage is a kind of model error. It occurs when M implies that events $y$, which are impossible given E, have positive probability. Leakage does not imply model falsification. Models with probability leakage cannot be calibrated empirically. Regression models, which are ubiquitous in statistical practice, often evince probability leakage.
Koo, Reginald; Jones, Martin L.
2011-01-01
Quite a number of interesting problems in probability feature an event with probability equal to 1/e. This article discusses three such problems and attempts to explain why this probability occurs with such frequency.
Goldberg, Samuel
1960-01-01
Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, more. Includes 360 problems with answers for half.
Failure probability under parameter uncertainty.
Gerrard, R; Tsanakas, A
2011-05-01
In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications. © 2010 Society for Risk Analysis.
Quantum probability measures and tomographic probability densities
Amosov, GG; Man'ko, [No Value
2004-01-01
Using a simple relation of the Dirac delta-function to generalized the theta-function, the relationship between the tomographic probability approach and the quantum probability measure approach with the description of quantum states is discussed. The quantum state tomogram expressed in terms of the
Influence of aging conditions on the quality of red Sangiovese wine.
Castellari, M; Piermattei, B; Arfelli, G; Amati, A
2001-08-01
A red Sangiovese wine was stored in barrels of different woods (oak and chestnut) and types (225-L "barriques" and 1000-L barrels) at 12 and 22 degrees C for 320 days to evaluate the effects of different aging conditions on wine quality. Chestnut barrels led to wines richer in phenolics, and which were more tannic, colored, and fruity. Oak barrels gave wines with more monomeric phenolics, but less astringent, with higher vanilla smell, and more harmonious. The type of barrel could be used as a parameter to regulate the extraction of wood components and the polymerization of monomeric phenolics. Storage at 22 degrees C favored the formation of polymerized phenolics and the increase of color density and color hue. The temperature produced less pronounced effects on aroma and taste, even if wines stored at 12 degrees C showed more harmony.
Linear positivity and virtual probability
International Nuclear Information System (INIS)
Hartle, James B.
2004-01-01
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. The objective of any quantum theory of a closed system, most generally the universe, is the prediction of probabilities for the individual members of sets of alternative coarse-grained histories of the system. Quantum interference between members of a set of alternative histories is an obstacle to assigning probabilities that are consistent with the rules of probability theory. A quantum theory of closed systems therefore requires two elements: (1) a condition specifying which sets of histories may be assigned probabilities and (2) a rule for those probabilities. The linear positivity condition of Goldstein and Page is the weakest of the general conditions proposed so far. Its general properties relating to exact probability sum rules, time neutrality, and conservation laws are explored. Its inconsistency with the usual notion of independent subsystems in quantum mechanics is reviewed. Its relation to the stronger condition of medium decoherence necessary for classicality is discussed. The linear positivity of histories in a number of simple model systems is investigated with the aim of exhibiting linearly positive sets of histories that are not decoherent. The utility of extending the notion of probability to include values outside the range of 0-1 is described. Alternatives with such virtual probabilities cannot be measured or recorded, but can be used in the intermediate steps of calculations of real probabilities. Extended probabilities give a simple and general way of formulating quantum theory. The various decoherence conditions are compared in terms of their utility for characterizing classicality and the role they might play in further generalizations of quantum mechanics
Toward a generalized probability theory: conditional probabilities
International Nuclear Information System (INIS)
Cassinelli, G.
1979-01-01
The main mathematical object of interest in the quantum logic approach to the foundations of quantum mechanics is the orthomodular lattice and a set of probability measures, or states, defined by the lattice. This mathematical structure is studied per se, independently from the intuitive or physical motivation of its definition, as a generalized probability theory. It is thought that the building-up of such a probability theory could eventually throw light on the mathematical structure of Hilbert-space quantum mechanics as a particular concrete model of the generalized theory. (Auth.)
Probable Inference and Quantum Mechanics
International Nuclear Information System (INIS)
Grandy, W. T. Jr.
2009-01-01
In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.
Probability Machines: Consistent Probability Estimation Using Nonparametric Learning Machines
Malley, J. D.; Kruppa, J.; Dasgupta, A.; Malley, K. G.; Ziegler, A.
2011-01-01
Summary Background Most machine learning approaches only provide a classification for binary responses. However, probabilities are required for risk estimation using individual patient characteristics. It has been shown recently that every statistical learning machine known to be consistent for a nonparametric regression problem is a probability machine that is provably consistent for this estimation problem. Objectives The aim of this paper is to show how random forests and nearest neighbors can be used for consistent estimation of individual probabilities. Methods Two random forest algorithms and two nearest neighbor algorithms are described in detail for estimation of individual probabilities. We discuss the consistency of random forests, nearest neighbors and other learning machines in detail. We conduct a simulation study to illustrate the validity of the methods. We exemplify the algorithms by analyzing two well-known data sets on the diagnosis of appendicitis and the diagnosis of diabetes in Pima Indians. Results Simulations demonstrate the validity of the method. With the real data application, we show the accuracy and practicality of this approach. We provide sample code from R packages in which the probability estimation is already available. This means that all calculations can be performed using existing software. Conclusions Random forest algorithms as well as nearest neighbor approaches are valid machine learning methods for estimating individual probabilities for binary responses. Freely available implementations are available in R and may be used for applications. PMID:21915433
Heterogeneous Calculation of {epsilon}
Energy Technology Data Exchange (ETDEWEB)
Jonsson, Alf
1961-02-15
A heterogeneous method of calculating the fast fission factor given by Naudet has been applied to the Carlvik - Pershagen definition of {epsilon}. An exact calculation of the collision probabilities is included in the programme developed for the Ferranti - Mercury computer.
Heterogeneous Calculation of ε
International Nuclear Information System (INIS)
Jonsson, Alf
1961-02-01
A heterogeneous method of calculating the fast fission factor given by Naudet has been applied to the Carlvik - Pershagen definition of ε. An exact calculation of the collision probabilities is included in the programme developed for the Ferranti - Mercury computer
Crosslinking of SAVY-4000 O-rings as a Function of Aging Conditions
Energy Technology Data Exchange (ETDEWEB)
Van Buskirk, Caleb Griffith [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-09-08
SAVY-4000 containers were developed as a part of DOE M 441.1-1 to protect workers who handle stored nuclear material from exposure due to loss of containment.1 The SAVY-4000 is comprised of three parts: a lid, a container, and a cross-linked fluoropolymer O-ring. Degradation of the O-ring during use could limit the lifetime of the SAVY-4000. In order to quantify the chemical changes of the Oring over time, the molecular weight between crosslinks was determined as a function of aging conditions using a swelling technique. Because the O-ring is a cross-linked polymer, it will absorb solvent into its matrix without dissolving. The relative amount of solvent uptake can be related to the degree of crosslinking using an equation developed by Paul Flory and John Rehner Jr3. This method was used to analyze O-ring samples aged under thermal and ionizing-radiation conditions. It was found that at the harsher thermal gaining conditions in absence of ionizing-radiation the average molecular weight between crosslinks decreased, indicating a rise in crosslinks, which may be attributable to advanced aging with no ionizing radiation present. Inversely, in the presence of ionizing radiation it was found that material has a higher level of cross-linking with age. This information could be used to help predict the lifetime of the O-rings in SAVY-4000 containers under service conditions.
Influence of Aging Conditions on Fatigue Fracture Behaviour of 6063 Aluminum Alloy
Directory of Open Access Journals (Sweden)
Rafiq Ahmed Siddiqui
2001-12-01
Full Text Available Aluminum - Magnesium - Silicon (Al-Mg-Si 6063 alloy was heat-treated using under aged, peak aged and overage temperatures. The numbers of cycles required to cause the fatigue fracture, at constant stress, was considered as criteria for the fatigue resistance. Moreover, the fractured surface of the alloy at different aging conditions was evaluated by optical microscopy and the Scanning Electron Microscopy (SEM. The SEM micrographs confirmed the cleavage surfaces with well-defined fatigue striations. It has been observed that the various aging time and temperature of the 6063 Al-alloy, produces different modes of fractures. The most suitable age hardening time and temperature was found to be between 4 to 5 hours and to occur at 460 K. The increase in fatigue fracture property of the alloy due to aging could be attributed to a vacancy assisted diffusion mechanism or due to pinning of dislocations movement by the precipitates produced during aging. However, the decrease in the fatigue resistance, for the over aged alloys, might be due to the coalescence of precipitates into larger grains.
Collision Probabilities for Finite Cylinders and Cuboids
Energy Technology Data Exchange (ETDEWEB)
Carlvik, I
1967-05-15
Analytical formulae have been derived for the collision probabilities of homogeneous finite cylinders and cuboids. The formula for the finite cylinder contains double integrals, and the formula for the cuboid only single integrals. Collision probabilities have been calculated by means of the formulae and compared with values obtained by other authors. It was found that the calculations using the analytical formulae are much quicker and give higher accuracy than Monte Carlo calculations.
Philosophical theories of probability
Gillies, Donald
2000-01-01
The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.
Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia
We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned
Interpretations of probability
Khrennikov, Andrei
2009-01-01
This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.
Energy Technology Data Exchange (ETDEWEB)
Grau Malonda, A; Garcia-Torano, E
1983-07-01
Interaction and absorption probabilities for gamma-rays with energies between 1 and 1000 KeV have been computed and tabulated. Toluene based scintillator solution has been assumed in the computation. Both, point sources and homogeneously dispersed radioactive material have been assumed. These tables may be applied to cylinders with radii between 1.25 cm and 0.25 cm and heights between 4.07 cm and 0.20 cm. (Author) 26 refs.
D'Alpino, Paulo Henrique Perlatti; Svizero, Nádia da Rocha; Bim Júnior, Odair; Valduga, Claudete Justina; Graeff, Carlos Frederico de Oliveira; Sauro, Salvatore
2016-06-01
The aim of this study is to evaluate the distribution of the filler size along with the zeta potential, and the integrity of silane-bonded filler surface in different types of restorative dental composites as a function of the material age condition. Filtek P60 (hybrid composite), Filtek Z250 (small-particle filled composite), Filtek Z350XT (nanofilled composite), and Filtek Silorane (silorane composite) (3M ESPE) were tested at different stage condition (i.e., fresh/new, aged, and expired). Composites were submitted to an accelerated aging protocol (Arrhenius model). Specimens were obtained by first diluting each composite specimen in ethanol and then dispersed in potassium chloride solution (0.001 mol%). Composite fillers were characterized for their zeta potential, mean particle size, size distribution, via poly-dispersion dynamic light scattering. The integrity of the silane-bonded surface of the fillers was characterized by FTIR. The material age influenced significantly the outcomes; Zeta potential, filler characteristics, and silane integrity varied both after aging and expiration. Silorane presented the broadest filler distribution and lowest zeta potential. Nanofilled and silorane composites exhibited decreased peak intensities in the FTIR analysis, indicating a deficiency of the silane integrity after aging or expiry time. Regardless to the material condition, the hybrid and the small-particle-filled composites were more stable overtime as no significant alteration in filler size distribution, diameter, and zeta potential occurred. A deficiency in the silane integrity in the nanofilled and silorane composites seems to be affected by the material stage condition. The materials conditions tested in this study influenced the filler size distribution, the zeta potential, and integrity of the silane adsorbed on fillers in the nanofilled and silorane composites. Thus, this may result in a decrease of the clinical performance of aforementioned composites, in
Stage line diagram: An age-conditional reference diagram for tracking development
Buuren, S. van; Ooms, J.C.L.
2009-01-01
This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and
Stage line diagram: an age-conditional reference diagram for tracking development.
Van Buuren, S.; Ooms, J.C.L.
2009-01-01
This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and
Phillips, C I; Newton, M; Duvall, J; Holloway, S; Levy, A M
1986-01-01
Two sibships, each with two affected males but no other affected family members, are described. All four patients at birth had small eyes with white masses visible behind clear lenses. Support for a diagnosis of Norrie's disease lies in the probable mental retardation and sudden death of one child and mental retardation in the other in one of the families, and strong support in the sensorineural deafness in one child in the other family. A necropsy was performed on the dead child. Both eyes s...
The quantum probability calculus
International Nuclear Information System (INIS)
Jauch, J.M.
1976-01-01
The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)
Choice Probability Generating Functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel L; Bierlaire, Michel
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications....
Probability of satellite collision
Mccarter, J. W.
1972-01-01
A method is presented for computing the probability of a collision between a particular artificial earth satellite and any one of the total population of earth satellites. The collision hazard incurred by the proposed modular Space Station is assessed using the technique presented. The results of a parametric study to determine what type of satellite orbits produce the greatest contribution to the total collision probability are presented. Collision probability for the Space Station is given as a function of Space Station altitude and inclination. Collision probability was also parameterized over miss distance and mission duration.
Choice probability generating functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2013-01-01
This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended...
Florescu, Ionut
2013-01-01
THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability. The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introductio
Ash, Robert B; Lukacs, E
1972-01-01
Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory.Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of var
Probability Issues in without Replacement Sampling
Joarder, A. H.; Al-Sabah, W. S.
2007-01-01
Sampling without replacement is an important aspect in teaching conditional probabilities in elementary statistics courses. Different methods proposed in different texts for calculating probabilities of events in this context are reviewed and their relative merits and limitations in applications are pinpointed. An alternative representation of…
Simulations of Probabilities for Quantum Computing
Zak, M.
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
Freund, John E
1993-01-01
Thorough, lucid coverage of permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, binomial distribution, geometric distribution, standard deviation, law of large numbers, and much more. Exercises with some solutions. Summary. Bibliography. Includes 42 black-and-white illustrations. 1973 edition.
Probability, Nondeterminism and Concurrency
DEFF Research Database (Denmark)
Varacca, Daniele
Nondeterminism is modelled in domain theory by the notion of a powerdomain, while probability is modelled by that of the probabilistic powerdomain. Some problems arise when we want to combine them in order to model computation in which both nondeterminism and probability are present. In particula...
Rocchi, Paolo
2014-01-01
The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability. Beyond the radical followers of the two schools, a circle of pluralist thinkers tends to reconcile the opposing concepts. The author uses two theorems in order to prove that the various interpretations of probability do not come into opposition and can be used in different contexts. The goal here is to clarify the multifold nature of probability by means of a purely mathematical approach and to show how philosophical arguments can only serve to deepen actual intellectual contrasts. The book can be considered as one of the most important contributions in the analysis of probability interpretation in the last 10-15 years.
Swedish earthquakes and acceleration probabilities
International Nuclear Information System (INIS)
Slunga, R.
1979-03-01
A method to assign probabilities to ground accelerations for Swedish sites is described. As hardly any nearfield instrumental data is available we are left with the problem of interpreting macroseismic data in terms of acceleration. By theoretical wave propagation computations the relation between seismic strength of the earthquake, focal depth, distance and ground accelerations are calculated. We found that most Swedish earthquake of the area, the 1904 earthquake 100 km south of Oslo, is an exception and probably had a focal depth exceeding 25 km. For the nuclear power plant sites an annual probability of 10 -5 has been proposed as interesting. This probability gives ground accelerations in the range 5-20 % for the sites. This acceleration is for a free bedrock site. For consistency all acceleration results in this study are given for bedrock sites. When applicating our model to the 1904 earthquake and assuming the focal zone to be in the lower crust we get the epicentral acceleration of this earthquake to be 5-15 % g. The results above are based on an analyses of macrosismic data as relevant instrumental data is lacking. However, the macroseismic acceleration model deduced in this study gives epicentral ground acceleration of small Swedish earthquakes in agreement with existent distant instrumental data. (author)
Billingsley, Patrick
2012-01-01
Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this
International Nuclear Information System (INIS)
Bitsakis, E.I.; Nicolaides, C.A.
1989-01-01
The concept of probability is now, and always has been, central to the debate on the interpretation of quantum mechanics. Furthermore, probability permeates all of science, as well as our every day life. The papers included in this volume, written by leading proponents of the ideas expressed, embrace a broad spectrum of thought and results: mathematical, physical epistemological, and experimental, both specific and general. The contributions are arranged in parts under the following headings: Following Schroedinger's thoughts; Probability and quantum mechanics; Aspects of the arguments on nonlocality; Bell's theorem and EPR correlations; Real or Gedanken experiments and their interpretation; Questions about irreversibility and stochasticity; and Epistemology, interpretation and culture. (author). refs.; figs.; tabs
Orthogonal Algorithm of Logic Probability and Syndrome-Testable Analysis
Institute of Scientific and Technical Information of China (English)
无
1990-01-01
A new method,orthogonal algoritm,is presented to compute the logic probabilities(i.e.signal probabilities)accurately,The transfer properties of logic probabilities are studied first,which are useful for the calculation of logic probability of the circuit with random independent inputs.Then the orthogonal algoritm is described to compute the logic probability of Boolean function realized by a combinational circuit.This algorithm can make Boolean function “ORTHOGONAL”so that the logic probabilities can be easily calculated by summing up the logic probabilities of all orthogonal terms of the Booleam function.
Shorack, Galen R
2017-01-01
This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians—a textbook for courses in probability for students in mathematical statistics. It is recommended to anyone interested in the probability underlying modern statistics, providing a solid grounding in the probabilistic tools and techniques necessary to do theoretical research in statistics. For the teaching of probability theory to post graduate statistics students, this is one of the most attractive books available. Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. Martingale coverage includes coverage of censored data martingales. The text includes measure theoretic...
Concepts of probability theory
Pfeiffer, Paul E
1979-01-01
Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
Probability and Statistical Inference
Prosper, Harrison B.
2006-01-01
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
Hartmann, Stephan
2011-01-01
Many results of modern physics--those of quantum mechanics, for instance--come in a probabilistic guise. But what do probabilistic statements in physics mean? Are probabilities matters of objective fact and part of the furniture of the world, as objectivists think? Or do they only express ignorance or belief, as Bayesians suggest? And how are probabilistic hypotheses justified and supported by empirical evidence? Finally, what does the probabilistic nature of physics imply for our understanding of the world? This volume is the first to provide a philosophical appraisal of probabilities in all of physics. Its main aim is to make sense of probabilistic statements as they occur in the various physical theories and models and to provide a plausible epistemology and metaphysics of probabilities. The essays collected here consider statistical physics, probabilistic modelling, and quantum mechanics, and critically assess the merits and disadvantages of objectivist and subjectivist views of probabilities in these fie...
Grimmett, Geoffrey
2014-01-01
Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit th...
Hemmo, Meir
2012-01-01
What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.
Probability in quantum mechanics
Directory of Open Access Journals (Sweden)
J. G. Gilson
1982-01-01
Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
Quantum computing and probability.
Ferry, David K
2009-11-25
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.
Quantum computing and probability
International Nuclear Information System (INIS)
Ferry, David K
2009-01-01
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction. (viewpoint)
The perception of probability.
Gallistel, C R; Krishan, Monika; Liu, Ye; Miller, Reilly; Latham, Peter E
2014-01-01
We present a computational model to explain the results from experiments in which subjects estimate the hidden probability parameter of a stepwise nonstationary Bernoulli process outcome by outcome. The model captures the following results qualitatively and quantitatively, with only 2 free parameters: (a) Subjects do not update their estimate after each outcome; they step from one estimate to another at irregular intervals. (b) The joint distribution of step widths and heights cannot be explained on the assumption that a threshold amount of change must be exceeded in order for them to indicate a change in their perception. (c) The mapping of observed probability to the median perceived probability is the identity function over the full range of probabilities. (d) Precision (how close estimates are to the best possible estimate) is good and constant over the full range. (e) Subjects quickly detect substantial changes in the hidden probability parameter. (f) The perceived probability sometimes changes dramatically from one observation to the next. (g) Subjects sometimes have second thoughts about a previous change perception, after observing further outcomes. (h) The frequency with which they perceive changes moves in the direction of the true frequency over sessions. (Explaining this finding requires 2 additional parametric assumptions.) The model treats the perception of the current probability as a by-product of the construction of a compact encoding of the experienced sequence in terms of its change points. It illustrates the why and the how of intermittent Bayesian belief updating and retrospective revision in simple perception. It suggests a reinterpretation of findings in the recent literature on the neurobiology of decision making. (PsycINFO Database Record (c) 2014 APA, all rights reserved).
Sensitivity analysis using probability bounding
International Nuclear Information System (INIS)
Ferson, Scott; Troy Tucker, W.
2006-01-01
Probability bounds analysis (PBA) provides analysts a convenient means to characterize the neighborhood of possible results that would be obtained from plausible alternative inputs in probabilistic calculations. We show the relationship between PBA and the methods of interval analysis and probabilistic uncertainty analysis from which it is jointly derived, and indicate how the method can be used to assess the quality of probabilistic models such as those developed in Monte Carlo simulations for risk analyses. We also illustrate how a sensitivity analysis can be conducted within a PBA by pinching inputs to precise distributions or real values
Irreversibility and conditional probability
International Nuclear Information System (INIS)
Stuart, C.I.J.M.
1989-01-01
The mathematical entropy - unlike physical entropy - is simply a measure of uniformity for probability distributions in general. So understood, conditional entropies have the same logical structure as conditional probabilities. If, as is sometimes supposed, conditional probabilities are time-reversible, then so are conditional entropies and, paradoxically, both then share this symmetry with physical equations of motion. The paradox is, of course that probabilities yield a direction to time both in statistical mechanics and quantum mechanics, while the equations of motion do not. The supposed time-reversibility of both conditionals seems also to involve a form of retrocausality that is related to, but possibly not the same as, that described by Costa de Beaurgard. The retrocausality is paradoxically at odds with the generally presumed irreversibility of the quantum mechanical measurement process. Further paradox emerges if the supposed time-reversibility of the conditionals is linked with the idea that the thermodynamic entropy is the same thing as 'missing information' since this confounds the thermodynamic and mathematical entropies. However, it is shown that irreversibility is a formal consequence of conditional entropies and, hence, of conditional probabilities also. 8 refs. (Author)
Isaac, Richard
1995-01-01
The ideas of probability are all around us. Lotteries, casino gambling, the al most non-stop polling which seems to mold public policy more and more these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac ing quantum mechanics, has a world view that is at its core probabilistic in nature, contrary to the deterministic one of classical physics. In addition to all this muscular evidence of the importance of probability ideas it should also be said that probability can be lots of fun. It is a subject where you can start thinking about amusing, interesting, and often difficult problems with very little mathematical background. In this book, I wanted to introduce a reader with at least a fairl...
Experimental Probability in Elementary School
Andrew, Lane
2009-01-01
Concepts in probability can be more readily understood if students are first exposed to probability via experiment. Performing probability experiments encourages students to develop understandings of probability grounded in real events, as opposed to merely computing answers based on formulae.
Improving Ranking Using Quantum Probability
Melucci, Massimo
2011-01-01
The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of ...
Choice probability generating functions
DEFF Research Database (Denmark)
Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel
2010-01-01
This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice...... probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications....... The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to competing risk survival models....
Probability and stochastic modeling
Rotar, Vladimir I
2012-01-01
Basic NotionsSample Space and EventsProbabilitiesCounting TechniquesIndependence and Conditional ProbabilityIndependenceConditioningThe Borel-Cantelli TheoremDiscrete Random VariablesRandom Variables and VectorsExpected ValueVariance and Other Moments. Inequalities for DeviationsSome Basic DistributionsConvergence of Random Variables. The Law of Large NumbersConditional ExpectationGenerating Functions. Branching Processes. Random Walk RevisitedBranching Processes Generating Functions Branching Processes Revisited More on Random WalkMarkov ChainsDefinitions and Examples. Probability Distributions of Markov ChainsThe First Step Analysis. Passage TimesVariables Defined on a Markov ChainErgodicity and Stationary DistributionsA Classification of States and ErgodicityContinuous Random VariablesContinuous DistributionsSome Basic Distributions Continuous Multivariate Distributions Sums of Independent Random Variables Conditional Distributions and ExpectationsDistributions in the General Case. SimulationDistribution F...
International Nuclear Information System (INIS)
Shimada, Yoshio
2000-01-01
It is anticipated that the change of frequency of surveillance tests, preventive maintenance or parts replacement of safety related components may cause the change of component failure probability and result in the change of core damage probability. It is also anticipated that the change is different depending on the initiating event frequency or the component types. This study assessed the change of core damage probability using simplified PSA model capable of calculating core damage probability in a short time period, which is developed by the US NRC to process accident sequence precursors, when various component's failure probability is changed between 0 and 1, or Japanese or American initiating event frequency data are used. As a result of the analysis, (1) It was clarified that frequency of surveillance test, preventive maintenance or parts replacement of motor driven pumps (high pressure injection pumps, residual heat removal pumps, auxiliary feedwater pumps) should be carefully changed, since the core damage probability's change is large, when the base failure probability changes toward increasing direction. (2) Core damage probability change is insensitive to surveillance test frequency change, since the core damage probability change is small, when motor operated valves and turbine driven auxiliary feed water pump failure probability changes around one figure. (3) Core damage probability change is small, when Japanese failure probability data are applied to emergency diesel generator, even if failure probability changes one figure from the base value. On the other hand, when American failure probability data is applied, core damage probability increase is large, even if failure probability changes toward increasing direction. Therefore, when Japanese failure probability data is applied, core damage probability change is insensitive to surveillance tests frequency change etc. (author)
Estimating Subjective Probabilities
DEFF Research Database (Denmark)
Andersen, Steffen; Fountain, John; Harrison, Glenn W.
2014-01-01
either construct elicitation mechanisms that control for risk aversion, or construct elicitation mechanisms which undertake 'calibrating adjustments' to elicited reports. We illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration adjustments...... that theory calls for. We illustrate this approach using data from a controlled experiment with real monetary consequences to the subjects. This allows the observer to make inferences about the latent subjective probability, under virtually any well-specified model of choice under subjective risk, while still...
