Cruz, Cristina D; Win, Jessicah K; Chantarachoti, Jiraporn; Mutukumira, Anthony N; Fletcher, Graham C
2012-02-15
The standard Bacteriological Analytical Manual (BAM) protocol for detecting Listeria in food and on environmental surfaces takes about 96 h. Some studies indicate that rapid methods, which produce results within 48 h, may be as sensitive and accurate as the culture protocol. As they only give presence/absence results, it can be difficult to compare the accuracy of results generated. We used the Most Probable Number (MPN) technique to evaluate the performance and detection limits of six rapid kits for detecting Listeria in seafood and on an environmental surface compared with the standard protocol. Three seafood products and an environmental surface were inoculated with similar known cell concentrations of Listeria and analyzed according to the manufacturers' instructions. The MPN was estimated using the MPN-BAM spreadsheet. For the seafood products no differences were observed among the rapid kits and efficiency was similar to the BAM method. On the environmental surface the BAM protocol had a higher recovery rate (sensitivity) than any of the rapid kits tested. Clearview™, Reveal®, TECRA® and VIDAS® LDUO detected the cells but only at high concentrations (>10(2) CFU/10 cm(2)). Two kits (VIP™ and Petrifilm™) failed to detect 10(4) CFU/10 cm(2). The MPN method was a useful tool for comparing the results generated by these presence/absence test kits. There remains a need to develop a rapid and sensitive method for detecting Listeria in environmental samples that performs as well as the BAM protocol, since none of the rapid tests used in this study achieved a satisfactory result. Copyright © 2011 Elsevier B.V. All rights reserved.
Munoz, E. F.; Silverman, M. P.
1979-01-01
A single-step most-probable-number method for determining the number of fecal coliform bacteria present in sewage treatment plant effluents is discussed. A single growth medium based on that of Reasoner et al. (1976) and consisting of 5.0 gr. proteose peptone, 3.0 gr. yeast extract, 10.0 gr. lactose, 7.5 gr. NaCl, 0.2 gr. sodium lauryl sulfate, and 0.1 gr. sodium desoxycholate per liter is used. The pH is adjusted to 6.5, and samples are incubated at 44.5 deg C. Bacterial growth is detected either by measuring the increase with time in the electrical impedance ratio between the innoculated sample vial and an uninnoculated reference vial or by visual examination for turbidity. Results obtained by the single-step method for chlorinated and unchlorinated effluent samples are in excellent agreement with those obtained by the standard method. It is suggested that in automated treatment plants impedance ratio data could be automatically matched by computer programs with the appropriate dilution factors and most probable number tables already in the computer memory, with the corresponding result displayed as fecal coliforms per 100 ml of effluent.
Clan structure analysis and rapidity gap probability
International Nuclear Information System (INIS)
Lupia, S.; Giovannini, A.; Ugoccioni, R.
1995-01-01
Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at TEVATRON and HERA. (orig.)
Clan structure analysis and rapidity gap probability
Energy Technology Data Exchange (ETDEWEB)
Lupia, S. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy); Giovannini, A. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy); Ugoccioni, R. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy)
1995-03-01
Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at TEVATRON and HERA. (orig.)
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
Talking probabilities: communicating probalistic information with words and numbers
Renooij, S.; Witteman, C.L.M.
1999-01-01
The number of knowledge-based systems that build on Bayesian belief networks is increasing. The construction of such a network however requires a large number of probabilities in numerical form. This is often considered a major obstacle, one of the reasons being that experts are reluctant to provide
Talking probabilities: communicating probabilistic information with words and numbers
Renooij, S.; Witteman, C.L.M.
1999-01-01
The number of knowledge-based systems that build on Bayesian belief networks is increasing. The construction of such a network however requires a large number of probabilities in numerical form. This is often considered a major obstacle, one of the reasons being that experts are reluctant to
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
Estimated probability of the number of buildings damaged by the ...
African Journals Online (AJOL)
The analysis shows that the probability estimator of the building damage ... and homeowners) should reserve the cost of repair at least worth the risk of loss, to face ... Keywords: Citarum River; logistic regression; genetic algorithm; losses risk; ...
Energy Technology Data Exchange (ETDEWEB)
O' Rourke, Patrick Francis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-10-27
The purpose of this report is to provide the reader with an understanding of how a Monte Carlo neutron transport code was written, developed, and evolved to calculate the probability distribution functions (PDFs) and their moments for the neutron number at a final time as well as the cumulative fission number, along with introducing several basic Monte Carlo concepts.
Learning Binomial Probability Concepts with Simulation, Random Numbers and a Spreadsheet
Rochowicz, John A., Jr.
2005-01-01
This paper introduces the reader to the concepts of binomial probability and simulation. A spreadsheet is used to illustrate these concepts. Random number generators are great technological tools for demonstrating the concepts of probability. Ideas of approximation, estimation, and mathematical usefulness provide numerous ways of learning…
Method for rapidly determining a pulp kappa number using spectrophotometry
Chai, Xin-Sheng; Zhu, Jun Yong
2002-01-01
A system and method for rapidly determining the pulp kappa number through direct measurement of the potassium permanganate concentration in a pulp-permanganate solution using spectrophotometry. Specifically, the present invention uses strong acidification to carry out the pulp-permanganate oxidation reaction in the pulp-permanganate solution to prevent the precipitation of manganese dioxide (MnO.sub.2). Consequently, spectral interference from the precipitated MnO.sub.2 is eliminated and the oxidation reaction becomes dominant. The spectral intensity of the oxidation reaction is then analyzed to determine the pulp kappa number.
Kidwai, Aneela Altaf; Jamal, Qaiser; Saher; Mehrunnisa; Farooqi, Faiz-ur-rehman; Saleem-Ullah
2010-11-01
To determine the frequency of seropositive dengue infection using rapid immunochromatographic assay in patients with probable dengue infection as per WHO criteria. A cross-sectional observational study was conducted at Abbasi Shaheed Hospital, Karachi from July 2008 to January 2009. Patients presenting with acute febrile illness, rashes, bleeding tendencies, leucopenia and or thrombocytopenia were evaluated according to WHO criteria for probable dengue infection. Acute phase sera were collected after 5 days of the onset of fever as per WHO criteria. Serology was performed using rapid immunochromatographic (ICT) assay with differential detection of IgM and IgG. A primary dengue infection was defined by a positive IgM band and a negative IgG band whereas secondary infection was defined by a positive IgG band with or without positive IgM band. Among 599 patients who met the WHO criteria for dengue infection, 251(41.9%) were found to be ICT reactive among whom 42 (16.73%) had primary infection. Secondary infection was reported in 209 (83.26%). Acute phase sera of 348 (58.09%) were ICT non reactive. Four patients died because of dengue shock syndrome among which three had secondary infection. Early identification of secondary infection in acute phase sera using rapid ICT is valuable in terms of disease progression and mortality. However in highly suspected cases of dengue infection clinical management should not rely on negative serological results.
International Nuclear Information System (INIS)
Kidwai, A.A.; Jamal, Q.; Mehrunnisa, S.; Farooqi, F.R.
2010-01-01
Objective: To determine the frequency of seropositive dengue infection using rapid immuno chromatographic assay in patients with probable dengue infection as per WHO criteria. Method: A cross-sectional observational study was conducted at Abbasi Shaheed Hospital, Karachi from July 2008 to January 2009. Patients presenting with acute febrile illness, rashes, bleeding tendencies, leucopenia and or thrombocytopenia were evaluated according to WHO criteria for probable dengue infection. Acute phase sera were collected after 5 days of the onset of fever as per WHO criteria. Serology was performed using rapid immuno chromatographic (ICT) assay with differential detection of IgM and IgG. A primary dengue infection was defined by a positive IgM band and a negative IgG band whereas secondary infection was defined by a positive IgG band with or without positive IgM band. Result: Among 599 patients who met the WHO criteria for dengue infection, 251(41.9%) were found to be ICT reactive among whom 42 (16.73%) had primary infection. Secondary infection was reported in 209 (83.26%). Acute phase sera of 348 (58.09%) were ICT non reactive. Four patients died because of dengue shock syndrome among which three had secondary infection. Conclusion: Early identification of secondary infection in acute phase sera using rapid ICT is valuable in terms of disease progression and mortality. However in highly suspected cases of dengue infection clinical management should not rely on negative serological results. (author)
Medicine in words and numbers: a cross-sectional survey comparing probability assessment scales
Directory of Open Access Journals (Sweden)
Koele Pieter
2007-06-01
Full Text Available Abstract Background In the complex domain of medical decision making, reasoning under uncertainty can benefit from supporting tools. Automated decision support tools often build upon mathematical models, such as Bayesian networks. These networks require probabilities which often have to be assessed by experts in the domain of application. Probability response scales can be used to support the assessment process. We compare assessments obtained with different types of response scale. Methods General practitioners (GPs gave assessments on and preferences for three different probability response scales: a numerical scale, a scale with only verbal labels, and a combined verbal-numerical scale we had designed ourselves. Standard analyses of variance were performed. Results No differences in assessments over the three response scales were found. Preferences for type of scale differed: the less experienced GPs preferred the verbal scale, the most experienced preferred the numerical scale, with the groups in between having a preference for the combined verbal-numerical scale. Conclusion We conclude that all three response scales are equally suitable for supporting probability assessment. The combined verbal-numerical scale is a good choice for aiding the process, since it offers numerical labels to those who prefer numbers and verbal labels to those who prefer words, and accommodates both more and less experienced professionals.
Hotspots ampersand other hidden targets: Probability of detection, number, frequency and area
International Nuclear Information System (INIS)
Vita, C.L.
1994-01-01
Concepts and equations are presented for making probability-based estimates of the detection probability, and the number, frequency, and area of hidden targets, including hotspots, at a given site. Targets include hotspots, which are areas of extreme or particular contamination, and any object or feature that is hidden from direct visual observation--including buried objects and geologic or hydrologic details or anomalies. Being Bayesian, results are fundamentally consistent with observational methods. Results are tools for planning or interpreting exploration programs used in site investigation or characterization, remedial design, construction, or compliance monitoring, including site closure. Used skillfully and creatively, these tools can help streamline and expedite environmental restoration, reducing time and cost, making site exploration cost-effective, and providing acceptable risk at minimum cost. 14 refs., 4 figs
Directory of Open Access Journals (Sweden)
FL Colla
2014-03-01
Full Text Available Salmonella is traditionally identified by conventional microbiological tests, but the enumeration of this bacterium is not used on a routine basis. Methods such as the most probable number (MPN, which utilize an array of multiple tubes, are time-consuming and expensive, whereas miniaturized most probable number (mMPN methods, which use microplates, can be adapted for the enumeration of bacteria, saving up time and materials. The aim of the present paper is to assess two mMPN methods for the enumeration of Salmonella sp in artificially-contaminated chicken meat samples. Microplates containing 24 wells (method A and 96 wells (method B, both with peptone water as pre-enrichment medium and modified semi-solid Rappaport-Vassiliadis (MSRV as selective enrichment medium, were used. The meat matrix consisted of 25g of autoclaved ground chicken breast contaminated with dilutions of up to 10(6 of Salmonella Typhimurium (ST and Escherichia coli (EC. In method A, the dilution 10-5 of Salmonella Typhimurium corresponded to >57 MPN/mL and the dilution 10-6 was equal to 30 MPN/mL. There was a correlation between the counts used for the artificial contamination of the samples and those recovered by mMPN, indicating that the method A was sensitive for the enumeration of different levels of contamination of the meat matrix. In method B, there was no correlation between the inoculated dilutions and the mMPN results.
DEFF Research Database (Denmark)
Kriegbaum, Margit; Larsen, Anne Mette; Christensen, Ulla
2011-01-01
and to study joint exposure to both. Methods Birth cohort study of smoking cessation of 6232 Danish men born in 1953 with a follow-up at age 51 (response rate 66.2%). History of unemployment and cohabitation was measured annually using register data. Information on smoking cessation was obtained...... by a questionnaire. Results The probability of smoking cessation decreased with the number of job losses (ranging from 1 OR 0.54 (95% CI 0.46 to 0.64) to 3+ OR 0.41 (95% CI 0.30 to 0.55)) and of broken partnerships (ranging from 1 OR 0.74 (95% CI 0.63 to 0.85) to 3+ OR 0.50 (95% CI 0.39 to 0.63)). Furthermore......–23 years (OR 0.44, 95% CI 0.37 to 0.52)). Those who never cohabited and experienced one or more job losses had a particular low chance of smoking cessation (OR 0.19, 95% CI 0.12 to 0.30). Conclusion The numbers of job losses and of broken partnerships were both inversely associated with probability...
Estimating the concordance probability in a survival analysis with a discrete number of risk groups.
Heller, Glenn; Mo, Qianxing
2016-04-01
A clinical risk classification system is an important component of a treatment decision algorithm. A measure used to assess the strength of a risk classification system is discrimination, and when the outcome is survival time, the most commonly applied global measure of discrimination is the concordance probability. The concordance probability represents the pairwise probability of lower patient risk given longer survival time. The c-index and the concordance probability estimate have been used to estimate the concordance probability when patient-specific risk scores are continuous. In the current paper, the concordance probability estimate and an inverse probability censoring weighted c-index are modified to account for discrete risk scores. Simulations are generated to assess the finite sample properties of the concordance probability estimate and the weighted c-index. An application of these measures of discriminatory power to a metastatic prostate cancer risk classification system is examined.
Francisco, E.; Pendás, A. Martín; Blanco, M. A.
2008-04-01
: 2.80 GHz Intel Pentium IV CPU Operating system: GNU/Linux RAM: 55 992 KB Word size: 32 bits Classification: 2.7 External routines: Netlib Nature of problem: Let us have an N-electron molecule and define an exhaustive partition of the physical space into m three-dimensional regions. The edf program computes the probabilities P(n,n,…,n)≡P({n}) of all possible allocations of n electrons to Ω, n electrons to Ω,…, and n electrons to Ω,{n} being integers. Solution method: Let us assume that the N-electron molecular wave function, Ψ(1,N), is a linear combination of M Slater determinants, Ψ(1,N)=∑rMCψ(1,N). Calling SΩrs the overlap matrix over the 3D region Ω between the (real) molecular spin-orbitals (MSO) in ψ(χ1r,…χNr) and the MSOs in ψ,(χ1s,…,χNs), edf finds all the P({n})'s by solving the linear system ∑{n}{∏kmtkn}P({n})=∑r,sMCCdet[∑kmtSΩrs], where t=1 and t,…,t are arbitrary real numbers. Restrictions: The number of {n} sets grows very fast with m and N, so that the dimension of the linear system (1) soon becomes very large. Moreover, the computer time required to obtain the determinants in the second member of Eq. (1) scales quadratically with M. These two facts limit the applicability of the method to relatively small molecules. Unusual features: Most of the real variables are of precision real*16. Running time: 0.030, 2.010, and 0.620 seconds for Test examples 1, 2, and 3, respectively. References: [1] A. Martín Pendás, E. Francisco, M.A. Blanco, Faraday Discuss. 135 (2007) 423-438. [2] A. Martín Pendás, E. Francisco, M.A. Blanco, J. Phys. Chem. A 111 (2007) 1084-1090. [3] A. Martín Pendás, E. Francisco, M.A. Blanco, Phys. Chem. Chem. Phys. 9 (2007) 1087-1092. [4] E. Francisco, A. Martín Pendás, M.A. Blanco, J. Chem. Phys. 126 (2007) 094102. [5] A. Martín Pendás, E. Francisco, M.A. Blanco, C. Gatti, Chemistry: A European Journal 113 (2007) 9362-9371.
A measure of mutual divergence among a number of probability distributions
Directory of Open Access Journals (Sweden)
J. N. Kapur
1987-01-01
major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.
The Most Probable Limit of Detection (MPL) for rapid microbiological methods
Verdonk, G.P.H.T.; Willemse, M.J.; Hoefs, S.G.G.; Cremers, G.; Heuvel, E.R. van den
Classical microbiological methods have nowadays unacceptably long cycle times. Rapid methods, available on the market for decades, are already applied within the clinical and food industry, but the implementation in pharmaceutical industry is hampered by for instance stringent regulations on
The most probable limit of detection (MPL) for rapid microbiological methods
Verdonk, G.P.H.T.; Willemse, M.J.; Hoefs, S.G.G.; Cremers, G.; Heuvel, van den E.R.
2010-01-01
Classical microbiological methods have nowadays unacceptably long cycle times. Rapid methods, available on the market for decades, are already applied within the clinical and food industry, but the implementation in pharmaceutical industry is hampered by for instance stringent regulations on
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)
Institute of Scientific and Technical Information of China (English)
Yi-Hua Zhu; Ding-Hua Shi; Yong Xiong; Ji Gao; He-Zhi Luo
2004-01-01
Mobility management is a challenging topic in mobile computing environment. Studying the situation of mobiles crossing the boundaries of location areas is significant for evaluating the costs and performances of various location management strategies. Hitherto, several formulae were derived to describe the probability of the number of location areas' boundaries crossed by a mobile. Some of them were widely used in analyzing the costs and performances of mobility management strategies. Utilizing the density evolution method of vector Markov processes, we propose a general probability formula of the number of location areas' boundaries crossed by a mobile between two successive calls. Fortunately, several widely-used formulae are special cases of the proposed formula.
Wu, Yunna; Chen, Kaifeng; Xu, Hu; Xu, Chuanbo; Zhang, Haobo; Yang, Meng
2017-12-01
There is insufficient research relating to offshore wind farm site selection in China. The current methods for site selection have some defects. First, information loss is caused by two aspects: the implicit assumption that the probability distribution on the interval number is uniform; and ignoring the value of decision makers' (DMs') common opinion on the criteria information evaluation. Secondly, the difference in DMs' utility function has failed to receive attention. An innovative method is proposed in this article to solve these drawbacks. First, a new form of interval number and its weighted operator are proposed to reflect the uncertainty and reduce information loss. Secondly, a new stochastic dominance degree is proposed to quantify the interval number with a probability distribution. Thirdly, a two-stage method integrating the weighted operator with stochastic dominance degree is proposed to evaluate the alternatives. Finally, a case from China proves the effectiveness of this method.
Selective genomic copy number imbalances and probability of recurrence in early-stage breast cancer.
Directory of Open Access Journals (Sweden)
Patricia A Thompson
Full Text Available A number of studies of copy number imbalances (CNIs in breast tumors support associations between individual CNIs and patient outcomes. However, no pattern or signature of CNIs has emerged for clinical use. We determined copy number (CN gains and losses using high-density molecular inversion probe (MIP arrays for 971 stage I/II breast tumors and applied a boosting strategy to fit hazards models for CN and recurrence, treating chromosomal segments in a dose-specific fashion (-1 [loss], 0 [no change] and +1 [gain]. The concordance index (C-Index was used to compare prognostic accuracy between a training (n = 728 and test (n = 243 set and across models. Twelve novel prognostic CNIs were identified: losses at 1p12, 12q13.13, 13q12.3, 22q11, and Xp21, and gains at 2p11.1, 3q13.12, 10p11.21, 10q23.1, 11p15, 14q13.2-q13.3, and 17q21.33. In addition, seven CNIs previously implicated as prognostic markers were selected: losses at 8p22 and 16p11.2 and gains at 10p13, 11q13.5, 12p13, 20q13, and Xq28. For all breast cancers combined, the final full model including 19 CNIs, clinical covariates, and tumor marker-approximated subtypes (estrogen receptor [ER], progesterone receptor, ERBB2 amplification, and Ki67 significantly outperformed a model containing only clinical covariates and tumor subtypes (C-Index(full model, train[test] = 0.72[0.71] ± 0.02 vs. C-Index(clinical + subtype model, train[test] = 0.62[0.62] ± 0.02; p<10(-6. In addition, the full model containing 19 CNIs significantly improved prognostication separately for ER-, HER2+, luminal B, and triple negative tumors over clinical variables alone. In summary, we show that a set of 19 CNIs discriminates risk of recurrence among early-stage breast tumors, independent of ER status. Further, our data suggest the presence of specific CNIs that promote and, in some cases, limit tumor spread.
Atwell, William; Tylka, Allan J.; Dietrich, William F.; Rojdev, Kristina; Matzkind, Courtney
2016-01-01
In an earlier paper presented at ICES in 2015, we investigated solar particle event (SPE) radiation exposures (absorbed dose) to small, thinly-shielded spacecraft during a period when the monthly smoothed sunspot number (SSN) was less than 30. Although such months are generally considered "solar-quiet", SPEs observed during these months even include Ground Level Events, the most energetic type of SPE. In this paper, we add to previous study those SPEs that occurred in 1973-2015 when the SSN was greater than 30 but less than 50. Based on the observable energy range of the solar protons, we classify the event as GLEs, sub-GLEs, and sub-sub-GLEs, all of which are potential contributors to the radiation hazard. We use the spectra of these events to construct a probabilistic model of the absorbed dose due to solar protons when SSN < 50 at various confidence levels for various depths of shielding and for various mission durations. We provide plots and tables of solar proton-induced absorbed dose as functions of confidence level, shielding thickness, and mission-duration that will be useful to system designers.
DEFF Research Database (Denmark)
Fredslund, Line; Ekelund, Flemming; Jacobsen, Carsten Suhr
2001-01-01
This paper reports on the first successful molecular detection and quantification of soil protozoa. Quantification of heterotrophic flagellates and naked amoebae in soil has traditionally relied on dilution culturing techniques, followed by most-probable-number (MPN) calculations. Such methods...... are biased by differences in the culturability of soil protozoa and are unable to quantify specific taxonomic groups, and the results are highly dependent on the choice of media and the skills of the microscopists. Successful detection of protozoa in soil by DNA techniques requires (i) the development...