Introduction to imprecise probabilities
Augustin, Thomas; de Cooman, Gert; Troffaes, Matthias C M
2014-01-01
In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, includin
Classic Problems of Probability
Gorroochurn, Prakash
2012-01-01
"A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin
Counterexamples in probability
Stoyanov, Jordan M
2013-01-01
While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix.
Plotnitsky, Arkady
2010-01-01
Offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schrodinger; in quantum mechanics; and in modern physics. This book considers the implications of these relationships and of quantum theory for our understanding of the nature of thinking and knowledge in general
Transition probabilities for atoms
International Nuclear Information System (INIS)
Kim, Y.K.
1980-01-01
Current status of advanced theoretical methods for transition probabilities for atoms and ions is discussed. An experiment on the f values of the resonance transitions of the Kr and Xe isoelectronic sequences is suggested as a test for the theoretical methods
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…
Negative probability in the framework of combined probability
Burgin, Mark
2013-01-01
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of conventional probability. So, it is natural that negative probability also has different axiomatic frameworks. In the previous publications (Burgin, 2009; 2010), negative probability was mathematically formalized and rigorously interpreted in the context of extende...
Contributions to quantum probability
International Nuclear Information System (INIS)
Fritz, Tobias
2010-01-01
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a finite set can occur as the outcome
von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo
2014-06-01
Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.
Contributions to quantum probability
Energy Technology Data Exchange (ETDEWEB)
Fritz, Tobias
2010-06-25
Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a
Probability theory and applications
Hsu, Elton P
1999-01-01
This volume, with contributions by leading experts in the field, is a collection of lecture notes of the six minicourses given at the IAS/Park City Summer Mathematics Institute. It introduces advanced graduates and researchers in probability theory to several of the currently active research areas in the field. Each course is self-contained with references and contains basic materials and recent results. Topics include interacting particle systems, percolation theory, analysis on path and loop spaces, and mathematical finance. The volume gives a balanced overview of the current status of probability theory. An extensive bibliography for further study and research is included. This unique collection presents several important areas of current research and a valuable survey reflecting the diversity of the field.
Paradoxes in probability theory
Eckhardt, William
2013-01-01
Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.
Model uncertainty and probability
International Nuclear Information System (INIS)
Parry, G.W.
1994-01-01
This paper discusses the issue of model uncertainty. The use of probability as a measure of an analyst's uncertainty as well as a means of describing random processes has caused some confusion, even though the two uses are representing different types of uncertainty with respect to modeling a system. The importance of maintaining the distinction between the two types is illustrated with a simple example
Retrocausality and conditional probability
International Nuclear Information System (INIS)
Stuart, C.I.J.M.
1989-01-01
Costa de Beauregard has proposed that physical causality be identified with conditional probability. The proposal is shown to be vulnerable on two accounts. The first, though mathematically trivial, seems to be decisive so far as the current formulation of the proposal is concerned. The second lies in a physical inconsistency which seems to have its source in a Copenhagenlike disavowal of realism in quantum mechanics. 6 refs. (Author)
Whittle, Peter
1992-01-01
This book is a complete revision of the earlier work Probability which ap peared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, de manding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept, and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 (reproduced below, together with that to the Russian edition of 1982) I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text...
Energy Technology Data Exchange (ETDEWEB)
Jasso G, J.; Diaz S, A.; Mendoza G, G.; Sainz M, E. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Garcia de la C, F. M., E-mail: angeles.diaz@inin.gob.mx [Comision Federal de Electricidad, Central Nucleoelectrica Laguna Verde, Km 44.5 Carretera Cardel-Nautla, 91476 Laguna Verde, Alto Lucero, Veracruz (Mexico)
2014-10-15
The growth and the cracks propagation by fatigue are a typical degradation mechanism that is presented in the nuclear industry as in the conventional industry; the unstable propagation of a crack can cause the catastrophic failure of a metallic component even with high ductility; for this reason, activities of programmed maintenance have been established in the industry using inspection and visual techniques and/or ultrasound with an established periodicity allowing to follow up to these growths, controlling the undesirable effects; however, these activities increase the operation costs; and in the peculiar case of the nuclear industry, they increase the radiation exposure to the participant personnel. The use of mathematical processes that integrate concepts of uncertainty, material properties and the probability associated to the inspection results, has been constituted as a powerful tool of evaluation of the component reliability, reducing costs and exposure levels. In this work the evaluation of the failure probability by cracks growth preexisting by fatigue is presented, in pipes of a Reactor Core Isolation Cooling system (Rcic) in a nuclear power station. The software WinPRAISE 07 (Piping Reliability Analysis Including Seismic Events) was used supported in the probabilistic fracture mechanics principles. The obtained values of failure probability evidenced a good behavior of the analyzed pipes with a maximum order of 1.0 E-6, therefore is concluded that the performance of the lines of these pipes is reliable even extrapolating the calculations at 10, 20, 30 and 40 years of service. (Author)
Upgrading Probability via Fractions of Events
Directory of Open Access Journals (Sweden)
Frič Roman
2016-08-01
Full Text Available The influence of “Grundbegriffe” by A. N. Kolmogorov (published in 1933 on education in the area of probability and its impact on research in stochastics cannot be overestimated. We would like to point out three aspects of the classical probability theory “calling for” an upgrade: (i classical random events are black-and-white (Boolean; (ii classical random variables do not model quantum phenomena; (iii basic maps (probability measures and observables { dual maps to random variables have very different “mathematical nature”. Accordingly, we propose an upgraded probability theory based on Łukasiewicz operations (multivalued logic on events, elementary category theory, and covering the classical probability theory as a special case. The upgrade can be compared to replacing calculations with integers by calculations with rational (and real numbers. Namely, to avoid the three objections, we embed the classical (Boolean random events (represented by the f0; 1g-valued indicator functions of sets into upgraded random events (represented by measurable {0; 1}-valued functions, the minimal domain of probability containing “fractions” of classical random events, and we upgrade the notions of probability measure and random variable.
Probability concepts in quality risk management.
Claycamp, H Gregg
2012-01-01
Essentially any concept of risk is built on fundamental concepts of chance, likelihood, or probability. Although risk is generally a probability of loss of something of value, given that a risk-generating event will occur or has occurred, it is ironic that the quality risk management literature and guidelines on quality risk management tools are relatively silent on the meaning and uses of "probability." The probability concept is typically applied by risk managers as a combination of frequency-based calculation and a "degree of belief" meaning of probability. Probability as a concept that is crucial for understanding and managing risk is discussed through examples from the most general, scenario-defining and ranking tools that use probability implicitly to more specific probabilistic tools in risk management. A rich history of probability in risk management applied to other fields suggests that high-quality risk management decisions benefit from the implementation of more thoughtful probability concepts in both risk modeling and risk management. Essentially any concept of risk is built on fundamental concepts of chance, likelihood, or probability. Although "risk" generally describes a probability of loss of something of value, given that a risk-generating event will occur or has occurred, it is ironic that the quality risk management literature and guidelines on quality risk management methodologies and respective tools focus on managing severity but are relatively silent on the in-depth meaning and uses of "probability." Pharmaceutical manufacturers are expanding their use of quality risk management to identify and manage risks to the patient that might occur in phases of the pharmaceutical life cycle from drug development to manufacture, marketing to product discontinuation. A probability concept is typically applied by risk managers as a combination of data-based measures of probability and a subjective "degree of belief" meaning of probability. Probability as
Calculating the probability of multitaxon evolutionary trees: bootstrappers Gambit.
Lake, J A
1995-01-01
The reconstruction of multitaxon trees from molecular sequences is confounded by the variety of algorithms and criteria used to evaluate trees, making it difficult to compare the results of different analyses. A global method of multitaxon phylogenetic reconstruction described here, Bootstrappers Gambit, can be used with any four-taxon algorithm, including distance, maximum likelihood, and parsimony methods. It incorporates a Bayesian-Jeffreys'-bootstrap analysis to provide a uniform probabil...
Probability mapping of contaminants
Energy Technology Data Exchange (ETDEWEB)
Rautman, C.A.; Kaplan, P.G. [Sandia National Labs., Albuquerque, NM (United States); McGraw, M.A. [Univ. of California, Berkeley, CA (United States); Istok, J.D. [Oregon State Univ., Corvallis, OR (United States); Sigda, J.M. [New Mexico Inst. of Mining and Technology, Socorro, NM (United States)
1994-04-01
Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. The probability mapping approach illustrated in this paper appears to offer site operators a reasonable, quantitative methodology for many environmental remediation decisions and allows evaluation of the risk associated with those decisions. For example, output from this approach can be used in quantitative, cost-based decision models for evaluating possible site characterization and/or remediation plans, resulting in selection of the risk-adjusted, least-cost alternative. The methodology is completely general, and the techniques are applicable to a wide variety of environmental restoration projects. The probability-mapping approach is illustrated by application to a contaminated site at the former DOE Feed Materials Production Center near Fernald, Ohio. Soil geochemical data, collected as part of the Uranium-in-Soils Integrated Demonstration Project, have been used to construct a number of geostatistical simulations of potential contamination for parcels approximately the size of a selective remediation unit (the 3-m width of a bulldozer blade). Each such simulation accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination (potential clean-up or personnel-hazard thresholds).
Probability mapping of contaminants
International Nuclear Information System (INIS)
Rautman, C.A.; Kaplan, P.G.; McGraw, M.A.; Istok, J.D.; Sigda, J.M.
1994-01-01
Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. The probability mapping approach illustrated in this paper appears to offer site operators a reasonable, quantitative methodology for many environmental remediation decisions and allows evaluation of the risk associated with those decisions. For example, output from this approach can be used in quantitative, cost-based decision models for evaluating possible site characterization and/or remediation plans, resulting in selection of the risk-adjusted, least-cost alternative. The methodology is completely general, and the techniques are applicable to a wide variety of environmental restoration projects. The probability-mapping approach is illustrated by application to a contaminated site at the former DOE Feed Materials Production Center near Fernald, Ohio. Soil geochemical data, collected as part of the Uranium-in-Soils Integrated Demonstration Project, have been used to construct a number of geostatistical simulations of potential contamination for parcels approximately the size of a selective remediation unit (the 3-m width of a bulldozer blade). Each such simulation accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination (potential clean-up or personnel-hazard thresholds)
Probability of causation approach
International Nuclear Information System (INIS)
Jose, D.E.
1988-01-01
Probability of causation (PC) is sometimes viewed as a great improvement by those persons who are not happy with the present rulings of courts in radiation cases. The author does not share that hope and expects that PC will not play a significant role in these issues for at least the next decade. If it is ever adopted in a legislative compensation scheme, it will be used in a way that is unlikely to please most scientists. Consequently, PC is a false hope for radiation scientists, and its best contribution may well lie in some of the spin-off effects, such as an influence on medical practice
Generalized Probability Functions
Directory of Open Access Journals (Sweden)
Alexandre Souto Martinez
2009-01-01
Full Text Available From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs. A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.
2014-06-30
precisely the content of the following result. The price we pay is that the assumption that A is a packing in (F, k ·k1) is too weak to make this happen...Regularité des trajectoires des fonctions aléatoires gaussiennes. In: École d’Été de Probabilités de Saint- Flour , IV-1974, pp. 1–96. Lecture Notes in...Lectures on probability theory and statistics (Saint- Flour , 1994), Lecture Notes in Math., vol. 1648, pp. 165–294. Springer, Berlin (1996) 50. Ledoux
International Nuclear Information System (INIS)
Moriyama, Michihiko; Takaki, Setsuo; Kawagoishi, Norio
2000-01-01
The influence of aging condition on fatigue strength of the 300 grade 18Ni maraging steel has been investigated in relation to the behavior of age hardening and the formation of reversion austenite. In this study, rotating bending fatigue tests were performed for three series of specimens with different aging condition; as solution-treated without aging, aged for various time at 753 K which is the temperature applied for the industrial aging treatment, and over-aged to form a small amount of reversion austenite. Effect of reversion austenite on fatigue strength was examined using specimens with the same static strength which had been controlled by varying aging temperature and time, namely under-aging or over-aging. The main results obtained are as follows. (1) In the case of 753 K aging, the fatigue limits of specimens aged for 11 ks to 48 ks were nearly the same value, although an under-aged (2.8 ks) specimen has as much lower value as a solution-treated specimen without aging treatment. (2) A small amount of reversion austenite is effective for increasing fatigue resistance. For instance, 2 vol% of austenite was enough for improving fatigue limit of the maraging steel used, from 580 MPa to 640 MPa at the same hardness level of Hv 610. (author)
Lectures on probability and statistics
International Nuclear Information System (INIS)
Yost, G.P.
1984-09-01
These notes are based on a set of statistics lectures delivered at Imperial College to the first-year postgraduate students in High Energy Physics. They are designed for the professional experimental scientist. We begin with the fundamentals of probability theory, in which one makes statements about the set of possible outcomes of an experiment, based upon a complete a priori understanding of the experiment. For example, in a roll of a set of (fair) dice, one understands a priori that any given side of each die is equally likely to turn up. From that, we can calculate the probability of any specified outcome. We finish with the inverse problem, statistics. Here, one begins with a set of actual data (e.g., the outcomes of a number of rolls of the dice), and attempts to make inferences about the state of nature which gave those data (e.g., the likelihood of seeing any given side of any given die turn up). This is a much more difficult problem, of course, and one's solutions often turn out to be unsatisfactory in one respect or another
Probable maximum flood control
International Nuclear Information System (INIS)
DeGabriele, C.E.; Wu, C.L.
1991-11-01
This study proposes preliminary design concepts to protect the waste-handling facilities and all shaft and ramp entries to the underground from the probable maximum flood (PMF) in the current design configuration for the proposed Nevada Nuclear Waste Storage Investigation (NNWSI) repository protection provisions were furnished by the United States Bureau of Reclamation (USSR) or developed from USSR data. Proposed flood protection provisions include site grading, drainage channels, and diversion dikes. Figures are provided to show these proposed flood protection provisions at each area investigated. These areas are the central surface facilities (including the waste-handling building and waste treatment building), tuff ramp portal, waste ramp portal, men-and-materials shaft, emplacement exhaust shaft, and exploratory shafts facility
On the Possibility of Assigning Probabilities to Singular Cases, or: Probability Is Subjective Too!
Directory of Open Access Journals (Sweden)
Mark R. Crovelli
2009-06-01
Full Text Available Both Ludwig von Mises and Richard von Mises claimed that numerical probability could not be legitimately applied to singular cases. This paper challenges this aspect of the von Mises brothers’ theory of probability. It is argued that their denial that numerical probability could be applied to singular cases was based solely upon Richard von Mises’ exceptionally restrictive definition of probability. This paper challenges Richard von Mises’ definition of probability by arguing that the definition of probability necessarily depends upon whether the world is governed by time-invariant causal laws. It is argued that if the world is governed by time-invariant causal laws, a subjective definition of probability must be adopted. It is further argued that both the nature of human action and the relative frequency method for calculating numerical probabilities both presuppose that the world is indeed governed by time-invariant causal laws. It is finally argued that the subjective definition of probability undercuts the von Mises claim that numerical probability cannot legitimately be applied to singular, non-replicable cases.
Probability & Perception: The Representativeness Heuristic in Action
Lu, Yun; Vasko, Francis J.; Drummond, Trevor J.; Vasko, Lisa E.
2014-01-01
If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…
Encounter Probability of Individual Wave Height
DEFF Research Database (Denmark)
Liu, Z.; Burcharth, H. F.
1998-01-01
wave height corresponding to a certain exceedence probability within a structure lifetime (encounter probability), based on the statistical analysis of long-term extreme significant wave height. Then the design individual wave height is calculated as the expected maximum individual wave height...... associated with the design significant wave height, with the assumption that the individual wave heights follow the Rayleigh distribution. However, the exceedence probability of such a design individual wave height within the structure lifetime is unknown. The paper presents a method for the determination...... of the design individual wave height corresponding to an exceedence probability within the structure lifetime, given the long-term extreme significant wave height. The method can also be applied for estimation of the number of relatively large waves for fatigue analysis of constructions....
Probability of crack-initiation and application to NDE
Energy Technology Data Exchange (ETDEWEB)
Prantl, G [Nuclear Safety Inspectorate HSK, (Switzerland)
1988-12-31
Fracture toughness is a property with a certain variability. When a statistical distribution is assumed, the probability of crack initiation may be calculated for a given problem defined by its geometry and the applied stress. Experiments have shown, that cracks which experience a certain small amount of ductile growth can reliably be detected by acoustic emission measurements. The probability of crack detection by AE-techniques may be estimated using this experimental finding and the calculated probability of crack initiation. (author).
Evaluation of probability and hazard in nuclear energy
International Nuclear Information System (INIS)
Novikov, V.Ya.; Romanov, N.L.
1979-01-01
Various methods of evaluation of accident probability on NPP are proposed because of NPP security statistic evaluation unreliability. The conception of subjective probability for quantitative analysis of security and hazard are described. Intrepretation of probability as real faith of an expert is assumed as a basis of the conception. It is suggested to study the event uncertainty in the framework of subjective probability theory which not only permits but demands to take into account expert opinions when evaluating the probability. These subjective expert evaluations effect to a certain extent the calculation of the usual mathematical event probability. The above technique is advantageous to use for consideration of a separate experiment or random event
Spallation reactions: calculations
International Nuclear Information System (INIS)
Bertini, H.W.
1975-01-01
Current methods for calculating spallation reactions over various energy ranges are described and evaluated. Recent semiempirical fits to existing data will probably yield the most accurate predictions for these reactions in general. However, if the products in question have binding energies appreciably different from their isotropic neighbors and if the cross section is approximately 30 mb or larger, then the intranuclear-cascade-evaporation approach is probably better suited. (6 tables, 12 figures, 34 references) (U.S.)
Probability of Criticality for MOX SNF
International Nuclear Information System (INIS)
P. Gottlieb
1999-01-01
The purpose of this calculation is to provide a conservative (upper bound) estimate of the probability of criticality for mixed oxide (MOX) spent nuclear fuel (SNF) of the Westinghouse pressurized water reactor (PWR) design that has been proposed for use. with the Plutonium Disposition Program (Ref. 1, p. 2). This calculation uses a Monte Carlo technique similar to that used for ordinary commercial SNF (Ref. 2, Sections 2 and 5.2). Several scenarios, covering a range of parameters, are evaluated for criticality. Parameters specifying the loss of fission products and iron oxide from the waste package are particularly important. This calculation is associated with disposal of MOX SNF
Probability and rational choice
Directory of Open Access Journals (Sweden)
David Botting
2014-05-01
Full Text Available http://dx.doi.org/10.5007/1808-1711.2014v18n1p1 In this paper I will discuss the rationality of reasoning about the future. There are two things that we might like to know about the future: which hypotheses are true and what will happen next. To put it in philosophical language, I aim to show that there are methods by which inferring to a generalization (selecting a hypothesis and inferring to the next instance (singular predictive inference can be shown to be normative and the method itself shown to be rational, where this is due in part to being based on evidence (although not in the same way and in part on a prior rational choice. I will also argue that these two inferences have been confused, being distinct not only conceptually (as nobody disputes but also in their results (the value given to the probability of the hypothesis being not in general that given to the next instance and that methods that are adequate for one are not by themselves adequate for the other. A number of debates over method founder on this confusion and do not show what the debaters think they show.
Approaches to Evaluating Probability of Collision Uncertainty
Hejduk, Matthew D.; Johnson, Lauren C.
2016-01-01
While the two-dimensional probability of collision (Pc) calculation has served as the main input to conjunction analysis risk assessment for over a decade, it has done this mostly as a point estimate, with relatively little effort made to produce confidence intervals on the Pc value based on the uncertainties in the inputs. The present effort seeks to try to carry these uncertainties through the calculation in order to generate a probability density of Pc results rather than a single average value. Methods for assessing uncertainty in the primary and secondary objects' physical sizes and state estimate covariances, as well as a resampling approach to reveal the natural variability in the calculation, are presented; and an initial proposal for operationally-useful display and interpretation of these data for a particular conjunction is given.
COVAL, Compound Probability Distribution for Function of Probability Distribution
International Nuclear Information System (INIS)
Astolfi, M.; Elbaz, J.
1979-01-01
1 - Nature of the physical problem solved: Computation of the probability distribution of a function of variables, given the probability distribution of the variables themselves. 'COVAL' has been applied to reliability analysis of a structure subject to random loads. 2 - Method of solution: Numerical transformation of probability distributions
Falk, Ruma; Kendig, Keith
2013-01-01
Two contestants debate the notorious probability problem of the sex of the second child. The conclusions boil down to explication of the underlying scenarios and assumptions. Basic principles of probability theory are highlighted.
Introduction to probability with R
Baclawski, Kenneth
2008-01-01
FOREWORD PREFACE Sets, Events, and Probability The Algebra of Sets The Bernoulli Sample Space The Algebra of Multisets The Concept of Probability Properties of Probability Measures Independent Events The Bernoulli Process The R Language Finite Processes The Basic Models Counting Rules Computing Factorials The Second Rule of Counting Computing Probabilities Discrete Random Variables The Bernoulli Process: Tossing a Coin The Bernoulli Process: Random Walk Independence and Joint Distributions Expectations The Inclusion-Exclusion Principle General Random Variable
Ross, Sheldon
2014-01-01
A First Course in Probability, Ninth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.
Hartikainen, Anni; Yli-Pirilä, Pasi; Tiitta, Petri; Leskinen, Ari; Kortelainen, Miika; Orasche, Jürgen; Schnelle-Kreis, Jürgen; Lehtinen, Kari E J; Zimmermann, Ralf; Jokiniemi, Jorma; Sippula, Olli
2018-04-17
Residential wood combustion (RWC) emits high amounts of volatile organic compounds (VOCs) into ambient air, leading to formation of secondary organic aerosol (SOA), and various health and climate effects. In this study, the emission factors of VOCs from a logwood-fired modern masonry heater were measured using a Proton-Transfer-Reactor Time-of-Flight Mass Spectrometer. Next, the VOCs were aged in a 29 m 3 Teflon chamber equipped with UV black lights, where dark and photochemical atmospheric conditions were simulated. The main constituents of the VOC emissions were carbonyls and aromatic compounds, which accounted for 50%-52% and 30%-46% of the detected VOC emission, respectively. Emissions were highly susceptible to different combustion conditions, which caused a 2.4-fold variation in emission factors. The overall VOC concentrations declined considerably during both dark and photochemical aging, with simultaneous increase in particulate organic aerosol mass. Especially furanoic and phenolic compounds decreased, and they are suggested to be the major precursors of RWC-originated SOA in all aging conditions. On the other hand, dark aging produced relatively high amounts of nitrogen-containing organic compounds in both gas and particulate phase, while photochemical aging increased especially the concentrations of certain gaseous carbonyls, particularly acid anhydrides.
Tensile and fracture behavior of boron and carbon modified Ti-15-3 alloys in aged conditions
Energy Technology Data Exchange (ETDEWEB)
Sarkar, R., E-mail: rajdeepsarkar@dmrl.drdo.in [Defence Metallurgical Research Laboratory, Kanchanbagh, Hyderabad 500058 (India); Ghosal, P.; Nandy, T.K. [Defence Metallurgical Research Laboratory, Kanchanbagh, Hyderabad 500058 (India); Ray, K.K. [Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur 721302 (India)
2016-02-22
This work illustrates the effect of boron and carbon addition on the mechanical behavior of a beta Ti alloy, Ti–15V–3Cr–3Al–3Sn (Ti-15-3), in differently aged conditions. The alloys were prepared by consumable vacuum arc melting followed by forging and hot rolling. These were subsequently solution treated and aged at different temperatures above 500 °C for 8 h. Standard tensile and plane strain fracture toughness tests were carried out to understand the mechanical behavior of the alloys and its correlation with the microstructural features characterized by scanning and transmission electron microscopy. Both the boron- and the carbon-containing alloys exhibit improved strength with comparable elongation to failure values as compared to the base Ti-15-3 alloy. The presence of TiB and TiC precipitates in a matrix of fine α with β results in lower fracture toughness (K{sub IC}) in the boron- and carbon-containing alloys as compared to the base alloy. However, at higher aging temperatures K{sub IC} improves due to more tortuous crack path because of the presence of coarse α-phase. An empirical relationship has been proposed correlating K{sub IC} with the volume fraction, size and interspacing of α in these alloys.
Aging, condition monitoring, and loss-of-coolant accident (LOCA) tests of class 1E electrical cables
International Nuclear Information System (INIS)
Jacobus, M.J.
1992-11-01
This report describes the results of aging, condition monitoring, and accident testing of miscellaneous cable types. Three sets of cables were aged for up to 9 months under simultaneous thermal (≅100 degrees C) and radiation (≅0.10 kGy/hr) conditions. A sequential accident consisting of high dose rate irradiation (≅6 kGy/hr) and high temperature steam followed the aging. Also exposed to the accident conditions was a fourth set of cables, which were unaged. The test results indicate that, properly installed, most of the various miscellaneous cable products tested should be able to survive an accident after 60 years for total aging doses of at least 150 kGy or higher (depending on the material) and for moderate ambient temperatures on the order of 45--55 degrees C (potentially higher or lower, depending on material specific activtion energies and total radiation doses). Mechanical measurements (primarily elongation, modulus, and density) were more effective than electrical measurements for monitoring age-related degradation
A brief introduction to probability.
Di Paola, Gioacchino; Bertani, Alessandro; De Monte, Lavinia; Tuzzolino, Fabio
2018-02-01
The theory of probability has been debated for centuries: back in 1600, French mathematics used the rules of probability to place and win bets. Subsequently, the knowledge of probability has significantly evolved and is now an essential tool for statistics. In this paper, the basic theoretical principles of probability will be reviewed, with the aim of facilitating the comprehension of statistical inference. After a brief general introduction on probability, we will review the concept of the "probability distribution" that is a function providing the probabilities of occurrence of different possible outcomes of a categorical or continuous variable. Specific attention will be focused on normal distribution that is the most relevant distribution applied to statistical analysis.
Fixation probability on clique-based graphs
Choi, Jeong-Ok; Yu, Unjong
2018-02-01
The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms graph changes from amplifier to suppressor as the fitness of the mutant increases. We demonstrate that the overall structure of a graph can be more important to determine the fixation probability than the degree or the heat heterogeneity. The dependence of the fixation probability on the position of the first mutant is discussed.
International Nuclear Information System (INIS)
Devooght, J.; Lefvert, T.; Stankiewiez, J.
1981-01-01
This chapter deals with the work done in reactor dynamics within the Coordinated Research Program on Transport Theory and Advanced Reactor Calculations by three groups in Belgium, Poland, Sweden and Italy. Discretization methods in diffusion theory, collision probability methods in time-dependent neutron transport and singular perturbation method are represented in this paper
Prediction of accident sequence probabilities in a nuclear power plant due to earthquake events
International Nuclear Information System (INIS)
Hudson, J.M.; Collins, J.D.
1980-01-01
This paper presents a methodology to predict accident probabilities in nuclear power plants subject to earthquakes. The resulting computer program accesses response data to compute component failure probabilities using fragility functions. Using logical failure definitions for systems, and the calculated component failure probabilities, initiating event and safety system failure probabilities are synthesized. The incorporation of accident sequence expressions allows the calculation of terminal event probabilities. Accident sequences, with their occurrence probabilities, are finally coupled to a specific release category. A unique aspect of the methodology is an analytical procedure for calculating top event probabilities based on the correlated failure of primary events
Escape probabilities for fluorescent x-rays
International Nuclear Information System (INIS)
Dance, D.R.; Day, G.J.
1985-01-01
Computation of the energy absorption efficiency of an x-ray photon detector involves consideration of the histories of the secondary particles produced in any initial or secondary interaction which may occur within the detector. In particular, the K or higher shell fluorescent x-rays which may be emitted following a photoelectric interaction can carry away a large fraction of the energy of the incident photon, especially if this energy is just above an absorption edge. The effects of such photons cannot be ignored and a correction term, depending upon the probability that the fluorescent x-rays will escape from the detector, must be applied to the energy absorption efficiency. For detectors such as x-ray intensifying screens, it has been usual to calculate this probability by numerical integration. In this note analytic expressions are derived for the escape probability of fluorescent photons from planar detectors in terms of exponential integral functions. Rational approximations for these functions are readily available and these analytic expressions therefore facilitate the computation of photon absorption efficiencies. A table is presented which should obviate the need for calculating the escape probability for most cases of interest. (author)
Probability of collective excited state decay
International Nuclear Information System (INIS)
Manykin, Eh.A.; Ozhovan, M.I.; Poluehktov, P.P.
1987-01-01
Decay mechanisms of condensed excited state formed of highly excited (Rydberg) atoms are considered, i.e. stability of so-called Rydberg substance is analyzed. It is shown that Auger recombination and radiation transitions are the basic processes. The corresponding probabilities are calculated and compared. It is ascertained that the ''Rydberg substance'' possesses macroscopic lifetime (several seconds) and in a sense it is metastable
Directory of Open Access Journals (Sweden)
Harcourt Robert G
2006-02-01
Full Text Available Abstract Background Chemical immobilization of Weddell seals (Leptonychotes weddellii has previously been, for the most part, problematic and this has been mainly attributed to the type of immobilizing agent used. In addition to individual sensitivity, physiological status may play an important role. We investigated the use of the intravenous administration of a 1:1 mixture of tiletamine and zolazepam (Telazol® to immobilize adult females at different points during a physiologically demanding 5–6 week lactation period. We also compared performance between IV and IM injection of the same mixture. Results The tiletamine:zolazepam mixture administered intravenously was an effective method for immobilization with no fatalities or pronounced apnoeas in 106 procedures; however, there was a 25 % (one animal in four mortality rate with intramuscular administration. Induction time was slightly longer for females at the end of lactation (54.9 ± 2.3 seconds than at post-parturition (48.2 ± 2.9 seconds. In addition, the number of previous captures had a positive effect on induction time. There was no evidence for effects due to age, condition (total body lipid, stage of lactation or number of captures on recovery time. Conclusion We suggest that intravenous administration of tiletamine and zolazepam is an effective and safe immobilizing agent for female Weddell seals. Although individual traits could not explain variation in recovery time, we suggest careful monitoring of recovery times during longitudinal studies (> 2 captures. We show that physiological pressures do not substantially affect response to chemical immobilization with this mixture; however, consideration must be taken for differences that may exist for immobilization of adult males and juveniles. Nevertheless, we recommend a mass-specific dose of 0.50 – 0.65 mg/kg for future procedures with adult female Weddell seals and a starting dose of 0.50 mg/kg for other age classes and other
Prediction and probability in sciences
International Nuclear Information System (INIS)
Klein, E.; Sacquin, Y.
1998-01-01
This book reports the 7 presentations made at the third meeting 'physics and fundamental questions' whose theme was probability and prediction. The concept of probability that was invented to apprehend random phenomena has become an important branch of mathematics and its application range spreads from radioactivity to species evolution via cosmology or the management of very weak risks. The notion of probability is the basis of quantum mechanics and then is bound to the very nature of matter. The 7 topics are: - radioactivity and probability, - statistical and quantum fluctuations, - quantum mechanics as a generalized probability theory, - probability and the irrational efficiency of mathematics, - can we foresee the future of the universe?, - chance, eventuality and necessity in biology, - how to manage weak risks? (A.C.)
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
Poisson Processes in Free Probability
An, Guimei; Gao, Mingchu
2015-01-01
We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisso...
PROBABILITY SURVEYS , CONDITIONAL PROBABILITIES AND ECOLOGICAL RISK ASSESSMENT
We show that probability-based environmental resource monitoring programs, such as the U.S. Environmental Protection Agency's (U.S. EPA) Environmental Monitoring and Assessment Program, and conditional probability analysis can serve as a basis for estimating ecological risk over ...
National Oceanic and Atmospheric Administration, Department of Commerce — Declination is calculated using the current International Geomagnetic Reference Field (IGRF) model. Declination is calculated using the current World Magnetic Model...
Numerical determination of transmission probabilities in cylindrical geometry
International Nuclear Information System (INIS)
Queiroz Bogado Leite, S. de.
1989-11-01
Efficient methods for numerical calculation of transmission probabilities in cylindrical geometry are presented. Relative errors of the order of 10 -5 or smaller are obtained using analytical solutions and low order quadrature integration schemes. (author) [pt
The estimation of collision probabilities in complicated geometries
International Nuclear Information System (INIS)
Roth, M.J.
1969-04-01
This paper demonstrates how collision probabilities in complicated geometries may be estimated. It is assumed that the reactor core may be divided into a number of cells each with simple geometry so that a collision probability matrix can be calculated for each cell by standard methods. It is then shown how these may be joined together. (author)
A note on the transition probability over Csup(*)-algebras
International Nuclear Information System (INIS)
Alberti, P.M.; Karl-Marx-Universitaet, Leipzig
1983-01-01
The algebraic structure of Uhlmann's transition probability between mixed states on unital Csup(*)-algebras is analyzed. Several improvements of methods to calculate the transition probability are fixed, examples are given (e.g., the case of quasi-local Csup(*)-algebras is dealt with) and two more functional characterizations are proved in general. (orig.)
Probability inequalities for decomposition integrals
Czech Academy of Sciences Publication Activity Database
Agahi, H.; Mesiar, Radko
2017-01-01
Roč. 315, č. 1 (2017), s. 240-248 ISSN 0377-0427 Institutional support: RVO:67985556 Keywords : Decomposition integral * Superdecomposition integral * Probability inequalities Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/E/mesiar-0470959.pdf
Expected utility with lower probabilities
DEFF Research Database (Denmark)
Hendon, Ebbe; Jacobsen, Hans Jørgen; Sloth, Birgitte
1994-01-01
An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory...
Bayesian maximum posterior probability method for interpreting plutonium urinalysis data
International Nuclear Information System (INIS)
Miller, G.; Inkret, W.C.
1996-01-01
A new internal dosimetry code for interpreting urinalysis data in terms of radionuclide intakes is described for the case of plutonium. The mathematical method is to maximise the Bayesian posterior probability using an entropy function as the prior probability distribution. A software package (MEMSYS) developed for image reconstruction is used. Some advantages of the new code are that it ensures positive calculated dose, it smooths out fluctuating data, and it provides an estimate of the propagated uncertainty in the calculated doses. (author)
Impact probabilities of meteoroid streams with artificial satellites: An assessment
International Nuclear Information System (INIS)
Foschini, L.; Cevolani, G.
1997-01-01
Impact probabilities of artificial satellites with meteoroid streams were calculated using data collected with the CNR forward scatter (FS) bistatic radar over the Bologna-Lecce baseline (about 700 km). Results show that impact probabilities are 2 times higher than other previously calculated values. Nevertheless, although catastrophic impacts are still rare even in the case of meteor storm conditions, it is expected that high meteoroid fluxes can erode satellites surfaces and weaken their external structures
Invariant probabilities of transition functions
Zaharopol, Radu
2014-01-01
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of t...
Introduction to probability with Mathematica
Hastings, Kevin J
2009-01-01
Discrete ProbabilityThe Cast of Characters Properties of Probability Simulation Random SamplingConditional ProbabilityIndependenceDiscrete DistributionsDiscrete Random Variables, Distributions, and ExpectationsBernoulli and Binomial Random VariablesGeometric and Negative Binomial Random Variables Poisson DistributionJoint, Marginal, and Conditional Distributions More on ExpectationContinuous ProbabilityFrom the Finite to the (Very) Infinite Continuous Random Variables and DistributionsContinuous ExpectationContinuous DistributionsThe Normal Distribution Bivariate Normal DistributionNew Random Variables from OldOrder Statistics Gamma DistributionsChi-Square, Student's t, and F-DistributionsTransformations of Normal Random VariablesAsymptotic TheoryStrong and Weak Laws of Large Numbers Central Limit TheoremStochastic Processes and ApplicationsMarkov ChainsPoisson Processes QueuesBrownian MotionFinancial MathematicsAppendixIntroduction to Mathematica Glossary of Mathematica Commands for Probability Short Answers...
The transmission probability method in one-dimensional cylindrical geometry
International Nuclear Information System (INIS)
Rubin, I.E.
1983-01-01
The collision probability method widely used in solving the problems of neutron transpopt in a reactor cell is reliable for simple cells with small number of zones. The increase of the number of zones and also taking into account the anisotropy of scattering greatly increase the scope of calculations. In order to reduce the time of calculation the transmission probability method is suggested to be used for flux calculation in one-dimensional cylindrical geometry taking into account the scattering anisotropy. The efficiency of the suggested method is verified using the one-group calculations for cylindrical cells. The use of the transmission probability method allows to present completely angular and spatial dependences is neutrons distributions without the increase in the scope of calculations. The method is especially effective in solving the multi-group problems
Probability with applications and R
Dobrow, Robert P
2013-01-01
An introduction to probability at the undergraduate level Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability. With real-life examples and thoughtful exercises from fields as diverse as biology, computer science, cryptology, ecology, public health, and sports, the book is accessible for a variety of readers. The book's emphasis on simulation through the use of the popular R software language c
A philosophical essay on probabilities
Laplace, Marquis de
1996-01-01
A classic of science, this famous essay by ""the Newton of France"" introduces lay readers to the concepts and uses of probability theory. It is of especial interest today as an application of mathematical techniques to problems in social and biological sciences.Generally recognized as the founder of the modern phase of probability theory, Laplace here applies the principles and general results of his theory ""to the most important questions of life, which are, in effect, for the most part, problems in probability."" Thus, without the use of higher mathematics, he demonstrates the application
The collision probability modules of WIMS-E
International Nuclear Information System (INIS)
Roth, M.J.
1985-04-01
This report describes how flat source first flight collision probabilities are calculated and used in the WIMS-E modular program. It includes a description of the input to the modules W-FLU, W-THES, W-PIP, W-PERS and W-MERGE. Input to other collision probability modules are described in separate reports. WIMS-E is capable of calculating collision probabilities in a wide variety of geometries, some of them quite complicated. It can also use them for a variety of purposes. (author)
Quantum processes: probability fluxes, transition probabilities in unit time and vacuum vibrations
International Nuclear Information System (INIS)
Oleinik, V.P.; Arepjev, Ju D.
1989-01-01
Transition probabilities in unit time and probability fluxes are compared in studying the elementary quantum processes -the decay of a bound state under the action of time-varying and constant electric fields. It is shown that the difference between these quantities may be considerable, and so the use of transition probabilities W instead of probability fluxes Π, in calculating the particle fluxes, may lead to serious errors. The quantity W represents the rate of change with time of the population of the energy levels relating partly to the real states and partly to the virtual ones, and it cannot be directly measured in experiment. The vacuum background is shown to be continuously distorted when a perturbation acts on a system. Because of this the viewpoint of an observer on the physical properties of real particles continuously varies with time. This fact is not taken into consideration in the conventional theory of quantum transitions based on using the notion of probability amplitude. As a result, the probability amplitudes lose their physical meaning. All the physical information on quantum dynamics of a system is contained in the mean values of physical quantities. The existence of considerable differences between the quantities W and Π permits one in principle to make a choice of the correct theory of quantum transitions on the basis of experimental data. (author)
Probabilities the little numbers that rule our lives
Olofsson, Peter
2014-01-01
Praise for the First Edition"If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real-world situations."- Keith Devlin, Stanford University, National Public Radio's "Math Guy" and author of The Math Gene and The Unfinished GameFrom probable improbabilities to regular irregularities, Probabilities: The Little Numbers That Rule Our Lives, Second Edition investigates the often surprising effects of risk and chance in our lives. Featur
Logic, probability, and human reasoning.
Johnson-Laird, P N; Khemlani, Sangeet S; Goodwin, Geoffrey P
2015-04-01
This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn - not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction. Copyright © 2015 Elsevier Ltd. All rights reserved.
Free probability and random matrices
Mingo, James A
2017-01-01
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Introduction to probability and measure
Parthasarathy, K R
2005-01-01
According to a remark attributed to Mark Kac 'Probability Theory is a measure theory with a soul'. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both these aesthetic and practical aspects into account.
Failure frequencies and probabilities applicable to BWR and PWR piping
International Nuclear Information System (INIS)
Bush, S.H.; Chockie, A.D.
1996-03-01
This report deals with failure probabilities and failure frequencies of nuclear plant piping and the failure frequencies of flanges and bellows. Piping failure probabilities are derived from Piping Reliability Analysis Including Seismic Events (PRAISE) computer code calculations based on fatigue and intergranular stress corrosion as failure mechanisms. Values for both failure probabilities and failure frequencies are cited from several sources to yield a better evaluation of the spread in mean and median values as well as the widths of the uncertainty bands. A general conclusion is that the numbers from WASH-1400 often used in PRAs are unduly conservative. Failure frequencies for both leaks and large breaks tend to be higher than would be calculated using the failure probabilities, primarily because the frequencies are based on a relatively small number of operating years. Also, failure probabilities are substantially lower because of the probability distributions used in PRAISE calculations. A general conclusion is that large LOCA probability values calculated using PRAISE will be quite small, on the order of less than 1E-8 per year (<1E-8/year). The values in this report should be recognized as having inherent limitations and should be considered as estimates and not absolute values. 24 refs 24 refs
Measurement of the resonance escape probability
International Nuclear Information System (INIS)
Anthony, J.P.; Bacher, P.; Lheureux, L.; Moreau, J.; Schmitt, A.P.
1957-01-01
The average cadmium ratio in natural uranium rods has been measured, using equal diameter natural uranium disks. These values correlated with independent measurements of the lattice buckling, enabled us to calculate values of the resonance escape probability for the G1 reactor with one or the other of two definitions. Measurements were performed on 26 mm and 32 mm rods, giving the following values for the resonance escape probability p: 0.8976 ± 0.005 and 0.912 ± 0.006 (d. 26 mm), 0.8627 ± 0.009 and 0.884 ± 0.01 (d. 32 mm). The influence of either definition on the lattice parameters is discussed, leading to values of the effective integral. Similar experiments have been performed with thorium rods. (author) [fr
Joint probabilities and quantum cognition
International Nuclear Information System (INIS)
Acacio de Barros, J.
2012-01-01
In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.
Joint probabilities and quantum cognition
Energy Technology Data Exchange (ETDEWEB)
Acacio de Barros, J. [Liberal Studies, 1600 Holloway Ave., San Francisco State University, San Francisco, CA 94132 (United States)
2012-12-18
In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.
Default probabilities and default correlations
Erlenmaier, Ulrich; Gersbach, Hans
2001-01-01
Starting from the Merton framework for firm defaults, we provide the analytics and robustness of the relationship between default correlations. We show that loans with higher default probabilities will not only have higher variances but also higher correlations between loans. As a consequence, portfolio standard deviation can increase substantially when loan default probabilities rise. This result has two important implications. First, relative prices of loans with different default probabili...
The Probabilities of Unique Events
2012-08-30
Washington, DC USA Max Lotstein and Phil Johnson-Laird Department of Psychology Princeton University Princeton, NJ USA August 30th 2012...social justice and also participated in antinuclear demonstrations. The participants ranked the probability that Linda is a feminist bank teller as...retorted that such a flagrant violation of the probability calculus was a result of a psychological experiment that obscured the rationality of the
Probability Matching, Fast and Slow
Koehler, Derek J.; James, Greta
2014-01-01
A prominent point of contention among researchers regarding the interpretation of probability-matching behavior is whether it represents a cognitively sophisticated, adaptive response to the inherent uncertainty of the tasks or settings in which it is observed, or whether instead it represents a fundamental shortcoming in the heuristics that support and guide human decision making. Put crudely, researchers disagree on whether probability matching is "smart" or "dumb." Here, we consider eviden...
Probably not future prediction using probability and statistical inference
Dworsky, Lawrence N
2008-01-01
An engaging, entertaining, and informative introduction to probability and prediction in our everyday lives Although Probably Not deals with probability and statistics, it is not heavily mathematical and is not filled with complex derivations, proofs, and theoretical problem sets. This book unveils the world of statistics through questions such as what is known based upon the information at hand and what can be expected to happen. While learning essential concepts including "the confidence factor" and "random walks," readers will be entertained and intrigued as they move from chapter to chapter. Moreover, the author provides a foundation of basic principles to guide decision making in almost all facets of life including playing games, developing winning business strategies, and managing personal finances. Much of the book is organized around easy-to-follow examples that address common, everyday issues such as: How travel time is affected by congestion, driving speed, and traffic lights Why different gambling ...
Transition probabilities between levels of K and K+
International Nuclear Information System (INIS)
Campos Gutierrez, J.; Martin Vicente, A.
1984-01-01
In this work transition probabilities between Ievels of n < 11 for K and for the known of K+ are calculated. Two computer programs based on the Coulomb approximation and the most suitable coupling schemes has been used. Lifetimes of all these levels are also calculated. (Author)
Representing Uncertainty by Probability and Possibility
DEFF Research Database (Denmark)
of uncertain parameters. Monte Carlo simulation is readily used for practical calculations. However, an alternative approach is offered by possibility theory making use of possibility distributions such as intervals and fuzzy intervals. This approach is well suited to represent lack of knowledge or imprecision......Uncertain parameters in modeling are usually represented by probability distributions reflecting either the objective uncertainty of the parameters or the subjective belief held by the model builder. This approach is particularly suited for representing the statistical nature or variance...
Normal probability plots with confidence.
Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank; Kiatsupaibul, Seksan; Hayter, Anthony J; Wan, Fang
2015-01-01
Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability 1-α. These simultaneous 1-α probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson-Darling and Shapiro-Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
International Nuclear Information System (INIS)
Scholtyssek, W.
1995-01-01
In the first phase of a benchmark comparison, the CONTAIN code was used to calculate an assumed EPR accident 'medium-sized leak in the cold leg', especially for the first two days after initiation of the accident. The results for global characteristics compare well with those of FIPLOC, MELCOR and WAVCO calculations, if the same materials data are used as input. However, significant differences show up for local quantities such as flows through leakages. (orig.)
Probability theory a foundational course
Pakshirajan, R P
2013-01-01
This book shares the dictum of J. L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics analysed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdos-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject.
VIBRATION ISOLATION SYSTEM PROBABILITY ANALYSIS
Directory of Open Access Journals (Sweden)
Smirnov Vladimir Alexandrovich
2012-10-01
Full Text Available The article deals with the probability analysis for a vibration isolation system of high-precision equipment, which is extremely sensitive to low-frequency oscillations even of submicron amplitude. The external sources of low-frequency vibrations may include the natural city background or internal low-frequency sources inside buildings (pedestrian activity, HVAC. Taking Gauss distribution into account, the author estimates the probability of the relative displacement of the isolated mass being still lower than the vibration criteria. This problem is being solved in the three dimensional space, evolved by the system parameters, including damping and natural frequency. According to this probability distribution, the chance of exceeding the vibration criteria for a vibration isolation system is evaluated. Optimal system parameters - damping and natural frequency - are being developed, thus the possibility of exceeding vibration criteria VC-E and VC-D is assumed to be less than 0.04.
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Model uncertainty: Probabilities for models?
International Nuclear Information System (INIS)
Winkler, R.L.
1994-01-01
Like any other type of uncertainty, model uncertainty should be treated in terms of probabilities. The question is how to do this. The most commonly-used approach has a drawback related to the interpretation of the probabilities assigned to the models. If we step back and look at the big picture, asking what the appropriate focus of the model uncertainty question should be in the context of risk and decision analysis, we see that a different probabilistic approach makes more sense, although it raise some implementation questions. Current work that is underway to address these questions looks very promising
Knowledge typology for imprecise probabilities.
Energy Technology Data Exchange (ETDEWEB)
Wilson, G. D. (Gregory D.); Zucker, L. J. (Lauren J.)
2002-01-01
When characterizing the reliability of a complex system there are often gaps in the data available for specific subsystems or other factors influencing total system reliability. At Los Alamos National Laboratory we employ ethnographic methods to elicit expert knowledge when traditional data is scarce. Typically, we elicit expert knowledge in probabilistic terms. This paper will explore how we might approach elicitation if methods other than probability (i.e., Dempster-Shafer, or fuzzy sets) prove more useful for quantifying certain types of expert knowledge. Specifically, we will consider if experts have different types of knowledge that may be better characterized in ways other than standard probability theory.
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
Probability, statistics, and queueing theory
Allen, Arnold O
1990-01-01
This is a textbook on applied probability and statistics with computer science applications for students at the upper undergraduate level. It may also be used as a self study book for the practicing computer science professional. The successful first edition of this book proved extremely useful to students who need to use probability, statistics and queueing theory to solve problems in other fields, such as engineering, physics, operations research, and management science. The book has also been successfully used for courses in queueing theory for operations research students. This second edit
Probability and Statistics: 5 Questions
DEFF Research Database (Denmark)
Probability and Statistics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in probability and statistics. We hear their views on the fields, aims, scopes, the future direction of research and how their work fits...... in these respects. Interviews with Nick Bingham, Luc Bovens, Terrence L. Fine, Haim Gaifman, Donald Gillies, James Hawthorne, Carl Hoefer, James M. Joyce, Joseph B. Kadane Isaac Levi, D.H. Mellor, Patrick Suppes, Jan von Plato, Carl Wagner, Sandy Zabell...
Pipe failure probability - the Thomas paper revisited
International Nuclear Information System (INIS)
Lydell, B.O.Y.
2000-01-01
Almost twenty years ago, in Volume 2 of Reliability Engineering (the predecessor of Reliability Engineering and System Safety), a paper by H. M. Thomas of Rolls Royce and Associates Ltd. presented a generalized approach to the estimation of piping and vessel failure probability. The 'Thomas-approach' used insights from actual failure statistics to calculate the probability of leakage and conditional probability of rupture given leakage. It was intended for practitioners without access to data on the service experience with piping and piping system components. This article revisits the Thomas paper by drawing on insights from development of a new database on piping failures in commercial nuclear power plants worldwide (SKI-PIPE). Partially sponsored by the Swedish Nuclear Power Inspectorate (SKI), the R and D leading up to this note was performed during 1994-1999. Motivated by data requirements of reliability analysis and probabilistic safety assessment (PSA), the new database supports statistical analysis of piping failure data. Against the background of this database development program, the article reviews the applicability of the 'Thomas approach' in applied risk and reliability analysis. It addresses the question whether a new and expanded database on the service experience with piping systems would alter the original piping reliability correlation as suggested by H. M. Thomas
Dynamic SEP event probability forecasts
Kahler, S. W.; Ling, A.
2015-10-01
The forecasting of solar energetic particle (SEP) event probabilities at Earth has been based primarily on the estimates of magnetic free energy in active regions and on the observations of peak fluxes and fluences of large (≥ M2) solar X-ray flares. These forecasts are typically issued for the next 24 h or with no definite expiration time, which can be deficient for time-critical operations when no SEP event appears following a large X-ray flare. It is therefore important to decrease the event probability forecast with time as a SEP event fails to appear. We use the NOAA listing of major (≥10 pfu) SEP events from 1976 to 2014 to plot the delay times from X-ray peaks to SEP threshold onsets as a function of solar source longitude. An algorithm is derived to decrease the SEP event probabilities with time when no event is observed to reach the 10 pfu threshold. In addition, we use known SEP event size distributions to modify probability forecasts when SEP intensity increases occur below the 10 pfu event threshold. An algorithm to provide a dynamic SEP event forecast, Pd, for both situations of SEP intensities following a large flare is derived.