The average number of partons per clan in rapidity intervals in parton showers
Energy Technology Data Exchange (ETDEWEB)
Giovannini, A. [Turin Univ. (Italy). Ist. di Fisica Teorica; Lupia, S. [Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut; Ugoccioni, R. [Lund Univ. (Sweden). Dept. of Theoretical Physics
1996-04-01
The dependence of the average number of partons per clan on virtuality and rapidity variables is analytically predicted in the framework of the Generalized Simplified Parton Shower model, based on the idea that clans are genuine elementary subprocesses. The obtained results are found to be qualitatively consistent with experimental trends. This study extends previous results on the behavior of the average number of clans in virtuality and rapidity and shows how important physical quantities can be calculated analytically in a model based on essentials of QCD allowing local violations of the energy-momentum conservation law, still requiring its global validity. (orig.)
The average number of partons per clan in rapidity intervals in parton showers
International Nuclear Information System (INIS)
Giovannini, A.; Lupia, S.; Ugoccioni, R.
1996-01-01
The dependence of the average number of partons per clan on virtuality and rapidity variables is analytically predicted in the framework of the Generalized Simplified Parton Shower model, based on the idea that clans are genuine elementary subprocesses. The obtained results are found to be qualitatively consistent with experimental trends. This study extends previous results on the behavior of the average number of clans in virtuality and rapidity and shows how important physical quantities can be calculated analytically in a model based on essentials of QCD allowing local violations of the energy-momentum conservation law, still requiring its global validity. (orig.)
Institute of Scientific and Technical Information of China (English)
HAN Li-Bo; GONG Xiao-Long; CAO Li; WU Da-Jin
2007-01-01
An approximate Fokker-P1anck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution (SPD) and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ, is in -1＜λ ≤ 0 and can be the double extrema in 0＜λ＜1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, 〈x〉, versus λ. The position and the value of the minimum are controlled by the noise-correlated times.
Directory of Open Access Journals (Sweden)
Randa Novalino
2016-09-01
Full Text Available AbstrakDiare merupakan salah satu penyakit yang ditularkan melalui air terkontaminasi oleh agen penyebab seperti bakteri Coliform. Menurut data Dinas Kesehatan Kota (DKK Padang pada tahun 2011, kejadian diare di Kelurahan Lubuk Buaya Kecamatan Koto Tangah, Kota Padang merupakan kasus tertinggi di Kota Padang. Tujuan penelitian ini adalah menentukan kualitas air sumur gali di Kelurahan Lubuk Buaya berdasarkan Indeks Most Probable Number (MPN menurut Peraturan Menteri Kesehatan Republik Indonesia (Permenkes RI No. 416 tahun 1990. Sampel penelitian ini adalah air sumur gali yang digunakan di beberapa Rukun Tetangga (RT, yang diambil secara acak dari beberapa Rukun Warga (RW yang telah dipilih sebelumnya, sehingga didapatkan 15 sampel. Penelitian ini dilaksanakan dalam 2 tahap yaitu pengambilan sampel air sumur gali sekaligus observasi faktor yang mempengaruhi kualitas air dan pemeriksaan mikrobiologi dengan metode Most Probable Number (MPN Test. Tes ini terdiri dari tes presumtif dan tes konfirmatif yang disesuaikan dengan Permenkes RI. Hasil penelitian ialah 73,33% dari jumlah sumur yang diperiksa tidak memenuhi standar Permenkes R.I. karena mengandung Coliform > 50 pada setiap 100 ml air. Hanya 26,6% sumur yang memenuhi standar yang telah ditetapkan. Beberapa faktor yang dapat mempengaruhi yaitu lokasi sumber pencemaran, dinding parapet, drainase, tutup sumur dan sarana pengambilan air.Kata kunci: kualitas air sumur gali, MPN, coliform AbstractDiarrhea is one of the diseases that transmitted through contaminated water by causative agent, one of which is coliform bacteria. According to data from City Health Department Padang in 2011, the incidence of diarrhea in Kelurahan Lubuk Buaya Kecamatan Koto Tangah – Padang is the highest case in the city of Padang. The objective of this study was to determine the water quality of wells dug in Kelurahan Lubuk Buaya by Most Probable Number Index (MPN according regulation of Indonesian health
Jenkins, M B; Endale, D M; Fisher, D S; Gay, P A
2009-02-01
To better understand the transport and enumeration of dilute densities of Escherichia coli O157:H7 in agricultural watersheds, we developed a culture-based, five tube-multiple dilution most probable number (MPN) method. The MPN method combined a filtration technique for large volumes of surface water with standard selective media, biochemical and immunological tests, and a TaqMan confirmation step. This method determined E. coli O157:H7 concentrations as low as 0.1 MPN per litre, with a 95% confidence level of 0.01-0.7 MPN per litre. Escherichia coli O157:H7 densities ranged from not detectable to 9 MPN per litre for pond inflow, from not detectable to 0.9 MPN per litre for pond outflow and from not detectable to 8.3 MPN per litre for within pond. The MPN methodology was extended to mass flux determinations. Fluxes of E. coli O157:H7 ranged from 10(4) MPN per hour. This culture-based method can detect small numbers of viable/culturable E. coli O157:H7 in surface waters of watersheds containing animal agriculture and wildlife. This MPN method will improve our understanding of the transport and fate of E. coli O157:H7 in agricultural watersheds, and can be the basis of collections of environmental E. coli O157:H7.
Directory of Open Access Journals (Sweden)
Adriana Zulay Argüello Navarro
2016-07-01
Full Text Available The objective of this research was to quantify diazotrophic bacteria and compare physicochemically rhizospheric soils of three cocoa plantations (Theobroma cacao L. in Norte de Santander Department, Colombia; for which they were characterized, differing in cultivated area, agronomic management and crop age. From serial dilutions of the samples and using the technique of Most Probable Number (MPN, In semisolid culture media (NFb, JMV, LGI, JNFb, the diazotrophs were quantified, evaluating as positive the formation of a subsurface film in the medium contained in sealed vials; equal samples were sent to the Bioambiental laboratory (UNET for physicochemical analyzes. As a result, the evaluated samples showed deficiencies in the percentage of organic matter and elements such as Potassium, Phosphorus and Magnesium. Statistically highly significant differences in MPN were reported. The highest quantification of diazotrophs was reported in the Florilandia farm, which was characterized by drip irrigation. The highest quantification of diazotrophs was recorded in the media NFb and JMV, demonstrating a greater presence of the presumed genera Azospirillum sp. and Burkholderia sp. which are easily isolated from rhizospheric soils, unlike the genera Herbaspirillum sp. and Gluconacetobacter sp. which by their endophytic character tend to be less predominant in this type of samples. It is also concluded that the physicochemical characteristics of the soil, humidity and climatic relationships at the moment of sampling, condition the amount of root exudates and therefore are factors that conditioned the presence of diazotrophs in the samples.
Chen, Yi; Pouillot, Régis; S Burall, Laurel; Strain, Errol A; Van Doren, Jane M; De Jesus, Antonio J; Laasri, Anna; Wang, Hua; Ali, Laila; Tatavarthy, Aparna; Zhang, Guodong; Hu, Lijun; Day, James; Sheth, Ishani; Kang, Jihun; Sahu, Surasri; Srinivasan, Devayani; Brown, Eric W; Parish, Mickey; Zink, Donald L; Datta, Atin R; Hammack, Thomas S; Macarisin, Dumitru
2017-01-16
A precise and accurate method for enumeration of low level of Listeria monocytogenes in foods is critical to a variety of studies. In this study, paired comparison of most probable number (MPN) and direct plating enumeration of L. monocytogenes was conducted on a total of 1730 outbreak-associated ice cream samples that were naturally contaminated with low level of L. monocytogenes. MPN was performed on all 1730 samples. Direct plating was performed on all samples using the RAPID'L.mono (RLM) agar (1600 samples) and agar Listeria Ottaviani and Agosti (ALOA; 130 samples). Probabilistic analysis with Bayesian inference model was used to compare paired direct plating and MPN estimates of L. monocytogenes in ice cream samples because assumptions implicit in ordinary least squares (OLS) linear regression analyses were not met for such a comparison. The probabilistic analysis revealed good agreement between the MPN and direct plating estimates, and this agreement showed that the MPN schemes and direct plating schemes using ALOA or RLM evaluated in the present study were suitable for enumerating low levels of L. monocytogenes in these ice cream samples. The statistical analysis further revealed that OLS linear regression analyses of direct plating and MPN data did introduce bias that incorrectly characterized systematic differences between estimates from the two methods. Published by Elsevier B.V.
Rapid enumeration of low numbers of moulds in tea based drinks using an automated system.
Tanaka, Kouichi; Yamaguchi, Nobuyasu; Baba, Takashi; Amano, Norihide; Nasu, Masao
2011-01-31
Aseptically prepared cold drinks based on tea have become popular worldwide. Contamination of these drinks with harmful microbes is a potential health problem because such drinks are kept free from preservatives to maximize aroma and flavour. Heat-tolerant conidia and ascospores of fungi can survive pasteurization, and need to be detected as quickly as possible. We were able to rapidly and accurately detect low numbers of conidia and ascospores in tea-based drinks using fluorescent staining followed by an automated counting system. Conidia or ascospores were inoculated into green tea and oolong tea, and samples were immediately filtered through nitrocellulose membranes (pore size: 0.8 μm) to concentrate fungal propagules. These were transferred onto potato dextrose agar and incubated for 23 h at 28 °C. Fungi germinating on the membranes were fluorescently stained for 30 min. The stained mycelia were counted selectively within 90s using an automated counting system (MGS-10LD; Chuo Electric Works, Osaka, Japan). Very low numbers (1 CFU/100ml) of conidia or ascospores could be rapidly counted, in contrast to traditional labour intensive techniques. All tested mould strains were detected within 24h while conventional plate counting required 72 h for colony enumeration. Counts of slow-growing fungi (Cladosporium cladosporioides) obtained by automated counting and by conventional plate counting were close (r(2) = 0.986). Our combination of methods enables counting of both fast- and slow-growing fungi, and should be useful for microbiological quality control of tea-based and also other drinks. Copyright © 2011 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Ekelund, Flemming; Christensen, Søren; Rønn, Regin
1999-01-01
An automated modification of the most-probable-number (MPN) technique has been developed for enumeration of phagotrophic protozoa. The method is based on detection of prey depletion in micro titre plates rather than on presence of protozoa. A transconjugant Pseudomonas fluorescens DR54 labelled w...
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Knuiman Matthew
2008-06-01
Full Text Available Abstract Background Treatments for coronary heart disease (CHD have evolved rapidly over the last 15 years with considerable change in the number and effectiveness of both medical and surgical treatments. This period has seen the rapid development and uptake of statin drugs and coronary artery revascularization procedures (CARPs that include Coronary Artery Bypass Graft procedures (CABGs and Percutaneous Coronary Interventions (PCIs. It is difficult in an era of such rapid change to accurately forecast requirements for treatment services such as CARPs. In a previous paper we have described and outlined the use of a Markov Monte Carlo simulation model for analyzing and predicting the requirements for CARPs for the population of Western Australia (Mannan et al, 2007. In this paper, we expand on the use of this model for forecasting CARPs in Western Australia with a focus on the lack of adequate performance of the (standard model for forecasting CARPs in a period during the mid 1990s when there were considerable changes to CARP technology and implementation policy and an exploration and demonstration of how the standard model may be adapted to achieve better performance. Methods Selected key CARP event model probabilities are modified based on information relating to changes in the effectiveness of CARPs from clinical trial evidence and an awareness of trends in policy and practice of CARPs. These modified model probabilities and the ones obtained by standard methods are used as inputs in our Markov simulation model. Results The projected numbers of CARPs in the population of Western Australia over 1995–99 only improve marginally when modifications to model probabilities are made to incorporate an increase in effectiveness of PCI procedures. However, the projected numbers improve substantially when, in addition, further modifications are incorporated that relate to the increased probability of a PCI procedure and the reduced probability of a CABG
Mannan, Haider R; Knuiman, Matthew; Hobbs, Michael
2008-06-25
Treatments for coronary heart disease (CHD) have evolved rapidly over the last 15 years with considerable change in the number and effectiveness of both medical and surgical treatments. This period has seen the rapid development and uptake of statin drugs and coronary artery revascularization procedures (CARPs) that include Coronary Artery Bypass Graft procedures (CABGs) and Percutaneous Coronary Interventions (PCIs). It is difficult in an era of such rapid change to accurately forecast requirements for treatment services such as CARPs. In a previous paper we have described and outlined the use of a Markov Monte Carlo simulation model for analyzing and predicting the requirements for CARPs for the population of Western Australia (Mannan et al, 2007). In this paper, we expand on the use of this model for forecasting CARPs in Western Australia with a focus on the lack of adequate performance of the (standard) model for forecasting CARPs in a period during the mid 1990s when there were considerable changes to CARP technology and implementation policy and an exploration and demonstration of how the standard model may be adapted to achieve better performance. Selected key CARP event model probabilities are modified based on information relating to changes in the effectiveness of CARPs from clinical trial evidence and an awareness of trends in policy and practice of CARPs. These modified model probabilities and the ones obtained by standard methods are used as inputs in our Markov simulation model. The projected numbers of CARPs in the population of Western Australia over 1995-99 only improve marginally when modifications to model probabilities are made to incorporate an increase in effectiveness of PCI procedures. However, the projected numbers improve substantially when, in addition, further modifications are incorporated that relate to the increased probability of a PCI procedure and the reduced probability of a CABG procedure stemming from changed CARP preference
Malizia, Agustina; Easdale, Tomás A; Grau, H Ricardo
2013-01-01
Recent studies have shown directional changes in old-growth tropical forests, but changes are complex and diverse, and their drivers unclear. Here, we report rapid net structural and compositional changes in an old-growth subtropical forest and we assess the functional nature of these changes to test hypothetical drivers including recovery from past disturbances, reduction in ungulate browsing, CO2 fertilization, and increases in rainfall and temperature. The study relies on 15 years of demographic monitoring within 8 ha of subtropical montane forest in Argentina. Between 1992 and 2007, stem density markedly increased by 50% (12 stems ha(-1) y(-1)) and basal area by 6% (0.13 m(2) ha(-1) y(-1)). Increased stem density resulted from enhanced recruitment of understory treelets (Piper tucumanum, Eugenia uniflora, Allophylus edulis) into small size classes. Among 27 common tree species, net population growth was negatively correlated with maximum tree size and longevity, and positively correlated with leaf size and leaf nutrient content, especially so when initial population size was controlled for. Changes were inconsistent with predictions derived from past disturbances (no increase in shade-tolerant or long-lived late-succesional species), rainfall or temperature increase (no increase in evergreen or deciduous species, respectively). However, the increase in nutrient-rich soft-leaved species was consistent with exclusion of large herbivores two decades before monitoring started; and CO2 fertilization could help explain the disproportionate increase in small stems. Reductions in populations of large vertebrates have been observed in many otherwise undisturbed tropical forests, and our results suggest they can have important structural and functional repercussions in these forests.
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.
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.
A staggered conservative scheme for every Froude number in rapidly varied shallow water flows
Stelling, G. S.; Duinmeijer, S. P. A.
2003-12-01
This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations.
On random number generators providing convergence more rapid than 1/√N
International Nuclear Information System (INIS)
Belov, V.A.
1982-01-01
To realize the simulation of processes in High Energy Physics a practical test of the efficiency in applying quasirandom numbers to check multiple integration with Monte-Karlo method is presented together with the comparison of the wellknown generators of quasirandom and pseudorandom numbers [ru
DEFF Research Database (Denmark)
Friggens, N C; Labouriau, R
2010-01-01
An improved understanding of the animal factors that affect measures such as conception rate would contribute to solving the problem of impaired reproductive performance in modern dairy cows. A question of particular interest relates to the observed improvement in conception rates from first...... to second and third oestrus cycle: is the increase in conception rate related to cycle number per se or to increasing days from calving? A 5-year study using three breeds (Holstein, Jersey and Danish Red) allowed this issue to be examined. In 560 lactations, from calving until confirmed pregnancy or until...... model. Danish Red cows had a significantly greater rate of occurrence of first oestrus over time. Generalized linear mixed models defined using a binomial distribution and logit link function were used to estimate probability of pregnancy as affected by: breed, parity, oestrus number and days from...
Ramos-Zapata, José A; Guadarrama, Patricia; Navarro-Alberto, Jorge; Orellana, Roger
2011-02-01
The present study was aimed at comparing the number of arbuscular mycorrhizal fungi (AMF) propagules found in soil from a mature tropical forest and that found in an abandoned cornfield in Noh-Bec Quintana Roo, Mexico, during three seasons. Agricultural practices can dramatically reduce the availability and viability of AMF propagules, and in this way delay the regeneration of tropical forests in abandoned agricultural areas. In addition, rainfall seasonality, which characterizes deciduous tropical forests, may strongly influence AMF propagules density. To compare AMF propagule numbers between sites and seasons (summer rainy, winter rainy and dry season), a "most probable number" (MPN) bioassay was conducted under greenhouse conditions employing Sorgum vulgare L. as host plant. Results showed an average value of 3.5 ± 0.41 propagules in 50 ml of soil for the mature forest while the abandoned cornfield had 15.4 ± 5.03 propagules in 50 ml of soil. Likelihood analysis showed no statistical differences in MPN of propagules between seasons within each site, or between sites, except for the summer rainy season for which soil from the abandoned cornfield had eight times as many propagules compared to soil from the mature forest site for this season. Propagules of arbuscular mycorrhizal fungi remained viable throughout the sampling seasons at both sites. Abandoned areas resulting from traditional slash and burn agriculture practices involving maize did not show a lower number of AMF propagules, which should allow the establishment of mycotrophic plants thus maintaining the AMF inoculum potential in these soils.
Energy Technology Data Exchange (ETDEWEB)
Katoh, K [Ibaraki Pref. Univ. Health Sci., (Japan)
1997-12-31
A problem of estimating stochastic characteristics of a population from a small number of samples is solved as an inverse problem, from view point of information theory and with the Bayesian statistics. For both Poisson-process and Bernoulli-process, the most probable values of the characteristics of the mother population and their accuracies and degrees of confidence are successfully obtained. Mathematical expressions are given to the general case where a limit amount of information and/or knowledge with the stochastic characteristics are available and a special case where no a priori information nor knowledge are available. Mathematical properties of the solutions obtained, practical appreciation to the problem to radiation measurement are also discussed.
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Manuel Restrepo-Llano
2014-01-01
Full Text Available The aim of this study was to evaluate the response of Pinus patula seedlings to two inocula types: soil from a Pinus plantation (ES and an in vitro produced inoculum (EM. The most probable number method (MPN was used to quantify ectomycorrhizal propagule density (EPD in both inocula in a 7-order dilution series ranging from 100 (undiluted inoculum to 10−6 (the most diluted inoculum. The MPN method allowed establishing differences in the number of infective ectomycorrhizal propagules’ density (EPD (ES=34 per g; EM=156 per g. The results suggest that the EPD of an inoculum may be a key factor that influences the successfulness of the inoculation. The low EPD of the ES inoculum suggests that soil extracted from forest plantations had very low effectiveness for promoting root colonization and plant growth. In contrast, the high EPD found in the formulated inoculum (EM reinforced the idea that it is better to use proven high quality inocula for forest nurseries than using soil from a forestry plantation.
Atwell, William; Tylka, Allan J.; Dietrich, William; Rojdev, Kristina; Matzkind, Courtney
2016-01-01
In an earlier paper (Atwell, et al., 2015), we investigated solar particle event (SPE) radiation exposures (absorbed dose) to small, thinly-shielded spacecraft during a period when the sunspot number (SSN) was less than 30. These SPEs contain Ground Level Events (GLE), sub-GLEs, and sub-sub-GLEs (Tylka and Dietrich, 2009, Tylka and Dietrich, 2008, and Atwell, et al., 2008). GLEs are extremely energetic solar particle events having proton energies extending into the several GeV range and producing secondary particles in the atmosphere, mostly neutrons, observed with ground station neutron monitors. Sub-GLE events are less energetic, extending into the several hundred MeV range, but do not produce secondary atmospheric particles. Sub-sub GLEs are even less energetic with an observable increase in protons at energies greater than 30 MeV, but no observable proton flux above 300 MeV. In this paper, we consider those SPEs that occurred during 1973-2010 when the SSN was greater than 30 but less than 50. In addition, we provide probability estimates of absorbed dose based on mission duration with a 95% confidence level (CL). We also discuss the implications of these data and provide some recommendations that may be useful to spacecraft designers of these smaller spacecraft.