Conditional Independence in Applied Probability.
Pfeiffer, Paul E.
This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…
Stretching Probability Explorations with Geoboards
Wheeler, Ann; Champion, Joe
2016-01-01
Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
DECOFF Probabilities of Failed Operations
DEFF Research Database (Denmark)
Gintautas, Tomas
2015-01-01
A statistical procedure of estimation of Probabilities of Failed Operations is described and exemplified using ECMWF weather forecasts and SIMO output from Rotor Lift test case models. Also safety factor influence is investigated. DECOFF statistical method is benchmarked against standard Alpha-factor...
Risk estimation using probability machines
2014-01-01
Background Logistic regression has been the de facto, and often the only, model used in the description and analysis of relationships between a binary outcome and observed features. It is widely used to obtain the conditional probabilities of the outcome given predictors, as well as predictor effect size estimates using conditional odds ratios. Results We show how statistical learning machines for binary outcomes, provably consistent for the nonparametric regression problem, can be used to provide both consistent conditional probability estimation and conditional effect size estimates. Effect size estimates from learning machines leverage our understanding of counterfactual arguments central to the interpretation of such estimates. We show that, if the data generating model is logistic, we can recover accurate probability predictions and effect size estimates with nearly the same efficiency as a correct logistic model, both for main effects and interactions. We also propose a method using learning machines to scan for possible interaction effects quickly and efficiently. Simulations using random forest probability machines are presented. Conclusions The models we propose make no assumptions about the data structure, and capture the patterns in the data by just specifying the predictors involved and not any particular model structure. So they do not run the same risks of model mis-specification and the resultant estimation biases as a logistic model. This methodology, which we call a “risk machine”, will share properties from the statistical machine that it is derived from. PMID:24581306
Probability and statistics: A reminder
International Nuclear Information System (INIS)
Clement, B.
2013-01-01
The main purpose of these lectures is to provide the reader with the tools needed to data analysis in the framework of physics experiments. Basic concepts are introduced together with examples of application in experimental physics. The lecture is divided into two parts: probability and statistics. It is build on the introduction from 'data analysis in experimental sciences' given in [1]. (authors)
Nash equilibrium with lower probabilities
DEFF Research Database (Denmark)
Groes, Ebbe; Jacobsen, Hans Jørgen; Sloth, Birgitte
1998-01-01
We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible...
On probability-possibility transformations
Klir, George J.; Parviz, Behzad
1992-01-01
Several probability-possibility transformations are compared in terms of the closeness of preserving second-order properties. The comparison is based on experimental results obtained by computer simulation. Two second-order properties are involved in this study: noninteraction of two distributions and projections of a joint distribution.
Salgado, C A; Salgado, Carlos A.; Wiedemann, Urs Achim
2003-01-01
We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus colli...
Directory of Open Access Journals (Sweden)
Jiefeng Liu
2018-02-01
Full Text Available The life expectancy of a transformer is largely depended on the service life of transformer polymer insulation materials. Nowadays, several papers have reported that the traditional system poles obtained from polarization and depolarization current (PDC data can be used to assess the condition of transformer insulation systems. However, the traditional system poles technique only provides limited ageing information for transformer polymer insulation. In this paper, the modified system poles obtained from PDC data are proposed to assess the ageing condition of transformer polymer insulation. The aim of the work is to focus on reporting a comparative investigation on the performance of modified system poles and traditional system poles for assessing the ageing condition of a transformer polymer insulation system. In the present work, a series of experiments have been performed under controlled laboratory conditions. The PDC measurement data, degree of polymerization (DP and moisture content of the oil-immersed polymer pressboard specimens were carefully monitored. It is observed that, compared to the relationships between traditional system poles and DP values, there are better correlations between the modified system poles and DP values, because the modified system poles can obtain much more ageing information on transformer polymer insulation. Therefore, the modified system poles proposed in the paper are more suitable for the diagnosis of the ageing condition of transformer polymer insulation.
PROCOPE, Collision Probability in Pin Clusters and Infinite Rod Lattices
International Nuclear Information System (INIS)
Amyot, L.; Daolio, C.; Benoist, P.
1984-01-01
1 - Nature of physical problem solved: Calculation of directional collision probabilities in pin clusters and infinite rod lattices. 2 - Method of solution: a) Gauss integration of analytical expressions for collision probabilities. b) alternately, an approximate closed expression (not involving integrals) may be used for pin-to-pin interactions. 3 - Restrictions on the complexity of the problem: number of fuel pins must be smaller than 62; maximum number of groups of symmetry is 300
Gluon saturation: Survival probability for leading neutrons in DIS
International Nuclear Information System (INIS)
Levin, Eugene; Tapia, Sebastian
2012-01-01
In this paper we discuss the example of one rapidity gap process: the inclusive cross sections of the leading neutrons in deep inelastic scattering with protons (DIS). The equations for this process are proposed and solved, giving the example of theoretical calculation of the survival probability for one rapidity gap processes. It turns out that the value of the survival probability is small and it decreases with energy.
Large deviations and idempotent probability
Puhalskii, Anatolii
2001-01-01
In the view of many probabilists, author Anatolii Puhalskii''s research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak convergence results.Large Deviations and Idempotent Probability expounds upon the recent methodology of building large deviation theory along the lines of weak convergence theory. The author develops an idempotent (or maxitive) probability theory, introduces idempotent analogues of martingales (maxingales), Wiener and Poisson processes, and Ito differential equations, and studies their properties. The large deviation principle for stochastic processes is formulated as a certain type of convergence of stochastic processes to idempotent processes. The author calls this large deviation convergence.The approach to establishing large deviation convergence uses novel com...
Probability biases as Bayesian inference
Directory of Open Access Journals (Sweden)
Andre; C. R. Martins
2006-11-01
Full Text Available In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions. %XX In that sense, it should be no surprise that humans reason with % probability as it has been observed.
Probability matching and strategy availability.
Koehler, Derek J; James, Greta
2010-09-01
Findings from two experiments indicate that probability matching in sequential choice arises from an asymmetry in strategy availability: The matching strategy comes readily to mind, whereas a superior alternative strategy, maximizing, does not. First, compared with the minority who spontaneously engage in maximizing, the majority of participants endorse maximizing as superior to matching in a direct comparison when both strategies are described. Second, when the maximizing strategy is brought to their attention, more participants subsequently engage in maximizing. Third, matchers are more likely than maximizers to base decisions in other tasks on their initial intuitions, suggesting that they are more inclined to use a choice strategy that comes to mind quickly. These results indicate that a substantial subset of probability matchers are victims of "underthinking" rather than "overthinking": They fail to engage in sufficient deliberation to generate a superior alternative to the matching strategy that comes so readily to mind.
Probability as a Physical Motive
Directory of Open Access Journals (Sweden)
Peter Martin
2007-04-01
Full Text Available Recent theoretical progress in nonequilibrium thermodynamics, linking thephysical principle of Maximum Entropy Production (Ã¢Â€ÂœMEPÃ¢Â€Â to the information-theoreticalÃ¢Â€ÂœMaxEntÃ¢Â€Â principle of scientific inference, together with conjectures from theoreticalphysics that there may be no fundamental causal laws but only probabilities for physicalprocesses, and from evolutionary theory that biological systems expand Ã¢Â€Âœthe adjacentpossibleÃ¢Â€Â as rapidly as possible, all lend credence to the proposition that probability shouldbe recognized as a fundamental physical motive. It is further proposed that spatial order andtemporal order are two aspects of the same thing, and that this is the essence of the secondlaw of thermodynamics.
Logic, Probability, and Human Reasoning
2015-01-01
accordingly suggest a way to integrate probability and deduction. The nature of deductive reasoning To be rational is to be able to make deductions...3–6] and they underlie mathematics, science, and tech- nology [7–10]. Plato claimed that emotions upset reason- ing. However, individuals in the grip...fundamental to human rationality . So, if counterexamples to its principal predictions occur, the theory will at least explain its own refutation
Probability Measures on Groups IX
1989-01-01
The latest in this series of Oberwolfach conferences focussed on the interplay between structural probability theory and various other areas of pure and applied mathematics such as Tauberian theory, infinite-dimensional rotation groups, central limit theorems, harmonizable processes, and spherical data. Thus it was attended by mathematicians whose research interests range from number theory to quantum physics in conjunction with structural properties of probabilistic phenomena. This volume contains 5 survey articles submitted on special invitation and 25 original research papers.
Probability matching and strategy availability
J. Koehler, Derek; Koehler, Derek J.; James, Greta
2010-01-01
Findings from two experiments indicate that probability matching in sequential choice arises from an asymmetry in strategy availability: The matching strategy comes readily to mind, whereas a superior alternative strategy, maximizing, does not. First, compared with the minority who spontaneously engage in maximizing, the majority of participants endorse maximizing as superior to matching in a direct comparison when both strategies are described. Second, when the maximizing strategy is brought...
Kheifets, Aaron; Gallistel, C R
2012-05-29
Animals successfully navigate the world despite having only incomplete information about behaviorally important contingencies. It is an open question to what degree this behavior is driven by estimates of stochastic parameters (brain-constructed models of the experienced world) and to what degree it is directed by reinforcement-driven processes that optimize behavior in the limit without estimating stochastic parameters (model-free adaptation processes, such as associative learning). We find that mice adjust their behavior in response to a change in probability more quickly and abruptly than can be explained by differential reinforcement. Our results imply that mice represent probabilities and perform calculations over them to optimize their behavior, even when the optimization produces negligible material gain.
On Farmer's line, probability density functions, and overall risk
International Nuclear Information System (INIS)
Munera, H.A.; Yadigaroglu, G.
1986-01-01
Limit lines used to define quantitative probabilistic safety goals can be categorized according to whether they are based on discrete pairs of event sequences and associated probabilities, on probability density functions (pdf's), or on complementary cumulative density functions (CCDFs). In particular, the concept of the well-known Farmer's line and its subsequent reinterpretations is clarified. It is shown that Farmer's lines are pdf's and, therefore, the overall risk (defined as the expected value of the pdf) that they represent can be easily calculated. It is also shown that the area under Farmer's line is proportional to probability, while the areas under CCDFs are generally proportional to expected value
International Nuclear Information System (INIS)
Li, D.
1980-01-01
Reviewed is the effect of heat flux of different system parameters on critical density in order to give an initial view on the value of several parameters. A thorough analysis of different equations is carried out to calculate burnout is steam-water flows in uniformly heated tubes, annular, and rectangular channels and rod bundles. Effect of heat flux density distribution and flux twisting on burnout and storage determination according to burnout are commended [ru
Evaluation of DNA match probability in criminal case.
Lee, J W; Lee, H S; Park, M; Hwang, J J
2001-02-15
The new emphasis on quantification of evidence has led to perplexing courtroom decisions and it has been difficult for forensic scientists to pursue logical arguments. Especially, for evaluating DNA evidence, though both the genetic relationship for two compared persons and the examined locus system should be considered, the understanding for this has not yet drawn much attention. In this paper, we suggest to calculate the match probability by using coancestry coefficient when the family relationship is considered, and thus the performances of the identification values depending on the calculation of match probability are compared under various situations.
Cross Check of NOvA Oscillation Probabilities
Energy Technology Data Exchange (ETDEWEB)
Parke, Stephen J. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States). Dept. of Theoretical Physics; Messier, Mark D. [Indiana Univ., Bloomington, IN (United States). Dept. of Physics
2018-01-12
In this note we perform a cross check of the programs used by NOvA to calculate the 3-flavor oscillation probabilities with a independent program using a different method. The comparison is performed at 6 significant figures and the agreement, $|\\Delta P|/P$ is better than $10^{-5}$, as good as can be expected with 6 significant figures. In addition, a simple and accurate alternative method to calculate the oscillation probabilities is outlined and compared in the L/E range and matter density relevant for the NOvA experiment.
Evaluations of Structural Failure Probabilities and Candidate Inservice Inspection Programs
Energy Technology Data Exchange (ETDEWEB)
Khaleel, Mohammad A.; Simonen, Fredric A.
2009-05-01
The work described in this report applies probabilistic structural mechanics models to predict the reliability of nuclear pressure boundary components. These same models are then applied to evaluate the effectiveness of alternative programs for inservice inspection to reduce these failure probabilities. Results of the calculations support the development and implementation of risk-informed inservice inspection of piping and vessels. Studies have specifically addressed the potential benefits of ultrasonic inspections to reduce failure probabilities associated with fatigue crack growth and stress-corrosion cracking. Parametric calculations were performed with the computer code pc-PRAISE to generate an extensive set of plots to cover a wide range of pipe wall thicknesses, cyclic operating stresses, and inspection strategies. The studies have also addressed critical inputs to fracture mechanics calculations such as the parameters that characterize the number and sizes of fabrication flaws in piping welds. Other calculations quantify uncertainties associated with the inputs calculations, the uncertainties in the fracture mechanics models, and the uncertainties in the resulting calculated failure probabilities. A final set of calculations address the effects of flaw sizing errors on the effectiveness of inservice inspection programs.
Probability for Weather and Climate
Smith, L. A.
2013-12-01
Over the last 60 years, the availability of large-scale electronic computers has stimulated rapid and significant advances both in meteorology and in our understanding of the Earth System as a whole. The speed of these advances was due, in large part, to the sudden ability to explore nonlinear systems of equations. The computer allows the meteorologist to carry a physical argument to its conclusion; the time scales of weather phenomena then allow the refinement of physical theory, numerical approximation or both in light of new observations. Prior to this extension, as Charney noted, the practicing meteorologist could ignore the results of theory with good conscience. Today, neither the practicing meteorologist nor the practicing climatologist can do so, but to what extent, and in what contexts, should they place the insights of theory above quantitative simulation? And in what circumstances can one confidently estimate the probability of events in the world from model-based simulations? Despite solid advances of theory and insight made possible by the computer, the fidelity of our models of climate differs in kind from the fidelity of models of weather. While all prediction is extrapolation in time, weather resembles interpolation in state space, while climate change is fundamentally an extrapolation. The trichotomy of simulation, observation and theory which has proven essential in meteorology will remain incomplete in climate science. Operationally, the roles of probability, indeed the kinds of probability one has access too, are different in operational weather forecasting and climate services. Significant barriers to forming probability forecasts (which can be used rationally as probabilities) are identified. Monte Carlo ensembles can explore sensitivity, diversity, and (sometimes) the likely impact of measurement uncertainty and structural model error. The aims of different ensemble strategies, and fundamental differences in ensemble design to support of
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2012-01-01
This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and
Probability, statistics, and computational science.
Beerenwinkel, Niko; Siebourg, Juliane
2012-01-01
In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.
Simulator data on human error probabilities
International Nuclear Information System (INIS)
Kozinsky, E.J.; Guttmann, H.E.
1982-01-01
Analysis of operator errors on NPP simulators is being used to determine Human Error Probabilities (HEP) for task elements defined in NUREG/CR 1278. Simulator data tapes from research conducted by EPRI and ORNL are being analyzed for operator error rates. The tapes collected, using Performance Measurement System software developed for EPRI, contain a history of all operator manipulations during simulated casualties. Analysis yields a time history or Operational Sequence Diagram and a manipulation summary, both stored in computer data files. Data searches yield information on operator errors of omission and commission. This work experimentally determines HEPs for Probabilistic Risk Assessment calculations. It is the only practical experimental source of this data to date
Future probabilities of coastal floods in Finland
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.
Simulator data on human error probabilities
International Nuclear Information System (INIS)
Kozinsky, E.J.; Guttmann, H.E.
1981-01-01
Analysis of operator errors on NPP simulators is being used to determine Human Error Probabilities (HEP) for task elements defined in NUREG/CR-1278. Simulator data tapes from research conducted by EPRI and ORNL are being analyzed for operator error rates. The tapes collected, using Performance Measurement System software developed for EPRI, contain a history of all operator manipulations during simulated casualties. Analysis yields a time history or Operational Sequence Diagram and a manipulation summary, both stored in computer data files. Data searches yield information on operator errors of omission and commission. This work experimentally determined HEP's for Probabilistic Risk Assessment calculations. It is the only practical experimental source of this data to date
International Nuclear Information System (INIS)
Petersen, K.E.
1986-03-01
Risk and reliability analysis is increasingly being used in evaluations of plant safety and plant reliability. The analysis can be performed either during the design process or during the operation time, with the purpose to improve the safety or the reliability. Due to plant complexity and safety and availability requirements, sophisticated tools, which are flexible and efficient, are needed. Such tools have been developed in the last 20 years and they have to be continuously refined to meet the growing requirements. Two different areas of application were analysed. In structural reliability probabilistic approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested. (author)
McCarty, George
1982-01-01
How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio...
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…
DEFF Research Database (Denmark)
Petersen, Kurt Erling
1986-01-01
Risk and reliability analysis is increasingly being used in evaluations of plant safety and plant reliability. The analysis can be performed either during the design process or during the operation time, with the purpose to improve the safety or the reliability. Due to plant complexity and safety...... and availability requirements, sophisticated tools, which are flexible and efficient, are needed. Such tools have been developed in the last 20 years and they have to be continuously refined to meet the growing requirements. Two different areas of application were analysed. In structural reliability probabilistic...... approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very...
Probability theory a comprehensive course
Klenke, Achim
2014-01-01
This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To address these concepts, the title covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: • limit theorems for sums of random variables • martingales • percolation • Markov chains and electrical networks • construction of stochastic processes • Poisson point process and infinite divisibility • large deviation principles and statistical physics • Brownian motion • stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the c...
On estimating the fracture probability of nuclear graphite components
International Nuclear Information System (INIS)
Srinivasan, Makuteswara
2008-01-01
The properties of nuclear grade graphites exhibit anisotropy and could vary considerably within a manufactured block. Graphite strength is affected by the direction of alignment of the constituent coke particles, which is dictated by the forming method, coke particle size, and the size, shape, and orientation distribution of pores in the structure. In this paper, a Weibull failure probability analysis for components is presented using the American Society of Testing Materials strength specification for nuclear grade graphites for core components in advanced high-temperature gas-cooled reactors. The risk of rupture (probability of fracture) and survival probability (reliability) of large graphite blocks are calculated for varying and discrete values of service tensile stresses. The limitations in these calculations are discussed from considerations of actual reactor environmental conditions that could potentially degrade the specification properties because of damage due to complex interactions between irradiation, temperature, stress, and variability in reactor operation
Using Fuzzy Probability Weights in Cumulative Prospect Theory
Directory of Open Access Journals (Sweden)
Užga-Rebrovs Oļegs
2016-12-01
Full Text Available During the past years, a rapid growth has been seen in the descriptive approaches to decision choice. As opposed to normative expected utility theory, these approaches are based on the subjective perception of probabilities by the individuals, which takes place in real situations of risky choice. The modelling of this kind of perceptions is made on the basis of probability weighting functions. In cumulative prospect theory, which is the focus of this paper, decision prospect outcome weights are calculated using the obtained probability weights. If the value functions are constructed in the sets of positive and negative outcomes, then, based on the outcome value evaluations and outcome decision weights, generalised evaluations of prospect value are calculated, which are the basis for choosing an optimal prospect.
Failure probability of PWR reactor coolant loop piping
International Nuclear Information System (INIS)
Lo, T.; Woo, H.H.; Holman, G.S.; Chou, C.K.
1984-02-01
This paper describes the results of assessments performed on the PWR coolant loop piping of Westinghouse and Combustion Engineering plants. For direct double-ended guillotine break (DEGB), consideration was given to crack existence probability, initial crack size distribution, hydrostatic proof test, preservice inspection, leak detection probability, crack growth characteristics, and failure criteria based on the net section stress failure and tearing modulus stability concept. For indirect DEGB, fragilities of major component supports were estimated. The system level fragility was then calculated based on the Boolean expression involving these fragilities. Indirect DEGB due to seismic effects was calculated by convolving the system level fragility and the seismic hazard curve. The results indicate that the probability of occurrence of both direct and indirect DEGB is extremely small, thus, postulation of DEGB in design should be eliminated and replaced by more realistic criteria
Simplified Freeman-Tukey test statistics for testing probabilities in ...
African Journals Online (AJOL)
This paper presents the simplified version of the Freeman-Tukey test statistic for testing hypothesis about multinomial probabilities in one, two and multidimensional contingency tables that does not require calculating the expected cell frequencies before test of significance. The simplified method established new criteria of ...
Relative transition probabilities for krypton.
Miller, M. H.; Roig, R. A.; Bengtson, R. D.
1972-01-01
First experimental line strength data for the visible Kr II lines and for several of the more prominent Kr I lines are given. The spectroscopic light source used is the thermal plasma behind the reflected shock wave in a gas-driven shock tube. A 3/4-m spectrograph and a 1-m spectrograph were employed simultaneously to provide redundant photometry. The data are compared with other measurements and with theoretical calculations.
Excluding joint probabilities from quantum theory
Allahverdyan, Armen E.; Danageozian, Arshag
2018-03-01
Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.
Reliability of structures by using probability and fatigue theories
International Nuclear Information System (INIS)
Lee, Ouk Sub; Kim, Dong Hyeok; Park, Yeon Chang
2008-01-01
Methodologies to calculate failure probability and to estimate the reliability of fatigue loaded structures are developed. The applicability of the methodologies is evaluated with the help of the fatigue crack growth models suggested by Paris and Walker. The probability theories such as the FORM (first order reliability method), the SORM (second order reliability method) and the MCS (Monte Carlo simulation) are utilized. It is found that the failure probability decreases with the increase of the design fatigue life and the applied minimum stress, the decrease of the initial edge crack size, the applied maximum stress and the slope of Paris equation. Furthermore, according to the sensitivity analysis of random variables, the slope of Pairs equation affects the failure probability dominantly among other random variables in the Paris and the Walker models
Wigner function and the probability representation of quantum states
Directory of Open Access Journals (Sweden)
Man’ko Margarita A.
2014-01-01
Full Text Available The relation of theWigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner–Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for directexperimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.
Probability theory and mathematical statistics for engineers
Pugachev, V S
1984-01-01
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Introduction to probability theory with contemporary applications
Helms, Lester L
2010-01-01
This introduction to probability theory transforms a highly abstract subject into a series of coherent concepts. Its extensive discussions and clear examples, written in plain language, expose students to the rules and methods of probability. Suitable for an introductory probability course, this volume requires abstract and conceptual thinking skills and a background in calculus.Topics include classical probability, set theory, axioms, probability functions, random and independent random variables, expected values, and covariance and correlations. Additional subjects include stochastic process
K-forbidden transition probabilities
International Nuclear Information System (INIS)
Saitoh, T.R.; Sletten, G.; Bark, R.A.; Hagemann, G.B.; Herskind, B.; Saitoh-Hashimoto, N.; Tsukuba Univ., Ibaraki
2000-01-01
Reduced hindrance factors of K-forbidden transitions are compiled for nuclei with A∝180 where γ-vibrational states are observed. Correlations between these reduced hindrance factors and Coriolis forces, statistical level mixing and γ-softness have been studied. It is demonstrated that the K-forbidden transition probabilities are related to γ-softness. The decay of the high-K bandheads has been studied by means of the two-state mixing, which would be induced by the γ-softness, with the use of a number of K-forbidden transitions compiled in the present work, where high-K bandheads are depopulated by both E2 and ΔI=1 transitions. The validity of the two-state mixing scheme has been examined by using the proposed identity of the B(M1)/B(E2) ratios of transitions depopulating high-K bandheads and levels of low-K bands. A break down of the identity might indicate that other levels would mediate transitions between high- and low-K states. (orig.)
Direct probability mapping of contaminants
International Nuclear Information System (INIS)
Rautman, C.A.
1993-01-01
Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. Geostatistical simulation provides powerful tools for investigating contaminant levels, and in particular, for identifying and using the spatial interrelationships among a set of isolated sample values. This additional information can be used to assess the likelihood of encountering contamination at unsampled locations and to evaluate the risk associated with decisions to remediate or not to remediate specific regions within a site. Past operation of the DOE Feed Materials Production Center has contaminated a site near Fernald, Ohio, with natural uranium. Soil geochemical data have been collected as part of the Uranium-in-Soils Integrated Demonstration Project. These data have been used to construct a number of stochastic images of potential contamination for parcels approximately the size of a selective remediation unit. Each such image accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely, statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination. Evaluation of the geostatistical simulations can yield maps representing the expected magnitude of the contamination for various regions and other information that may be important in determining a suitable remediation process or in sizing equipment to accomplish the restoration
Psychophysics of the probability weighting function
Takahashi, Taiki
2011-03-01
A probability weighting function w(p) for an objective probability p in decision under risk plays a pivotal role in Kahneman-Tversky prospect theory. Although recent studies in econophysics and neuroeconomics widely utilized probability weighting functions, psychophysical foundations of the probability weighting functions have been unknown. Notably, a behavioral economist Prelec (1998) [4] axiomatically derived the probability weighting function w(p)=exp(-() (01e)=1e,w(1)=1), which has extensively been studied in behavioral neuroeconomics. The present study utilizes psychophysical theory to derive Prelec's probability weighting function from psychophysical laws of perceived waiting time in probabilistic choices. Also, the relations between the parameters in the probability weighting function and the probability discounting function in behavioral psychology are derived. Future directions in the application of the psychophysical theory of the probability weighting function in econophysics and neuroeconomics are discussed.
THE BLACK HOLE FORMATION PROBABILITY
Energy Technology Data Exchange (ETDEWEB)
Clausen, Drew; Piro, Anthony L.; Ott, Christian D., E-mail: dclausen@tapir.caltech.edu [TAPIR, Walter Burke Institute for Theoretical Physics, California Institute of Technology, Mailcode 350-17, Pasadena, CA 91125 (United States)
2015-02-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P {sub BH}(M {sub ZAMS}). Although we find that it is difficult to derive a unique P {sub BH}(M {sub ZAMS}) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P {sub BH}(M {sub ZAMS}) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P {sub BH}(M {sub ZAMS}) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment.
THE BLACK HOLE FORMATION PROBABILITY
International Nuclear Information System (INIS)
Clausen, Drew; Piro, Anthony L.; Ott, Christian D.
2015-01-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P BH (M ZAMS ). Although we find that it is difficult to derive a unique P BH (M ZAMS ) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P BH (M ZAMS ) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P BH (M ZAMS ) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment
The Black Hole Formation Probability
Clausen, Drew; Piro, Anthony L.; Ott, Christian D.
2015-02-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P BH(M ZAMS). Although we find that it is difficult to derive a unique P BH(M ZAMS) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P BH(M ZAMS) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P BH(M ZAMS) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment.
Assigning probability gain for precursors of four large Chinese earthquakes
Energy Technology Data Exchange (ETDEWEB)
Cao, T.; Aki, K.
1983-03-10
We extend the concept of probability gain associated with a precursor (Aki, 1981) to a set of precursors which may be mutually dependent. Making use of a new formula, we derive a criterion for selecting precursors from a given data set in order to calculate the probability gain. The probabilities per unit time immediately before four large Chinese earthquakes are calculated. They are approximately 0.09, 0.09, 0.07 and 0.08 per day for 1975 Haicheng (M = 7.3), 1976 Tangshan (M = 7.8), 1976 Longling (M = 7.6), and Songpan (M = 7.2) earthquakes, respectively. These results are encouraging because they suggest that the investigated precursory phenomena may have included the complete information for earthquake prediction, at least for the above earthquakes. With this method, the step-by-step approach to prediction used in China may be quantified in terms of the probability of earthquake occurrence. The ln P versus t curve (where P is the probability of earthquake occurrence at time t) shows that ln P does not increase with t linearly but more rapidly as the time of earthquake approaches.
Neutronic calculation of reactor cells
International Nuclear Information System (INIS)
Jaliff, J.O.
1981-01-01
Multigroup calculations of cylindrical pin cells were programmed, in Fortran IV, upon the basis of collision probabilities in each energy group. A rational approximation to the fuel-to-fuel collision probability in resonance groups was used. Together with the intermediate resonance theory, cross sections corrected for heterogeneity and absorber interactions were found. For the optimization of the program, the cell of a BWR reactor was taken as reference. Data for such a cell and the reactor's operating conditions are presented. PINCEL is a fast and flexible program, with checked results, around a 69-group library. (M.E.L.) [es
Foundations of the theory of probability
Kolmogorov, AN
2018-01-01
This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.
Conditional Probability Modulates Visual Search Efficiency
Directory of Open Access Journals (Sweden)
Bryan eCort
2013-10-01
Full Text Available We investigated the effects of probability on visual search. Previous work has shown that people can utilize spatial and sequential probability information to improve target detection. We hypothesized that performance improvements from probability information would extend to the efficiency of visual search. Our task was a simple visual search in which the target was always present among a field of distractors, and could take one of two colors. The absolute probability of the target being either color was 0.5; however, the conditional probability – the likelihood of a particular color given a particular combination of two cues – varied from 0.1 to 0.9. We found that participants searched more efficiently for high conditional probability targets and less efficiently for low conditional probability targets, but only when they were explicitly informed of the probability relationship between cues and target color.
Analytic Neutrino Oscillation Probabilities in Matter: Revisited
Energy Technology Data Exchange (ETDEWEB)
Parke, Stephen J. [Fermilab; Denton, Peter B. [Copenhagen U.; Minakata, Hisakazu [Madrid, IFT
2018-01-02
We summarize our recent paper on neutrino oscillation probabilities in matter, explaining the importance, relevance and need for simple, highly accurate approximations to the neutrino oscillation probabilities in matter.
Non-equilibrium random matrix theory. Transition probabilities
Energy Technology Data Exchange (ETDEWEB)
Pedro, Francisco Gil [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie
2016-06-15
In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Non-equilibrium random matrix theory. Transition probabilities
International Nuclear Information System (INIS)
Pedro, Francisco Gil; Westphal, Alexander
2016-06-01
In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large N limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.
Emptiness formation probability and quantum Knizhnik-Zamolodchikov equation
International Nuclear Information System (INIS)
Boos, H.E.; Korepin, V.E.; Smirnov, F.A.
2003-01-01
We consider the one-dimensional XXX spin-1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability (EFP). We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik-Zamolodchikov equation (qKZ). We calculate EFP for n≤6 for inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbitrary n
The case of escape probability as linear in short time
Marchewka, A.; Schuss, Z.
2018-02-01
We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more.
Impact of proof test interval and coverage on probability of failure of safety instrumented function
International Nuclear Information System (INIS)
Jin, Jianghong; Pang, Lei; Hu, Bin; Wang, Xiaodong
2016-01-01
Highlights: • Introduction of proof test coverage makes the calculation of the probability of failure for SIF more accurate. • The probability of failure undetected by proof test is independently defined as P TIF and calculated. • P TIF is quantified using reliability block diagram and simple formula of PFD avg . • Improving proof test coverage and adopting reasonable test period can reduce the probability of failure for SIF. - Abstract: Imperfection of proof test can result in the safety function failure of safety instrumented system (SIS) at any time in its life period. IEC61508 and other references ignored or only elementarily analyzed the imperfection of proof test. In order to further study the impact of the imperfection of proof test on the probability of failure for safety instrumented function (SIF), the necessity of proof test and influence of its imperfection on system performance was first analyzed theoretically. The probability of failure for safety instrumented function resulted from the imperfection of proof test was defined as probability of test independent failures (P TIF ), and P TIF was separately calculated by introducing proof test coverage and adopting reliability block diagram, with reference to the simplified calculation formula of average probability of failure on demand (PFD avg ). Research results show that: the shorter proof test period and the higher proof test coverage indicate the smaller probability of failure for safety instrumented function. The probability of failure for safety instrumented function which is calculated by introducing proof test coverage will be more accurate.
Void probability scaling in hadron nucleus interactions
International Nuclear Information System (INIS)
Ghosh, Dipak; Deb, Argha; Bhattacharyya, Swarnapratim; Ghosh, Jayita; Bandyopadhyay, Prabhat; Das, Rupa; Mukherjee, Sima
2002-01-01
Heygi while investigating with the rapidity gap probability (that measures the chance of finding no particle in the pseudo-rapidity interval Δη) found that a scaling behavior in the rapidity gap probability has a close correspondence with the scaling of a void probability in galaxy correlation study. The main aim in this paper is to study the scaling behavior of the rapidity gap probability
Pre-Service Teachers' Conceptions of Probability
Odafe, Victor U.
2011-01-01
Probability knowledge and skills are needed in science and in making daily decisions that are sometimes made under uncertain conditions. Hence, there is the need to ensure that the pre-service teachers of our children are well prepared to teach probability. Pre-service teachers' conceptions of probability are identified, and ways of helping them…
Using Playing Cards to Differentiate Probability Interpretations
López Puga, Jorge
2014-01-01
The aprioristic (classical, naïve and symmetric) and frequentist interpretations of probability are commonly known. Bayesian or subjective interpretation of probability is receiving increasing attention. This paper describes an activity to help students differentiate between the three types of probability interpretations.
Dependent Human Error Probability Assessment
International Nuclear Information System (INIS)
Simic, Z.; Mikulicic, V.; Vukovic, I.
2006-01-01
This paper presents an assessment of the dependence between dynamic operator actions modeled in a Nuclear Power Plant (NPP) PRA and estimate the associated impact on Core damage frequency (CDF). This assessment was done improve HEP dependencies implementation inside existing PRA. All of the dynamic operator actions modeled in the NPP PRA are included in this assessment. Determining the level of HEP dependence and the associated influence on CDF are the major steps of this assessment. A decision on how to apply the results, i.e., should permanent HEP model changes be made, is based on the resulting relative CDF increase. Some CDF increase was selected as a threshold based on the NPP base CDF value and acceptance guidelines from the Regulatory Guide 1.174. HEP dependence resulting in a CDF increase of > 5E-07 would be considered potential candidates for specific incorporation into the baseline model. The approach used to judge the level of dependence between operator actions is based on dependency level categories and conditional probabilities developed in the Handbook of Human Reliability Analysis with Emphasis on Nuclear Power Plant Applications NUREG/CR-1278. To simplify the process, NUREG/CR-1278 identifies five levels of dependence: ZD (zero dependence), LD (low dependence), MD (moderate dependence), HD (high dependence), and CD (complete dependence). NUREG/CR-1278 also identifies several qualitative factors that could be involved in determining the level of dependence. Based on the NUREG/CR-1278 information, Time, Function, and Spatial attributes were judged to be the most important considerations when determining the level of dependence between operator actions within an accident sequence. These attributes were used to develop qualitative criteria (rules) that were used to judge the level of dependence (CD, HD, MD, LD, ZD) between the operator actions. After the level of dependence between the various HEPs is judged, quantitative values associated with the
Probability evolution method for exit location distribution
Zhu, Jinjie; Chen, Zhen; Liu, Xianbin
2018-03-01
The exit problem in the framework of the large deviation theory has been a hot topic in the past few decades. The most probable escape path in the weak-noise limit has been clarified by the Freidlin-Wentzell action functional. However, noise in real physical systems cannot be arbitrarily small while noise with finite strength may induce nontrivial phenomena, such as noise-induced shift and noise-induced saddle-point avoidance. Traditional Monte Carlo simulation of noise-induced escape will take exponentially large time as noise approaches zero. The majority of the time is wasted on the uninteresting wandering around the attractors. In this paper, a new method is proposed to decrease the escape simulation time by an exponentially large factor by introducing a series of interfaces and by applying the reinjection on them. This method can be used to calculate the exit location distribution. It is verified by examining two classical examples and is compared with theoretical predictions. The results show that the method performs well for weak noise while may induce certain deviations for large noise. Finally, some possible ways to improve our method are discussed.
Lectures on probability and statistics. Revision
International Nuclear Information System (INIS)
Yost, G.P.
1985-06-01
These notes are based on a set of statistics lectures delivered at Imperial College to the first-year postgraduate students in High Energy Physics. They are designed for the professional experimental scientist. They begin with the fundamentals of probability theory, in which one makes statements about the set of possible outcomes of an experiment, based upon a complete a priori understanding of the experiment. For example, in a roll of a set of (fair) dice, one understands a priori that any given side of each die is equally likely to turn up. From that, we can calculate the probabilty of any specified outcome. They finish with the inverse problem, statistics. Here, one begins with a set of actual data (e.g., the outcomes of a number of rolls of the dice), and attempts to make inferences about the state of nature which gave those data (e.g., the likelihood of seeing any given side of any given die turn up). This is a much more difficult problem, of course, and one's solutions often turn out to be unsatisfactory in one respect or another. Hopefully, the reader will come away from these notes with a feel for some of the problems and uncertainties involved. Although there are standard approaches, most of the time there is no cut and dried ''best'' solution - ''best'' according to every criterion
Probability based calibration of pressure coefficients
DEFF Research Database (Denmark)
Hansen, Svend Ole; Pedersen, Marie Louise; Sørensen, John Dalsgaard
2015-01-01
Normally, a consistent basis for calculating partial factors focuses on a homogeneous reliability index neither depending on which material the structure is constructed of nor the ratio between the permanent and variable actions acting on the structure. Furthermore, the reliability index should n...... the characteristic shape coefficients are based on mean values as specified in background documents to the Eurocodes. Importance of hidden safeties judging the reliability is discussed for wind actions on low-rise structures....... not depend on the type of variable action. A probability based calibration of pressure coefficients have been carried out using pressure measurements on the standard CAARC building modelled on scale of 1:383. The extreme pressures measured on the CAARC building model in the wind tunnel have been fitted.......3, the Eurocode partial factor of 1.5 for variable actions agrees well with the inherent uncertainties of wind actions when the pressure coefficients are determined using wind tunnel test results. The increased bias and uncertainty when pressure coefficients mainly are based on structural codes lead to a larger...
Fundamentals of applied probability and random processes
Ibe, Oliver
2014-01-01
The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability t
Probability of Failure in Random Vibration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
1988-01-01
Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out......-crossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval and thus for the first-passage probability...
An Objective Theory of Probability (Routledge Revivals)
Gillies, Donald
2012-01-01
This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises' views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises' definition of probability in terms of limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axioma
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
Methodologies of Uncertainty Propagation Calculation
International Nuclear Information System (INIS)
Chojnacki, Eric
2002-01-01
After recalling the theoretical principle and the practical difficulties of the methodologies of uncertainty propagation calculation, the author discussed how to propagate input uncertainties. He said there were two kinds of input uncertainty: - variability: uncertainty due to heterogeneity, - lack of knowledge: uncertainty due to ignorance. It was therefore necessary to use two different propagation methods. He demonstrated this in a simple example which he generalised, treating the variability uncertainty by the probability theory and the lack of knowledge uncertainty by the fuzzy theory. He cautioned, however, against the systematic use of probability theory which may lead to unjustifiable and illegitimate precise answers. Mr Chojnacki's conclusions were that the importance of distinguishing variability and lack of knowledge increased as the problem was getting more and more complex in terms of number of parameters or time steps, and that it was necessary to develop uncertainty propagation methodologies combining probability theory and fuzzy theory
Calculation of the quantities of radiation risk in Japanese population
International Nuclear Information System (INIS)
Nakamura, Yuji
1993-01-01
The purpose of this study was to reevaluate various kinds of indicators of radiation risks using additive projection and multiplicative projection models, as proposed by ICRP. Total death probability rate (1985) and probability rate of cancer death (1983 to 1987) were used as data base. The following indicators were calculated: total conditional death probability rate and conditional death probability rate; normalized death age probability density and unconditional death probability rate; attributable life-time probability of cancer death; and other risk indicators, including mean loss of life expectancy, reduction of life expectancy, mean annually committed probability of attributable cancer deaths, annual extra probability of cancer death, probability density of the age of death, maximum relative death probability rate (age at maximum relative rate), and probabilistic aging. In terms of calculations of these risk indicators for the comprehensive cancer death, there was no great difference between the Japanese population and ICRP. When calculating according to sites of cancer, calculations of indicators for cancer mortality (or cancer cure rate) in the Japanese population might bedifferent from ICRP's calculation. (N.K.) different from ICRP's calculations. (N.K.)
Flux continuity and probability conservation in complexified Bohmian mechanics
International Nuclear Information System (INIS)
Poirier, Bill
2008-01-01
Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems as both a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy probability conservation to ensure they are always guided to where they are most needed. We consider probability conservation for complexified Bohmian trajectories. The analysis relies on time-reversal symmetry considerations, leading to a generalized expression for the conjugation of wave functions of complexified variables. This in turn enables meaningful discussion of complexified flux continuity, which turns out not to be satisfied in general, though a related property is found to be true. The main conclusion, though, is that even under a weak interpretation, probability is not conserved along complex Bohmian trajectories
Incidence Probability of Delayed Health Consequences of the Chernobyl Accident
International Nuclear Information System (INIS)
Abdel-Ghani, A.H.; El-Naggar, A.M.; El-Kadi, A.A.
2000-01-01
During the first international Conference on the long -term consequences of the Chernobyl disaster in 1995 at Kiev, and also during the 1996 International Conference at Vienna, Summing up the consequences of the Chernobyl accident, the data regarding the delayed health consequences were mainly related to thyroid cancer, hereditary disorders, general morbidity, mortality and psychological disturbances. Contrary to expectations, the incidences of Leukemia and Soft Tissue tumors were similar to the spontaneous incident. The expected delayed effects, however, among the accident survivors, the liquidators and populations resident in contaminated areas would show higher incidence probability to Leukemia. These population groups have been continuously exposed to low level radiation both externally and internally. Application of the new ICRP concept of radiation-induced Detriment, and the Nominal Probability Coefficient for Cancer and hereditary effects for both workers and populations are used as the rationale to calculate the incidence probability of occurrence of delayed health effects of the Chernobyl accidents
Approximation of ruin probabilities via Erlangized scale mixtures
DEFF Research Database (Denmark)
Peralta, Oscar; Rojas-Nandayapa, Leonardo; Xie, Wangyue
2018-01-01
In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale...... a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size...... distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed....
Computing exact bundle compliance control charts via probability generating functions.
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.
[Inverse probability weighting (IPW) for evaluating and "correcting" selection bias].
Narduzzi, Silvia; Golini, Martina Nicole; Porta, Daniela; Stafoggia, Massimo; Forastiere, Francesco
2014-01-01
the Inverse probability weighting (IPW) is a methodology developed to account for missingness and selection bias caused by non-randomselection of observations, or non-random lack of some information in a subgroup of the population. to provide an overview of IPW methodology and an application in a cohort study of the association between exposure to traffic air pollution (nitrogen dioxide, NO₂) and 7-year children IQ. this methodology allows to correct the analysis by weighting the observations with the probability of being selected. The IPW is based on the assumption that individual information that can predict the probability of inclusion (non-missingness) are available for the entire study population, so that, after taking account of them, we can make inferences about the entire target population starting from the nonmissing observations alone.The procedure for the calculation is the following: firstly, we consider the entire population at study and calculate the probability of non-missing information using a logistic regression model, where the response is the nonmissingness and the covariates are its possible predictors.The weight of each subject is given by the inverse of the predicted probability. Then the analysis is performed only on the non-missing observations using a weighted model. IPW is a technique that allows to embed the selection process in the analysis of the estimates, but its effectiveness in "correcting" the selection bias depends on the availability of enough information, for the entire population, to predict the non-missingness probability. In the example proposed, the IPW application showed that the effect of exposure to NO2 on the area of verbal intelligence quotient of children is stronger than the effect showed from the analysis performed without regard to the selection processes.
Time Dependence of Collision Probabilities During Satellite Conjunctions
Hall, Doyle T.; Hejduk, Matthew D.; Johnson, Lauren C.
2017-01-01
The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.
Bremsstrahlung emission probability in the α decay of 210Po
International Nuclear Information System (INIS)
Boie, Hans-Hermann
2009-01-01
A high-statistics measurement of bremsstrahlung emitted in the α decay of 210 Po has been performed. The measured differential emission probabilities, which could be followed up to γ-energies of ∝ 500 keV, allow for the first time for a serious test of various model calculations of the bremsstrahlung accompanied α decay. It is shown that corrections to the α-γ angular correlation due to the interference between the electric dipole and quadrupole amplitudes and due to the relativistic character of the process have to be taken into account. With the experimentally derived angular correlation the measured energydifferential bremsstrahlung emission probabilities show excellent agreement with the fully quantum mechanical calculation. (orig.)
The extinction probability in systems randomly varying in time
Directory of Open Access Journals (Sweden)
Imre Pázsit
2017-09-01
Full Text Available The extinction probability of a branching process (a neutron chain in a multiplying medium is calculated for a system randomly varying in time. The evolution of the first two moments of such a process was calculated previously by the authors in a system randomly shifting between two states of different multiplication properties. The same model is used here for the investigation of the extinction probability. It is seen that the determination of the extinction probability is significantly more complicated than that of the moments, and it can only be achieved by pure numerical methods. The numerical results indicate that for systems fluctuating between two subcritical or two supercritical states, the extinction probability behaves as expected, but for systems fluctuating between a supercritical and a subcritical state, there is a crucial and unexpected deviation from the predicted behaviour. The results bear some significance not only for neutron chains in a multiplying medium, but also for the evolution of biological populations in a time-varying environment.
Generic Degraded Configuration Probability Analysis for the Codisposal Waste Package
International Nuclear Information System (INIS)
S.F.A. Deng; M. Saglam; L.J. Gratton
2001-01-01
In accordance with the technical work plan, ''Technical Work Plan For: Department of Energy Spent Nuclear Fuel Work Packages'' (CRWMS M and O 2000c), this Analysis/Model Report (AMR) is developed for the purpose of screening out degraded configurations for U.S. Department of Energy (DOE) spent nuclear fuel (SNF) types. It performs the degraded configuration parameter and probability evaluations of the overall methodology specified in the ''Disposal Criticality Analysis Methodology Topical Report'' (YMP 2000, Section 3) to qualifying configurations. Degradation analyses are performed to assess realizable parameter ranges and physical regimes for configurations. Probability calculations are then performed for configurations characterized by k eff in excess of the Critical Limit (CL). The scope of this document is to develop a generic set of screening criteria or models to screen out degraded configurations having potential for exceeding a criticality limit. The developed screening criteria include arguments based on physical/chemical processes and probability calculations and apply to DOE SNF types when codisposed with the high-level waste (HLW) glass inside a waste package. The degradation takes place inside the waste package and is long after repository licensing has expired. The emphasis of this AMR is on degraded configuration screening and the probability analysis is one of the approaches used for screening. The intended use of the model is to apply the developed screening criteria to each DOE SNF type following the completion of the degraded mode criticality analysis internal to the waste package
Reach/frequency for printed media: Personal probabilities or models
DEFF Research Database (Denmark)
Mortensen, Peter Stendahl
2000-01-01
The author evaluates two different ways of estimating reach and frequency of plans for printed media. The first assigns reading probabilities to groups of respondents and calculates reach and frequency by simulation. the second estimates parameters to a model for reach/frequency. It is concluded ...... and estiamtes from such models are shown to be closer to panel data. the problem, however, is to get valid input for such models from readership surveys. Means for this are discussed....
Absolute Kr I and Kr II transition probabilities
International Nuclear Information System (INIS)
Brandt, T.; Helbig, V.; Nick, K.P.
1982-01-01
Transition probabilities for 11 KrI and 9 KrII lines between 366.5 and 599.3nm were obtained from measurements with a wall-stabilised arc at atmospheric pressure in pure krypton. The population densities of the excited krypton levels were calculated under the assumption of LTE from electron densities measured by laser interferometry. The uncertainties for the KrI and the KrII data are 15 and 25% respectively. (author)
Transition probability spaces in loop quantum gravity
Guo, Xiao-Kan
2018-03-01
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.
Towards a Categorical Account of Conditional Probability
Directory of Open Access Journals (Sweden)
Robert Furber
2015-11-01
Full Text Available This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condition. The latter is a predicate in the logic of effect modules on this Kleisli category. This same approach can be transferred to the category of C*-algebras (with positive unital maps, whose predicate logic is also expressed in terms of effect modules. Conditional probabilities can again be expressed via a triangle-fill-in property. In the literature, there are several proposals for what quantum conditional probability should be, and also there are extra difficulties not present in the classical case. At this stage, we only describe quantum systems with classical parametrization.
UT Biomedical Informatics Lab (BMIL) probability wheel
Huang, Sheng-Cheng; Lee, Sara; Wang, Allen; Cantor, Scott B.; Sun, Clement; Fan, Kaili; Reece, Gregory P.; Kim, Min Soon; Markey, Mia K.
A probability wheel app is intended to facilitate communication between two people, an "investigator" and a "participant", about uncertainties inherent in decision-making. Traditionally, a probability wheel is a mechanical prop with two colored slices. A user adjusts the sizes of the slices to indicate the relative value of the probabilities assigned to them. A probability wheel can improve the adjustment process and attenuate the effect of anchoring bias when it is used to estimate or communicate probabilities of outcomes. The goal of this work was to develop a mobile application of the probability wheel that is portable, easily available, and more versatile. We provide a motivating example from medical decision-making, but the tool is widely applicable for researchers in the decision sciences.
A probability space for quantum models
Lemmens, L. F.
2017-06-01
A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.
Fundamentals of applied probability and random processes
Ibe, Oliver
2005-01-01
This book is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book''s clear writing style and homework problems make it ideal for the classroom or for self-study.* Good and solid introduction to probability theory and stochastic processes * Logically organized; writing is presented in a clear manner * Choice of topics is comprehensive within the area of probability * Ample homework problems are organized into chapter sections
Striatal activity is modulated by target probability.
Hon, Nicholas
2017-06-14
Target probability has well-known neural effects. In the brain, target probability is known to affect frontal activity, with lower probability targets producing more prefrontal activation than those that occur with higher probability. Although the effect of target probability on cortical activity is well specified, its effect on subcortical structures such as the striatum is less well understood. Here, I examined this issue and found that the striatum was highly responsive to target probability. This is consistent with its hypothesized role in the gating of salient information into higher-order task representations. The current data are interpreted in light of that fact that different components of the striatum are sensitive to different types of task-relevant information.
Defining Probability in Sex Offender Risk Assessment.
Elwood, Richard W
2016-12-01
There is ongoing debate and confusion over using actuarial scales to predict individuals' risk of sexual recidivism. Much of the debate comes from not distinguishing Frequentist from Bayesian definitions of probability. Much of the confusion comes from applying Frequentist probability to individuals' risk. By definition, only Bayesian probability can be applied to the single case. The Bayesian concept of probability resolves most of the confusion and much of the debate in sex offender risk assessment. Although Bayesian probability is well accepted in risk assessment generally, it has not been widely used to assess the risk of sex offenders. I review the two concepts of probability and show how the Bayesian view alone provides a coherent scheme to conceptualize individuals' risk of sexual recidivism.