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Suzuki Keisuke
2013-02-01
Full Text Available Abstract Background Increasing evidence provides a clear association between rapid eye movement sleep behavior disorders (RBD and Parkinson’s disease (PD, but the clinical features that determine the co-morbidity of RBD and PD are not yet fully understood. Methods We evaluated the characteristics of nocturnal disturbances and other motor and non-motor features related to RBD in patients with PD and the impact of RBD on their quality of life. Probable RBD (pRBD was evaluated using the Japanese version of the RBD screening questionnaire (RBDSQ-J. Results A significantly higher frequency of pRBD was observed in PD patients than in the controls (RBDSQ-J ≥ 5 or ≥ 6: 29.0% vs. 8.6%; 17.2% vs. 2.2%, respectively. After excluding restless legs syndrome and snorers in the PD patients, the pRBD group (RBDSQ-J≥5 showed higher scores compared with the non-pRBD group on the Parkinson’s disease sleep scale-2 (PDSS-2 total and three-domain scores. Early morning dystonia was more frequent in the pRBD group. The Parkinson’s Disease Questionnaire (PDQ-39 domain scores for cognition and emotional well-being were higher in the patients with pRBD than in the patients without pRBD. There were no differences between these two groups with respect to the clinical subtype, disease severity or motor function. When using a cut-off of RBDSQ-J = 6, a similar trend was observed for the PDSS-2 and PDQ-39 scores. Patients with PD and pRBD had frequent sleep onset insomnia, distressing dreams and hallucinations. The stepwise linear regression analysis showed that the PDSS-2 domain “motor symptoms at night”, particularly the PDSS sub-item 6 “distressing dreams”, was the only predictor of RBDSQ-J in PD. Conclusion Our results indicate a significant impact of RBD co-morbidity on night-time disturbances and quality of life in PD, particularly on cognition and emotional well-being. RBDSQ may be a useful tool for not only screening RBD in PD patients
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Anderlise Borsoi
2010-11-01
Full Text Available A Salmonella permanece um importante problema na avicultura e, considerando os patógenos transmitidos por alimentos, aparece como um dos agentes principais em surtos de toxinfecções alimentares. Para auxiliar na avaliação de riscos em adquirir infecção alimentar via carne de frangos que sofreram cocção inadequada, ou através de contaminação cruzada a partir desses animais, torna-se importante determinar a extensão de contaminação por patógenos em carne crua. No presente trabalho, foram analisadas 180 carcaças de frangos resfriadas, adquiridas em varejos, para pesquisa de Salmonella com determinação do número de células da bactéria. Foi utilizado o método do número mais provável (NMP nos ágares para isolamento verde brilhante com novobiocina (BGN e xilose-lisina tergitol 4 (XLT4. Os resultados mostraram 12,2% de ocorrência de Salmonella nas carcaças de frangos resfriadas e a média de NMP de Salmonella por mL, na leitura pelo ágar XLT4 foi de 2,7 células e no ágar BGN foi de 1,3 células. Os sorovares de Salmonella isolados das carcaças de frangos no estudo foram S. Enteritidis, S. Agona, S.Rissen, S. Heidelberg e S. Livingstone. A análise dos resultados demonstrou existir um número variável de células de Salmonella contaminando as carcaças de frango resfriadas que estão à venda ao consumidor.Salmonella in poultry remains an important worldwide problem, and among foodborne pathogens, the Salmonella appears as one of the most important outbreaks agents. To assess the risks of acquiring infection via undercooked poultry or cross contamination from chickens, it is important to determine the extent of the contamination on raw poultry with this pathogen. In this study, 180 refrigerated broiler carcasses, obtained from local stores, were assessed to recover Salmonella by the most probable number (MPN method to quantify bacterias cells onto brilliant green agar with novobiocin (BGN and xylose lysin tergitol 4 agar
Hansen, John P
2003-01-01
Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.
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Antoine Abou Rached
2017-11-01
Full Text Available Helicobacter pylori (H. pylori can cause a wide variety of illnesses such as peptic ulcer disease, gastric adenocarcinoma and mucosa-associated lymphoid tissue (MALT lymphoma. The diagnosis and eradication of H. pylori are crucial. The diagnosis of H. pylori is usually based on the rapid urease test (RUT and gastric antral biopsy for histology. The aim of this study is to evaluate the numbers of needed biopsies and their location (antrum/fundus to obtain optimal result for the diagnosis of H. pylori. Three hundred fifty consecutive patients were recruited, 210 fulfill the inclusion criteria and had nine gastric biopsies for the detection of H. pylori infection: two antral for the first RUT (RUT1, one antral and one fundic for the second (RUT2, one antral for the third (RUT3 and two antral with two fundic for histology (HES, Giemsa, PAS. The reading of the 3 types of RUT was performed at 1 hour, 3 hours and 24 hours and biopsies were read by two experienced pathologists not informed about the result of RUT. Results of RUT were considered positive if H. pylori was found on histology of at least one biopsy. The RUT1 at 1h, 3h and 24h has a sensitivity of 72%, 82% and 89% and a specificity of 100%, 99% and 87% respectively. The positive predictive value (PPV was 100%, 99% and 85% respectively and the negative predictive value (NPV of 81%, 87% and 90%. The RUT2 at 1h, 3h and 24h, respectively, had a sensitivity of 86%, 87% and 91% and a specificity of 99%, 97% and 90%. The PPV was 99%, 96% and 88% and NPV of 89%, 90%, 94%. The RUT3 at 1h, 3h and 24h, respectively, had a sensitivity of 70%, 74% and 84% and a specificity of 99%, 99% and 94%. The PPV was 99%, 99% and 92% and NPV of 79%, 81% and 87%. The best sensitivity and specificity were obtained for RUT1 read at 3h, for RUT2 read 1h and 3h, and the RUT3 read at 24h.This study demonstrates that the best sensitivity and specificity of rapid test for urease is obtained when fundic plus antral biopsy
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Dehghan fatemeh
2014-05-01
Conclusions: Multiplex PCR method with shortened operation time was used for the simultaneous detection of total coliforms and Escherichia coli in distribution system of Arak city. It's recommended to be used at least as an initial screening test, and then the positive samples could be randomly tested by MPN.
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
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...
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Cooper W James
2009-01-01
data support a tight and biomechanically defined link between structure and the functional ecology of fish skulls, and indicate that certain mechanisms for transmitting motion through their jaw linkages may require particular anatomical configurations, a conclusion that contravenes the concept of "many-to-one mapping" for fish jaw mechanics. Damselfish trophic evolution is characterized by rapid and repeated shifts between a small number of eco-morphological states, an evolutionary pattern that we describe as reticulate adaptive radiation.
Cooper, W James; Westneat, Mark W
2009-01-30
between structure and the functional ecology of fish skulls, and indicate that certain mechanisms for transmitting motion through their jaw linkages may require particular anatomical configurations, a conclusion that contravenes the concept of "many-to-one mapping" for fish jaw mechanics. Damselfish trophic evolution is characterized by rapid and repeated shifts between a small number of eco-morphological states, an evolutionary pattern that we describe as reticulate adaptive radiation.
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.
Quantum Probabilities as Behavioral Probabilities
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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...
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
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
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Noelle Suemi Wassano
2017-03-01
Full Text Available Solid organ transplantation provides life-saving therapy for patients with end-stage organ disease, and its outcomes have been improving dramatically over the past few decades. However, substantial morbidity results from chronic immunosuppressive therapy administered to prevent graft rejection. It predisposes patients to several life-threatening complications, such as opportunistic microbial infections and the development of different types of cancers. Here, we presented the case of a young man with probable Lynch syndrome, who developed an aggressive colon carcinoma after long-term immunosuppressive therapy due to a prior liver transplantation. Based on this case report, we attempt to find an answer to the question about the risk of cancer development or recurrence in patients with familial syndromes receiving long-term immunosuppressive therapy and to find out how it can be minimized. Answering these questions is particularly important, given the facts that disease course is substantially more aggressive among transplanted patients and that prognosis is poor due to lack of immunocompetence, especially in the setting of Lynch syndrome.
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.
Che Hsin, Lin; Lung Ming, Fu; 10.1088/0960-1317/15/5/006
2005-01-01
This paper proposes a novel three-dimensional (3D) vortex micromixer for micro-total-analysis-systems ( mu TAS) applications which utilizes self-rotation effects to mix fluids in a circular chamber at low Reynolds numbers (Re). The microfluidic mixer is fabricated in a three-layer glass structure for delivering fluid samples in parallel. The fluids are driven into the circular mixing chamber by means of hydrodynamic pumps from two fluid inlet ports. The two inlet channels divide into eight individual channels tangent to a 3D circular chamber for the purpose of mixing. Numerical simulation of the microfluidic dynamics is employed to predict the self-rotation phenomenon and to estimate the mixing performance under various Reynolds number conditions. Experimental flow visualization by mixing dye samples is performed in order to verify the numerical simulation results. A good agreement is found to exist between the two sets of results. The numerical results indicate that the mixing performance can be as high as 9...
Maricq, M Matti; Chase, Richard E; Xu, Ning; Podsiadlik, Diane H
2003-10-01
An improved version of the constant volume sampling (CVS) methodology that overcomes a number of obstacles that exist with the current CVS dilution tunnel system used in most diesel and gasoline vehicle emissions test facilities is presented. The key feature of the new sampling system is the introduction of dilution air immediately at the vehicle tailpipe. In the present implementation, this is done concentrically through a cylindrical air filter. Elimination of the transfer hose conventionally used to connect the tailpipe to the dilution tunnel significantly reduces the hydrocarbon and particulate matter (PM) storage release artifacts that can lead to wildly incorrect particle number counts and to erroneous filter-collected PM mass. It provides accurate representations of particle size distributions for diesel vehicles by avoiding the particle coagulation that occurs in the transfer hose. Furthermore, it removes the variable delay time that otherwise exists between the time that emissions exit the tailpipe and when they are detected in the dilution tunnel. The performance of the improved CVS system is examined with respect to diesel, gasoline, and compressed natural gas vehicles.
Rapid methods for detection of bacteria
DEFF Research Database (Denmark)
Corfitzen, Charlotte B.; Andersen, B.Ø.; Miller, M.
2006-01-01
Traditional methods for detection of bacteria in drinking water e.g. Heterotrophic Plate Counts (HPC) or Most Probable Number (MNP) take 48-72 hours to give the result. New rapid methods for detection of bacteria are needed to protect the consumers against contaminations. Two rapid methods...
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...
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...
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...
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...
Niu, Ao-lei; Wang, Yin-qiu; Zhang, Hui; Liao, Cheng-hong; Wang, Jin-kai; Zhang, Rui; Che, Jun; Su, Bing
2011-10-12
Homeobox genes are the key regulators during development, and they are in general highly conserved with only a few reported cases of rapid evolution. RHOXF2 is an X-linked homeobox gene in primates. It is highly expressed in the testicle and may play an important role in spermatogenesis. As male reproductive system is often the target of natural and/or sexual selection during evolution, in this study, we aim to dissect the pattern of molecular evolution of RHOXF2 in primates and its potential functional consequence. We studied sequences and copy number variation of RHOXF2 in humans and 16 nonhuman primate species as well as the expression patterns in human, chimpanzee, white-browed gibbon and rhesus macaque. The gene copy number analysis showed that there had been parallel gene duplications/losses in multiple primate lineages. Our evidence suggests that 11 nonhuman primate species have one RHOXF2 copy, and two copies are present in humans and four Old World monkey species, and at least 6 copies in chimpanzees. Further analysis indicated that the gene duplications in primates had likely been mediated by endogenous retrovirus (ERV) sequences flanking the gene regions. In striking contrast to non-human primates, humans appear to have homogenized their two RHOXF2 copies by the ERV-mediated non-allelic recombination mechanism. Coding sequence and phylogenetic analysis suggested multi-lineage strong positive selection on RHOXF2 during primate evolution, especially during the origins of humans and chimpanzees. All the 8 coding region polymorphic sites in human populations are non-synonymous, implying on-going selection. Gene expression analysis demonstrated that besides the preferential expression in the reproductive system, RHOXF2 is also expressed in the brain. The quantitative data suggests expression pattern divergence among primate species. RHOXF2 is a fast-evolving homeobox gene in primates. The rapid evolution and copy number changes of RHOXF2 had been driven by
Directory of Open Access Journals (Sweden)
Zhang Rui
2011-10-01
Full Text Available Abstract Background Homeobox genes are the key regulators during development, and they are in general highly conserved with only a few reported cases of rapid evolution. RHOXF2 is an X-linked homeobox gene in primates. It is highly expressed in the testicle and may play an important role in spermatogenesis. As male reproductive system is often the target of natural and/or sexual selection during evolution, in this study, we aim to dissect the pattern of molecular evolution of RHOXF2 in primates and its potential functional consequence. Results We studied sequences and copy number variation of RHOXF2 in humans and 16 nonhuman primate species as well as the expression patterns in human, chimpanzee, white-browed gibbon and rhesus macaque. The gene copy number analysis showed that there had been parallel gene duplications/losses in multiple primate lineages. Our evidence suggests that 11 nonhuman primate species have one RHOXF2 copy, and two copies are present in humans and four Old World monkey species, and at least 6 copies in chimpanzees. Further analysis indicated that the gene duplications in primates had likely been mediated by endogenous retrovirus (ERV sequences flanking the gene regions. In striking contrast to non-human primates, humans appear to have homogenized their two RHOXF2 copies by the ERV-mediated non-allelic recombination mechanism. Coding sequence and phylogenetic analysis suggested multi-lineage strong positive selection on RHOXF2 during primate evolution, especially during the origins of humans and chimpanzees. All the 8 coding region polymorphic sites in human populations are non-synonymous, implying on-going selection. Gene expression analysis demonstrated that besides the preferential expression in the reproductive system, RHOXF2 is also expressed in the brain. The quantitative data suggests expression pattern divergence among primate species. Conclusions RHOXF2 is a fast-evolving homeobox gene in primates. The rapid
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...
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
Directory of Open Access Journals (Sweden)
Renato Travassos Beltrame
2009-08-01
Full Text Available Several models have been developed to evaluate reproductive status of cows through concentration of progesterone in milk, the effect of sex selection in the commercial production of herds and bioeconomic performance of the multiple ovulation and embryo transfer system in select herds. However, models describing the production of embryos in superovulated females have yet to be developed. A probability density function of the number of embryos collected by donors of the Nelore breed was determined. Records of 61,928 embryo collections from 26,767 donors from 1991 to 2005 were analyzed. Data were provided by the Brazilian Association of Creators of Zebu and Controlmax Consultoria e Sistemas Ltda. The probability density function of the number of viable embryos was modeled using exponential and gamma distributions. Parameter fitting was carried out for maximum likelihood using a non-linear gradient method. Both distributions presented similar level of precision: root mean square error (RMSE = 0.0072 and 0.0071 for the exponential and gamma distributions, respectively; both distributions are thus deemed suitable for representing the probability density function of embryo production by Nelore females.Diversos modelos têm sido desenvolvidos para avaliar o estado reprodutivo de vacas por meio da concentração de progesterona no leite, o efeito da seleção do sexo na produção comercial de rebanhos e o desempenho bioeconômico da ovulação múltipla e transferência de embriões em rebanhos selecionados. No entanto, modelos que descrevem a produção de embriões em fêmeas superovulados ainda têm de ser desenvolvidos. Uma função de densidade probabilidade para o número de embriões viáveis recuperados de doadoras da raça Nelore foi determinada. Dados de 61.928 coletas de 26.767 doadoras entre 1991 e 2005 foram analisados. Os resultados foram fornecidos pela Associação Brasileira de Criadores de Zebu (ABCZ e pela empresa Controlmax
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.
Directory of Open Access Journals (Sweden)
Sureeporn Narongwongwattana
2015-09-01
Full Text Available Volatile Fatty Acid number (VFA no. is one of the parameters indicating the state of quality of Para rubber latex at that particular time. Most factories analyze this parameter using standard analytical method as in ISO 506:1992(E. Nevertheless, this procedure is complicated, chemical and time consuming, as well as skilled analyst required. Therefore, near infrared (NIR spectroscopy which is rapid, accurate and nonchemicals method was applied to determine the VFA no. in field latex and concentrated latex based on quantification and discriminant model. The best calibration equation was obtained from standard normal variate (SNV spectra in the region of 6109.7–5770.3, 4613.1–4242.9 cm-1 with R = 0.832, SECV = 0.036 and no bias. From the performance check, statistically it was found that SECV and bias were low enough for practical acceptance and the predicted VFA no. was not different significantly from actual VFA no. at 95% confidence intervals. In addition, discriminant model was developed to separate good quality latex from the deteriorated latex using VFA no. at 0.06 as standard as in ISO 2004:2010(E. The discriminant model can be used to screen the latex with overall accuracy of 91.86% in validation set.
Lee, Tzong-Hsi; Lin, Chien-Chu; Chung, Chen-Shuan; Lin, Cheng-Kuan; Liang, Cheng-Chao; Tsai, Kuang-Chau
2015-02-01
Previous studies demonstrated that the sensitivity of rapid urease test (RUT) for diagnosis of Helicobacter pylori infection decreased during peptic ulcer bleeding. We designed this study and tried to find a better method to improve the detection rate of H. pylori infection at the same session of endoscopic diagnosis of peptic ulcer bleeding. We prospectively enrolled 116 patients with peptic ulcer bleeding. These patients received intravenous proton pump inhibitor and then received upper gastrointestinal endoscopy within 24 h after arrival. We took one piece of biopsy from gastric antrum (Group 1), four pieces from gastric antrum (Group 2), and one piece from the gastric body (Group 3) for three separate RUTs, respectively. (13)C-urease breath test was used as gold standard for diagnosis of H. pylori infection. There were 74 patients (64 %) with positive (13)C-urease breath test. Among these 74 patients, 45 patients had positive RUT (sensitivity: 61 %) in Group 1; 55 patients had positive RUT (sensitivity: 74 %) in Group 2; 54 patients had positive RUT (sensitivity: 73 %) in Group 3. There were significant differences between Group 1 and Group 2 (p = 0.02) and between Group 1 and Group 3 (p = 0.022). The sensitivity of RUT was 61 % during peptic ulcer bleeding. The sensitivity of RUT can be increased significantly by increased biopsy number from gastric antrum or biopsy from gastric body.
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.
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.
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)
Harper, Nigel M; Getty, Kelly J K; Schmidt, Karen A; Nutsch, Abbey L; Linton, Richard H
2011-03-01
The U.S. Food and Drug Administration's Bacteriological Analytical Manual recommends two enumeration methods for Bacillus cereus: (i) standard plate count method with mannitol-egg yolk-polymyxin (MYP) agar and (ii) a most-probable-number (MPN) method with tryptic soy broth (TSB) supplemented with 0.1% polymyxin sulfate. This study compared the effectiveness of MYP and MPN methods for detecting and enumerating B. cereus in raw and high-temperature, short-time pasteurized skim (0.5%), 2%, and whole (3.5%) bovine milk stored at 4°C for 96 h. Each milk sample was inoculated with B. cereus EZ-Spores and sampled at 0, 48, and 96 h after inoculation. There were no differences (P > 0.05) in B. cereus populations among sampling times for all milk types, so data were pooled to obtain overall mean values for each treatment. The overall B. cereus population mean of pooled sampling times for the MPN method (2.59 log CFU/ml) was greater (P milk samples ranged from 2.36 to 3.46 and 2.66 to 3.58 log CFU/ml for inoculated milk treatments for the MYP plate count and MPN methods, respectively, which is below the level necessary for toxin production. The MPN method recovered more B. cereus, which makes it useful for validation research. However, the MYP plate count method for enumeration of B. cereus also had advantages, including its ease of use and faster time to results (2 versus 5 days for MPN).
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
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...
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.)
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
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.
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…
Keng, Shao-Hsun; Lin, Chun-Hung; Orazem, Peter
2014-01-01
Since 1990, Taiwan increased the college share of its labor force from 7% to 28% by converting junior colleges to 4-year colleges. Such a rapid surge in skill supply should suppress college wages and lower income inequality. Instead, inequality rose steadily. The surge of weaker college graduates made them weak substitutes for better trained college graduates, increasing wage inequality within skill groups. The college premium would have been 15% higher had college quality remained unchanged ...
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.)
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.
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
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.
Directory of Open Access Journals (Sweden)
Rajiv Advani
2014-06-01
Full Text Available Aims: This study aims to evaluate the implementation of a rapid response treatment protocol for patients presenting with acute onset ischemic stroke. Improvements of routines surrounding the admission and treatment of patients with intravenous thrombolysis (IVT, such as door-to-needle (DTN times, and increasing the numbers of patients treated are discussed. Methods: We conducted a retrospective analysis of all patients (n = 320 treated with IVT for acute onset ischemic stroke at the Stavanger University Hospital, Norway, between 2003 and 2012. In 2009, a succession of changes to pre- and intra-hospital routines were made as well as an improvement in the education of primary health care physicians, nurses and paramedics involved in the treatment of acute onset stroke patients (rapid response treatment protocol. Analyses of DTN times, onset-to-needle times and the number of patients treated per year were carried out to ascertain the effect of the changes made. The primary aim was to analyze DTN times to look for any changes, and the secondary aim was to analyze changes in the number of patients treated per year. Results: In the years after the implementation of the rapid treatment protocol, we saw an improvement in the median DTN time with a decrease from 73 to 50 min in the first year (p = 0.03, a decrease of 45 min in the second year (p = 0.01 and a decrease of 31 min in the third year (p Conclusions: The implementation of the rapid treatment protocol for acute onset ischemic stroke patients led to a significant decrease in the DTN time at our center. These improvements also produced an increase in the number of patients treated per year. The extension of the therapeutic window from 3 to 4.5 h for the use of intravenous recombinant tissue plasminogen activator also played a role in the increased treatment numbers.
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.
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
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.
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...
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)
Maeda, Shinji; Murase, Yoshiro; Mitarai, Satoshi; Sugawara, Isamu; Kato, Seiya
2008-10-01
The discriminatory power of each locus in variable numbers of tandem repeats (VNTR) analyses was evaluated for development of the genotyping method of Mycobacterium tuberculosis (TB) in Japan. By using 325 TB strains collected from whole Japan and 24 mass infection cases (74 isolates), IS6110 restriction fragment length polymorphism (RFLP), spoligotyping and VNTR (35 loci) were analyzed. We excluded 4 loci (VNTRs 2163a, 3232, 3820, and 4120) and selected in top 12 loci (VNTRs 0424, 0960, 1955, 2074, 2163b, 2372, 2996, 3155, 3192, 3336, 4052, and 4156). The cluster rate of IS6110 RFLP was higher than that of 12-locus [Japan Anti-Tuberculosis Association (JATA)] VNTR. And in comparison of the discriminatory power of 12-locus JATA VNTR and that of Supply (15)-VNTR, the JATA (12)-VNTR was superior, even though less loci analyses. Therefore, this JATA (12)-VNTR could be used for TB genotyping in areas where Beijing strains are prevalent.
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).
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.
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.
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....
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
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...
Scale-invariant transition probabilities in free word association trajectories
Directory of Open Access Journals (Sweden)
Martin Elias Costa
2009-09-01
Full Text Available Free-word association has been used as a vehicle to understand the organization of human thoughts. The original studies relied mainly on qualitative assertions, yielding the widely intuitive notion that trajectories of word associations are structured, yet considerably more random than organized linguistic text. Here we set to determine a precise characterization of this space, generating a large number of word association trajectories in a web implemented game. We embedded the trajectories in the graph of word co-occurrences from a linguistic corpus. To constrain possible transport models we measured the memory loss and the cycling probability. These two measures could not be reconciled by a bounded diffusive model since the cycling probability was very high (16 % of order-2 cycles implying a majority of short-range associations whereas the memory loss was very rapid (converging to the asymptotic value in ∼ 7 steps which, in turn, forced a high fraction of long-range associations. We show that memory loss and cycling probabilities of free word association trajectories can be simultaneously accounted by a model in which transitions are determined by a scale invariant probability distribution.
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.
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.
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
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)
Detection probability of Campylobacter
Evers, E.G.; Post, J.; Putirulan, F.F.; Wal, van der F.J.
2010-01-01
A rapid presence/absence test for Campylobacter in chicken faeces is being evaluated to support the scheduling of highly contaminated broiler flocks as a measure to reduce public health risks [Nauta, M. J., & Havelaar, A. H. (2008). Risk-based standards for Campylobacter in the broiler meat
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...
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
Indian Academy of Sciences (India)
the event A) such that the frequencies v get closer "generally speaking" to p as the number of ... Before showing how this is done, we must enumerate .... sequences is obviously equal to the number of combinations of n things taken k at a time, ...
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
Quantum probability for probabilists
Meyer, Paul-André
1993-01-01
In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide anintroduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of stochastic calculus for physicists familiar with Fock space analysis.
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
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
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
Box-particle probability hypothesis density filtering
Schikora, M.; Gning, A.; Mihaylova, L.; Cremers, D.; Koch, W.
2014-01-01
This paper develops a novel approach for multitarget tracking, called box-particle probability hypothesis density filter (box-PHD filter). The approach is able to track multiple targets and estimates the unknown number of targets. Furthermore, it is capable of dealing with three sources of uncertainty: stochastic, set-theoretic, and data association uncertainty. The box-PHD filter reduces the number of particles significantly, which improves the runtime considerably. The small number of box-p...
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
Indian Academy of Sciences (India)
An axiomatic development of such a model is given below. It is also shown ... teacher needs to decide which students deserve to be promoted to the next class - it is not ... whether an unborn child would be a boy or a girl, the total number of births in a ..... that the outcome of the previous trials has no influence on the next trial.
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.
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
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.
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....
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.
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
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
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.
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.
Probability of brittle failure
Kim, A.; Bosnyak, C. P.; Chudnovsky, A.
1991-01-01
A methodology was developed for collecting statistically representative data for crack initiation and arrest from small number of test specimens. An epoxy (based on bisphenol A diglycidyl ether and polyglycol extended diglycyl ether and cured with diethylene triamine) is selected as a model material. A compact tension specimen with displacement controlled loading is used to observe multiple crack initiation and arrests. The energy release rate at crack initiation is significantly higher than that at a crack arrest, as has been observed elsewhere. The difference between these energy release rates is found to depend on specimen size (scale effect), and is quantitatively related to the fracture surface morphology. The scale effect, similar to that in statistical strength theory, is usually attributed to the statistics of defects which control the fracture process. Triangular shaped ripples (deltoids) are formed on the fracture surface during the slow subcritical crack growth, prior to the smooth mirror-like surface characteristic of fast cracks. The deltoids are complementary on the two crack faces which excludes any inelastic deformation from consideration. Presence of defects is also suggested by the observed scale effect. However, there are no defects at the deltoid apexes detectable down to the 0.1 micron level.
Probability shapes perceptual precision: A study in orientation estimation.
Jabar, Syaheed B; Anderson, Britt
2015-12-01
Probability is known to affect perceptual estimations, but an understanding of mechanisms is lacking. Moving beyond binary classification tasks, we had naive participants report the orientation of briefly viewed gratings where we systematically manipulated contingent probability. Participants rapidly developed faster and more precise estimations for high-probability tilts. The shapes of their error distributions, as indexed by a kurtosis measure, also showed a distortion from Gaussian. This kurtosis metric was robust, capturing probability effects that were graded, contextual, and varying as a function of stimulus orientation. Our data can be understood as a probability-induced reduction in the variability or "shape" of estimation errors, as would be expected if probability affects the perceptual representations. As probability manipulations are an implicit component of many endogenous cuing paradigms, changes at the perceptual level could account for changes in performance that might have traditionally been ascribed to "attention." (c) 2015 APA, all rights reserved).
Finite-size scaling of survival probability in branching processes
Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Alvaro
2014-01-01
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival probability for a given branching process ruled by a probability distribution of the number of offspring per element whose standard deviation is finite, obtaining the exact scaling function as well as the critical exponents. Our findings prove the universal behavi...
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...
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.)
Impact of controlling the sum of error probability in the sequential probability ratio test
Directory of Open Access Journals (Sweden)
Bijoy Kumarr Pradhan
2013-05-01
Full Text Available A generalized modified method is proposed to control the sum of error probabilities in sequential probability ratio test to minimize the weighted average of the two average sample numbers under a simple null hypothesis and a simple alternative hypothesis with the restriction that the sum of error probabilities is a pre-assigned constant to find the optimal sample size and finally a comparison is done with the optimal sample size found from fixed sample size procedure. The results are applied to the cases when the random variate follows a normal law as well as Bernoullian law.
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 ...
Foundations of quantization for probability distributions
Graf, Siegfried
2000-01-01
Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.
Prospect evaluation as a function of numeracy and probability denominator.
Millroth, Philip; Juslin, Peter
2015-05-01
This study examines how numeracy and probability denominator (a direct-ratio probability, a relative frequency with denominator 100, a relative frequency with denominator 10,000) affect the evaluation of prospects in an expected-value based pricing task. We expected that numeracy would affect the results due to differences in the linearity of number perception and the susceptibility to denominator neglect with different probability formats. An analysis with functional measurement verified that participants integrated value and probability into an expected value. However, a significant interaction between numeracy and probability format and subsequent analyses of the parameters of cumulative prospect theory showed that the manipulation of probability denominator changed participants' psychophysical response to probability and value. Standard methods in decision research may thus confound people's genuine risk attitude with their numerical capacities and the probability format used. Copyright © 2015 Elsevier B.V. All rights reserved.
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...
Hristova-Veleva, S. M.; Chen, H.; Gopalakrishnan, S.; Haddad, Z. S.
2017-12-01
Tropical cyclones (TCs) are the product of complex multi-scale processes and interactions. The role of the environment has long been recognized. However, recent research has shown that convective-scale processes in the hurricane core might also play a crucial role in determining TCs intensity and size. Several studies have linked Rapid Intensification to the characteristics of the convective clouds (shallow versus deep), their organization (isolated versus wide-spread) and their location with respect to dynamical controls (the vertical shear, the radius of maximum wind). Yet a third set of controls signifies the interaction between the storm-scale and large-scale processes. Our goal is to use observations and models to advance the still-lacking understanding of these processes. Recently, hurricane models have improved significantly. However, deterministic forecasts have limitations due to the uncertainty in the representation of the physical processes and initial conditions. A crucial step forward is the use of high-resolution ensembles. We adopt the following approach: i) generate a high resolution ensemble forecast using HWRF; ii) produce synthetic data (e.g. brightness temperature) from the model fields for direct comparison to satellite observations; iii) develop metrics to allow us to sub-select the realistic members of the ensemble, based on objective measures of the similarity between observed and forecasted structures; iv) for these most-realistic members, determine the skill in forecasting TCs to provide"guidance on guidance"; v) use the members with the best predictive skill to untangle the complex multi-scale interactions. We will report on the first three goals of our research, using forecasts and observations of hurricane Edouard (2014), focusing on RI. We will focus on describing the metrics for the selection of the most appropriate ensemble members, based on applying low-wave number analysis (WNA - Hristova-Veleva et al., 2016) to the observed and
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
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.
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.
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
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.
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...
STRIP: stream learning of influence probabilities
DEFF Research Database (Denmark)
Kutzkov, Konstantin
2013-01-01
cascades, and developing applications such as viral marketing. Motivated by modern microblogging platforms, such as twitter, in this paper we study the problem of learning influence probabilities in a data-stream scenario, in which the network topology is relatively stable and the challenge of a learning...... algorithm is to keep up with a continuous stream of tweets using a small amount of time and memory. Our contribution is a number of randomized approximation algorithms, categorized according to the available space (superlinear, linear, and sublinear in the number of nodes n) and according to dierent models...
Establishment probability in newly founded populations
Directory of Open Access Journals (Sweden)
Gusset Markus
2012-06-01
Full Text Available Abstract Background Establishment success in newly founded populations relies on reaching the established phase, which is defined by characteristic fluctuations of the population’s state variables. Stochastic population models can be used to quantify the establishment probability of newly founded populations; however, so far no simple but robust method for doing so existed. To determine a critical initial number of individuals that need to be released to reach the established phase, we used a novel application of the “Wissel plot”, where –ln(1 – P0(t is plotted against time t. This plot is based on the equation P0t=1–c1e–ω1t, which relates the probability of extinction by time t, P0(t, to two constants: c1 describes the probability of a newly founded population to reach the established phase, whereas ω1 describes the population’s probability of extinction per short time interval once established. Results For illustration, we applied the method to a previously developed stochastic population model of the endangered African wild dog (Lycaon pictus. A newly founded population reaches the established phase if the intercept of the (extrapolated linear parts of the “Wissel plot” with the y-axis, which is –ln(c1, is negative. For wild dogs in our model, this is the case if a critical initial number of four packs, consisting of eight individuals each, are released. Conclusions The method we present to quantify the establishment probability of newly founded populations is generic and inferences thus are transferable to other systems across the field of conservation biology. In contrast to other methods, our approach disaggregates the components of a population’s viability by distinguishing establishment from persistence.
On the shake-off probability for atomic systems
Energy Technology Data Exchange (ETDEWEB)
Santos, A.C.F., E-mail: toniufrj@gmail.com [Instituto de Física, Universidade Federal do Rio de Janeiro, P.O. Box 68528, 21941-972 Rio de Janeiro, RJ (Brazil); Almeida, D.P. [Departamento de Física, Universidade Federal de Santa Catarina, 88040-900 Florianópolis (Brazil)
2016-07-15
Highlights: • The scope is to find the relationship among SO probabilities, Z and electron density. • A scaling law is suggested, allowing us to find the SO probabilities for atoms. • SO probabilities have been scaled as a function of target Z and polarizability. - Abstract: The main scope in this work has been upon the relationship between shake-off probabilities, target atomic number and electron density. By comparing the saturation values of measured double-to-single photoionization ratios from the literature, a simple scaling law has been found, which allows us to predict the shake-off probabilities for several elements up to Z = 54 within a factor 2. The electron shake-off probabilities accompanying valence shell photoionization have been scaled as a function of the target atomic number, Z, and polarizability, α. This behavior is in qualitative agreement with the experimental results.
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 ...
Bennett, Ruth, Ed.; And Others
An introduction to the Hupa number system is provided in this workbook, one in a series of numerous materials developed to promote the use of the Hupa language. The book is written in English with Hupa terms used only for the names of numbers. The opening pages present the numbers from 1-10, giving the numeral, the Hupa word, the English word, and…
Indian Academy of Sciences (India)
Admin
Triangular number, figurate num- ber, rangoli, Brahmagupta–Pell equation, Jacobi triple product identity. Figure 1. The first four triangular numbers. Left: Anuradha S Garge completed her PhD from. Pune University in 2008 under the supervision of Prof. S A Katre. Her research interests include K-theory and number theory.
Directory of Open Access Journals (Sweden)
Schwarzweller Christoph
2015-02-01
Full Text Available In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.
Counting problems for number rings
Brakenhoff, Johannes Franciscus
2009-01-01
In this thesis we look at three counting problems connected to orders in number fields. First we study the probability that for a random polynomial f in Z[X] the ring Z[X]/f is the maximal order in Q[X]/f. Connected to this is the probability that a random polynomial has a squarefree
Mendonça, J. Ricardo G.
2012-01-01
We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.
International Nuclear Information System (INIS)
Coveyou, R.R.
1974-01-01
The subject of random number generation is currently controversial. Differing opinions on this subject seem to stem from implicit or explicit differences in philosophy; in particular, from differing ideas concerning the role of probability in the real world of physical processes, electronic computers, and Monte Carlo calculations. An attempt is made here to reconcile these views. The role of stochastic ideas in mathematical models is discussed. In illustration of these ideas, a mathematical model of the use of random number generators in Monte Carlo calculations is constructed. This model is used to set up criteria for the comparison and evaluation of random number generators. (U.S.)
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.
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)
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.
Characterizing the Frequency and Elevation of Rapid Drainage Events in West Greenland
Cooley, S.; Christoffersen, P.
2016-12-01
Rapid drainage of supraglacial lakes on the Greenland Ice Sheet is critical for the establishment of surface-to-bed hydrologic connections and the subsequent transfer of water from surface to bed. Yet, estimates of the number and spatial distribution of rapidly draining lakes vary widely due to limitations in the temporal frequency of image collection and obscureness by cloud. So far, no study has assessed the impact of these observation biases. In this study, we examine the frequency and elevation of rapidly draining lakes in central West Greenland, from 68°N to 72.6°N, and we make a robust statistical analysis to estimate more accurately the likelihood of lakes draining rapidly. Using MODIS imagery and a fully automated lake detection method, we map more than 500 supraglacial lakes per year over a 63000 km2 study area from 2000-2015. Through testing four different definitions of rapidly draining lakes from previously published studies, we find that the number of rapidly draining lakes varies from 3% to 38%. Logistic regression between rapid drainage events and image sampling frequency demonstrates that the number of rapid drainage events is strongly dependent on cloud-free observation percentage. We then develop three new drainage criteria and apply an observation bias correction that suggests a true rapid drainage probability between 36% and 45%, considerably higher than previous studies without bias assessment have reported. We find rapid-draining lakes are on average larger and disappear earlier than slow-draining lakes, and we also observe no elevation differences for the lakes detected as rapidly draining. We conclude a) that methodological problems in rapid drainage research caused by observation bias and varying detection methods have obscured large-scale rapid drainage characteristics and b) that the lack of evidence for an elevation limit on rapid drainage suggests surface-to-bed hydrologic connections may continue to propagate inland as climate warms.
Petersen, T Kyle
2015-01-01
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...
Probability Distribution for Flowing Interval Spacing
International Nuclear Information System (INIS)
S. Kuzio
2004-01-01
Fracture spacing is a key hydrologic parameter in analyses of matrix diffusion. Although the individual fractures that transmit flow in the saturated zone (SZ) cannot be identified directly, it is possible to determine the fractured zones that transmit flow from flow meter survey observations. The fractured zones that transmit flow as identified through borehole flow meter surveys have been defined in this report as flowing intervals. The flowing interval spacing is measured between the midpoints of each flowing interval. The determination of flowing interval spacing is important because the flowing interval spacing parameter is a key hydrologic parameter in SZ transport modeling, which impacts the extent of matrix diffusion in the SZ volcanic matrix. The output of this report is input to the ''Saturated Zone Flow and Transport Model Abstraction'' (BSC 2004 [DIRS 170042]). Specifically, the analysis of data and development of a data distribution reported herein is used to develop the uncertainty distribution for the flowing interval spacing parameter for the SZ transport abstraction model. Figure 1-1 shows the relationship of this report to other model reports that also pertain to flow and transport in the SZ. Figure 1-1 also shows the flow of key information among the SZ reports. It should be noted that Figure 1-1 does not contain a complete representation of the data and parameter inputs and outputs of all SZ reports, nor does it show inputs external to this suite of SZ reports. Use of the developed flowing interval spacing probability distribution is subject to the limitations of the assumptions discussed in Sections 5 and 6 of this analysis report. The number of fractures in a flowing interval is not known. Therefore, the flowing intervals are assumed to be composed of one flowing zone in the transport simulations. This analysis may overestimate the flowing interval spacing because the number of fractures that contribute to a flowing interval cannot be
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
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
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...
Optimal design of unit hydrographs using probability distribution and ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
optimization formulation is solved using binary-coded genetic algorithms. The number of variables to ... Unit hydrograph; rainfall-runoff; hydrology; genetic algorithms; optimization; probability ..... Application of the model. Data derived from the ...
Multiple model cardinalized probability hypothesis density filter
Georgescu, Ramona; Willett, Peter
2011-09-01
The Probability Hypothesis Density (PHD) filter propagates the first-moment approximation to the multi-target Bayesian posterior distribution while the Cardinalized PHD (CPHD) filter propagates both the posterior likelihood of (an unlabeled) target state and the posterior probability mass function of the number of targets. Extensions of the PHD filter to the multiple model (MM) framework have been published and were implemented either with a Sequential Monte Carlo or a Gaussian Mixture approach. In this work, we introduce the multiple model version of the more elaborate CPHD filter. We present the derivation of the prediction and update steps of the MMCPHD particularized for the case of two target motion models and proceed to show that in the case of a single model, the new MMCPHD equations reduce to the original CPHD equations.
Tumor control probability after a radiation of animal tumors
International Nuclear Information System (INIS)
Urano, Muneyasu; Ando, Koichi; Koike, Sachiko; Nesumi, Naofumi
1975-01-01
Tumor control and regrowth probability of animal tumors irradiated with a single x-ray dose were determined, using a spontaneous C3H mouse mammary carcinoma. Cellular radiation sensitivity of tumor cells and tumor control probability of the tumor were examined by the TD 50 and TCD 50 assays respectively. Tumor growth kinetics were measured by counting the percentage of labelled mitosis and by measuring the growth curve. A mathematical analysis of tumor control probability was made from these results. A formula proposed, accounted for cell population kinetics or division probability model, cell sensitivity to radiation and number of tumor cells. (auth.)
On the universality of knot probability ratios
Energy Technology Data Exchange (ETDEWEB)
Janse van Rensburg, E J [Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3 (Canada); Rechnitzer, A, E-mail: rensburg@yorku.ca, E-mail: andrewr@math.ubc.ca [Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2 (Canada)
2011-04-22
Let p{sub n} denote the number of self-avoiding polygons of length n on a regular three-dimensional lattice, and let p{sub n}(K) be the number which have knot type K. The probability that a random polygon of length n has knot type K is p{sub n}(K)/p{sub n} and is known to decay exponentially with length (Sumners and Whittington 1988 J. Phys. A: Math. Gen. 21 1689-94, Pippenger 1989 Discrete Appl. Math. 25 273-8). Little is known rigorously about the asymptotics of p{sub n}(K), but there is substantial numerical evidence. It is believed that the entropic exponent, {alpha}, is universal, while the exponential growth rate is independent of the knot type but varies with the lattice. The amplitude, C{sub K}, depends on both the lattice and the knot type. The above asymptotic form implies that the relative probability of a random polygon of length n having prime knot type K over prime knot type L. In the thermodynamic limit this probability ratio becomes an amplitude ratio; it should be universal and depend only on the knot types K and L. In this communication we examine the universality of these probability ratios for polygons in the simple cubic, face-centred cubic and body-centred cubic lattices. Our results support the hypothesis that these are universal quantities. For example, we estimate that a long random polygon is approximately 28 times more likely to be a trefoil than be a figure-eight, independent of the underlying lattice, giving an estimate of the intrinsic entropy associated with knot types in closed curves. (fast track communication)
Indian Academy of Sciences (India)
Transfinite Numbers. What is Infinity? S M Srivastava. In a series of revolutionary articles written during the last quarter of the nineteenth century, the great Ger- man mathematician Georg Cantor removed the age-old mistrust of infinity and created an exceptionally beau- tiful and useful theory of transfinite numbers. This is.
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…
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…
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)
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.
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
Ji, Caleb; Khovanova, Tanya; Park, Robin; Song, Angela
2015-01-01
In this paper, we consider a game played on a rectangular $m \\times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain. This paper enumerates the number of ways to break an $m \\times n$ bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we p...
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Exploring non-signalling polytopes with negative probability
International Nuclear Information System (INIS)
Oas, G; Barros, J Acacio de; Carvalhaes, C
2014-01-01
Bipartite and tripartite EPR–Bell type systems are examined via joint quasi-probability distributions where probabilities are permitted to be negative. It is shown that such distributions exist only when the no-signalling condition is satisfied. A characteristic measure, the probability mass, is introduced and, via its minimization, limits the number of quasi-distributions describing a given marginal probability distribution. The minimized probability mass is shown to be an alternative way to characterize non-local systems. Non-signalling polytopes for two to eight settings in the bipartite scenario are examined and compared to prior work. Examining perfect cloning of non-local systems within the tripartite scenario suggests defining two categories of signalling. It is seen that many properties of non-local systems can be efficiently described by quasi-probability theory. (paper)
Energy Technology Data Exchange (ETDEWEB)
Netter, F; Faraggi, H; Garin-Bonnet, A; Julien, J; Corge, C [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires; Turkiewicz, J [Institut de Recherches Nucleaire de Varsovie (Poland)
1958-07-01
The authors describe relative cross-section measurements of fission of the isotopes of uranium and plutonium (more particularly {sup 235}U, {sup 238}U, {sup 239}Pu), with emission of long range particles, under the action of neutrons of various energies: thermal neutrons, pile neutrons, neutrons produced with the Van de Graaff accelerator by reaction of protons on tritium. The measurements are carried out: 1) with the aid of photographic plates, by submitting to the action of the neutrons a layer of fissile material coupled with an Ilford nuclear emulsion of 200 microns; a tin sheet laying between the plate and the layer stops the {alpha} particles and the fission fragments. By an appropriate development the tracks of the long range particles can be distinguished in the emulsion, from the tracks of the recoil protons resulting of fission neutrons, or of the last primary neutrons. For neutrons of energy under 1 MeV, the compared frequency of the tracks of long range particles and of the recoils caused by the fission neutrons gives a measurement of the fission cross-section with emission of long range particles relative to the product of the fission cross-section by the mean number of neutrons emitted by fission. For neutrons of higher energy, one measures only the frequency of the tracks of long range particles, comparatively with the flux of primary neutrons. Some precautions are taken to eliminate the action of thermal neutrons in the measurements with fast neutrons. 2) with the aid of a system of ionization chamber and proportional counter, the rate of coincidence between the impulsions caused by the long range particles and the impulsions provided by one of the fission fragments is measured comparatively with the counting rate of fission fragme (author) [French] Les auteurs decrivent des mesures relatives a la section efficace de fission des isotopes de l'uranium et du plutonium (notamment {sup 235}U, {sup 238}U, {sup 239}Pu) avec emission de particules de long
Barnes, John
2016-01-01
In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...