On the probability of cure for heavy-ion radiotherapy
International Nuclear Information System (INIS)
Hanin, Leonid; Zaider, Marco
2014-01-01
The probability of a cure in radiation therapy (RT)—viewed as the probability of eventual extinction of all cancer cells—is unobservable, and the only way to compute it is through modeling the dynamics of cancer cell population during and post-treatment. The conundrum at the heart of biophysical models aimed at such prospective calculations is the absence of information on the initial size of the subpopulation of clonogenic cancer cells (also called stem-like cancer cells), that largely determines the outcome of RT, both in an individual and population settings. Other relevant parameters (e.g. potential doubling time, cell loss factor and survival probability as a function of dose) are, at least in principle, amenable to empirical determination. In this article we demonstrate that, for heavy-ion RT, microdosimetric considerations (justifiably ignored in conventional RT) combined with an expression for the clone extinction probability obtained from a mechanistic model of radiation cell survival lead to useful upper bounds on the size of the pre-treatment population of clonogenic cancer cells as well as upper and lower bounds on the cure probability. The main practical impact of these limiting values is the ability to make predictions about the probability of a cure for a given population of patients treated to newer, still unexplored treatment modalities from the empirically determined probability of a cure for the same or similar population resulting from conventional low linear energy transfer (typically photon/electron) RT. We also propose that the current trend to deliver a lower total dose in a smaller number of fractions with larger-than-conventional doses per fraction has physical limits that must be understood before embarking on a particular treatment schedule. (paper)
CONDOR: neutronic code for fuel elements calculation with rods
International Nuclear Information System (INIS)
Villarino, E.A.
1990-01-01
CONDOR neutronic code is used for the calculation of fuel elements formed by fuel rods. The method employed to obtain the neutronic flux is that of collision probabilities in a multigroup scheme on two-dimensional geometry. This code utilizes new calculation algorithms and normalization of such collision probabilities. Burn-up calculations can be made before the alternative of applying variational methods for response flux calculations or those corresponding to collision normalization. (Author) [es
Spatial probability aids visual stimulus discrimination
Directory of Open Access Journals (Sweden)
Michael Druker
2010-08-01
Full Text Available We investigated whether the statistical predictability of a target's location would influence how quickly and accurately it was classified. Recent results have suggested that spatial probability can be a cue for the allocation of attention in visual search. One explanation for probability cuing is spatial repetition priming. In our two experiments we used probability distributions that were continuous across the display rather than relying on a few arbitrary screen locations. This produced fewer spatial repeats and allowed us to dissociate the effect of a high probability location from that of short-term spatial repetition. The task required participants to quickly judge the color of a single dot presented on a computer screen. In Experiment 1, targets were more probable in an off-center hotspot of high probability that gradually declined to a background rate. Targets garnered faster responses if they were near earlier target locations (priming and if they were near the high probability hotspot (probability cuing. In Experiment 2, target locations were chosen on three concentric circles around fixation. One circle contained 80% of targets. The value of this ring distribution is that it allowed for a spatially restricted high probability zone in which sequentially repeated trials were not likely to be physically close. Participant performance was sensitive to the high-probability circle in addition to the expected effects of eccentricity and the distance to recent targets. These two experiments suggest that inhomogeneities in spatial probability can be learned and used by participants on-line and without prompting as an aid for visual stimulus discrimination and that spatial repetition priming is not a sufficient explanation for this effect. Future models of attention should consider explicitly incorporating the probabilities of targets locations and features.
Is probability of frequency too narrow?
International Nuclear Information System (INIS)
Martz, H.F.
1993-01-01
Modern methods of statistical data analysis, such as empirical and hierarchical Bayesian methods, should find increasing use in future Probabilistic Risk Assessment (PRA) applications. In addition, there will be a more formalized use of expert judgment in future PRAs. These methods require an extension of the probabilistic framework of PRA, in particular, the popular notion of probability of frequency, to consideration of frequency of frequency, frequency of probability, and probability of probability. The genesis, interpretation, and examples of these three extended notions are discussed
ICPP - a collision probability module for the AUS neutronics code system
International Nuclear Information System (INIS)
Robinson, G.S.
1985-10-01
The isotropic collision probability program (ICPP) is a module of the AUS neutronics code system which calculates first flight collision probabilities for neutrons in one-dimensional geometries and in clusters of rods. Neutron sources, including scattering, are assumed to be isotropic and to be spatially flat within each mesh interval. The module solves the multigroup collision probability equations for eigenvalue or fixed source problems
International Nuclear Information System (INIS)
Coleman, J.H.
1980-10-01
A technique is discussed for computing the probability distribution of the accumulated dose received by an arbitrary receptor resulting from several single releases from an intermittent source. The probability density of the accumulated dose is the convolution of the probability densities of doses from the intermittent releases. Emissions are not assumed to be constant over the brief release period. The fast fourier transform is used in the calculation of the convolution
Probability theory and statistical applications a profound treatise for self-study
Zörnig, Peter
2016-01-01
This accessible and easy-to-read book provides many examples to illustrate diverse topics in probability and statistics, from initial concepts up to advanced calculations. Special attention is devoted e.g. to independency of events, inequalities in probability and functions of random variables. The book is directed to students of mathematics, statistics, engineering, and other quantitative sciences.
Interpretation of the results of statistical measurements. [search for basic probability model
Olshevskiy, V. V.
1973-01-01
For random processes, the calculated probability characteristic, and the measured statistical estimate are used in a quality functional, which defines the difference between the two functions. Based on the assumption that the statistical measurement procedure is organized so that the parameters for a selected model are optimized, it is shown that the interpretation of experimental research is a search for a basic probability model.
Impact of MCNP unresolved resonance probability-table treatment on uranium and plutonium benchmarks
International Nuclear Information System (INIS)
Mosteller, R.D.; Little, R.C.
1998-01-01
Versions of MCNP up through and including 4B have not accurately modeled neutron self-shielding effects in the unresolved resonance energy region. Recently, a probability-table treatment has been incorporated into a developmental version of MCNP. This paper presents MCNP results for a variety of uranium and plutonium critical benchmarks, calculated with and without the probability-table treatment
Compact baby universe model in ten dimension and probability function of quantum gravity
International Nuclear Information System (INIS)
Yan Jun; Hu Shike
1991-01-01
The quantum probability functions are calculated for ten-dimensional compact baby universe model. The authors find that the probability for the Yang-Mills baby universe to undergo a spontaneous compactification down to a four-dimensional spacetime is greater than that to remain in the original homogeneous multidimensional state. Some questions about large-wormhole catastrophe are also discussed
On the properties of collision probability integrals in annular geometry-II evaluation
International Nuclear Information System (INIS)
Milgram, M.S.; Sly, K.N.
1979-02-01
To calculate neutron flux distributions in infinitely long annular regions, the inner-outer and outer-outer transmission probabilities psup(io) and psup(oo) are required. Efficient algorithms for the computation of these probabilities as functions of two variables (the ratio of inner/outer radii kappa, and cross-section Σ) are given for 0 -5 . (author)
Probability of Grounding and Collision Events
DEFF Research Database (Denmark)
Pedersen, Preben Terndrup
1996-01-01
To quantify the risks involved in ship traffic, rational criteria for collision and grounding accidents are developed. This implies that probabilities as well as inherent consequences can be analysed and assessed. The presnt paper outlines a method for evaluation of the probability of ship...
Probability of Grounding and Collision Events
DEFF Research Database (Denmark)
Pedersen, Preben Terndrup
1996-01-01
To quantify the risks involved in ship traffic, rational criteria for collision and grounding accidents have to be developed. This implies that probabilities as well as inherent consequences have to be analyzed and assessed.The present notes outline a method for evaluation of the probability...
Introducing Disjoint and Independent Events in Probability.
Kelly, I. W.; Zwiers, F. W.
Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…
Selected papers on probability and statistics
2009-01-01
This volume contains translations of papers that originally appeared in the Japanese journal Sūgaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.
Examples of Neutrosophic Probability in Physics
Directory of Open Access Journals (Sweden)
Fu Yuhua
2015-01-01
Full Text Available This paper re-discusses the problems of the so-called “law of nonconservation of parity” and “accelerating expansion of the universe”, and presents the examples of determining Neutrosophic Probability of the experiment of Chien-Shiung Wu et al in 1957, and determining Neutrosophic Probability of accelerating expansion of the partial universe.
Eliciting Subjective Probabilities with Binary Lotteries
DEFF Research Database (Denmark)
Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd
objective probabilities. Drawing a sample from the same subject population, we find evidence that the binary lottery procedure induces linear utility in a subjective probability elicitation task using the Quadratic Scoring Rule. We also show that the binary lottery procedure can induce direct revelation...
Some open problems in noncommutative probability
International Nuclear Information System (INIS)
Kruszynski, P.
1981-01-01
A generalization of probability measures to non-Boolean structures is discussed. The starting point of the theory is the Gleason theorem about the form of measures on closed subspaces of a Hilbert space. The problems are formulated in terms of probability on lattices of projections in arbitrary von Neumann algebras. (Auth.)
Probability: A Matter of Life and Death
Hassani, Mehdi; Kippen, Rebecca; Mills, Terence
2016-01-01
Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…
Teaching Probability: A Socio-Constructivist Perspective
Sharma, Sashi
2015-01-01
There is a considerable and rich literature on students' misconceptions in probability. However, less attention has been paid to the development of students' probabilistic thinking in the classroom. This paper offers a sequence, grounded in socio-constructivist perspective for teaching probability.
Stimulus Probability Effects in Absolute Identification
Kent, Christopher; Lamberts, Koen
2016-01-01
This study investigated the effect of stimulus presentation probability on accuracy and response times in an absolute identification task. Three schedules of presentation were used to investigate the interaction between presentation probability and stimulus position within the set. Data from individual participants indicated strong effects of…
Against All Odds: When Logic Meets Probability
van Benthem, J.; Katoen, J.-P.; Langerak, R.; Rensink, A.
2017-01-01
This paper is a light walk along interfaces between logic and probability, triggered by a chance encounter with Ed Brinksma. It is not a research paper, or a literature survey, but a pointer to issues. I discuss both direct combinations of logic and probability and structured ways in which logic can
An introduction to probability and stochastic processes
Melsa, James L
2013-01-01
Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
The probability of the false vacuum decay
International Nuclear Information System (INIS)
Kiselev, V.; Selivanov, K.
1983-01-01
The closed expession for the probability of the false vacuum decay in (1+1) dimensions is given. The probability of false vacuum decay is expessed as the product of exponential quasiclassical factor and a functional determinant of the given form. The method for calcutation of this determinant is developed and a complete answer for (1+1) dimensions is given
Probability elements of the mathematical theory
Heathcote, C R
2000-01-01
Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.
The transition probabilities of the reciprocity model
Snijders, T.A.B.
1999-01-01
The reciprocity model is a continuous-time Markov chain model used for modeling longitudinal network data. A new explicit expression is derived for its transition probability matrix. This expression can be checked relatively easily. Some properties of the transition probabilities are given, as well
Probability numeracy and health insurance purchase
Dillingh, Rik; Kooreman, Peter; Potters, Jan
2016-01-01
This paper provides new field evidence on the role of probability numeracy in health insurance purchase. Our regression results, based on rich survey panel data, indicate that the expenditure on two out of three measures of health insurance first rises with probability numeracy and then falls again.
The enigma of probability and physics
International Nuclear Information System (INIS)
Mayants, L.
1984-01-01
This volume contains a coherent exposition of the elements of two unique sciences: probabilistics (science of probability) and probabilistic physics (application of probabilistics to physics). Proceeding from a key methodological principle, it starts with the disclosure of the true content of probability and the interrelation between probability theory and experimental statistics. This makes is possible to introduce a proper order in all the sciences dealing with probability and, by conceiving the real content of statistical mechanics and quantum mechanics in particular, to construct both as two interconnected domains of probabilistic physics. Consistent theories of kinetics of physical transformations, decay processes, and intramolecular rearrangements are also outlined. The interrelation between the electromagnetic field, photons, and the theoretically discovered subatomic particle 'emon' is considered. Numerous internal imperfections of conventional probability theory, statistical physics, and quantum physics are exposed and removed - quantum physics no longer needs special interpretation. EPR, Bohm, and Bell paradoxes are easily resolved, among others. (Auth.)
Optimizing Probability of Detection Point Estimate Demonstration
Koshti, Ajay M.
2017-01-01
Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.
Alternative probability theories for cognitive psychology.
Narens, Louis
2014-01-01
Various proposals for generalizing event spaces for probability functions have been put forth in the mathematical, scientific, and philosophic literatures. In cognitive psychology such generalizations are used for explaining puzzling results in decision theory and for modeling the influence of context effects. This commentary discusses proposals for generalizing probability theory to event spaces that are not necessarily boolean algebras. Two prominent examples are quantum probability theory, which is based on the set of closed subspaces of a Hilbert space, and topological probability theory, which is based on the set of open sets of a topology. Both have been applied to a variety of cognitive situations. This commentary focuses on how event space properties can influence probability concepts and impact cognitive modeling. Copyright © 2013 Cognitive Science Society, Inc.
Conditional probability of the tornado missile impact given a tornado occurrence
International Nuclear Information System (INIS)
Goodman, J.; Koch, J.E.
1982-01-01
Using an approach based on statistical mechanics, an expression for the probability of the first missile strike is developed. The expression depends on two generic parameters (injection probability eta(F) and height distribution psi(Z,F)), which are developed in this study, and one plant specific parameter (number of potential missiles N/sub p/). The expression for the joint probability of simultaneous impact of muitiple targets is also developed. This espression is applicable to calculation of the probability of common cause failure due to tornado missiles. It is shown that the probability of the first missile strike can be determined using a uniform missile distribution model. It is also shown that the conditional probability of the second strike, given the first, is underestimated by the uniform model. The probability of the second strike is greatly increased if the missiles are in clusters large enough to cover both targets
International Nuclear Information System (INIS)
Detrano, R.; Yiannikas, J.; Salcedo, E.E.; Rincon, G.; Go, R.T.; Williams, G.; Leatherman, J.
1984-01-01
One hundred fifty-four patients referred for coronary arteriography were prospectively studied with stress electrocardiography, stress thallium scintigraphy, cine fluoroscopy (for coronary calcifications), and coronary angiography. Pretest probabilities of coronary disease were determined based on age, sex, and type of chest pain. These and pooled literature values for the conditional probabilities of test results based on disease state were used in Bayes theorem to calculate posttest probabilities of disease. The results of the three noninvasive tests were compared for statistical independence, a necessary condition for their simultaneous use in Bayes theorem. The test results were found to demonstrate pairwise independence in patients with and those without disease. Some dependencies that were observed between the test results and the clinical variables of age and sex were not sufficient to invalidate application of the theorem. Sixty-eight of the study patients had at least one major coronary artery obstruction of greater than 50%. When these patients were divided into low-, intermediate-, and high-probability subgroups according to their pretest probabilities, noninvasive test results analyzed by Bayesian probability analysis appropriately advanced 17 of them by at least one probability subgroup while only seven were moved backward. Of the 76 patients without disease, 34 were appropriately moved into a lower probability subgroup while 10 were incorrectly moved up. We conclude that posttest probabilities calculated from Bayes theorem more accurately classified patients with and without disease than did pretest probabilities, thus demonstrating the utility of the theorem in this application
Assessing the clinical probability of pulmonary embolism
International Nuclear Information System (INIS)
Miniati, M.; Pistolesi, M.
2001-01-01
Clinical assessment is a cornerstone of the recently validated diagnostic strategies for pulmonary embolism (PE). Although the diagnostic yield of individual symptoms, signs, and common laboratory tests is limited, the combination of these variables, either by empirical assessment or by a prediction rule, can be used to express a clinical probability of PE. The latter may serve as pretest probability to predict the probability of PE after further objective testing (posterior or post-test probability). Over the last few years, attempts have been made to develop structured prediction models for PE. In a Canadian multicenter prospective study, the clinical probability of PE was rated as low, intermediate, or high according to a model which included assessment of presenting symptoms and signs, risk factors, and presence or absence of an alternative diagnosis at least as likely as PE. Recently, a simple clinical score was developed to stratify outpatients with suspected PE into groups with low, intermediate, or high clinical probability. Logistic regression was used to predict parameters associated with PE. A score ≤ 4 identified patients with low probability of whom 10% had PE. The prevalence of PE in patients with intermediate (score 5-8) and high probability (score ≥ 9) was 38 and 81%, respectively. As opposed to the Canadian model, this clinical score is standardized. The predictor variables identified in the model, however, were derived from a database of emergency ward patients. This model may, therefore, not be valid in assessing the clinical probability of PE in inpatients. In the PISA-PED study, a clinical diagnostic algorithm was developed which rests on the identification of three relevant clinical symptoms and on their association with electrocardiographic and/or radiographic abnormalities specific for PE. Among patients who, according to the model, had been rated as having a high clinical probability, the prevalence of proven PE was 97%, while it was 3
Grieshop, A. P.; Reece, S. M.; Sinha, A.; Wathore, R.
2016-12-01
Combustion in rudimentary and improved cook-stoves used by billions in developing countries can be a regionally dominant contributor to black carbon (BC), primary organic aerosols (POA) and precursors for secondary organic aerosol (SOA). Recent studies suggest that SOA formed during photo-oxidation of primary emissions from biomass burning may make important contribution to its atmospheric impacts. However, the extent to which stove type and operating conditions affect the amount, composition and characteristics of SOA formed from the aging of cookstoves emissions is still largely undetermined. Here we present results from experiments with a field portable oxidation flow reactor (F-OFR) designed to assess aging of cook-stove emissions in both laboratory and field settings. Laboratory tests results are used to compare the quantity and properties of fresh and aged emissions from a traditional open fire and twp alternative stove designs operated on the standard and alternate testing protocols. Diluted cookstove emissions were exposed to a range of oxidant concentrations in the F-OFR. Primary emissions were aged both on-line, to study the influence of combustion variability, and sampled from batched emissions in a smog chamber to examine different aging conditions. Data from real-time particle- and gas-phase instruments and integrated filter samples were collected up and down stream of the OFR. The properties of primary emissions vary strongly with stove type and combustion conditions (e.g. smoldering versus flaming). Experiments aging diluted biomass emissions from distinct phases of stove operation (smoldering and flaming) showed peak SOA production for both phases occurred between 3 and 6 equivalent days of aging with slightly greater production observed in flaming phase emissions. Changing combustion conditions had a stronger influence than aging on POA+SOA `emission factors'. Aerosol Chemical Speciation Monitor data show a substantial evolution of aerosol
Zhou, Jun; Zotter, Peter; Bruns, Emily A.; Stefenelli, Giulia; Bhattu, Deepika; Brown, Samuel; Bertrand, Amelie; Marchand, Nicolas; Lamkaddam, Houssni; Slowik, Jay G.; Prévôt, André S. H.; Baltensperger, Urs; Nussbaumer, Thomas; El-Haddad, Imad; Dommen, Josef
2018-05-01
Wood combustion emissions can induce oxidative stress in the human respiratory tract by reactive oxygen species (ROS) in the aerosol particles, which are emitted either directly or formed through oxidation in the atmosphere. To improve our understanding of the particle-bound ROS (PB-ROS) generation potential of wood combustion emissions, a suite of smog chamber (SC) and potential aerosol mass (PAM) chamber experiments were conducted under well-determined conditions for different combustion devices and technologies, different fuel types, operation methods, combustion regimes, combustion phases, and aging conditions. The PB-ROS content and the chemical properties of the aerosols were quantified by a novel ROS analyzer using the DCFH (2',7'-dichlorofluorescin) assay and a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS). For all eight combustion devices tested, primary PB-ROS concentrations substantially increased upon aging. The level of primary and aged PB-ROS emission factors (EFROS) were dominated by the combustion device (within different combustion technologies) and to a greater extent by the combustion regimes: the variability within one device was much higher than the variability of EFROS from different devices. Aged EFROS under bad combustion conditions were ˜ 2-80 times higher than under optimum combustion conditions. EFROS from automatically operated combustion devices were on average 1 order of magnitude lower than those from manually operated devices, which indicates that automatic combustion devices operated at optimum conditions to achieve near-complete combustion should be employed to minimize PB-ROS emissions. The use of an electrostatic precipitator decreased the primary and aged ROS emissions by a factor of ˜ 1.5 which is however still within the burn-to-burn variability. The parameters controlling the PB-ROS formation in secondary organic aerosol were investigated by employing a regression model, including the fractions of
Failure probability analysis of optical grid
Zhong, Yaoquan; Guo, Wei; Sun, Weiqiang; Jin, Yaohui; Hu, Weisheng
2008-11-01
Optical grid, the integrated computing environment based on optical network, is expected to be an efficient infrastructure to support advanced data-intensive grid applications. In optical grid, the faults of both computational and network resources are inevitable due to the large scale and high complexity of the system. With the optical network based distributed computing systems extensive applied in the processing of data, the requirement of the application failure probability have been an important indicator of the quality of application and an important aspect the operators consider. This paper will present a task-based analysis method of the application failure probability in optical grid. Then the failure probability of the entire application can be quantified, and the performance of reducing application failure probability in different backup strategies can be compared, so that the different requirements of different clients can be satisfied according to the application failure probability respectively. In optical grid, when the application based DAG (directed acyclic graph) is executed in different backup strategies, the application failure probability and the application complete time is different. This paper will propose new multi-objective differentiated services algorithm (MDSA). New application scheduling algorithm can guarantee the requirement of the failure probability and improve the network resource utilization, realize a compromise between the network operator and the application submission. Then differentiated services can be achieved in optical grid.
The Misapplication of Probability Theory in Quantum Mechanics
Racicot, Ronald
2014-03-01
This article is a revision of two papers submitted to the APS in the past two and a half years. In these papers, arguments and proofs are summarized for the following: (1) The wrong conclusion by EPR that Quantum Mechanics is incomplete, perhaps requiring the addition of ``hidden variables'' for completion. Theorems that assume such ``hidden variables,'' such as Bell's theorem, are also wrong. (2) Quantum entanglement is not a realizable physical phenomenon and is based entirely on assuming a probability superposition model for quantum spin. Such a model directly violates conservation of angular momentum. (3) Simultaneous multiple-paths followed by a quantum particle traveling through space also cannot possibly exist. Besides violating Noether's theorem, the multiple-paths theory is based solely on probability calculations. Probability calculations by themselves cannot possibly represent simultaneous physically real events. None of the reviews of the submitted papers actually refuted the arguments and evidence that was presented. These analyses should therefore be carefully evaluated since the conclusions reached have such important impact in quantum mechanics and quantum information theory.
Posterior probability of linkage and maximal lod score.
Génin, E; Martinez, M; Clerget-Darpoux, F
1995-01-01
To detect linkage between a trait and a marker, Morton (1955) proposed to calculate the lod score z(theta 1) at a given value theta 1 of the recombination fraction. If z(theta 1) reaches +3 then linkage is concluded. However, in practice, lod scores are calculated for different values of the recombination fraction between 0 and 0.5 and the test is based on the maximum value of the lod score Zmax. The impact of this deviation of the test on the probability that in fact linkage does not exist, when linkage was concluded, is documented here. This posterior probability of no linkage can be derived by using Bayes' theorem. It is less than 5% when the lod score at a predetermined theta 1 is used for the test. But, for a Zmax of +3, we showed that it can reach 16.4%. Thus, considering a composite alternative hypothesis instead of a single one decreases the reliability of the test. The reliability decreases rapidly when Zmax is less than +3. Given a Zmax of +2.5, there is a 33% chance that linkage does not exist. Moreover, the posterior probability depends not only on the value of Zmax but also jointly on the family structures and on the genetic model. For a given Zmax, the chance that linkage exists may then vary.
Uncertainty about probability: a decision analysis perspective
International Nuclear Information System (INIS)
Howard, R.A.
1988-01-01
The issue of how to think about uncertainty about probability is framed and analyzed from the viewpoint of a decision analyst. The failure of nuclear power plants is used as an example. The key idea is to think of probability as describing a state of information on an uncertain event, and to pose the issue of uncertainty in this quantity as uncertainty about a number that would be definitive: it has the property that you would assign it as the probability if you knew it. Logical consistency requires that the probability to assign to a single occurrence in the absence of further information be the mean of the distribution of this definitive number, not the medium as is sometimes suggested. Any decision that must be made without the benefit of further information must also be made using the mean of the definitive number's distribution. With this formulation, they find further that the probability of r occurrences in n exchangeable trials will depend on the first n moments of the definitive number's distribution. In making decisions, the expected value of clairvoyance on the occurrence of the event must be at least as great as that on the definitive number. If one of the events in question occurs, then the increase in probability of another such event is readily computed. This means, in terms of coin tossing, that unless one is absolutely sure of the fairness of a coin, seeing a head must increase the probability of heads, in distinction to usual thought. A numerical example for nuclear power shows that the failure of one plant of a group with a low probability of failure can significantly increase the probability that must be assigned to failure of a second plant in the group
Fixation probability in a two-locus intersexual selection model.
Durand, Guillermo; Lessard, Sabin
2016-06-01
We study a two-locus model of intersexual selection in a finite haploid population reproducing according to a discrete-time Moran model with a trait locus expressed in males and a preference locus expressed in females. We show that the probability of ultimate fixation of a single mutant allele for a male ornament introduced at random at the trait locus given any initial frequency state at the preference locus is increased by weak intersexual selection and recombination, weak or strong. Moreover, this probability exceeds the initial frequency of the mutant allele even in the case of a costly male ornament if intersexual selection is not too weak. On the other hand, the probability of ultimate fixation of a single mutant allele for a female preference towards a male ornament introduced at random at the preference locus is increased by weak intersexual selection and weak recombination if the female preference is not costly, and is strong enough in the case of a costly male ornament. The analysis relies on an extension of the ancestral recombination-selection graph for samples of haplotypes to take into account events of intersexual selection, while the symbolic calculation of the fixation probabilities is made possible in a reasonable time by an optimizing algorithm. Copyright © 2016 Elsevier Inc. All rights reserved.
Computation of Probabilities in Causal Models of History of Science
Directory of Open Access Journals (Sweden)
Osvaldo Pessoa Jr.
2006-12-01
Full Text Available : The aim of this paper is to investigate the ascription of probabilities in a causal model of an episode in the history of science. The aim of such a quantitative approach is to allow the implementation of the causal model in a computer, to run simulations. As an example, we look at the beginning of the science of magnetism, “explaining” — in a probabilistic way, in terms of a single causal model — why the field advanced in China but not in Europe (the difference is due to different prior probabilities of certain cultural manifestations. Given the number of years between the occurrences of two causally connected advances X and Y, one proposes a criterion for stipulating the value pY=X of the conditional probability of an advance Y occurring, given X. Next, one must assume a specific form for the cumulative probability function pY=X(t, which we take to be the time integral of an exponential distribution function, as is done in physics of radioactive decay. Rules for calculating the cumulative functions for more than two events are mentioned, involving composition, disjunction and conjunction of causes. We also consider the problems involved in supposing that the appearance of events in time follows an exponential distribution, which are a consequence of the fact that a composition of causes does not follow an exponential distribution, but a “hypoexponential” one. We suggest that a gamma distribution function might more adequately represent the appearance of advances.
METHOD OF FOREST FIRES PROBABILITY ASSESSMENT WITH POISSON LAW
Directory of Open Access Journals (Sweden)
A. S. Plotnikova
2016-01-01
Full Text Available The article describes the method for the forest fire burn probability estimation on a base of Poisson distribution. The λ parameter is assumed to be a mean daily number of fires detected for each Forest Fire Danger Index class within specific period of time. Thus, λ was calculated for spring, summer and autumn seasons separately. Multi-annual daily Forest Fire Danger Index values together with EO-derived hot spot map were input data for the statistical analysis. The major result of the study is generation of the database on forest fire burn probability. Results were validated against EO daily data on forest fires detected over Irkutsk oblast in 2013. Daily weighted average probability was shown to be linked with the daily number of detected forest fires. Meanwhile, there was found a number of fires which were developed when estimated probability was low. The possible explanation of this phenomenon was provided.
Methods for estimating drought streamflow probabilities for Virginia streams
Austin, Samuel H.
2014-01-01
Maximum likelihood logistic regression model equations used to estimate drought flow probabilities for Virginia streams are presented for 259 hydrologic basins in Virginia. Winter streamflows were used to estimate the likelihood of streamflows during the subsequent drought-prone summer months. The maximum likelihood logistic regression models identify probable streamflows from 5 to 8 months in advance. More than 5 million streamflow daily values collected over the period of record (January 1, 1900 through May 16, 2012) were compiled and analyzed over a minimum 10-year (maximum 112-year) period of record. The analysis yielded the 46,704 equations with statistically significant fit statistics and parameter ranges published in two tables in this report. These model equations produce summer month (July, August, and September) drought flow threshold probabilities as a function of streamflows during the previous winter months (November, December, January, and February). Example calculations are provided, demonstrating how to use the equations to estimate probable streamflows as much as 8 months in advance.
Probability an introduction with statistical applications
Kinney, John J
2014-01-01
Praise for the First Edition""This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory."" - The StatisticianThoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, h
Dependency models and probability of joint events
International Nuclear Information System (INIS)
Oerjasaeter, O.
1982-08-01
Probabilistic dependencies between components/systems are discussed with reference to a broad classification of potential failure mechanisms. Further, a generalized time-dependency model, based on conditional probabilities for estimation of the probability of joint events and event sequences is described. The applicability of this model is clarified/demonstrated by various examples. It is concluded that the described model of dependency is a useful tool for solving a variety of practical problems concerning the probability of joint events and event sequences where common cause and time-dependent failure mechanisms are involved. (Auth.)
Handbook of probability theory and applications
Rudas, Tamas
2008-01-01
""This is a valuable reference guide for readers interested in gaining a basic understanding of probability theory or its applications in problem solving in the other disciplines.""-CHOICEProviding cutting-edge perspectives and real-world insights into the greater utility of probability and its applications, the Handbook of Probability offers an equal balance of theory and direct applications in a non-technical, yet comprehensive, format. Editor Tamás Rudas and the internationally-known contributors present the material in a manner so that researchers of vari
Probabilities on Streams and Reflexive Games
Directory of Open Access Journals (Sweden)
Andrew Schumann
2014-01-01
Full Text Available Probability measures on streams (e.g. on hypernumbers and p-adic numbers have been defined. It was shown that these probabilities can be used for simulations of reflexive games. In particular, it can be proved that Aumann's agreement theorem does not hold for these probabilities. Instead of this theorem, there is a statement that is called the reflexion disagreement theorem. Based on this theorem, probabilistic and knowledge conditions can be defined for reflexive games at various reflexion levels up to the infinite level. (original abstract
Concept of probability in statistical physics
Guttmann, Y M
1999-01-01
Foundational issues in statistical mechanics and the more general question of how probability is to be understood in the context of physical theories are both areas that have been neglected by philosophers of physics. This book fills an important gap in the literature by providing a most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics. The book explores both subjectivist and objectivist accounts of probability, and takes full measure of work in the foundations of probability theory, in statistical mechanics, and in mathematical theory. It will be of particular interest to philosophers of science, physicists and mathematicians interested in foundational issues, and also to historians of science.
Computation of the Complex Probability Function
Energy Technology Data Exchange (ETDEWEB)
Trainer, Amelia Jo [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ledwith, Patrick John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-08-22
The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the n^{th} degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.
Pre-aggregation for Probability Distributions
DEFF Research Database (Denmark)
Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach
Motivated by the increasing need to analyze complex uncertain multidimensional data (e.g., in order to optimize and personalize location-based services), this paper proposes novel types of {\\em probabilistic} OLAP queries that operate on aggregate values that are probability distributions...... and the techniques to process these queries. The paper also presents the methods for computing the probability distributions, which enables pre-aggregation, and for using the pre-aggregated distributions for further aggregation. In order to achieve good time and space efficiency, the methods perform approximate...... multidimensional data analysis that is considered in this paper (i.e., approximate processing of probabilistic OLAP queries over probability distributions)....
Comparing linear probability model coefficients across groups
DEFF Research Database (Denmark)
Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt
2015-01-01
of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate......This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more...... these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons....
Modeling experiments using quantum and Kolmogorov probability
International Nuclear Information System (INIS)
Hess, Karl
2008-01-01
Criteria are presented that permit a straightforward partition of experiments into sets that can be modeled using both quantum probability and the classical probability framework of Kolmogorov. These new criteria concentrate on the operational aspects of the experiments and lead beyond the commonly appreciated partition by relating experiments to commuting and non-commuting quantum operators as well as non-entangled and entangled wavefunctions. In other words the space of experiments that can be understood using classical probability is larger than usually assumed. This knowledge provides advantages for areas such as nanoscience and engineering or quantum computation.
Keren, G.; Teigen, K.H.
2001-01-01
This article presents a framework for lay people's internal representations of probabilities, which supposedly reflect the strength of underlying dispositions, or propensities, associated with the predicted event. From this framework, we derive the probability-outcome correspondence principle, which
International Nuclear Information System (INIS)
Eedy, W.; Hart, D.
1988-05-01
The risk to human health from radioactive waste management sites can be calculated as the product of the probability of accidental exposure (intrusion) times the probability of a health effect from such exposure. This report reviews the literature and evaluates methods used to predict the probabilities for unintentional intrusion into radioactive waste management areas in Canada over a 10,000-year period. Methods to predict such probabilities are available. They generally assume a long-term stability in terms of existing resource uses and society in the management area. The major potential for errors results from the unlikeliness of these assumptions holding true over such lengthy periods of prediction
International Nuclear Information System (INIS)
Wen Xiaoqiong; Li Qiang; Zhou Guangming; Li Wenjian; Wei Zengquan
2001-01-01
In order to estimate the influence of the un-uniform dose distribution on the clinical treatment result, the Influence of dose distribution homogeneity on the tumor control probability was investigated. Basing on the formula deduced previously for survival fraction of cells irradiated by the un-uniform heavy-ion irradiation field and the theory of tumor control probability, the tumor control probability was calculated for a tumor mode exposed to different dose distribution homogeneity. The results show that the tumor control probability responding to the same total dose will decrease if the dose distribution homogeneity gets worse. In clinical treatment, the dose distribution homogeneity should be better than 95%
Modelling the probability of building fires
Directory of Open Access Journals (Sweden)
Vojtěch Barták
2014-12-01
Full Text Available Systematic spatial risk analysis plays a crucial role in preventing emergencies.In the Czech Republic, risk mapping is currently based on the risk accumulationprinciple, area vulnerability, and preparedness levels of Integrated Rescue Systemcomponents. Expert estimates are used to determine risk levels for individualhazard types, while statistical modelling based on data from actual incidents andtheir possible causes is not used. Our model study, conducted in cooperation withthe Fire Rescue Service of the Czech Republic as a model within the Liberec andHradec Králové regions, presents an analytical procedure leading to the creation ofbuilding fire probability maps based on recent incidents in the studied areas andon building parameters. In order to estimate the probability of building fires, aprediction model based on logistic regression was used. Probability of fire calculatedby means of model parameters and attributes of specific buildings can subsequentlybe visualized in probability maps.
Predicting binary choices from probability phrase meanings.
Wallsten, Thomas S; Jang, Yoonhee
2008-08-01
The issues of how individuals decide which of two events is more likely and of how they understand probability phrases both involve judging relative likelihoods. In this study, we investigated whether derived scales representing probability phrase meanings could be used within a choice model to predict independently observed binary choices. If they can, this simultaneously provides support for our model and suggests that the phrase meanings are measured meaningfully. The model assumes that, when deciding which of two events is more likely, judges take a single sample from memory regarding each event and respond accordingly. The model predicts choice probabilities by using the scaled meanings of individually selected probability phrases as proxies for confidence distributions associated with sampling from memory. Predictions are sustained for 34 of 41 participants but, nevertheless, are biased slightly low. Sequential sampling models improve the fit. The results have both theoretical and applied implications.
Certainties and probabilities of the IPCC
International Nuclear Information System (INIS)
2004-01-01
Based on an analysis of information about the climate evolution, simulations of a global warming and the snow coverage monitoring of Meteo-France, the IPCC presented its certainties and probabilities concerning the greenhouse effect. (A.L.B.)
The probability factor in establishing causation
International Nuclear Information System (INIS)
Hebert, J.
1988-01-01
This paper discusses the possibilities and limitations of methods using the probability factor in establishing the causal link between bodily injury, whether immediate or delayed, and the nuclear incident presumed to have caused it (NEA) [fr
Bayesian optimization for computationally extensive probability distributions.
Tamura, Ryo; Hukushima, Koji
2018-01-01
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.
Characteristic length of the knotting probability revisited
International Nuclear Information System (INIS)
Uehara, Erica; Deguchi, Tetsuo
2015-01-01
We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of impermeable cylindrical segments corresponds to the screening length of double-stranded DNA surrounded by counter ions. For the model we evaluate the probability for a generated SAP with N segments having a given knot K through simulation. We call it the knotting probability of a knot K with N segments for the SAP model. We show that when N is large the most significant factor in the knotting probability is given by the exponentially decaying part exp(−N/N K ), where the estimates of parameter N K are consistent with the same value for all the different knots we investigated. We thus call it the characteristic length of the knotting probability. We give formulae expressing the characteristic length as a function of the cylindrical radius r ex , i.e. the screening length of double-stranded DNA. (paper)
Probability of Survival Decision Aid (PSDA)
National Research Council Canada - National Science Library
Xu, Xiaojiang; Amin, Mitesh; Santee, William R
2008-01-01
A Probability of Survival Decision Aid (PSDA) is developed to predict survival time for hypothermia and dehydration during prolonged exposure at sea in both air and water for a wide range of environmental conditions...
Probability and statistics with integrated software routines
Deep, Ronald
2005-01-01
Probability & Statistics with Integrated Software Routines is a calculus-based treatment of probability concurrent with and integrated with statistics through interactive, tailored software applications designed to enhance the phenomena of probability and statistics. The software programs make the book unique.The book comes with a CD containing the interactive software leading to the Statistical Genie. The student can issue commands repeatedly while making parameter changes to observe the effects. Computer programming is an excellent skill for problem solvers, involving design, prototyping, data gathering, testing, redesign, validating, etc, all wrapped up in the scientific method.See also: CD to accompany Probability and Stats with Integrated Software Routines (0123694698)* Incorporates more than 1,000 engaging problems with answers* Includes more than 300 solved examples* Uses varied problem solving methods
Determining probabilities of geologic events and processes
International Nuclear Information System (INIS)
Hunter, R.L.; Mann, C.J.; Cranwell, R.M.
1985-01-01
The Environmental Protection Agency has recently published a probabilistic standard for releases of high-level radioactive waste from a mined geologic repository. The standard sets limits for contaminant releases with more than one chance in 100 of occurring within 10,000 years, and less strict limits for releases of lower probability. The standard offers no methods for determining probabilities of geologic events and processes, and no consensus exists in the waste-management community on how to do this. Sandia National Laboratories is developing a general method for determining probabilities of a given set of geologic events and processes. In addition, we will develop a repeatable method for dealing with events and processes whose probability cannot be determined. 22 refs., 4 figs
Pre-Aggregation with Probability Distributions
DEFF Research Database (Denmark)
Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach
2006-01-01
Motivated by the increasing need to analyze complex, uncertain multidimensional data this paper proposes probabilistic OLAP queries that are computed using probability distributions rather than atomic values. The paper describes how to create probability distributions from base data, and how...... the distributions can be subsequently used in pre-aggregation. Since the probability distributions can become large, we show how to achieve good time and space efficiency by approximating the distributions. We present the results of several experiments that demonstrate the effectiveness of our methods. The work...... is motivated with a real-world case study, based on our collaboration with a leading Danish vendor of location-based services. This paper is the first to consider the approximate processing of probabilistic OLAP queries over probability distributions....
Probability of spent fuel transportation accidents
International Nuclear Information System (INIS)
McClure, J.D.
1981-07-01
The transported volume of spent fuel, incident/accident experience and accident environment probabilities were reviewed in order to provide an estimate of spent fuel accident probabilities. In particular, the accident review assessed the accident experience for large casks of the type that could transport spent (irradiated) nuclear fuel. This review determined that since 1971, the beginning of official US Department of Transportation record keeping for accidents/incidents, there has been one spent fuel transportation accident. This information, coupled with estimated annual shipping volumes for spent fuel, indicated an estimated annual probability of a spent fuel transport accident of 5 x 10 -7 spent fuel accidents per mile. This is consistent with ordinary truck accident rates. A comparison of accident environments and regulatory test environments suggests that the probability of truck accidents exceeding regulatory test for impact is approximately 10 -9 /mile
Sampling, Probability Models and Statistical Reasoning Statistical
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Sampling, Probability Models and Statistical Reasoning Statistical Inference. Mohan Delampady V R Padmawar. General Article Volume 1 Issue 5 May 1996 pp 49-58 ...
STADIC: a computer code for combining probability distributions
International Nuclear Information System (INIS)
Cairns, J.J.; Fleming, K.N.
1977-03-01
The STADIC computer code uses a Monte Carlo simulation technique for combining probability distributions. The specific function for combination of the input distribution is defined by the user by introducing the appropriate FORTRAN statements to the appropriate subroutine. The code generates a Monte Carlo sampling from each of the input distributions and combines these according to the user-supplied function to provide, in essence, a random sampling of the combined distribution. When the desired number of samples is obtained, the output routine calculates the mean, standard deviation, and confidence limits for the resultant distribution. This method of combining probability distributions is particularly useful in cases where analytical approaches are either too difficult or undefined
Voltage dependency of transmission probability of aperiodic DNA molecule
Wiliyanti, V.; Yudiarsah, E.
2017-07-01
Characteristics of electron transports in aperiodic DNA molecules have been studied. Double stranded DNA model with the sequences of bases, GCTAGTACGTGACGTAGCTAGGATATGCCTGA, in one chain and its complements on the other chains has been used. Tight binding Hamiltonian is used to model DNA molecules. In the model, we consider that on-site energy of the basis has a linearly dependency on the applied electric field. Slater-Koster scheme is used to model electron hopping constant between bases. The transmission probability of electron from one electrode to the next electrode is calculated using a transfer matrix technique and scattering matrix method simultaneously. The results show that, generally, higher voltage gives a slightly larger value of the transmission probability. The applied voltage seems to shift extended states to lower energy. Meanwhile, the value of the transmission increases with twisting motion frequency increment.
Imprecise Probability Methods for Weapons UQ
Energy Technology Data Exchange (ETDEWEB)
Picard, Richard Roy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vander Wiel, Scott Alan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-13
Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.
Escape and transmission probabilities in cylindrical geometry
International Nuclear Information System (INIS)
Bjerke, M.A.
1980-01-01
An improved technique for the generation of escape and transmission probabilities in cylindrical geometry was applied to the existing resonance cross section processing code ROLAIDS. The algorithm of Hwang and Toppel, [ANL-FRA-TM-118] (with modifications) was employed. The probabilities generated were found to be as accurate as those given by the method previously applied in ROLAIDS, while requiring much less computer core storage and CPU time
Probability and statistics for computer science
Johnson, James L
2011-01-01
Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: ""to present the mathematical analysis underlying probability results"" Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra in an appendix Mathematical interludes (in each chapter) which examine mathematical techniques in the context of probabilistic or statistical importance Numerous section exercises, summaries, historical notes, and Further Readings for reinforcem
Rare gases transition probabilities for plasma diagnostics
International Nuclear Information System (INIS)
Katsonis, K.; Siskos, A.; Ndiaye, A.; Clark, R.E.H.; Cornille, M.; Abdallah, J. Jr
2005-01-01
Emission spectroscopy is a powerful optical diagnostics tool which has been largely used in studying and monitoring various industrial, laboratory and natural plasmas. As these plasmas are rarely in Local Thermodynamic Equilibrium (LTE) a prerequisite of satisfactory evaluation of the plasma electron density n e and temperature T e is the existence of a detailed Collisional-Radiative (C-R) model taking into account the main physical processes influencing the plasma state and dynamics of its main constituents. The theoretical spectra which such a model generates match the experimental ones whenever the experimental values of ne and T e are introduced. In practice, in validating such models, discrepancies are observed which often are due to the atomic data included in the C-R model. In generating theoretical spectra pertaining to each atom(ion) multiplet, the most sensible atomic data are the relevant transition probabilities A j→i and electron collision excitation cross sections σ i→j . We note that the latter are actually poorly known, especially for low ionization stages and near the excitation threshold. We address here the evaluation of the former, especially of the A j→i of the Ar 2+ ion responsible for the Ar III spectra and of those of the Xe 2+ ion which are evaluated in an analogous way. Extensive studies of the Ar III and Xe III spectra exist, but the present status of Aj i cannot be considered sufficient for the generation of the theoretical spectra even of the most prominent visible lines coming from the Ar III multiplets 4s - 4p, 5p (corresponding to the well known '' red '' and 'blue' lines of Ar I) 4p - 4d, 5d and 3p - 4s, 5s (resonant) and the analogous Xe III multiplets (which have principal quantum numbers increased by two). Due to the gap observed in the Grotrian diagrams, the resonant lines which, together with the important metastable ones, belong to the 3p - 4s, 5s multiplets, (5p - 6s, 7s for Xe III), give spectra in the UV region. On
High throughput nonparametric probability density estimation.
Farmer, Jenny; Jacobs, Donald
2018-01-01
In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.
Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution
DEFF Research Database (Denmark)
Fog, Agner
2008-01-01
Two different probability distributions are both known in the literature as "the" noncentral hypergeometric distribution. Wallenius' noncentral hypergeometric distribution can be described by an urn model without replacement with bias. Fisher's noncentral hypergeometric distribution...... is the conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...... distribution are derived. Range of applicability, numerical problems, and efficiency are discussed for each method. Approximations to the mean and variance are also discussed. This distribution has important applications in models of biased sampling and in models of evolutionary systems....
Fixation Probabilities of Evolutionary Graphs Based on the Positions of New Appearing Mutants
Directory of Open Access Journals (Sweden)
Pei-ai Zhang
2014-01-01
Full Text Available Evolutionary graph theory is a nice measure to implement evolutionary dynamics on spatial structures of populations. To calculate the fixation probability is usually regarded as a Markov chain process, which is affected by the number of the individuals, the fitness of the mutant, the game strategy, and the structure of the population. However the position of the new mutant is important to its fixation probability. Here the position of the new mutant is laid emphasis on. The method is put forward to calculate the fixation probability of an evolutionary graph (EG of single level. Then for a class of bilevel EGs, their fixation probabilities are calculated and some propositions are discussed. The conclusion is obtained showing that the bilevel EG is more stable than the corresponding one-rooted EG.
Generic Degraded Congiguration Probability Analysis for DOE Codisposal Waste Package
Energy Technology Data Exchange (ETDEWEB)
S.F.A. Deng; M. Saglam; L.J. Gratton
2001-05-23
In accordance with the technical work plan, ''Technical Work Plan For: Department of Energy Spent Nuclear Fuel Work Packages'' (CRWMS M&O 2000c), this Analysis/Model Report (AMR) is developed for the purpose of screening out degraded configurations for U.S. Department of Energy (DOE) spent nuclear fuel (SNF) types. It performs the degraded configuration parameter and probability evaluations of the overall methodology specified in the ''Disposal Criticality Analysis Methodology Topical Report'' (YMP 2000, Section 3) to qualifying configurations. Degradation analyses are performed to assess realizable parameter ranges and physical regimes for configurations. Probability calculations are then performed for configurations characterized by k{sub eff} in excess of the Critical Limit (CL). The scope of this document is to develop a generic set of screening criteria or models to screen out degraded configurations having potential for exceeding a criticality limit. The developed screening criteria include arguments based on physical/chemical processes and probability calculations and apply to DOE SNF types when codisposed with the high-level waste (HLW) glass inside a waste package. The degradation takes place inside the waste package and is long after repository licensing has expired. The emphasis of this AMR is on degraded configuration screening and the probability analysis is one of the approaches used for screening. The intended use of the model is to apply the developed screening criteria to each DOE SNF type following the completion of the degraded mode criticality analysis internal to the waste package.
Model-Based Calculations of the Probability of a Country's Nuclear Proliferation Decisions
International Nuclear Information System (INIS)
Li, Jun; Yim, Man-Sung; McNelis, David N.
2007-01-01
The first nuclear weapon was detonated in August 1945 over Japan to end World War II. During the past six decades, the majority of the world's countries have abstained from acquiring nuclear weapons. However, a number of countries have explored the nuclear weapons option, 23 in all. Among them, 14 countries have dropped their interest in nuclear weapons after initiating some efforts. And nine of them today possess nuclear weapons. These countries include the five nuclear weapons states - U.S., Russia, U.K., France, and China - and the four non- NPT member states - Israel, India, Pakistan, and North Korea. Many of these countries initially used civilian nuclear power technology development as a basis or cover for their military program. Recent proliferation incidents in Iraq, Iran, and North Korea brought the world together to pay much attention to nuclear nonproliferation. With the expected surge in the use of nuclear energy for power generation by developing countries, the world's nuclear nonproliferation regime needs to be better prepared for potential future challenges. For the world's nuclear nonproliferation regime to effectively cope with any future proliferation attempts, early detection of potentially proliferation-related activities is highly desirable. Early detection allows the international community to respond and take necessary actions - ideally using political and diplomatic influences without resorting to harsh measures such as sanctions or military actions. In this regard, a capability to quantitatively predict the chance of a country's nuclear proliferation intent or activities is of significant interest. There have been various efforts in the research community to understand the determinants of nuclear proliferation and develop quantitative tools to predict nuclear proliferation events. These efforts have shown that information about the political issues surrounding a country's security along with economic development data can be useful to explain the occurrences of proliferation decisions. However, predicting major historical proliferation events using model-based predictions has been unreliable. Nuclear proliferation decisions by a country is affected by three main factors: (1) technology; (2) finance; and (3) political motivation [1]. Technological capability is important as nuclear weapons development needs special materials, detonation mechanism, delivery capability, and the supporting human resources and knowledge base. Financial capability is likewise important as the development of the technological capabilities requires a serious financial commitment. It would be difficult for any state with a gross national product (GNP) significantly less than that of about $100 billion to devote enough annual governmental funding to a nuclear weapon program to actually achieve positive results within a reasonable time frame (i.e., 10 years). At the same time, nuclear proliferation is not a matter determined by a mastery of technical details or overcoming financial constraints. Technology or finance is a necessary condition but not a sufficient condition for nuclear proliferation. At the most fundamental level, the proliferation decision by a state is controlled by its political motivation. To effectively address the issue of predicting proliferation events, all three of the factors must be included in the model. To the knowledge of the authors, none of the exiting models considered the 'technology' variable as part of the modeling. This paper presents an attempt to develop a methodology for statistical modeling and predicting a country's nuclear proliferation decisions. The approach is based on the combined use of data on a country's nuclear technical capability profiles economic development status, security environment factors and internal political and cultural factors. All of the information utilized in the study was from open source literature. (authors)
Modeling highway travel time distribution with conditional probability models
Energy Technology Data Exchange (ETDEWEB)
Oliveira Neto, Francisco Moraes [ORNL; Chin, Shih-Miao [ORNL; Hwang, Ho-Ling [ORNL; Han, Lee [University of Tennessee, Knoxville (UTK)
2014-01-01
ABSTRACT Under the sponsorship of the Federal Highway Administration's Office of Freight Management and Operations, the American Transportation Research Institute (ATRI) has developed performance measures through the Freight Performance Measures (FPM) initiative. Under this program, travel speed information is derived from data collected using wireless based global positioning systems. These telemetric data systems are subscribed and used by trucking industry as an operations management tool. More than one telemetric operator submits their data dumps to ATRI on a regular basis. Each data transmission contains truck location, its travel time, and a clock time/date stamp. Data from the FPM program provides a unique opportunity for studying the upstream-downstream speed distributions at different locations, as well as different time of the day and day of the week. This research is focused on the stochastic nature of successive link travel speed data on the continental United States Interstates network. Specifically, a method to estimate route probability distributions of travel time is proposed. This method uses the concepts of convolution of probability distributions and bivariate, link-to-link, conditional probability to estimate the expected distributions for the route travel time. Major contribution of this study is the consideration of speed correlation between upstream and downstream contiguous Interstate segments through conditional probability. The established conditional probability distributions, between successive segments, can be used to provide travel time reliability measures. This study also suggests an adaptive method for calculating and updating route travel time distribution as new data or information is added. This methodology can be useful to estimate performance measures as required by the recent Moving Ahead for Progress in the 21st Century Act (MAP 21).