An introduction to probability and statistical inference
Roussas, George G
2003-01-01
"The text is wonderfully written and has the mostcomprehensive range of exercise problems that I have ever seen." - Tapas K. Das, University of South Florida"The exposition is great; a mixture between conversational tones and formal mathematics; the appropriate combination for a math text at [this] level. In my examination I could find no instance where I could improve the book." - H. Pat Goeters, Auburn, University, Alabama* Contains more than 200 illustrative examples discussed in detail, plus scores of numerical examples and applications* Chapters 1-8 can be used independently for an introductory course in probability* Provides a substantial number of proofs
Stochastics introduction to probability and statistics
Georgii, Hans-Otto
2012-01-01
This second revised and extended edition presents the fundamental ideas and results of both, probability theory and statistics, and comprises the material of a one-year course. It is addressed to students with an interest in the mathematical side of stochastics. Stochastic concepts, models and methods are motivated by examples and developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems offer applications and supplements to the text.
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.
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 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...
School and conference on probability theory
International Nuclear Information System (INIS)
Lawler, G.F.
2004-01-01
This volume includes expanded lecture notes from the School and Conference in Probability Theory held at ICTP in May, 2001. Probability theory is a very large area, too large for a single school and conference. The organizers, G. Lawler, C. Newman, and S. Varadhan chose to focus on a number of active research areas that have their roots in statistical physics. The pervasive theme in these lectures is trying to find the large time or large space behaviour of models defined on discrete lattices. Usually the definition of the model is relatively simple: either assigning a particular weight to each possible configuration (equilibrium statistical mechanics) or specifying the rules under which the system evolves (nonequilibrium statistical mechanics). Interacting particle systems is the area of probability that studies the evolution of particles (either finite or infinite in number) under random motions. The evolution of particles depends on the positions of the other particles; often one assumes that it depends only on the particles that are close to the particular particle. Thomas Liggett's lectures give an introduction to this very large area. Claudio Landim's follows up by discussing hydrodynamic limits of particle systems. The goal of this area is to describe the long time, large system size dynamics in terms of partial differential equations. The area of random media is concerned with the properties of materials or environments that are not homogeneous. Percolation theory studies one of the simplest stated models for impurities - taking a lattice and removing some of the vertices or bonds. Luiz Renato G. Fontes and Vladas Sidoravicius give a detailed introduction to this area. Random walk in random environment combines two sources of randomness - a particle performing stochastic motion in which the transition probabilities depend on position and have been chosen from some probability distribution. Alain-Sol Sznitman gives a survey of recent developments in this
Number names and number understanding
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
2014-01-01
This paper concerns the results from the first year of a three-year research project involving the relationship between Danish number names and their corresponding digits in the canonical base 10 system. The project aims to develop a system to help the students’ understanding of the base 10 syste...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....
Neutron transport by collision probability method in complicated geometries
International Nuclear Information System (INIS)
Constantin, Marin
2000-01-01
For the first flight collision probability (FFCP) method a rapidly increasing of the memory requirements and execution time with the number of discrete regions occurs. Generally, the use of the method is restricted at cell/supercell level. However, the amazing developments both in computer hardware and computer architecture allow a real extending of the problems' domain and a more detailed treatment of the geometry. Two ways are discussed into the paper: the direct design of new codes and the improving of the mainframe old versions. The author's experience is focused on the performances' improving of the 3D integral transport code PIJXYZ (from an old version to a modern one) and on the design and developing of the 2D transport code CP 2 D in the last years. In the first case an optimization process have been performed before the parallelization. In the second a modular design and the newest techniques (factorization of the geometry, the macrobands method, the mobile set of chords, the automatic calculation of the integration error, optimal algorithms for the innermost programming level, the mixed method for tracking process and CPs calculation, etc.) were adopted. In both cases the parallelization uses a PCs network system. Some short examples for CP 2 D and PIJXYZ calculation are presented: reactivity void effect in typical CANDU cells using a multistratified coolant model, a problem of some adjacent fuel assemblies, CANDU reactivity devices 3D simulation. (author)
Directory of Open Access Journals (Sweden)
Theodore M. Porter
2012-12-01
Full Text Available The struggle over cure rate measures in nineteenth-century asylums provides an exemplary instance of how, when used for official assessments of institutions, these numbers become sites of contestation. The evasion of goals and corruption of measures tends to make these numbers “funny” in the sense of becoming dis-honest, while the mismatch between boring, technical appearances and cunning backstage manipulations supplies dark humor. The dangers are evident in recent efforts to decentralize the functions of governments and corporations using incen-tives based on quantified targets.
Murty, M Ram
2014-01-01
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Normal tissue complication probability for salivary glands
International Nuclear Information System (INIS)
Rana, B.S.
2008-01-01
The purpose of radiotherapy is to make a profitable balance between the morbidity (due to side effects of radiation) and cure of malignancy. To achieve this, one needs to know the relation between NTCP (normal tissue complication probability) and various treatment variables of a schedule viz. daily dose, duration of treatment, total dose and fractionation along with tissue conditions. Prospective studies require that a large number of patients be treated with varied schedule parameters and a statistically acceptable number of patients develop complications so that a true relation between NTCP and a particular variable is established. In this study Salivary Glands Complications have been considered. The cases treated in 60 Co teletherapy machine during the period 1994 to 2002 were analyzed and the clinicians judgement in ascertaining the end points was the only means of observations. The only end points were early and late xerestomia which were considered for NTCP evaluations for a period of 5 years
Indian Academy of Sciences (India)
this is a characteristic difference between finite and infinite sets and created an immensely useful branch of mathematics based on this idea which had a great impact on the whole of mathe- matics. For example, the question of what is a number (finite or infinite) is almost a philosophical one. However Cantor's work turned it ...
Electrofishing capture probability of smallmouth bass in streams
Dauwalter, D.C.; Fisher, W.L.
2007-01-01
Abundance estimation is an integral part of understanding the ecology and advancing the management of fish populations and communities. Mark-recapture and removal methods are commonly used to estimate the abundance of stream fishes. Alternatively, abundance can be estimated by dividing the number of individuals sampled by the probability of capture. We conducted a mark-recapture study and used multiple repeated-measures logistic regression to determine the influence of fish size, sampling procedures, and stream habitat variables on the cumulative capture probability for smallmouth bass Micropterus dolomieu in two eastern Oklahoma streams. The predicted capture probability was used to adjust the number of individuals sampled to obtain abundance estimates. The observed capture probabilities were higher for larger fish and decreased with successive electrofishing passes for larger fish only. Model selection suggested that the number of electrofishing passes, fish length, and mean thalweg depth affected capture probabilities the most; there was little evidence for any effect of electrofishing power density and woody debris density on capture probability. Leave-one-out cross validation showed that the cumulative capture probability model predicts smallmouth abundance accurately. ?? Copyright by the American Fisheries Society 2007.
[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.
Traffic simulation based ship collision probability modeling
Energy Technology Data Exchange (ETDEWEB)
Goerlandt, Floris, E-mail: floris.goerlandt@tkk.f [Aalto University, School of Science and Technology, Department of Applied Mechanics, Marine Technology, P.O. Box 15300, FI-00076 AALTO, Espoo (Finland); Kujala, Pentti [Aalto University, School of Science and Technology, Department of Applied Mechanics, Marine Technology, P.O. Box 15300, FI-00076 AALTO, Espoo (Finland)
2011-01-15
Maritime traffic poses various risks in terms of human, environmental and economic loss. In a risk analysis of ship collisions, it is important to get a reasonable estimate for the probability of such accidents and the consequences they lead to. In this paper, a method is proposed to assess the probability of vessels colliding with each other. The method is capable of determining the expected number of accidents, the locations where and the time when they are most likely to occur, while providing input for models concerned with the expected consequences. At the basis of the collision detection algorithm lays an extensive time domain micro-simulation of vessel traffic in the given area. The Monte Carlo simulation technique is applied to obtain a meaningful prediction of the relevant factors of the collision events. Data obtained through the Automatic Identification System is analyzed in detail to obtain realistic input data for the traffic simulation: traffic routes, the number of vessels on each route, the ship departure times, main dimensions and sailing speed. The results obtained by the proposed method for the studied case of the Gulf of Finland are presented, showing reasonable agreement with registered accident and near-miss data.
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.
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
Detection probabilities for time-domain velocity estimation
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt
1991-01-01
programs, it is demonstrated that the probability of correct estimation depends on the signal-to-noise ratio, transducer bandwidth, number of A-lines and number of samples used in the correlation estimate. The influence of applying a stationary echo-canceler is explained. The echo canceling can be modeled...
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.
International Nuclear Information System (INIS)
Ismail, M.; Adel, A.
2013-01-01
A realistic density-dependent nucleon–nucleon (NN) interaction with finite-range exchange part which produces the nuclear matter saturation curve and the energy dependence of the nucleon–nucleus optical model potential is used to calculate the preformation probability, S α , of α-decay from different isotones with neutron numbers N=124,126,128,130 and 132. We studied the variation of S α with the proton number, Z, for each isotone and found the effect of neutron and proton energy levels of parent nuclei on the behavior of the α-particle preformation probability. We found that S α increases regularly with the proton number when the proton pair in α-particle is emitted from the same level and the neutron level sequence is not changed during the Z-variation. In this case the neutron–proton (n–p) interaction of the two levels, contributing to emission process, is too small. On the contrary, if the proton or neutron level sequence is changed during the emission process, S α behaves irregularly, the irregular behavior increases if both proton and neutron levels are changed. This behavior is accompanied by change or rapid increase in the strength of n–p interaction
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...
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
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.
Directory of Open Access Journals (Sweden)
Maria Magdalena Ferreira Ribas
2009-12-01
ênico foi encontrado 103 microrganismos/mL no MC e 1015 microrganismos/mL no MM e uma contagem máxima de 1010 em MC. No efluente do reator metanogênico, foi encontrado 109 em MM microrganismos/mL e 1010 em MC. Para o MD, os valores foram intermediários para MC e MM em todas as amostras. Para testar a técnica de avaliação da atividade microbiana, uma dose única de choque de 750 mg/L de cianeto (CN- foi adicionada ao afluente do reator acidogênico. Depois de 48 horas, foi detectada redução na produção de gás e queda equivalente (104 no número de todos os grupos de microrganismos pela entrada do cianeto. A alimentação do reator foi retornada à concentração inicial de água residuária de processamento de mandioca e, depois de quinze dias o reator voltou a apresentar estabilidade. Em decorrência, observou-se aumento de todos os grupos de microrganismos. Portanto, as contagens microbianas obtidas foram condizentes com as condições de funcionamento dos reatores anaeróbios no período avaliado, validando a metodologia proposta.AbstractAbstractAnaerobic microbiology evaluation is an expensive and very difficult method. Simple techniques are available for the assessment of microorganism in several uses, such as medical, food, environment and anaerobic systems for wastewater treatment. A methodology was developed to assess the activity of microorganisms groups in anaerobic digestion with possible application to specific substrata. The technique applies oxygen-free gases in serum bottles closed with a rubber cover and an aluminum seal with the addition of a reducing indicator, nutrient complements and reducing agents after sterilization. The metabolism of the microorganisms was observed in these closed serum bottles after an incubation period of fourteen days, and regarding turbidness variation, pH variation measured by Arrhenius’s indicator and gas captured in Duran tubes. The Most Probable Number (MPN technique was used for microorganism counting in
Biagini, Francesca
2016-01-01
This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics.
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
Atomic Transition Probabilities Scandium through Manganese
International Nuclear Information System (INIS)
Martin, G.A.; Fuhr, J.R.; Wiese, W.L.
1988-01-01
Atomic transition probabilities for about 8,800 spectral lines of five iron-group elements, Sc(Z = 21) to Mn(Z = 25), are critically compiled, based on all available literature sources. The data are presented in separate tables for each element and stage of ionization and are further subdivided into allowed (i.e., electric dipole-E1) and forbidden (magnetic dipole-M1, electric quadrupole-E2, and magnetic quadrupole-M2) transitions. Within each data table the spectral lines are grouped into multiplets, which are in turn arranged according to parent configurations, transition arrays, and ascending quantum numbers. For each line the transition probability for spontaneous emission and the line strength are given, along with the spectroscopic designation, the wavelength, the statistical weights, and the energy levels of the upper and lower states. For allowed lines the absorption oscillator strength is listed, while for forbidden transitions the type of transition is identified (M1, E2, etc.). In addition, the estimated accuracy and the source are indicated. In short introductions, which precede the tables for each ion, the main justifications for the choice of the adopted data and for the accuracy rating are discussed. A general introduction contains a discussion of our method of evaluation and the principal criteria for our judgements
Applied probability and stochastic processes. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Feldman, Richard M. [Texas A and M Univ., College Station, TX (United States). Industrial and Systems Engineering Dept.; Valdez-Flores, Ciriaco [Sielken and Associates Consulting, Inc., Bryan, TX (United States)
2010-07-01
This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications of the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queuing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues. Included in the second edition are appendices at the end of several chapters giving suggestions for the use of Excel in solving the problems of the chapter. Also new in this edition are an introductory chapter on statistics and a chapter on Poisson processes that includes some techniques used in risk assessment. The old chapter on queues has been expanded and broken into two new chapters: one for simple queuing processes and one for queuing networks. Support is provided through the web site http://apsp.tamu.edu where students will have the answers to odd numbered problems and instructors will have access to full solutions and Excel files for homework. (orig.)
Collection of offshore human error probability data
International Nuclear Information System (INIS)
Basra, Gurpreet; Kirwan, Barry
1998-01-01
Accidents such as Piper Alpha have increased concern about the effects of human errors in complex systems. Such accidents can in theory be predicted and prevented by risk assessment, and in particular human reliability assessment (HRA), but HRA ideally requires qualitative and quantitative human error data. A research initiative at the University of Birmingham led to the development of CORE-DATA, a Computerised Human Error Data Base. This system currently contains a reasonably large number of human error data points, collected from a variety of mainly nuclear-power related sources. This article outlines a recent offshore data collection study, concerned with collecting lifeboat evacuation data. Data collection methods are outlined and a selection of human error probabilities generated as a result of the study are provided. These data give insights into the type of errors and human failure rates that could be utilised to support offshore risk analyses
Audio feature extraction using probability distribution function
Suhaib, A.; Wan, Khairunizam; Aziz, Azri A.; Hazry, D.; Razlan, Zuradzman M.; Shahriman A., B.
2015-05-01
Voice recognition has been one of the popular applications in robotic field. It is also known to be recently used for biometric and multimedia information retrieval system. This technology is attained from successive research on audio feature extraction analysis. Probability Distribution Function (PDF) is a statistical method which is usually used as one of the processes in complex feature extraction methods such as GMM and PCA. In this paper, a new method for audio feature extraction is proposed which is by using only PDF as a feature extraction method itself for speech analysis purpose. Certain pre-processing techniques are performed in prior to the proposed feature extraction method. Subsequently, the PDF result values for each frame of sampled voice signals obtained from certain numbers of individuals are plotted. From the experimental results obtained, it can be seen visually from the plotted data that each individuals' voice has comparable PDF values and shapes.
Some applications of the fractional Poisson probability distribution
International Nuclear Information System (INIS)
Laskin, Nick
2009-01-01
Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind. The appearance of fractional Bell polynomials is natural if one evaluates the diagonal matrix element of the evolution operator in the basis of newly introduced quantum coherent states. Fractional Stirling numbers of the second kind have been introduced and applied to evaluate the skewness and kurtosis of the fractional Poisson probability distribution function. A representation of the Bernoulli numbers in terms of fractional Stirling numbers of the second kind has been found. In the limit case when the fractional Poisson probability distribution becomes the Poisson probability distribution, all of the above listed developments and implementations turn into the well-known results of the quantum optics and the theory of combinatorial numbers.
Probability Distribution for Flowing Interval Spacing
International Nuclear Information System (INIS)
Kuzio, S.
2001-01-01
The purpose of this analysis is to develop a probability distribution for flowing interval spacing. A flowing interval is defined as a fractured zone that transmits flow in the Saturated Zone (SZ), as identified through borehole flow meter surveys (Figure 1). This analysis uses the term ''flowing interval spacing'' as opposed to fractured spacing, which is typically used in the literature. The term fracture spacing was not used in this analysis because the data used identify a zone (or a flowing interval) that contains fluid-conducting fractures but does not distinguish how many or which fractures comprise the flowing interval. The flowing interval spacing is measured between the midpoints of each flowing interval. Fracture spacing within the SZ is defined as the spacing between fractures, with no regard to which fractures are carrying flow. The Development Plan associated with this analysis is entitled, ''Probability Distribution for Flowing Interval Spacing'', (CRWMS M and O 2000a). The parameter from this analysis may be used in the TSPA SR/LA Saturated Zone Flow and Transport Work Direction and Planning Documents: (1) ''Abstraction of Matrix Diffusion for SZ Flow and Transport Analyses'' (CRWMS M and O 1999a) and (2) ''Incorporation of Heterogeneity in SZ Flow and Transport Analyses'', (CRWMS M and O 1999b). A limitation of this analysis is that the probability distribution of flowing interval spacing may underestimate the effect of incorporating matrix diffusion processes in the SZ transport model because of the possible overestimation of the flowing interval spacing. Larger flowing interval spacing results in a decrease in the matrix diffusion processes. This analysis may overestimate the flowing interval spacing because the number of fractures that contribute to a flowing interval cannot be determined from the data. Because each flowing interval probably has more than one fracture contributing to a flowing interval, the true flowing interval spacing could be
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.
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.
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.
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.
Finding upper bounds for software failure probabilities - experiments and results
International Nuclear Information System (INIS)
Kristiansen, Monica; Winther, Rune
2005-09-01
This report looks into some aspects of using Bayesian hypothesis testing to find upper bounds for software failure probabilities. In the first part, the report evaluates the Bayesian hypothesis testing approach for finding upper bounds for failure probabilities of single software components. The report shows how different choices of prior probability distributions for a software component's failure probability influence the number of tests required to obtain adequate confidence in a software component. In the evaluation, both the effect of the shape of the prior distribution as well as one's prior confidence in the software component were investigated. In addition, different choices of prior probability distributions are discussed based on their relevance in a software context. In the second part, ideas on how the Bayesian hypothesis testing approach can be extended to assess systems consisting of multiple software components are given. One of the main challenges when assessing systems consisting of multiple software components is to include dependency aspects in the software reliability models. However, different types of failure dependencies between software components must be modelled differently. Identifying different types of failure dependencies are therefore an important condition for choosing a prior probability distribution, which correctly reflects one's prior belief in the probability for software components failing dependently. In this report, software components include both general in-house software components, as well as pre-developed software components (e.g. COTS, SOUP, etc). (Author)
International Nuclear Information System (INIS)
1996-01-01
The present collection of rapid communications from JINR, Dubna, contains five separate reports on analytic QCD running coupling with finite IR behaviour and universal α bar s (0) value, quark condensate in the interacting pion- nucleon medium at finite temperature and baryon number density, γ-π 0 discrimination with a shower maximum detector using neural networks for the solenoidal tracker at RHIC, off-specular neutron reflection from magnetic media with nondiagonal reflectivity matrices and molecular cytogenetics of radiation-induced gene mutations in Drosophila melanogaster. 21 fig., 1 tab
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.
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.)
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.
Franceschetti, Donald R; Gire, Elizabeth
2013-06-01
Quantum probability theory offers a viable alternative to classical probability, although there are some ambiguities inherent in transferring the quantum formalism to a less determined realm. A number of physicists are now looking at the applicability of quantum ideas to the assessment of physics learning, an area particularly suited to quantum probability ideas.
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.
Measures, Probability and Holography in Cosmology
Phillips, Daniel
comment on the general implications of this view, and specifically question the application of classical probability theory to cosmology in cases where key questions are known to have no quantum answer. We argue that the ideas developed here may offer a way out of the notorious measure problems of eternal inflation. The fourth project looks at finite universes as alternatives to multiverse theories of cosmology. We compare two holographic arguments that impose especially strong bounds on the amount of inflation. One comes from the de Sitter Equilibrium cosmology and the other from the work of Banks and Fischler. We find that simple versions of these two approaches yield the same bound on the number of e-foldings. A careful examination reveals that while these pictures are similar in spirit, they are not necessarily identical prescriptions. We apply the two pictures to specific cosmologies which expose potentially important differences and which also demonstrate ways these seemingly simple proposals can be tricky to implement in practice.
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.
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
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
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.
Efficient Simulation of the Outage Probability of Multihop Systems
Ben Issaid, Chaouki; Alouini, Mohamed-Slim; Tempone, Raul
2017-01-01
In this paper, we present an efficient importance sampling estimator for the evaluation of the outage probability of multihop systems with amplify-and-forward channel state-information-assisted. The proposed estimator is endowed with the bounded relative error property. Simulation results show a significant reduction in terms of number of simulation runs compared to naive Monte Carlo.
A comparison of probability of ruin and expected discounted utility ...
African Journals Online (AJOL)
Individuals in defined-contribution retirement funds currently have a number of options as to how to finance their post-retirement spending. The paper considers the ranking of selected annuitisation strategies by the probability of ruin and by expected discounted utility under different scenarios. 'Ruin' is defined as occurring ...
Introduction to the Interface of Probability and Algorithms
Aldous, David; Steele, J. Michael
1993-01-01
Probability and algorithms enjoy an almost boisterous interaction that has led to an active, extensive literature that touches fields as diverse as number theory and the design of computer hardware. This article offers a gentle introduction to the simplest, most basic ideas that underlie this development.
Efficient Simulation of the Outage Probability of Multihop Systems
Ben Issaid, Chaouki
2017-10-23
In this paper, we present an efficient importance sampling estimator for the evaluation of the outage probability of multihop systems with amplify-and-forward channel state-information-assisted. The proposed estimator is endowed with the bounded relative error property. Simulation results show a significant reduction in terms of number of simulation runs compared to naive Monte Carlo.
A Short History of Probability Theory and Its Applications
Debnath, Lokenath; Basu, Kanadpriya
2015-01-01
This paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013…
Statistical complexity without explicit reference to underlying probabilities
Pennini, F.; Plastino, A.
2018-06-01
We show that extremely simple systems of a not too large number of particles can be simultaneously thermally stable and complex. To such an end, we extend the statistical complexity's notion to simple configurations of non-interacting particles, without appeal to probabilities, and discuss configurational properties.
Probable essential thrombocythemia in a dog
Energy Technology Data Exchange (ETDEWEB)
Hopper, P.E.; Mandell, C.P.; Turrel, J.M.; Jain, N.C.; Tablin, F.; Zinkl, J.G.
1989-04-01
Essential thrombocythemia (ET), in an 11-year-old dog was characterized by persistently high platelet counts range, 4.19 X 10(6)/microliters to 4.95 X 10(6)/microliters, abnormal platelet morphology, marked megakaryocytic hyperplasia in the bone marrow, absence of circulating megakaryoblasts, and history of splenomegaly and gastrointestinal bleeding. Increased numbers of megakaryocytes and megakaryoblasts (15% to 20%) in the bone marrow were confirmed by a positive acetylcholinesterase reaction. Another significant finding was the presence of a basophilia in blood (4,836/microliters) and bone marrow. The marked persistent thrombocytosis, absence of reactive (secondary) thrombocytosis, abnormal platelet morphology, and quantitative and qualitative changes in the megakaryocytic series in the bone marrow suggested the presence of a myeloproliferative disease. Cytochemical and ultrastructural findings aided in the diagnosis of ET. The dog was treated with radiophosphorus. The results was a rapid decline in the numbers of megakaryoblasts and megakaryocytes in the bone marrow and platelets and basophils in the peripheral blood. The dog died unexpectedly of acute necrotizing pancreatitis and diabetes mellitus before a complete remission was achieved.
Tachypnea; Breathing - rapid and shallow; Fast shallow breathing; Respiratory rate - rapid and shallow ... Shallow, rapid breathing has many possible medical causes, including: Asthma Blood clot in an artery in the ...
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
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.
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
XI Symposium on Probability and Stochastic Processes
Pardo, Juan; Rivero, Víctor; Bravo, Gerónimo
2015-01-01
This volume features lecture notes and a collection of contributed articles from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes. The book starts with notes from the mini-course given by Louigi Addario-Berry with an accessible description of some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. It includes a number of exercises and a section on unanswered questions. Further contributions provide the reader with a broad perspective on the state-of-the art of active areas of research. Contributions by: Louigi Addario-Berry Octavio Arizmendi Fabrice Baudoin Jochen Blath Loïc Chaumont J. Armando Domínguez-Molina Bjarki Eldon Shui Feng Tulio Gaxiola Adrián González Casanova Evgueni Gordienko Daniel...
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.
Digital dice computational solutions to practical probability problems
Nahin, Paul J
2013-01-01
Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the
Lower Confidence Bounds for the Probabilities of Correct Selection
Directory of Open Access Journals (Sweden)
Radhey S. Singh
2011-01-01
Full Text Available We extend the results of Gupta and Liang (1998, derived for location parameters, to obtain lower confidence bounds for the probability of correctly selecting the t best populations (PCSt simultaneously for all t=1,…,k−1 for the general scale parameter models, where k is the number of populations involved in the selection problem. The application of the results to the exponential and normal probability models is discussed. The implementation of the simultaneous lower confidence bounds for PCSt is illustrated through real-life datasets.
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
On the probability of occurrence of rogue waves
Directory of Open Access Journals (Sweden)
E. M. Bitner-Gregersen
2012-03-01
Full Text Available A number of extreme and rogue wave studies have been conducted theoretically, numerically, experimentally and based on field data in the last years, which have significantly advanced our knowledge of ocean waves. So far, however, consensus on the probability of occurrence of rogue waves has not been achieved. The present investigation is addressing this topic from the perspective of design needs. Probability of occurrence of extreme and rogue wave crests in deep water is here discussed based on higher order time simulations, experiments and hindcast data. Focus is given to occurrence of rogue waves in high sea states.
A probability model for the failure of pressure containing parts
International Nuclear Information System (INIS)
Thomas, H.M.
1978-01-01
The model provides a method of estimating the order of magnitude of the leakage failure probability of pressure containing parts. It is a fatigue based model which makes use of the statistics available for both specimens and vessels. Some novel concepts are introduced but essentially the model simply quantifies the obvious i.e. that failure probability increases with increases in stress levels, number of cycles, volume of material and volume of weld metal. A further model based on fracture mechanics estimates the catastrophic fraction of leakage failures. (author)
Allelic drop-out probabilities estimated by logistic regression
DEFF Research Database (Denmark)
Tvedebrink, Torben; Eriksen, Poul Svante; Asplund, Maria
2012-01-01
We discuss the model for estimating drop-out probabilities presented by Tvedebrink et al. [7] and the concerns, that have been raised. The criticism of the model has demonstrated that the model is not perfect. However, the model is very useful for advanced forensic genetic work, where allelic drop-out...... is occurring. With this discussion, we hope to improve the drop-out model, so that it can be used for practical forensic genetics and stimulate further discussions. We discuss how to estimate drop-out probabilities when using a varying number of PCR cycles and other experimental conditions....
International Nuclear Information System (INIS)
Otsuka, Naoto
2013-01-01
Highlights: • A theoretical foundation is presented for more efficient Integrated Safeguards (IS). • Probability of undetected nuclear proliferation activities should be maintained low. • For nations under IS, the probability to start proliferation activities is very low. • The fact can decrease the detection probability of IS by dozens of percentage points. • The cost of IS per nation can be cut down by reducing inspection frequencies etc. - Abstract: A theoretical foundation is presented for implementing more efficiently the present International Atomic Energy Agency (IAEA) integrated safeguards (ISs) on the basis of fuzzy evaluation of the probability that the evaluated nation will continue peaceful activities. It is shown that by determining the presence probability of undetected nuclear proliferating activities, nations under IS can be maintained at acceptably low proliferation risk levels even if the detection probability of current IS is decreased by dozens of percentage from the present value. This makes it possible to reduce inspection frequency and the number of collected samples, allowing the IAEA to cut costs per nation. This will contribute to further promotion and application of IS to more nations by the IAEA, and more efficient utilization of IAEA resources from the viewpoint of whole IS framework
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.
Finite-size scaling of survival probability in branching processes.
Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Álvaro
2015-04-01
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We derive analytically the existence of finite-size scaling for the survival probability as a function of the control parameter and the maximum number of generations, obtaining the critical exponents as well as the exact scaling function, which is G(y)=2ye(y)/(e(y)-1), with y the rescaled distance to the critical point. Our findings are valid for any branching process of the Galton-Watson type, independently of the distribution of the number of offspring, provided its variance is finite. This proves the universal behavior of the finite-size effects in branching processes, including the universality of the metric factors. The direct relation to mean-field percolation is also discussed.
Charge transfer and rapidity gap analysis in p(π+)n interactions at 195 GeV/c
International Nuclear Information System (INIS)
Eisenberg, Y.; Haber, B.; Hochmann, D.; Karshon, U.; Ronat, E.E.; Shapira, A.; Yekutieli, G.
1980-01-01
We present charge transfer probabilities between CM hemispheres in pn and π + n interactions at 195 GeV/c. The relative probabilities for charge exchanges ΔQ > 1 as a function of rapidity gap length, r, are given. Both results are compared with those of π - p interactions at 200 GeV/c. The average of r, viz. , is given as a function of the gap number and of ΔQ for various multiplicities, and the reduced average gap lengths /ysub(max) for pn interactions are compared with data at a lower energy. (orig.)
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
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
Generation of pseudo-random numbers
Howell, L. W.; Rheinfurth, M. H.
1982-01-01
Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.
LOGISTIC REGRESSION AS A TOOL FOR DETERMINATION OF THE PROBABILITY OF DEFAULT FOR ENTERPRISES
Directory of Open Access Journals (Sweden)
Erika SPUCHLAKOVA
2017-12-01
Full Text Available In a rapidly changing world it is necessary to adapt to new conditions. From a day to day approaches can vary. For the proper management of the company it is essential to know the financial situation. Assessment of the company financial health can be carried out by financial analysis which provides a number of methods how to evaluate the company financial health. Analysis indicators are often included in the company assessment, in obtaining bank loans and other financial resources to ensure the functioning of the company. As company focuses on the future and its planning, it is essential to forecast the future financial situation. According to the results of company´s financial health prediction, the company decides on the extension or limitation of its business. It depends mainly on the capabilities of company´s management how they will use information obtained from financial analysis in practice. The findings of logistic regression methods were published firstly in the 60s, as an alternative to the least squares method. The essence of logistic regression is to determine the relationship between being explained (dependent variable and explanatory (independent variables. The basic principle of this static method is based on the regression analysis, but unlike linear regression, it can predict the probability of a phenomenon that has occurred or not. The aim of this paper is to determine the probability of bankruptcy enterprises.
Implications of Cognitive Load for Hypothesis Generation and Probability Judgment
Sprenger, Amber M.; Dougherty, Michael R.; Atkins, Sharona M.; Franco-Watkins, Ana M.; Thomas, Rick P.; Lange, Nicholas; Abbs, Brandon
2011-01-01
We tested the predictions of HyGene (Thomas et al., 2008) that both divided attention at encoding and judgment should affect the degree to which participants’ probability judgments violate the principle of additivity. In two experiments, we showed that divided attention during judgment leads to an increase in subadditivity, suggesting that the comparison process for probability judgments is capacity limited. Contrary to the predictions of HyGene, a third experiment revealed that divided attention during encoding leads to an increase in later probability judgment made under full attention. The effect of divided attention during encoding on judgment was completely mediated by the number of hypotheses participants generated, indicating that limitations in both encoding and recall can cascade into biases in judgments. PMID:21734897
Implications of Cognitive Load for Hypothesis Generation and Probability Judgment.
Directory of Open Access Journals (Sweden)
Amber M Sprenger
2011-06-01
Full Text Available We tested the predictions of HyGene (Thomas, Dougherty, Sprenger, & Harbison, 2008 that both divided attention at encoding and judgment should affect degree to which participants’ probability judgments violate the principle of additivity. In two experiments, we showed that divided attention during judgment leads to an increase in subadditivity, suggesting that the comparison process for probability judgments is capacity limited. Contrary to the predictions of HyGene, a third experiment revealed that divided attention during encoding leads to an increase in later probability judgment made under full attention. The effect of divided attention at encoding on judgment was completely mediated by the number of hypotheses participants generated, indicating that limitations in both encoding and recall can cascade into biases in judgments.
International Nuclear Information System (INIS)
1997-01-01
The present collection of rapid communications from JINR, Dubna, contains nine separate reports on effects arising from charged particles overcoming of the light velocity barrier, deformable templates for circle recognition, scintillation detectors for precise time measurements, atomic form factors and incoherent scattering functions of atoms and ions with the number of electrons N ≤ 10, experimental set-up ANOMALON for measurement of relativistic nuclear fragmentation cross sections, superconducting dipole magnet for ALICE dimuon arm spectrometer, analysis of transverse mass dependence of Bose-Einstein correlation radii using the DELPHI data, low-energy theorem in softly broken supersymmetry and study of the characteristics of particles in reactions π - , p, d, He, C + C with the total disintegration on carbon nucleus
Earthquake number forecasts testing
Kagan, Yan Y.
2017-10-01
and kurtosis both tend to zero for large earthquake rates: for the Gaussian law, these values are identically zero. A calculation of the NBD skewness and kurtosis levels based on the values of the first two statistical moments of the distribution, shows rapid increase of these upper moments levels. However, the observed catalogue values of skewness and kurtosis are rising even faster. This means that for small time intervals, the earthquake number distribution is even more heavy-tailed than the NBD predicts. Therefore for small time intervals, we propose using empirical number distributions appropriately smoothed for testing forecasted earthquake numbers.
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
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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...
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…
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…
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...
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.
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)
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)
Decision making generalized by a cumulative probability weighting function
dos Santos, Lindomar Soares; Destefano, Natália; Martinez, Alexandre Souto
2018-01-01
Typical examples of intertemporal decision making involve situations in which individuals must choose between a smaller reward, but more immediate, and a larger one, delivered later. Analogously, probabilistic decision making involves choices between options whose consequences differ in relation to their probability of receiving. In Economics, the expected utility theory (EUT) and the discounted utility theory (DUT) are traditionally accepted normative models for describing, respectively, probabilistic and intertemporal decision making. A large number of experiments confirmed that the linearity assumed by the EUT does not explain some observed behaviors, as nonlinear preference, risk-seeking and loss aversion. That observation led to the development of new theoretical models, called non-expected utility theories (NEUT), which include a nonlinear transformation of the probability scale. An essential feature of the so-called preference function of these theories is that the probabilities are transformed by decision weights by means of a (cumulative) probability weighting function, w(p) . We obtain in this article a generalized function for the probabilistic discount process. This function has as particular cases mathematical forms already consecrated in the literature, including discount models that consider effects of psychophysical perception. We also propose a new generalized function for the functional form of w. The limiting cases of this function encompass some parametric forms already proposed in the literature. Far beyond a mere generalization, our function allows the interpretation of probabilistic decision making theories based on the assumption that individuals behave similarly in the face of probabilities and delays and is supported by phenomenological models.
Probability Maps for the Visualization of Assimilation Ensemble Flow Data
Hollt, Thomas
2015-05-25
Ocean forecasts nowadays are created by running ensemble simulations in combination with data assimilation techniques. Most of these techniques resample the ensemble members after each assimilation cycle. This means that in a time series, after resampling, every member can follow up on any of the members before resampling. Tracking behavior over time, such as all possible paths of a particle in an ensemble vector field, becomes very difficult, as the number of combinations rises exponentially with the number of assimilation cycles. In general a single possible path is not of interest but only the probabilities that any point in space might be reached by a particle at some point in time. In this work we present an approach using probability-weighted piecewise particle trajectories to allow such a mapping interactively, instead of tracing quadrillions of individual particles. We achieve interactive rates by binning the domain and splitting up the tracing process into the individual assimilation cycles, so that particles that fall into the same bin after a cycle can be treated as a single particle with a larger probability as input for the next time step. As a result we loose the possibility to track individual particles, but can create probability maps for any desired seed at interactive rates.
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
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
An empirical probability model of detecting species at low densities.
Delaney, David G; Leung, Brian
2010-06-01
False negatives, not detecting things that are actually present, are an important but understudied problem. False negatives are the result of our inability to perfectly detect species, especially those at low density such as endangered species or newly arriving introduced species. They reduce our ability to interpret presence-absence survey data and make sound management decisions (e.g., rapid response). To reduce the probability of false negatives, we need to compare the efficacy and sensitivity of different sampling approaches and quantify an unbiased estimate of the probability of detection. We conducted field experiments in the intertidal zone of New England and New York to test the sensitivity of two sampling approaches (quadrat vs. total area search, TAS), given different target characteristics (mobile vs. sessile). Using logistic regression we built detection curves for each sampling approach that related the sampling intensity and the density of targets to the probability of detection. The TAS approach reduced the probability of false negatives and detected targets faster than the quadrat approach. Mobility of targets increased the time to detection but did not affect detection success. Finally, we interpreted two years of presence-absence data on the distribution of the Asian shore crab (Hemigrapsus sanguineus) in New England and New York, using our probability model for false negatives. The type of experimental approach in this paper can help to reduce false negatives and increase our ability to detect species at low densities by refining sampling approaches, which can guide conservation strategies and management decisions in various areas of ecology such as conservation biology and invasion ecology.
Effects of amphibian chytrid fungus on individual survival probability in wild boreal toads
Pilliod, D.S.; Muths, E.; Scherer, R. D.; Bartelt, P.E.; Corn, P.S.; Hossack, B.R.; Lambert, B.A.; Mccaffery, R.; Gaughan, C.
2010-01-01
Chytridiomycosis is linked to the worldwide decline of amphibians, yet little is known about the demographic effects of the disease. We collected capture-recapture data on three populations of boreal toads (Bufo boreas [Bufo = Anaxyrus]) in the Rocky Mountains (U.S.A.). Two of the populations were infected with chytridiomycosis and one was not. We examined the effect of the presence of amphibian chytrid fungus (Batrachochytrium dendrobatidis [Bd]; the agent of chytridiomycosis) on survival probability and population growth rate. Toads that were infected with Bd had lower average annual survival probability than uninfected individuals at sites where Bd was detected, which suggests chytridiomycosis may reduce survival by 31-42% in wild boreal toads. Toads that were negative for Bd at infected sites had survival probabilities comparable to toads at the uninfected site. Evidence that environmental covariates (particularly cold temperatures during the breeding season) influenced toad survival was weak. The number of individuals in diseased populations declined by 5-7%/year over the 6 years of the study, whereas the uninfected population had comparatively stable population growth. Our data suggest that the presence of Bd in these toad populations is not causing rapid population declines. Rather, chytridiomycosis appears to be functioning as a low-level, chronic disease whereby some infected individuals survive but the overall population effects are still negative. Our results show that some amphibian populations may be coexisting with Bd and highlight the importance of quantitative assessments of survival in diseased animal populations. Journal compilation. ?? 2010 Society for Conservation Biology. No claim to original US government works.
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.
Evolution of an array of elements with logistic transition probability
International Nuclear Information System (INIS)
Majernik, Vladimir; Surda, Anton
1996-01-01
The paper addresses the problem how the state of an array of elements changes if the transition probabilities of its elements is chosen in the form of a logistic map. This problem leads to a special type of a discrete-time Markov which we simulated numerically for the different transition probabilities and the number of elements in the array. We show that the time evolution of the array exhibits a wide scale of behavior depending on the value of the total number of its elements and on the logistic constant a. We point out that this problem can be applied for description of a spin system with a certain type of mean field and of the multispecies ecosystems with an internal noise. (authors)
Maximizing probable oil field profit: uncertainties on well spacing
International Nuclear Information System (INIS)
MacKay, J.A.; Lerche, I.
1997-01-01
The influence of uncertainties in field development costs, well costs, lifting costs, selling price, discount factor, and oil field reserves are evaluated for their impact on assessing probable ranges of uncertainty on present day worth (PDW), oil field lifetime τ 2/3 , optimum number of wells (OWI), and the minimum (n-) and maximum (n+) number of wells to produce a PDW ≥ O. The relative importance of different factors in contributing to the uncertainties in PDW, τ 2/3 , OWI, nsub(-) and nsub(+) is also analyzed. Numerical illustrations indicate how the maximum PDW depends on the ranges of parameter values, drawn from probability distributions using Monte Carlo simulations. In addition, the procedure illustrates the relative importance of contributions of individual factors to the total uncertainty, so that one can assess where to place effort to improve ranges of uncertainty; while the volatility of each estimate allows one to determine when such effort is needful. (author)
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
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
Triangulation based inclusion probabilities: a design-unbiased sampling approach
Fehrmann, Lutz; Gregoire, Timothy; Kleinn, Christoph
2011-01-01
A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. ...
Unitarity corrections to short-range order long-range rapidity correlations
Capella, A
1978-01-01
Although the effective hadronic forces have short range in rapidity space, one nevertheless expects long-range dynamical correlations induced by unitarity constraints. This paper contains a thorough discussion of long-range rapidity correlations in high-multiplicity events. In particular, the authors analyze in detail the forward- backward multiplicity correlations, measured recently in the whole CERN ISR energy range. They find from these data that the normalized variance of the number n of exchanged cut Pomerons, ((n/(n)-1)/sup 2/) , is most probably in the range 0.32 to 0.36. They show that such a number is obtained from Reggeon theory in the eikonal approximation. The authors also predict a very specific violation of local compensation of charge in multiparticle events: The violation should appear in the fourth-order zone correlation function and is absent in the second-order correlation function, the only one measured until now. (48 refs).
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
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 ...
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
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.
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.
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
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.)
Rejecting probability summation for radial frequency patterns, not so Quick!
Baldwin, Alex S; Schmidtmann, Gunnar; Kingdom, Frederick A A; Hess, Robert F
2016-05-01
Radial frequency (RF) patterns are used to assess how the visual system processes shape. They are thought to be detected globally. This is supported by studies that have found summation for RF patterns to be greater than what is possible if the parts were being independently detected and performance only then improved with an increasing number of cycles by probability summation between them. However, the model of probability summation employed in these previous studies was based on High Threshold Theory (HTT), rather than Signal Detection Theory (SDT). We conducted rating scale experiments to investigate the receiver operating characteristics. We find these are of the curved form predicted by SDT, rather than the straight lines predicted by HTT. This means that to test probability summation we must use a model based on SDT. We conducted a set of summation experiments finding that thresholds decrease as the number of modulated cycles increases at approximately the same rate as previously found. As this could be consistent with either additive or probability summation, we performed maximum-likelihood fitting of a set of summation models (Matlab code provided in our Supplementary material) and assessed the fits using cross validation. We find we are not able to distinguish whether the responses to the parts of an RF pattern are combined by additive or probability summation, because the predictions are too similar. We present similar results for summation between separate RF patterns, suggesting that the summation process there may be the same as that within a single RF. Copyright © 2016 Elsevier Ltd. All rights reserved.
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.
1972-01-01
At the current rate of population growth, world population by 2000 is expected to reach 7 billion or more, with developing countries accounting for some 5.4 billion, and economically advanced nations accounting for 1.6 billion. 'Population explosion' is the result of falling mortality rates and continuing high birth rates. Many European countries, and Japan, have already completed what is termed as demographic transition, that is, birth rates have fallen to below 20 births per 1000 population, death rates to 10/1000 population, and annual growth rates are 1% or less; annual growth rates for less developed countries ranged from 2 to 3.5%. Less developed countries can be divided into 3 groups: 1) countries with both high birth and death rates; 2) countries with high birth rates and low death rates; and 3) countries with intermediate and declining birth rates and low death rates. Rapid population growth has serious economic consequences. It encourages inequities in income distribution; it limits rate of growth of gross national product by holding down level of savings and capital investments; it exerts pressure on agricultural production and land; and it creates unemployment problems. In addition, the quality of education for increasing number of chidren is adversely affected, as high proportions of children reduce the amount that can be spent for the education of each child out of the educational budget; the cost and adequacy of health and welfare services are affected in a similar way. Other serious consequences of rapid population growth are maternal death and illness, and physical and mental retardation of children of very poor families. It is very urgent that over a billion births be prevented in the next 30 years to reduce annual population growth rate from the current 2% to 1% per year.
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.
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...
Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory
Yushkevich, A
1992-01-01
This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend...
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
Number Sense on the Number Line
Woods, Dawn Marie; Ketterlin Geller, Leanne; Basaraba, Deni
2018-01-01
A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…
In vitro activity of flomoxef against rapidly growing mycobacteria.
Tsai, Moan-Shane; Tang, Ya-Fen; Eng, Hock-Liew
2008-06-01
The aim of this study was to determine the in vitro sensitivity of rapidly growing mycobacteria (RGM) to flomoxef in respiratory secretions collected from 61 consecutive inpatients and outpatients at Chang Gung Memorial Hospital-Kaohsiung medical center between July and December, 2005. Minimal inhibitory concentrations (MIC) of flomoxef were determined by the broth dilution method for the 61 clinical isolates of RGMs. The MICs of flomoxef at which 90% of clinical isolates were inhibited was >128 microg/mL in 26 isolates of Mycobacterium abscessus and 4 microg/mL in 31 isolates of M. fortuitum. Three out of 4 clinical M. peregrinum isolates were inhibited by flomoxef at concentrations of 4 microg/mL or less. Although the numbers of the clinical isolates of RGMs were small, these preliminary in vitro results demonstrate the potential activity of flomoxef in the management of infections due to M. fortuitum, and probably M. peregrinum in humans.
Richardson, Thomas M.
2014-01-01
We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analagous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.
A fluctuation relation for the probability of energy backscatter
Vela-Martin, Alberto; Jimenez, Javier
2017-11-01
We simulate the large scales of an inviscid turbulent flow in a triply periodic box using a dynamic Smagorinsky model for the sub-grid stresses. The flow, which is forced to constant kinetic energy, is fully reversible and can develop a sustained inverse energy cascade. However, due to the large number of degrees freedom, the probability of spontaneous mean inverse energy flux is negligible. In order to quantify the probability of inverse energy cascades, we test a local fluctuation relation of the form log P(A) = - c(V , t) A , where P(A) = p(| Cs|V,t = A) / p(| Cs|V , t = - A) , p is probability, and | Cs|V,t is the average of the least-squared dynamic model coefficient over volume V and time t. This is confirmed when Cs is averaged over sufficiently large domains and long times, and c is found to depend linearly on V and t. In the limit in which V 1 / 3 is of the order of the integral scale and t is of the order of the eddy-turnover time, we recover a global fluctuation relation that predicts a negligible probability of a sustained inverse energy cascade. For smaller V and t, the local fluctuation relation provides useful predictions on the occurrence of local energy backscatter. Funded by the ERC COTURB project.
Estimating the probability of rare events: addressing zero failure data.
Quigley, John; Revie, Matthew
2011-07-01
Traditional statistical procedures for estimating the probability of an event result in an estimate of zero when no events are realized. Alternative inferential procedures have been proposed for the situation where zero events have been realized but often these are ad hoc, relying on selecting methods dependent on the data that have been realized. Such data-dependent inference decisions violate fundamental statistical principles, resulting in estimation procedures whose benefits are difficult to assess. In this article, we propose estimating the probability of an event occurring through minimax inference on the probability that future samples of equal size realize no more events than that in the data on which the inference is based. Although motivated by inference on rare events, the method is not restricted to zero event data and closely approximates the maximum likelihood estimate (MLE) for nonzero data. The use of the minimax procedure provides a risk adverse inferential procedure where there are no events realized. A comparison is made with the MLE and regions of the underlying probability are identified where this approach is superior. Moreover, a comparison is made with three standard approaches to supporting inference where no event data are realized, which we argue are unduly pessimistic. We show that for situations of zero events the estimator can be simply approximated with 1/2.5n, where n is the number of trials. © 2011 Society for Risk Analysis.
Maximum parsimony, substitution model, and probability phylogenetic trees.
Weng, J F; Thomas, D A; Mareels, I
2011-01-01
The problem of inferring phylogenies (phylogenetic trees) is one of the main problems in computational biology. There are three main methods for inferring phylogenies-Maximum Parsimony (MP), Distance Matrix (DM) and Maximum Likelihood (ML), of which the MP method is the most well-studied and popular method. In the MP method the optimization criterion is the number of substitutions of the nucleotides computed by the differences in the investigated nucleotide sequences. However, the MP method is often criticized as it only counts the substitutions observable at the current time and all the unobservable substitutions that really occur in the evolutionary history are omitted. In order to take into account the unobservable substitutions, some substitution models have been established and they are now widely used in the DM and ML methods but these substitution models cannot be used within the classical MP method. Recently the authors proposed a probability representation model for phylogenetic trees and the reconstructed trees in this model are called probability phylogenetic trees. One of the advantages of the probability representation model is that it can include a substitution model to infer phylogenetic trees based on the MP principle. In this paper we explain how to use a substitution model in the reconstruction of probability phylogenetic trees and show the advantage of this approach with examples.
Heads or tails an introduction to limit theorems in probability
Lesigne, Emmanuel
2005-01-01
Everyone knows some of the basics of probability, perhaps enough to play cards. Beyond the introductory ideas, there are many wonderful results that are unfamiliar to the layman, but which are well within our grasp to understand and appreciate. Some of the most remarkable results in probability are those that are related to limit theorems--statements about what happens when the trial is repeated many times. The most famous of these is the Law of Large Numbers, which mathematicians, engineers, economists, and many others use every day. In this book, Lesigne has made these limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails. In this way, the analysis becomes much clearer, helping establish the reader's intuition about probability. Moreover, very little generality is lost, as many situations can be modelled from combinations of coin tosses. This book is suitable for anyone who would like to learn more about mathematical probability and has had a one-year underg...
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.
International Nuclear Information System (INIS)
Bickel, J.H.
1983-01-01
The quantification of the containment event trees in the Millstone Unit 3 Probabilistic Safety Study utilizes a conditional probability of failure given high pressure which is based on a new approach. The generation of this conditional probability was based on a weakest link failure mode model which considered contributions from a number of overlapping failure modes. This overlap effect was due to a number of failure modes whose mean failure pressures were clustered within a 5 psi range and which had uncertainties due to variances in material strengths and analytical uncertainties which were between 9 and 15 psi. Based on a review of possible probability laws to describe the failure probability of individual structural failure modes, it was determined that a Weibull probability law most adequately described the randomness in the physical process of interest. The resultant conditional probability of failure is found to have a median failure pressure of 132.4 psia. The corresponding 5-95 percentile values are 112 psia and 146.7 psia respectively. The skewed nature of the conditional probability of failure vs. pressure results in a lower overall containment failure probability for an appreciable number of the severe accident sequences of interest, but also probabilities which are more rigorously traceable from first principles
A procedure for estimation of pipe break probabilities due to IGSCC
International Nuclear Information System (INIS)
Bergman, M.; Brickstad, B.; Nilsson, F.
1998-06-01
A procedure has been developed for estimation of the failure probability of welds joints in nuclear piping susceptible to intergranular stress corrosion cracking. The procedure aims at a robust and rapid estimate of the failure probability for a specific weld with known stress state. Random properties are taken into account of the crack initiation rate, the initial crack length, the in-service inspection efficiency and the leak rate. A computer realization of the procedure has been developed for user friendly applications by design engineers. Some examples are considered to investigate the sensitivity of the failure probability to different input quantities. (au)
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.
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.
2011-06-23
... DEPARTMENT OF HEALTH AND HUMAN SERVICES 42 CFR Part 81 [Docket Number NIOSH-0209] RIN 0920-AA39 Guidelines for Determining Probability of Causation Under the Energy Employees Occupational Illness...: HHS published a proposed rule entitled ``Guidelines for Determining Probability of Causation Under the...
Universal critical wrapping probabilities in the canonical ensemble
Directory of Open Access Journals (Sweden)
Hao Hu
2015-09-01
Full Text Available Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in the random-cluster representation, under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We derive that, in the limit L→∞, the critical values of the wrapping probability are different from those of the unconstrained model, i.e. the model in the grand-canonical ensemble, but still universal, for systems with 2yt−d>0 where yt=1/ν is the thermal renormalization exponent and d is the spatial dimension. Similar modifications apply to other dimensionless quantities, such as Binder ratios. For systems with 2yt−d≤0, these quantities share same critical universal values in the two ensembles. It is also derived that new finite-size corrections are induced. These findings apply more generally to systems in the canonical ensemble, e.g. the dilute Potts model with a fixed total number of vacancies. Finally, we formulate an efficient cluster-type algorithm for the canonical ensemble, and confirm these predictions by extensive simulations.
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...
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.
Nilsson, Håkan; Juslin, Peter; Winman, Anders
2016-01-01
Costello and Watts (2014) present a model assuming that people's knowledge of probabilities adheres to probability theory, but that their probability judgments are perturbed by a random noise in the retrieval from memory. Predictions for the relationships between probability judgments for constituent events and their disjunctions and conjunctions, as well as for sums of such judgments were derived from probability theory. Costello and Watts (2014) report behavioral data showing that subjective probability judgments accord with these predictions. Based on the finding that subjective probability judgments follow probability theory, Costello and Watts (2014) conclude that the results imply that people's probability judgments embody the rules of probability theory and thereby refute theories of heuristic processing. Here, we demonstrate the invalidity of this conclusion by showing that all of the tested predictions follow straightforwardly from an account assuming heuristic probability integration (Nilsson, Winman, Juslin, & Hansson, 2009). We end with a discussion of a number of previous findings that harmonize very poorly with the predictions by the model suggested by Costello and Watts (2014). (c) 2015 APA, all rights reserved).
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...
Probability densities and Lévy densities
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler
For positive Lévy processes (i.e. subordinators) formulae are derived that express the probability density or the distribution function in terms of power series in time t. The applicability of the results to finance and to turbulence is briefly indicated.......For positive Lévy processes (i.e. subordinators) formulae are derived that express the probability density or the distribution function in terms of power series in time t. The applicability of the results to finance and to turbulence is briefly indicated....
Probabilities from entanglement, Born's rule from envariance
International Nuclear Information System (INIS)
Zurek, W.
2005-01-01
Full text: I shall discuss consequences of envariance (environment - assisted invariance) symmetry exhibited by entangled quantum states. I shall focus on the implications of envariance for the understanding of the origins and nature of ignorance, and, hence, for the origin of probabilities in physics. While the derivation of the Born's rule for probabilities (pk IykI2) is the principal accomplishment of this research, I shall explore the possibility that several other symptoms of the quantum - classical transition that are a consequence of decoherence can be justified directly by envariance -- i.e., without invoking Born's rule. (author)
Risk Probability Estimating Based on Clustering
DEFF Research Database (Denmark)
Chen, Yong; Jensen, Christian D.; Gray, Elizabeth
2003-01-01
of prior experiences, recommendations from a trusted entity or the reputation of the other entity. In this paper we propose a dynamic mechanism for estimating the risk probability of a certain interaction in a given environment using hybrid neural networks. We argue that traditional risk assessment models...... from the insurance industry do not directly apply to ubiquitous computing environments. Instead, we propose a dynamic mechanism for risk assessment, which is based on pattern matching, classification and prediction procedures. This mechanism uses an estimator of risk probability, which is based...
Fifty challenging problems in probability with solutions
Mosteller, Frederick
1987-01-01
Can you solve the problem of ""The Unfair Subway""? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to chall
Path probabilities of continuous time random walks
International Nuclear Information System (INIS)
Eule, Stephan; Friedrich, Rudolf
2014-01-01
Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
Probable Gastrointestinal Toxicity of Kombucha Tea
Srinivasan, Radhika; Smolinske, Susan; Greenbaum, David
1997-01-01
Kombucha tea is a health beverage made by incubating the Kombucha “mushroom” in tea and sugar. Although therapeutic benefits have been attributed to the drink, neither its beneficial effects nor adverse side effects have been reported widely in the scientific literature. Side effects probably related to consumption of Kombucha tea are reported in four patients. Two presented with symptoms of allergic reaction, the third with jaundice, and the fourth with nausea, vomiting, and head and neck pain. In all four, use of Kombucha tea in proximity to onset of symptoms and symptom resolution on cessation of tea drinking suggest a probable etiologic association. PMID:9346462
Quantum probability and quantum decision-making.
Yukalov, V I; Sornette, D
2016-01-13
A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary. © 2015 The Author(s).
Lady luck the theory of probability
Weaver, Warren
1982-01-01
""Should I take my umbrella?"" ""Should I buy insurance?"" ""Which horse should I bet on?"" Every day ― in business, in love affairs, in forecasting the weather or the stock market questions arise which cannot be answered by a simple ""yes"" or ""no."" Many of these questions involve probability. Probabilistic thinking is as crucially important in ordinary affairs as it is in the most abstruse realms of science. This book is the best nontechnical introduction to probability ever written. Its author, the late Dr. Warren Weaver, was a professor of mathematics, active in the Rockefeller and Sloa
Bayesian estimation of core-melt probability
International Nuclear Information System (INIS)
Lewis, H.W.
1984-01-01
A very simple application of the canonical Bayesian algorithm is made to the problem of estimation of the probability of core melt in a commercial power reactor. An approximation to the results of the Rasmussen study on reactor safety is used as the prior distribution, and the observation that there has been no core melt yet is used as the single experiment. The result is a substantial decrease in the mean probability of core melt--factors of 2 to 4 for reasonable choices of parameters. The purpose is to illustrate the procedure, not to argue for the decrease
Description of atomic burials in compact globular proteins by Fermi-Dirac probability distributions.
Gomes, Antonio L C; de Rezende, Júlia R; Pereira de Araújo, Antônio F; Shakhnovich, Eugene I
2007-02-01
We perform a statistical analysis of atomic distributions as a function of the distance R from the molecular geometrical center in a nonredundant set of compact globular proteins. The number of atoms increases quadratically for small R, indicating a constant average density inside the core, reaches a maximum at a size-dependent distance R(max), and falls rapidly for larger R. The empirical curves turn out to be consistent with the volume increase of spherical concentric solid shells and a Fermi-Dirac distribution in which the distance R plays the role of an effective atomic energy epsilon(R) = R. The effective chemical potential mu governing the distribution increases with the number of residues, reflecting the size of the protein globule, while the temperature parameter beta decreases. Interestingly, betamu is not as strongly dependent on protein size and appears to be tuned to maintain approximately half of the atoms in the high density interior and the other half in the exterior region of rapidly decreasing density. A normalized size-independent distribution was obtained for the atomic probability as a function of the reduced distance, r = R/R(g), where R(g) is the radius of gyration. The global normalized Fermi distribution, F(r), can be reasonably decomposed in Fermi-like subdistributions for different atomic types tau, F(tau)(r), with Sigma(tau)F(tau)(r) = F(r), which depend on two additional parameters mu(tau) and h(tau). The chemical potential mu(tau) affects a scaling prefactor and depends on the overall frequency of the corresponding atomic type, while the maximum position of the subdistribution is determined by h(tau), which appears in a type-dependent atomic effective energy, epsilon(tau)(r) = h(tau)r, and is strongly correlated to available hydrophobicity scales. Better adjustments are obtained when the effective energy is not assumed to be necessarily linear, or epsilon(tau)*(r) = h(tau)*r(alpha,), in which case a correlation with hydrophobicity
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
Safeguarding a Lunar Rover with Wald's Sequential Probability Ratio Test
Furlong, Michael; Dille, Michael; Wong, Uland; Nefian, Ara
2016-01-01
The virtual bumper is a safeguarding mechanism for autonomous and remotely operated robots. In this paper we take a new approach to the virtual bumper system by using an old statistical test. By using a modified version of Wald's sequential probability ratio test we demonstrate that we can reduce the number of false positive reported by the virtual bumper, thereby saving valuable mission time. We use the concept of sequential probability ratio to control vehicle speed in the presence of possible obstacles in order to increase certainty about whether or not obstacles are present. Our new algorithm reduces the chances of collision by approximately 98 relative to traditional virtual bumper safeguarding without speed control.
Fitting the Probability Distribution Functions to Model Particulate Matter Concentrations
International Nuclear Information System (INIS)
El-Shanshoury, Gh.I.
2017-01-01
The main objective of this study is to identify the best probability distribution and the plotting position formula for modeling the concentrations of Total Suspended Particles (TSP) as well as the Particulate Matter with an aerodynamic diameter<10 μm (PM 10 ). The best distribution provides the estimated probabilities that exceed the threshold limit given by the Egyptian Air Quality Limit value (EAQLV) as well the number of exceedance days is estimated. The standard limits of the EAQLV for TSP and PM 10 concentrations are 24-h average of 230 μg/m 3 and 70 μg/m 3 , respectively. Five frequency distribution functions with seven formula of plotting positions (empirical cumulative distribution functions) are compared to fit the average of daily TSP and PM 10 concentrations in year 2014 for Ain Sokhna city. The Quantile-Quantile plot (Q-Q plot) is used as a method for assessing how closely a data set fits a particular distribution. A proper probability distribution that represents the TSP and PM 10 has been chosen based on the statistical performance indicator values. The results show that Hosking and Wallis plotting position combined with Frechet distribution gave the highest fit for TSP and PM 10 concentrations. Burr distribution with the same plotting position follows Frechet distribution. The exceedance probability and days over the EAQLV are predicted using Frechet distribution. In 2014, the exceedance probability and days for TSP concentrations are 0.052 and 19 days, respectively. Furthermore, the PM 10 concentration is found to exceed the threshold limit by 174 days
Failure probability estimate of type 304 stainless steel piping
International Nuclear Information System (INIS)
Daugherty, W.L.; Awadalla, N.G.; Sindelar, R.L.; Mehta, H.S.; Ranganath, S.
1989-01-01
The primary source of in-service degradation of the SRS production reactor process water piping is intergranular stress corrosion cracking (IGSCC). IGSCC has occurred in a limited number of weld heat affected zones, areas known to be susceptible to IGSCC. A model has been developed to combine crack growth rates, crack size distributions, in-service examination reliability estimates and other considerations to estimate the pipe large-break frequency. This frequency estimates the probability that an IGSCC crack will initiate, escape detection by ultrasonic (UT) examination, and grow to instability prior to extending through-wall and being detected by the sensitive leak detection system. These events are combined as the product of four factors: (1) the probability that a given weld heat affected zone contains IGSCC; (2) the conditional probability, given the presence of IGSCC, that the cracking will escape detection during UT examination; (3) the conditional probability, given a crack escapes detection by UT, that it will not grow through-wall and be detected by leakage; (4) the conditional probability, given a crack is not detected by leakage, that it grows to instability prior to the next UT exam. These four factors estimate the occurrence of several conditions that must coexist in order for a crack to lead to a large break of the process water piping. When evaluated for the SRS production reactors, they produce an extremely low break frequency. The objective of this paper is to present the assumptions, methodology, results and conclusions of a probabilistic evaluation for the direct failure of the primary coolant piping resulting from normal operation and seismic loads. This evaluation was performed to support the ongoing PRA effort and to complement deterministic analyses addressing the credibility of a double-ended guillotine break
Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces
International Nuclear Information System (INIS)
Vourdas, A.
2014-01-01
The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H 1 ,H 2 ), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H 1 ),P(H 2 ), to the subspaces H 1 , H 2 . As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities
RAPID TRANSFER ALIGNMENT USING FEDERATED KALMAN FILTER
Institute of Scientific and Technical Information of China (English)
GUDong-qing; QINYong-yuan; PENGRong; LIXin
2005-01-01
The dimension number of the centralized Kalman filter (CKF) for the rapid transfer alignment (TA) is as high as 21 if the aircraft wing flexure motion is considered in the rapid TA. The 21-dimensional CKF brings the calculation burden on the computer and the difficulty to meet a high filtering updating rate desired by rapid TA. The federated Kalman filter (FKF) for the rapid TA is proposed to solve the dilemma. The structure and the algorithm of the FKF, which can perform parallel computation and has less calculation burden, are designed.The wing flexure motion is modeled, and then the 12-order velocity matching local filter and the 15-order attitud ematching local filter are devised. Simulation results show that the proposed EKE for the rapid TA almost has the same performance as the CKF. Thus the calculation burden of the proposed FKF for the rapid TA is markedly decreased.
Tropical Cyclone Wind Probability Forecasting (WINDP).
1981-04-01
llq. h. ,c ilrac (t’ small probabilities (below 107c) is limited II(t’h, numb(r o!, significant digits given: therefore 1t( huld lU r~ruidvd as being...APPLIED SCI. CORP. ENGLAMD ;7MOS. SCIENCES OEPT., LIBRARY ATTN: LIBARY , SUITE 500 400 WASHINGTON AVE. 6811 KENILWORTH AVE. EUROPEAN CENTRE FOR MEDIUM
The Probability Heuristics Model of Syllogistic Reasoning.
Chater, Nick; Oaksford, Mike
1999-01-01
Proposes a probability heuristic model for syllogistic reasoning and confirms the rationality of this heuristic by an analysis of the probabilistic validity of syllogistic reasoning that treats logical inference as a limiting case of probabilistic inference. Meta-analysis and two experiments involving 40 adult participants and using generalized…
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®…
Critique of `Elements of Quantum Probability'
Gill, R.D.
1998-01-01
We analyse the thesis of Kummerer and Maassen that classical probability is unable to model the the stochastic nature of the Aspect experiment in which violation of Bells inequality was experimentally demonstrated According to these authors the experiment shows the need to introduce the extension
Independent Events in Elementary Probability Theory
Csenki, Attila
2011-01-01
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): If the n events E[subscript 1],…
Probable Unusual Transmission of Zika Virus
Centers for Disease Control (CDC) Podcasts
This podcast discusses a study about the probable unusual transmission of Zika Virus Infection from a scientist to his wife, published in the May 2011 issue of Emerging Infectious Diseases. Dr. Brian Foy, Associate Professor at Colorado State University, shares details of this event.
Error probabilities in default Bayesian hypothesis testing
Gu, Xin; Hoijtink, Herbert; Mulder, J,
2016-01-01
This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for
Spatial Probability Cuing and Right Hemisphere Damage
Shaqiri, Albulena; Anderson, Britt
2012-01-01
In this experiment we studied statistical learning, inter-trial priming, and visual attention. We assessed healthy controls and right brain damaged (RBD) patients with and without neglect, on a simple visual discrimination task designed to measure priming effects and probability learning. All participants showed a preserved priming effect for item…
Sampling, Probability Models and Statistical Reasoning -RE ...
Indian Academy of Sciences (India)
random sampling allows data to be modelled with the help of probability ... g based on different trials to get an estimate of the experimental error. ... research interests lie in the .... if e is indeed the true value of the proportion of defectives in the.
Virus isolation: Specimen type and probable transmission
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Virus isolation: Specimen type and probable transmission. Over 500 CHIK virus isolations were made. 4 from male Ae. Aegypti (?TOT). 6 from CSF (neurological involvement). 1 from a 4-day old child (transplacental transmission.
Estimating the Probability of Negative Events
Harris, Adam J. L.; Corner, Adam; Hahn, Ulrike
2009-01-01
How well we are attuned to the statistics of our environment is a fundamental question in understanding human behaviour. It seems particularly important to be able to provide accurate assessments of the probability with which negative events occur so as to guide rational choice of preventative actions. One question that arises here is whether or…
Concurrency meets probability: theory and practice (abstract)
Katoen, Joost P.
Treating random phenomena in concurrency theory has a long tradition. Petri nets [18, 10] and process algebras [14] have been extended with probabilities. The same applies to behavioural semantics such as strong and weak (bi)simulation [1], and testing pre-orders [5]. Beautiful connections between
Confusion between Odds and Probability, a Pandemic?
Fulton, Lawrence V.; Mendez, Francis A.; Bastian, Nathaniel D.; Musal, R. Muzaffer
2012-01-01
This manuscript discusses the common confusion between the terms probability and odds. To emphasize the importance and responsibility of being meticulous in the dissemination of information and knowledge, this manuscript reveals five cases of sources of inaccurate statistical language imbedded in the dissemination of information to the general…
Probability in Action: The Red Traffic Light
Shanks, John A.
2007-01-01
Emphasis on problem solving in mathematics has gained considerable attention in recent years. While statistics teaching has always been problem driven, the same cannot be said for the teaching of probability where discrete examples involving coins and playing cards are often the norm. This article describes an application of simple probability…
Probability & Statistics: Modular Learning Exercises. Teacher Edition
Actuarial Foundation, 2012
2012-01-01
The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…
Probability & Statistics: Modular Learning Exercises. Student Edition
Actuarial Foundation, 2012
2012-01-01
The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…
Conditional probability on MV-algebras
Czech Academy of Sciences Publication Activity Database
Kroupa, Tomáš
2005-01-01
Roč. 149, č. 2 (2005), s. 369-381 ISSN 0165-0114 R&D Projects: GA AV ČR IAA2075302 Institutional research plan: CEZ:AV0Z10750506 Keywords : conditional probability * tribe * MV-algebra Subject RIV: BA - General Mathematics Impact factor: 1.039, year: 2005
Investigating Probability with the NBA Draft Lottery.
Quinn, Robert J.
1997-01-01
Investigates an interesting application of probability in the world of sports. Considers the role of permutations in the lottery system used by the National Basketball Association (NBA) in the United States to determine the order in which nonplayoff teams select players from the college ranks. Presents a lesson on this topic in which students work…
Probability from a Socio-Cultural Perspective
Sharma, Sashi
2016-01-01
There exists considerable and rich literature on students' misconceptions about probability; less attention has been paid to the development of students' probabilistic thinking in the classroom. Grounded in an analysis of the literature, this article offers a lesson sequence for developing students' probabilistic understanding. In particular, a…
Neutrosophic Probability, Set, And Logic (first version)
Smarandache, Florentin
2000-01-01
This project is a part of a National Science Foundation interdisciplinary project proposal. Starting from a new viewpoint in philosophy, the neutrosophy, one extends the classical "probability theory", "fuzzy set" and "fuzzy logic" to , and respectively. They are useful in artificial intelligence, neural networks, evolutionary programming, neutrosophic dynamic systems, and quantum mechanics.
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)
On a paradox of probability theory
International Nuclear Information System (INIS)
Stuart, C.I.J.M.
1989-01-01
Costa de Beauregard's proposal concerning physical retrocausality has been shown to fail on two crucial points. However, it is argued that his proposal still merits serious attention. The argument arises from showing that his proposal reveals a paradox involving relations between conditional probabilities, statistical correlations and reciprocal causalities of the type exhibited by cooperative dynamics in physical systems. 4 refs. (Author)
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)
Sequential Probability Ration Tests : Conservative and Robust
Kleijnen, J.P.C.; Shi, Wen
2017-01-01
In practice, most computers generate simulation outputs sequentially, so it is attractive to analyze these outputs through sequential statistical methods such as sequential probability ratio tests (SPRTs). We investigate several SPRTs for choosing between two hypothesized values for the mean output
Applied probability models with optimization applications
Ross, Sheldon M
1992-01-01
Concise advanced-level introduction to stochastic processes that frequently arise in applied probability. Largely self-contained text covers Poisson process, renewal theory, Markov chains, inventory theory, Brownian motion and continuous time optimization models, much more. Problems and references at chapter ends. ""Excellent introduction."" - Journal of the American Statistical Association. Bibliography. 1970 edition.
Quantum probability and conceptual combination in conjunctions.
Hampton, James A
2013-06-01
I consider the general problem of category conjunctions in the light of Pothos & Busemeyer (P&B)'s quantum probability (QP) account of the conjunction fallacy. I argue that their account as presented cannot capture the "guppy effect" - the case in which a class is a better member of a conjunction A^B than it is of either A or B alone.
Occupation probabilities and fluctuations in the asymmetric simple inclusion process
Reuveni, Shlomi; Hirschberg, Ori; Eliazar, Iddo; Yechiali, Uri
2014-04-01
The asymmetric simple inclusion process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an "inclusion" counterpart of the asymmetric simple exclusion process. In this paper we present an exact closed-form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites. Our results are expressed in terms of the entries of Catalan's trapezoids—number arrays which generalize Catalan's numbers and Catalan's triangle. We further prove that the ASIP is asymptotically governed by the following: (i) an inverse square-root law of occupation, (ii) a square-root law of fluctuation, and (iii) a Rayleigh law for the distribution of interexit times. The universality of these results is discussed.
Survival probability of diffusion with trapping in cellular neurobiology
Holcman, David; Marchewka, Avi; Schuss, Zeev
2005-09-01
The problem of diffusion with absorption and trapping sites arises in the theory of molecular signaling inside and on the membranes of biological cells. In particular, this problem arises in the case of spine-dendrite communication, where the number of calcium ions, modeled as random particles, is regulated across the spine microstructure by pumps, which play the role of killing sites, while the end of the dendritic shaft is an absorbing boundary. We develop a general mathematical framework for diffusion in the presence of absorption and killing sites and apply it to the computation of the time-dependent survival probability of ions. We also compute the ratio of the number of absorbed particles at a specific location to the number of killed particles. We show that the ratio depends on the distribution of killing sites. The biological consequence is that the position of the pumps regulates the fraction of calcium ions that reach the dendrite.
Sondergaard, Kathrine B; Hansen, Steen Moller; Pallisgaard, Jannik L; Gerds, Thomas Alexander; Wissenberg, Mads; Karlsson, Lena; Lippert, Freddy K; Gislason, Gunnar H; Torp-Pedersen, Christian; Folke, Fredrik
2018-03-01
Despite wide dissemination of automated external defibrillators (AEDs), bystander defibrillation rates remain low. We aimed to investigate how route distance to the nearest accessible AED was associated with probability of bystander defibrillation in public and residential locations. We used data from the nationwide Danish Cardiac Arrest Registry and the Danish AED Network to identify out-of-hospital cardiac arrests and route distances to nearest accessible registered AED during 2008-2013. The association between route distance and bystander defibrillation was described using restricted cubic spline logistic regression. We included 6971 out-of-hospital cardiac arrest cases. The proportion of arrests according to distance in meters (≤100, 101-200, >200) to the nearest accessible AED was: 4.6% (n=320), 5.3% (n=370), and 90.1% (n=6281), respectively. For cardiac arrests in public locations, the probability of bystander defibrillation at 0, 100 and 200m from the nearest AED was 35.7% (95% confidence interval 28.0%-43.5%), 21.3% (95% confidence interval 17.4%-25.2%), and 13.7% (95% confidence interval 10.1%-16.8%), respectively. The corresponding numbers for cardiac arrests in residential locations were 7.0% (95% confidence interval -2.1%-16.1%), 1.5% (95% confidence interval 0.002%-2.8%), and 0.9% (95% confidence interval 0.0005%-1.7%), respectively. In public locations, the probability of bystander defibrillation decreased rapidly within the first 100m route distance from cardiac arrest to nearest accessible AED whereas the probability of bystander defibrillation was low for all distances in residential areas. Copyright © 2017 Elsevier B.V. All rights reserved.
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
Federal Laboratory Consortium — The ARDEC Rapid Prototyping (RP) Laboratory was established in December 1992 to provide low cost RP capabilities to the ARDEC engineering community. The Stratasys,...
Bounding probabilistic safety assessment probabilities by reality
International Nuclear Information System (INIS)
Fragola, J.R.; Shooman, M.L.
1991-01-01
The investigation of the failure in systems where failure is a rare event makes the continual comparisons between the developed probabilities and empirical evidence difficult. The comparison of the predictions of rare event risk assessments with historical reality is essential to prevent probabilistic safety assessment (PSA) predictions from drifting into fantasy. One approach to performing such comparisons is to search out and assign probabilities to natural events which, while extremely rare, have a basis in the history of natural phenomena or human activities. For example the Segovian aqueduct and some of the Roman fortresses in Spain have existed for several millennia and in many cases show no physical signs of earthquake damage. This evidence could be used to bound the probability of earthquakes above a certain magnitude to less than 10 -3 per year. On the other hand, there is evidence that some repetitive actions can be performed with extremely low historical probabilities when operators are properly trained and motivated, and sufficient warning indicators are provided. The point is not that low probability estimates are impossible, but continual reassessment of the analysis assumptions, and a bounding of the analysis predictions by historical reality. This paper reviews the probabilistic predictions of PSA in this light, attempts to develop, in a general way, the limits which can be historically established and the consequent bounds that these limits place upon the predictions, and illustrates the methodology used in computing such limits. Further, the paper discusses the use of empirical evidence and the requirement for disciplined systematic approaches within the bounds of reality and the associated impact on PSA probabilistic estimates
The probability and severity of decompression sickness
Hada, Ethan A.; Vann, Richard D.; Denoble, Petar J.
2017-01-01
Decompression sickness (DCS), which is caused by inert gas bubbles in tissues, is an injury of concern for scuba divers, compressed air workers, astronauts, and aviators. Case reports for 3322 air and N2-O2 dives, resulting in 190 DCS events, were retrospectively analyzed and the outcomes were scored as (1) serious neurological, (2) cardiopulmonary, (3) mild neurological, (4) pain, (5) lymphatic or skin, and (6) constitutional or nonspecific manifestations. Following standard U.S. Navy medical definitions, the data were grouped into mild—Type I (manifestations 4–6)–and serious–Type II (manifestations 1–3). Additionally, we considered an alternative grouping of mild–Type A (manifestations 3–6)–and serious–Type B (manifestations 1 and 2). The current U.S. Navy guidance allows for a 2% probability of mild DCS and a 0.1% probability of serious DCS. We developed a hierarchical trinomial (3-state) probabilistic DCS model that simultaneously predicts the probability of mild and serious DCS given a dive exposure. Both the Type I/II and Type A/B discriminations of mild and serious DCS resulted in a highly significant (p probability of ‘mild’ DCS resulted in a longer allowable bottom time for the same 2% limit. However, for the 0.1% serious DCS limit, we found a vastly decreased allowable bottom dive time for all dive depths. If the Type A/B scoring was assigned to outcome severity, the no decompression limits (NDL) for air dives were still controlled by the acceptable serious DCS risk limit rather than the acceptable mild DCS risk limit. However, in this case, longer NDL limits were allowed than with the Type I/II scoring. The trinomial model mild and serious probabilities agree reasonably well with the current air NDL only with the Type A/B scoring and when 0.2% risk of serious DCS is allowed. PMID:28296928
Directory of Open Access Journals (Sweden)
M.P. Silva
2006-06-01
coliforms at 45ºC and to compare the methods of Most Probable Number Method (MPN and Petrifilm EC in their efficiency to detect E. coli in Minas cheese, sausage, fresh vegetables and corn flower samples. Petrifilm EC was more accurate method than MNP method, which presented false negative results or underestimation of E. coli. In conclusion, Petrifilm EC was an efficient and practical method to detect E. coli. Therefore, it may be alternatively used for enumeration of total coliforms and E. coli in foods.
High-resolution urban flood modelling - a joint probability approach
Hartnett, Michael; Olbert, Agnieszka; Nash, Stephen
2017-04-01
The hydrodynamic modelling of rapid flood events due to extreme climatic events in urban environment is both a complex and challenging task. The horizontal resolution necessary to resolve complexity of urban flood dynamics is a critical issue; the presence of obstacles of varying shapes and length scales, gaps between buildings and the complex geometry of the city such as slopes affect flow paths and flood levels magnitudes. These small scale processes require a high resolution grid to be modelled accurately (2m or less, Olbert et al., 2015; Hunter et al., 2008; Brown et al., 2007) and, therefore, altimetry data of at least the same resolution. Along with availability of high-resolution LiDAR data and computational capabilities, as well as state of the art nested modelling approaches, these problems can now be overcome. Flooding and drying, domain definition, frictional resistance and boundary descriptions are all important issues to be addressed when modelling urban flooding. In recent years, the number of urban flood models dramatically increased giving a good insight into various modelling problems and solutions (Mark et al., 2004; Mason et al., 2007; Fewtrell et al., 2008; Shubert et al., 2008). Despite extensive modelling work conducted for fluvial (e.g. Mignot et al., 2006; Hunter et al., 2008; Yu and Lane, 2006) and coastal mechanisms of flooding (e.g. Gallien et al., 2011; Yang et al., 2012), the amount of investigations into combined coastal-fluvial flooding is still very limited (e.g. Orton et al., 2012; Lian et al., 2013). This is surprising giving the extent of flood consequences when both mechanisms occur simultaneously, which usually happens when they are driven by one process such as a storm. The reason for that could be the fact that the likelihood of joint event is much smaller than those of any of the two contributors occurring individually, because for fast moving storms the rainfall-driven fluvial flood arrives usually later than the storm surge
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
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)
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…
Wilson, Jason; Lawman, Joshua; Murphy, Rachael; Nelson, Marissa
2011-01-01
This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…
Massey, J. L.
1976-01-01
The very low error probability obtained with long error-correcting codes results in a very small number of observed errors in simulation studies of practical size and renders the usual confidence interval techniques inapplicable to the observed error probability. A natural extension of the notion of a 'confidence interval' is made and applied to such determinations of error probability by simulation. An example is included to show the surprisingly great significance of as few as two decoding errors in a very large number of decoding trials.
VOLCANIC RISK ASSESSMENT - PROBABILITY AND CONSEQUENCES
International Nuclear Information System (INIS)
G.A. Valentine; F.V. Perry; S. Dartevelle
2005-01-01
Risk is the product of the probability and consequences of an event. Both of these must be based upon sound science that integrates field data, experiments, and modeling, but must also be useful to decision makers who likely do not understand all aspects of the underlying science. We review a decision framework used in many fields such as performance assessment for hazardous and/or radioactive waste disposal sites that can serve to guide the volcanological community towards integrated risk assessment. In this framework the underlying scientific understanding of processes that affect probability and consequences drive the decision-level results, but in turn these results can drive focused research in areas that cause the greatest level of uncertainty at the decision level. We review two examples of the determination of volcanic event probability: (1) probability of a new volcano forming at the proposed Yucca Mountain radioactive waste repository, and (2) probability that a subsurface repository in Japan would be affected by the nearby formation of a new stratovolcano. We also provide examples of work on consequences of explosive eruptions, within the framework mentioned above. These include field-based studies aimed at providing data for ''closure'' of wall rock erosion terms in a conduit flow model, predictions of dynamic pressure and other variables related to damage by pyroclastic flow into underground structures, and vulnerability criteria for structures subjected to conditions of explosive eruption. Process models (e.g., multiphase flow) are important for testing the validity or relative importance of possible scenarios in a volcanic risk assessment. We show how time-dependent multiphase modeling of explosive ''eruption'' of basaltic magma into an open tunnel (drift) at the Yucca Mountain repository provides insight into proposed scenarios that include the development of secondary pathways to the Earth's surface. Addressing volcanic risk within a decision
The Problem with Probability: Why rare hazards feel even rarer
Thompson, K. J.
2013-12-01
Even as scientists improve the accuracy of their forecasts for large-scale events like natural hazards and climate change, a gap remains between the confidence the scientific community has in those estimates, and the skepticism with which the lay public tends to view statements of uncertainty. Beyond the challenges of helping the public to understand probabilistic forecasts lies yet another barrier to effective communication: the fact that even when humans can estimate or state the correct probability of a rare event, we tend to distort that probability in our minds, acting as if the likelihood is higher or lower than we know it to be. A half century of empirical research in psychology and economics leaves us with a clear view of the ways that people interpret stated, or described probabilities--e.g., "There is a 6% chance of a Northridge-sized earthquake occurring in your area in the next 10 years." In the past decade, the focus of cognitive scientists has turned to the other method humans use to learn probabilities: intuitively estimating the chances of a rare event by assessing our personal experience with various outcomes. While it is well understood that described probabilities are over-weighted when they are small (e.g., a 5% chance might be treated more like a 10% or 12% chance), it appears that in many cases, experienced rare probabilities are in fact under-weighted. This distortion is not an under-estimation, and therefore cannot be prevented by reminding people of the described probability. This paper discusses the mechanisms and effects of this difference in the way probability is used when a number is provided, as opposed to when the frequency of a rare event is intuited. In addition to recommendations based on the current state of research on the way people appear to make decisions from experience, suggestions are made for how to present probabilistic information to best take advantage of people's tendencies to either amplify risk or ignore it, as well
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.
Mental status and suicide probability of young people: A cross-sectional study
Directory of Open Access Journals (Sweden)
Selen Ozakar Akca
Full Text Available Summary Objective: The most important determinant of suicide ideation, tendency and initiative is the presence of mental disorders. Since the number of those who lost their lives due to suicide in the world rose rapidly among the young population, the World Health Organization emphasizes the importance of assessing young people in the high-risk age group to prevent suicidal behavior. This study aimed to determine psychological symptom levels and suicide probability in young people. Method: The cross-sectional research consisted of 15-24 year-old individuals (N=348, who have sought a psychiatric clinic between February and June, 2015. The Research Data was collected by applying Data Collection Form, Suicide Probability Scale (SPS and Brief Symptom Inventory (BSI. SPSS 22.0 statistical package program was used for data analysis. Results: There was a statistically significant difference (p<0.05 between the mean SPS scores according to education, psychiatric treatment, self-harm, smoking and drinking status of the participants in the study. Apart from this, there was also a statistically significant correlation between anxiety, depression, negative self and hostility according to the SPS and BSI subscales (p<0.001, r=0.739; p<0.001, r=0.729; p<0.001, r=0.747; p<0.001, r=0.715; respectively. Conclusion: The results of our study show that suicide risk is significantly higher in young people with depression, anxiety, negative self-perception and hostility symptoms. In this regard, we suggest the relevance of assessing the suicide risk of young people seeking a psychiatric clinic, with thorough attention to those who have high potential for suicide.
Rapid Tooling via Stereolithography
Montgomery, Eva
2006-01-01
Approximately three years ago, composite stereolithography (SL) resins were introduced to the marketplace, offering performance features beyond what traditional SL resins could offer. In particular, the high heat deflection temperatures and high stiffness of these highly filled resins have opened the door to several new rapid prototyping (RP) applications, including wind tunnel test modelling and, more recently, rapid tooling.
Rapid arc - clinical rationale and results
International Nuclear Information System (INIS)
Cozzi, Lucca
2008-01-01
The presentation will focus on the background of Intensity modulation volumetric arc therapy Rapid Arc from Varian Medical Systems aiming to highlight the technical and clinical rational also from an historical perspective to the founding pillars of fast delivery with a minimum number of arcs and a minimum number of monitor units
A Probability-Based Hybrid User Model for Recommendation System
Directory of Open Access Journals (Sweden)
Jia Hao
2016-01-01
Full Text Available With the rapid development of information communication technology, the available information or knowledge is exponentially increased, and this causes the well-known information overload phenomenon. This problem is more serious in product design corporations because over half of the valuable design time is consumed in knowledge acquisition, which highly extends the design cycle and weakens the competitiveness. Therefore, the recommender systems become very important in the domain of product domain. This research presents a probability-based hybrid user model, which is a combination of collaborative filtering and content-based filtering. This hybrid model utilizes user ratings and item topics or classes, which are available in the domain of product design, to predict the knowledge requirement. The comprehensive analysis of the experimental results shows that the proposed method gains better performance in most of the parameter settings. This work contributes a probability-based method to the community for implement recommender system when only user ratings and item topics are available.