Analysis of probability of defects in the disposal canisters
International Nuclear Information System (INIS)
Holmberg, J.-E.; Kuusela, P.
2011-06-01
This report presents a probability model for the reliability of the spent nuclear waste final disposal canister. Reliability means here that the welding of the canister lid has no critical defects from the long-term safety point of view. From the reliability point of view, both the reliability of the welding process (that no critical defects will be born) and the non-destructive testing (NDT) process (all critical defects will be detected) are equally important. In the probability model, critical defects in a weld were simplified into a few types. Also the possibility of human errors in the NDT process was taken into account in a simple manner. At this moment there is very little representative data to determine the reliability of welding and also the data on NDT is not well suited for the needs of this study. Therefore calculations presented here are based on expert judgements and on several assumptions that have not been verified yet. The Bayesian probability model shows the importance of the uncertainty in the estimation of the reliability parameters. The effect of uncertainty is that the probability distribution of the number of defective canisters becomes flat for larger numbers of canisters compared to the binomial probability distribution in case of known parameter values. In order to reduce the uncertainty, more information is needed from both the reliability of the welding and NDT processes. It would also be important to analyse the role of human factors in these processes since their role is not reflected in typical test data which is used to estimate 'normal process variation'.The reported model should be seen as a tool to quantify the roles of different methods and procedures in the weld inspection process. (orig.)
FRELIB, Failure Reliability Index Calculation
International Nuclear Information System (INIS)
Parkinson, D.B.; Oestergaard, C.
1984-01-01
1 - Description of problem or function: Calculation of the reliability index given the failure boundary. A linearization point (design point) is found on the failure boundary for a stationary reliability index (min) and a stationary failure probability density function along the failure boundary, provided that the basic variables are normally distributed. 2 - Method of solution: Iteration along the failure boundary which must be specified - together with its partial derivatives with respect to the basic variables - by the user in a subroutine FSUR. 3 - Restrictions on the complexity of the problem: No distribution information included (first-order-second-moment-method). 20 basic variables (could be extended)
Transition Dipole Moments and Transition Probabilities of the CN Radical
Yin, Yuan; Shi, Deheng; Sun, Jinfeng; Zhu, Zunlue
2018-04-01
This paper studies the transition probabilities of electric dipole transitions between 10 low-lying states of the CN radical. These states are X2Σ+, A2Π, B2Σ+, a4Σ+, b4Π, 14Σ‑, 24Π, 14Δ, 16Σ+, and 16Π. The potential energy curves are calculated using the CASSCF method, which is followed by the icMRCI approach with the Davidson correction. The transition dipole moments between different states are calculated. To improve the accuracy of potential energy curves, core–valence correlation and scalar relativistic corrections, as well as the extrapolation of potential energies to the complete basis set limit are included. The Franck–Condon factors and Einstein coefficients of emissions are calculated. The radiative lifetimes are determined for the vibrational levels of the A2Π, B2Σ+, b4Π, 14Σ‑, 24Π, 14Δ, and 16Π states. According to the transition probabilities and radiative lifetimes, some guidelines for detecting these states spectroscopically are proposed. The spin–orbit coupling effect on the spectroscopic and vibrational properties is evaluated. The splitting energy in the A2Π state is determined to be 50.99 cm‑1, which compares well with the experimental ones. The potential energy curves, transition dipole moments, spectroscopic parameters, and transition probabilities reported in this paper can be considered to be very reliable. The results obtained here can be used as guidelines for detecting these transitions, in particular those that have not been measured in previous experiments or have not been observed in the Sun, comets, stellar atmospheres, dark interstellar clouds, and diffuse interstellar clouds.
VISA-2, Reactor Vessel Failure Probability Under Thermal Shock
International Nuclear Information System (INIS)
Simonen, F.; Johnson, K.
1992-01-01
1 - Description of program or function: VISA2 (Vessel Integrity Simulation Analysis) was developed to estimate the failure probability of nuclear reactor pressure vessels under pressurized thermal shock conditions. The deterministic portion of the code performs heat transfer, stress, and fracture mechanics calculations for a vessel subjected to a user-specified temperature and pressure transient. The probabilistic analysis performs a Monte Carlo simulation to estimate the probability of vessel failure. Parameters such as initial crack size and position, copper and nickel content, fluence, and the fracture toughness values for crack initiation and arrest are treated as random variables. Linear elastic fracture mechanics methods are used to model crack initiation and growth. This includes cladding effects in the heat transfer, stress, and fracture mechanics calculations. The simulation procedure treats an entire vessel and recognizes that more than one flaw can exist in a given vessel. The flaw model allows random positioning of the flaw within the vessel wall thickness, and the user can specify either flaw length or length-to-depth aspect ratio for crack initiation and arrest predictions. The flaw size distribution can be adjust on the basis of different inservice inspection techniques and inspection conditions. The toughness simulation model includes a menu of alternative equations for predicting the shift in the reference temperature of the nil-ductility transition. 2 - Method of solution: The solution method uses closed form equations for temperatures, stresses, and stress intensity factors. A polynomial fitting procedure approximates the specified pressure and temperature transient. Failure probabilities are calculated by a Monte Carlo simulation. 3 - Restrictions on the complexity of the problem: Maxima of 30 welds. VISA2 models only the belt-line (cylindrical) region of a reactor vessel. The stresses are a function of the radial (through-wall) coordinate only
Oscillator strengths and transition probabilities for the intercombination transitions in Fe XXII
International Nuclear Information System (INIS)
Glass, R.
1979-01-01
Oscillator strengths and transition probabilities are evaluated for the intercombination transitions between the 2s 2 2p, 2s 2p 2 and 2p 3 states of Fe XXII using configuration interaction wavefunctions. The fine-structure splittings have also been calculated. Some significant differences with previous calculations are obtained
K-shell ionization probability in energetic nearly symmetric heavy-ion collisions
International Nuclear Information System (INIS)
Tserruya, I.; Schmidt-Boecking, H.; Schuch, R.
1977-01-01
Impact parameter dependent K-x-ray emission probabilities for the projectile and target atoms have been measured in 35 MeV Cl on Cl, Cl on Ti and Cl on Ni collisions. The sum of projectile plus target K-shell ionization probability is taken as a measure of the total 2psigma ionization probability. The 2pπ-2psigma totational coupling model is in clear disagreement with the present results. On the other hand the sum of probabilities is reproduced both in shape and absolute magnitude by the statistical model for inner-shell ionization. The K-shell ionization probability of the higher -Z collision partner is well described by this model including the 2psigma-1ssigma vacancy sharing probability calculated as a function of the impact parameter. (author)
Collective fluctuations in magnetized plasma: Transition probability approach
International Nuclear Information System (INIS)
Sosenko, P.P.
1997-01-01
Statistical plasma electrodynamics is elaborated with special emphasis on the transition probability approach and quasi-particles, and on modern applications to magnetized plasmas. Fluctuation spectra in the magnetized plasma are calculated in the range of low frequencies (with respect to the cyclotron one), and the conditions for the transition from incoherent to collective fluctuations are established. The role of finite-Larmor-radius effects and particle polarization drift in such a transition is explained. The ion collective features in fluctuation spectra are studied. 63 refs., 30 figs
Probability analysis of MCO over-pressurization during staging
International Nuclear Information System (INIS)
Pajunen, A.L.
1997-01-01
The purpose of this calculation is to determine the probability of Multi-Canister Overpacks (MCOs) over-pressurizing during staging at the Canister Storage Building (CSB). Pressurization of an MCO during staging is dependent upon changes to the MCO gas temperature and the build-up of reaction products during the staging period. These effects are predominantly limited by the amount of water that remains in the MCO following cold vacuum drying that is available for reaction during staging conditions. Because of the potential for increased pressure within an MCO, provisions for a filtered pressure relief valve and rupture disk have been incorporated into the MCO design. This calculation provides an estimate of the frequency that an MCO will contain enough water to pressurize beyond the limits of these design features. The results of this calculation will be used in support of further safety analyses and operational planning efforts. Under the bounding steady state CSB condition assumed for this analysis, an MCO must contain less than 1.6 kg (3.7 lbm) of water available for reaction to preclude actuation of the pressure relief valve at 100 psid. To preclude actuation of the MCO rupture disk at 150 psid, an MCO must contain less than 2.5 kg (5.5 lbm) of water available for reaction. These limits are based on the assumption that hydrogen generated by uranium-water reactions is the sole source of gas produced within the MCO and that hydrates in fuel particulate are the primary source of water available for reactions during staging conditions. The results of this analysis conclude that the probability of the hydrate water content of an MCO exceeding 1.6 kg is 0.08 and the probability that it will exceed 2.5 kg is 0.01. This implies that approximately 32 of 400 staged MCOs may experience pressurization to the point where the pressure relief valve actuates. In the event that an MCO pressure relief valve fails to open, the probability is 1 in 100 that the MCO would experience
Estimating probable flaw distributions in PWR steam generator tubes
International Nuclear Information System (INIS)
Gorman, J.A.; Turner, A.P.L.
1997-01-01
This paper describes methods for estimating the number and size distributions of flaws of various types in PWR steam generator tubes. These estimates are needed when calculating the probable primary to secondary leakage through steam generator tubes under postulated accidents such as severe core accidents and steam line breaks. The paper describes methods for two types of predictions: (1) the numbers of tubes with detectable flaws of various types as a function of time, and (2) the distributions in size of these flaws. Results are provided for hypothetical severely affected, moderately affected and lightly affected units. Discussion is provided regarding uncertainties and assumptions in the data and analyses
Parallel computational in nuclear group constant calculation
International Nuclear Information System (INIS)
Su'ud, Zaki; Rustandi, Yaddi K.; Kurniadi, Rizal
2002-01-01
In this paper parallel computational method in nuclear group constant calculation using collision probability method will be discuss. The main focus is on the calculation of collision matrix which need large amount of computational time. The geometry treated here is concentric cylinder. The calculation of collision probability matrix is carried out using semi analytic method using Beckley Naylor Function. To accelerate computation speed some computer parallel used to solve the problem. We used LINUX based parallelization using PVM software with C or fortran language. While in windows based we used socket programming using DELPHI or C builder. The calculation results shows the important of optimal weight for each processor in case there area many type of processor speed
Causal inference, probability theory, and graphical insights.
Baker, Stuart G
2013-11-10
Causal inference from observational studies is a fundamental topic in biostatistics. The causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies. In contrast, the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons. First, probability theory is generally more flexible than causal graphs: Besides explaining such causal graph topics as M-bias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical controls, which does not fit into a causal graph framework. Second, probability theory is the basis for insightful graphical displays including the BK-Plot for understanding Simpson's paradox with a binary confounder, the BK2-Plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder, and the PAD-Plot for understanding the principal stratification component of the paired availability design. Published 2013. This article is a US Government work and is in the public domain in the USA.
Evolvement simulation of the probability of neutron-initiating persistent fission chain
International Nuclear Information System (INIS)
Wang Zhe; Hong Zhenying
2014-01-01
Background: Probability of neutron-initiating persistent fission chain, which has to be calculated in analysis of critical safety, start-up of reactor, burst waiting time on pulse reactor, bursting time on pulse reactor, etc., is an inherent parameter in a multiplying assembly. Purpose: We aim to derive time-dependent integro-differential equation for such probability in relative velocity space according to the probability conservation, and develop the deterministic code Dynamic Segment Number Probability (DSNP) based on the multi-group S N method. Methods: The reliable convergence of dynamic calculation was analyzed and numerical simulation of the evolvement process of dynamic probability for varying concentration was performed under different initial conditions. Results: On Highly Enriched Uranium (HEU) Bare Spheres, when the time is long enough, the results of dynamic calculation approach to those of static calculation. The most difference of such results between DSNP and Partisn code is less than 2%. On Baker model, over the range of about 1 μs after the first criticality, the most difference between the dynamic and static calculation is about 300%. As for a super critical system, the finite fission chains decrease and the persistent fission chains increase as the reactivity aggrandizes, the dynamic evolvement curve of initiation probability is close to the static curve within the difference of 5% when the K eff is more than 1.2. The cumulative probability curve also indicates that the difference of integral results between the dynamic calculation and the static calculation decreases from 35% to 5% as the K eff increases. This demonstrated that the ability of initiating a self-sustaining fission chain reaction approaches stabilization, while the former difference (35%) showed the important difference of the dynamic results near the first criticality with the static ones. The DSNP code agrees well with Partisn code. Conclusions: There are large numbers of
Estimation of post-test probabilities by residents: Bayesian reasoning versus heuristics?
Hall, Stacey; Phang, Sen Han; Schaefer, Jeffrey P; Ghali, William; Wright, Bruce; McLaughlin, Kevin
2014-08-01
Although the process of diagnosing invariably begins with a heuristic, we encourage our learners to support their diagnoses by analytical cognitive processes, such as Bayesian reasoning, in an attempt to mitigate the effects of heuristics on diagnosing. There are, however, limited data on the use ± impact of Bayesian reasoning on the accuracy of disease probability estimates. In this study our objective was to explore whether Internal Medicine residents use a Bayesian process to estimate disease probabilities by comparing their disease probability estimates to literature-derived Bayesian post-test probabilities. We gave 35 Internal Medicine residents four clinical vignettes in the form of a referral letter and asked them to estimate the post-test probability of the target condition in each case. We then compared these to literature-derived probabilities. For each vignette the estimated probability was significantly different from the literature-derived probability. For the two cases with low literature-derived probability our participants significantly overestimated the probability of these target conditions being the correct diagnosis, whereas for the two cases with high literature-derived probability the estimated probability was significantly lower than the calculated value. Our results suggest that residents generate inaccurate post-test probability estimates. Possible explanations for this include ineffective application of Bayesian reasoning, attribute substitution whereby a complex cognitive task is replaced by an easier one (e.g., a heuristic), or systematic rater bias, such as central tendency bias. Further studies are needed to identify the reasons for inaccuracy of disease probability estimates and to explore ways of improving accuracy.
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
National Oceanic and Atmospheric Administration, Department of Commerce — The Magnetic Field Calculator will calculate the total magnetic field, including components (declination, inclination, horizontal intensity, northerly intensity,...
Uncertainty relation and probability. Numerical illustration
International Nuclear Information System (INIS)
Fujikawa, Kazuo; Umetsu, Koichiro
2011-01-01
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty product of suitably sampled events with a very small probability. We have shown elsewhere that some examples of the evasion of the uncertainty relation noted in the past are in fact understood in this way. We here numerically illustrate that a very small uncertainty product is realized if one performs a suitable sampling of measured data that occur with a very small probability. We introduce a notion of cyclic measurements. It is also shown that our analysis is consistent with the Landau-Pollak-type uncertainty relation. It is suggested that the present analysis may help reconcile the contradicting views about the 'standard quantum limit' in the detection of gravitational waves. (author)
Scoring Rules for Subjective Probability Distributions
DEFF Research Database (Denmark)
Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd
The theoretical literature has a rich characterization of scoring rules for eliciting the subjective beliefs that an individual has for continuous events, but under the restrictive assumption of risk neutrality. It is well known that risk aversion can dramatically affect the incentives to correctly...... report the true subjective probability of a binary event, even under Subjective Expected Utility. To address this one can “calibrate” inferences about true subjective probabilities from elicited subjective probabilities over binary events, recognizing the incentives that risk averse agents have...... to distort reports. We characterize the comparable implications of the general case of a risk averse agent when facing a popular scoring rule over continuous events, and find that these concerns do not apply with anything like the same force. For empirically plausible levels of risk aversion, one can...
Comparing coefficients of nested nonlinear probability models
DEFF Research Database (Denmark)
Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders
2011-01-01
In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...
A basic course in probability theory
Bhattacharya, Rabi
2016-01-01
This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of thei...
Ignition probabilities for Compact Ignition Tokamak designs
International Nuclear Information System (INIS)
Stotler, D.P.; Goldston, R.J.
1989-09-01
A global power balance code employing Monte Carlo techniques had been developed to study the ''probability of ignition'' and has been applied to several different configurations of the Compact Ignition Tokamak (CIT). Probability distributions for the critical physics parameters in the code were estimated using existing experimental data. This included a statistical evaluation of the uncertainty in extrapolating the energy confinement time. A substantial probability of ignition is predicted for CIT if peaked density profiles can be achieved or if one of the two higher plasma current configurations is employed. In other cases, values of the energy multiplication factor Q of order 10 are generally obtained. The Ignitor-U and ARIES designs are also examined briefly. Comparisons of our empirically based confinement assumptions with two theory-based transport models yield conflicting results. 41 refs., 11 figs
Independent events in elementary probability theory
Csenki, Attila
2011-07-01
In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): quote specific-use="indent"> If the n events E 1, E 2, … , E n are jointly independent then any two events A and B built in finitely many steps from two disjoint subsets of E 1, E 2, … , E n are also independent. The operations 'union', 'intersection' and 'complementation' are permitted only when forming the events A and B. quote>Here we examine this statement from the point of view of elementary probability theory. The approach described here is accessible also to users of probability theory and is believed to be novel.
Pointwise probability reinforcements for robust statistical inference.
Frénay, Benoît; Verleysen, Michel
2014-02-01
Statistical inference using machine learning techniques may be difficult with small datasets because of abnormally frequent data (AFDs). AFDs are observations that are much more frequent in the training sample that they should be, with respect to their theoretical probability, and include e.g. outliers. Estimates of parameters tend to be biased towards models which support such data. This paper proposes to introduce pointwise probability reinforcements (PPRs): the probability of each observation is reinforced by a PPR and a regularisation allows controlling the amount of reinforcement which compensates for AFDs. The proposed solution is very generic, since it can be used to robustify any statistical inference method which can be formulated as a likelihood maximisation. Experiments show that PPRs can be easily used to tackle regression, classification and projection: models are freed from the influence of outliers. Moreover, outliers can be filtered manually since an abnormality degree is obtained for each observation. Copyright © 2013 Elsevier Ltd. All rights reserved.
Uncertainty the soul of modeling, probability & statistics
Briggs, William
2016-01-01
This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance". The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, suc...
Introduction to probability with statistical applications
Schay, Géza
2016-01-01
Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises
Python for probability, statistics, and machine learning
Unpingco, José
2016-01-01
This book covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules in these areas. The entire text, including all the figures and numerical results, is reproducible using the Python codes and their associated Jupyter/IPython notebooks, which are provided as supplementary downloads. The author develops key intuitions in machine learning by working meaningful examples using multiple analytical methods and Python codes, thereby connecting theoretical concepts to concrete implementations. Modern Python modules like Pandas, Sympy, and Scikit-learn are applied to simulate and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, and regularization. Many abstract mathematical ideas, such as convergence in probability theory, are developed and illustrated with numerical examples. This book is suitable for anyone with an undergraduate-level exposure to probability, statistics, or machine learning and with rudimentary knowl...
EARLY HISTORY OF GEOMETRIC PROBABILITY AND STEREOLOGY
Directory of Open Access Journals (Sweden)
Magdalena Hykšová
2012-03-01
Full Text Available The paper provides an account of the history of geometric probability and stereology from the time of Newton to the early 20th century. It depicts the development of two parallel ways: on one hand, the theory of geometric probability was formed with minor attention paid to other applications than those concerning spatial chance games. On the other hand, practical rules of the estimation of area or volume fraction and other characteristics, easily deducible from geometric probability theory, were proposed without the knowledge of this branch. A special attention is paid to the paper of J.-É. Barbier published in 1860, which contained the fundamental stereological formulas, but remained almost unnoticed both by mathematicians and practicians.
Probability analysis of nuclear power plant hazards
International Nuclear Information System (INIS)
Kovacs, Z.
1985-01-01
The probability analysis of risk is described used for quantifying the risk of complex technological systems, especially of nuclear power plants. Risk is defined as the product of the probability of the occurrence of a dangerous event and the significance of its consequences. The process of the analysis may be divided into the stage of power plant analysis to the point of release of harmful material into the environment (reliability analysis) and the stage of the analysis of the consequences of this release and the assessment of the risk. The sequence of operations is characterized in the individual stages. The tasks are listed which Czechoslovakia faces in the development of the probability analysis of risk, and the composition is recommended of the work team for coping with the task. (J.C.)
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Probability of causation for radiogenic cancer in Indian population
International Nuclear Information System (INIS)
Bhatia, D.P.; Murthy, M.S.S.
1992-01-01
The National Institute of Health (NIH), USA has generated tables for probability of causation (PC) for various radiogenic cancers for the population of United States, (NIH 1985). These are based on cancer incidence rates derived from data on the Japanese survivors of atomic bomb, followed up to 1977 and T65D dosimetry system. In 1987, Radiation Effects Research Foundation (RERF), a cooperative Japan-United States research organisation published radiation induced risk estimates (absolute and relative) using revised system of dosimetry DS86 and extended follow up of 35 years (Yukiko et al., 1988). In this paper PC has been calculated for the Indian population: i) using absolute risk estimates of RERF and NIH methodology, and ii) using the constant relative risk coefficients (CRR) of RERF. Calculations with new risk coefficients have been extended to the American population and results compared with Indian population. (author). 3 refs., 2 figs
Cladding failure probability modeling for risk evaluations of fast reactors
International Nuclear Information System (INIS)
Mueller, C.J.; Kramer, J.M.
1987-01-01
This paper develops the methodology to incorporate cladding failure data and associated modeling into risk evaluations of liquid metal-cooled fast reactors (LMRs). Current US innovative designs for metal-fueled pool-type LMRs take advantage of inherent reactivity feedback mechanisms to limit reactor temperature increases in response to classic anticipated-transient-without-scram (ATWS) initiators. Final shutdown without reliance on engineered safety features can then be accomplished if sufficient time is available for operator intervention to terminate fission power production and/or provide auxiliary cooling prior to significant core disruption. Coherent cladding failure under the sustained elevated temperatures of ATWS events serves as one indicator of core disruption. In this paper we combine uncertainties in cladding failure data with uncertainties in calculations of ATWS cladding temperature conditions to calculate probabilities of cladding failure as a function of the time for accident recovery
Cladding failure probability modeling for risk evaluations of fast reactors
International Nuclear Information System (INIS)
Mueller, C.J.; Kramer, J.M.
1987-01-01
This paper develops the methodology to incorporate cladding failure data and associated modeling into risk evaluations of liquid metal-cooled fast reactors (LMRs). Current U.S. innovative designs for metal-fueled pool-type LMRs take advantage of inherent reactivity feedback mechanisms to limit reactor temperature increases in response to classic anticipated-transient-without-scram (ATWS) initiators. Final shutdown without reliance on engineered safety features can then be accomplished if sufficient time is available for operator intervention to terminate fission power production and/or provide auxiliary cooling prior to significant core disruption. Coherent cladding failure under the sustained elevated temperatures of ATWS events serves as one indicator of core disruption. In this paper we combine uncertainties in cladding failure data with uncertainties in calculations of ATWS cladding temperature conditions to calculate probabilities of cladding failure as a function of the time for accident recovery. (orig.)
Wei, Wei; Larrey-Lassalle, Pyrène; Faure, Thierry; Dumoulin, Nicolas; Roux, Philippe; Mathias, Jean-Denis
2016-03-01
Comparative decision making process is widely used to identify which option (system, product, service, etc.) has smaller environmental footprints and for providing recommendations that help stakeholders take future decisions. However, the uncertainty problem complicates the comparison and the decision making. Probability-based decision support in LCA is a way to help stakeholders in their decision-making process. It calculates the decision confidence probability which expresses the probability of a option to have a smaller environmental impact than the one of another option. Here we apply the reliability theory to approximate the decision confidence probability. We compare the traditional Monte Carlo method with a reliability method called FORM method. The Monte Carlo method needs high computational time to calculate the decision confidence probability. The FORM method enables us to approximate the decision confidence probability with fewer simulations than the Monte Carlo method by approximating the response surface. Moreover, the FORM method calculates the associated importance factors that correspond to a sensitivity analysis in relation to the probability. The importance factors allow stakeholders to determine which factors influence their decision. Our results clearly show that the reliability method provides additional useful information to stakeholders as well as it reduces the computational time.
Duelling idiots and other probability puzzlers
Nahin, Paul J
2002-01-01
What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the worki
Proposal for Modified Damage Probability Distribution Functions
DEFF Research Database (Denmark)
Pedersen, Preben Terndrup; Hansen, Peter Friis
1996-01-01
Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub-committee on st......Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub...