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Sample records for probability learning

  1. Rethinking the learning of belief network probabilities

    SciTech Connect

    Musick, R.

    1996-03-01

    Belief networks are a powerful tool for knowledge discovery that provide concise, understandable probabilistic models of data. There are methods grounded in probability theory to incrementally update the relationships described by the belief network when new information is seen, to perform complex inferences over any set of variables in the data, to incorporate domain expertise and prior knowledge into the model, and to automatically learn the model from data. This paper concentrates on part of the belief network induction problem, that of learning the quantitative structure (the conditional probabilities), given the qualitative structure. In particular, the current practice of rote learning the probabilities in belief networks can be significantly improved upon. We advance the idea of applying any learning algorithm to the task of conditional probability learning in belief networks, discuss potential benefits, and show results of applying neural networks and other algorithms to a medium sized car insurance belief network. The results demonstrate from 10 to 100% improvements in model error rates over the current approaches.

  2. Probability density function learning by unsupervised neurons.

    PubMed

    Fiori, S

    2001-10-01

    In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals. PMID:11709808

  3. Probability & Statistics: Modular Learning Exercises. Teacher Edition

    ERIC Educational Resources Information Center

    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…

  4. Probability & Statistics: Modular Learning Exercises. Student Edition

    ERIC Educational Resources Information Center

    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…

  5. Fostering Positive Attitude in Probability Learning Using Graphing Calculator

    ERIC Educational Resources Information Center

    Tan, Choo-Kim; Harji, Madhubala Bava; Lau, Siong-Hoe

    2011-01-01

    Although a plethora of research evidence highlights positive and significant outcomes of the incorporation of the Graphing Calculator (GC) in mathematics education, its use in the teaching and learning process appears to be limited. The obvious need to revisit the teaching and learning of Probability has resulted in this study, i.e. to incorporate…

  6. Probably good diagrams for learning: representational epistemic recodification of probability theory.

    PubMed

    Cheng, Peter C-H

    2011-07-01

    The representational epistemic approach to the design of visual displays and notation systems advocates encoding the fundamental conceptual structure of a knowledge domain directly in the structure of a representational system. It is claimed that representations so designed will benefit from greater semantic transparency, which enhances comprehension and ease of learning, and plastic generativity, which makes the meaningful manipulation of the representation easier and less error prone. Epistemic principles for encoding fundamental conceptual structures directly in representational schemes are described. The diagrammatic recodification of probability theory is undertaken to demonstrate how the fundamental conceptual structure of a knowledge domain can be analyzed, how the identified conceptual structure may be encoded in a representational system, and the cognitive benefits that follow. An experiment shows the new probability space diagrams are superior to the conventional approach for learning this conceptually challenging topic.

  7. Learning about Posterior Probability: Do Diagrams and Elaborative Interrogation Help?

    ERIC Educational Resources Information Center

    Clinton, Virginia; Alibali, Martha W.; Nathan, Mitchell J.

    2016-01-01

    To learn from a text, students must make meaningful connections among related ideas in that text. This study examined the effectiveness of two methods of improving connections--elaborative interrogation and diagrams--in written lessons about posterior probability. Undergraduate students (N = 198) read a lesson in one of three questioning…

  8. Computational Modelling and Simulation Fostering New Approaches in Learning Probability

    ERIC Educational Resources Information Center

    Kuhn, Markus; Hoppe, Ulrich; Lingnau, Andreas; Wichmann, Astrid

    2006-01-01

    Discovery learning in mathematics in the domain of probability based on hands-on experiments is normally limited because of the difficulty in providing sufficient materials and data volume in terms of repetitions of the experiments. Our cooperative, computational modelling and simulation environment engages students and teachers in composing and…

  9. Dual-Processes in Learning and Judgment: Evidence from the Multiple Cue Probability Learning Paradigm

    ERIC Educational Resources Information Center

    Rolison, Jonathan J.; Evans, Jonathan St. B. T.; Dennis, Ian; Walsh, Clare R.

    2012-01-01

    Multiple cue probability learning (MCPL) involves learning to predict a criterion based on a set of novel cues when feedback is provided in response to each judgment made. But to what extent does MCPL require controlled attention and explicit hypothesis testing? The results of two experiments show that this depends on cue polarity. Learning about…

  10. A Mathematical Microworld for Students to Learn Introductory Probability.

    ERIC Educational Resources Information Center

    Jiang, Zhonghong; Potter, Walter D.

    1993-01-01

    Describes the Microworld Chance, a simulation-oriented computer environment that allows students to explore probability concepts in five subenvironments: coins, dice, spinners, thumbtacks, and marbles. Results of a teaching experiment to examine the effectiveness of the microworld in changing students' misconceptions about probability are…

  11. Paradoxes and Counterexamples in Teaching and Learning of Probability at University

    ERIC Educational Resources Information Center

    Klymchuk, Sergiy; Kachapova, Farida

    2012-01-01

    This article is devoted to practical aspects of teaching and learning of probability at university. It presents the difficulties and attitudes of first-year university science and engineering students towards using paradoxes and counterexamples as a pedagogical strategy in teaching and learning of probability. It also presents a student's point of…

  12. Quantum probability and cognitive modeling: some cautions and a promising direction in modeling physics learning.

    PubMed

    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.

  13. The feedback-related negativity is modulated by feedback probability in observational learning.

    PubMed

    Kobza, Stefan; Thoma, Patrizia; Daum, Irene; Bellebaum, Christian

    2011-12-01

    The feedback-related negativity (FRN), an event-related potentials (ERPs) component reflecting activity of the anterior cingulate cortex (ACC), has been shown to be modulated by feedback expectancy following active choices in feedback-based learning tasks. A general reduction of FRN amplitude has been described in observational feedback learning, raising the question whether FRN amplitude is modulated in a similar way in this type of learning. The present study investigated whether the FRN and the P300 - a second ERP component related to feedback processing - are modulated by feedback probability in observational learning. Thirty-two subjects participated in the experiment. They observed a virtual person choosing between two symbols and receiving positive or negative feedback. Learning about stimulus-specific feedback probabilities was assessed in active test trials without feedback. In addition, the bias to learn from positive or negative feedback and - in a subsample of 17 subjects - empathy scores were obtained. General FRN and P300 modulations by feedback probability were found across all subjects. Only for the FRN in learners, an interaction between probability and valence was observed. Larger FRN amplitudes for negative relative to positive feedback only emerged for the lowest outcome probability. The results show that feedback expectancy modulates FRN amplitude also in observational learning, suggesting a similar ACC function as in active learning. On the other hand, the modulation is only seen for very low feedback expectancy, which suggests that brain regions other than those of the reward system contribute to feedback processing in an observation setting.

  14. The Effect of Simulation-Based Learning on Prospective Teachers' Inference Skills in Teaching Probability

    ERIC Educational Resources Information Center

    Koparan, Timur; Yilmaz, Gül Kaleli

    2015-01-01

    The effect of simulation-based probability teaching on the prospective teachers' inference skills has been examined with this research. In line with this purpose, it has been aimed to examine the design, implementation and efficiency of a learning environment for experimental probability. Activities were built on modeling, simulation and the…

  15. Sequence Learning in Infancy: The Independent Contributions of Conditional Probability and Pair Frequency Information

    ERIC Educational Resources Information Center

    Marcovitch, Stuart; Lewkowicz, David J.

    2009-01-01

    The ability to perceive sequences is fundamental to cognition. Previous studies have shown that infants can learn visual sequences as early as 2 months of age and it has been suggested that this ability is mediated by sensitivity to conditional probability information. Typically, conditional probability information has covaried with frequency…

  16. Illustrating Probability in Genetics with Hands-On Learning: Making the Math Real

    ERIC Educational Resources Information Center

    Pierce, Benjamin A.; Honeycutt, Brenda B.

    2007-01-01

    Probability is an essential tool for understanding heredity and modern genetics, yet many students have difficulty with this topic due to the abstract and quantitative nature of the subject. To facilitate student learning of probability in genetics, we have developed a set of hands-on, cooperative activities that allow students to determine…

  17. Probability and Statistics in Astronomical Machine Learning and Data Minin

    NASA Astrophysics Data System (ADS)

    Scargle, Jeffrey

    2012-03-01

    Statistical issues peculiar to astronomy have implications for machine learning and data mining. It should be obvious that statistics lies at the heart of machine learning and data mining. Further it should be no surprise that the passive observational nature of astronomy, the concomitant lack of sampling control, and the uniqueness of its realm (the whole universe!) lead to some special statistical issues and problems. As described in the Introduction to this volume, data analysis technology is largely keeping up with major advances in astrophysics and cosmology, even driving many of them. And I realize that there are many scientists with good statistical knowledge and instincts, especially in the modern era I like to call the Age of Digital Astronomy. Nevertheless, old impediments still lurk, and the aim of this chapter is to elucidate some of them. Many experiences with smart people doing not-so-smart things (cf. the anecdotes collected in the Appendix here) have convinced me that the cautions given here need to be emphasized. Consider these four points: 1. Data analysis often involves searches of many cases, for example, outcomes of a repeated experiment, for a feature of the data. 2. The feature comprising the goal of such searches may not be defined unambiguously until the search is carried out, or perhaps vaguely even then. 3. The human visual system is very good at recognizing patterns in noisy contexts. 4. People are much easier to convince of something they want to believe, or already believe, as opposed to unpleasant or surprising facts. One can argue that all four are good things during the initial, exploratory phases of most data analysis. They represent the curiosity and creativity of the scientific process, especially during the exploration of data collections from new observational programs such as all-sky surveys in wavelengths not accessed before or sets of images of a planetary surface not yet explored. On the other hand, confirmatory scientific

  18. Learning Probabilities in Computer Engineering by Using a Competency- and Problem-Based Approach

    ERIC Educational Resources Information Center

    Khoumsi, Ahmed; Hadjou, Brahim

    2005-01-01

    Our department has redesigned its electrical and computer engineering programs by adopting a learning methodology based on competence development, problem solving, and the realization of design projects. In this article, we show how this pedagogical approach has been successfully used for learning probabilities and their application to computer…

  19. Word Learning by Preschoolers with SLI: Effect of Phonotactic Probability and Object Familiarity

    ERIC Educational Resources Information Center

    Gray, Shelley; Brinkley, Shara; Svetina, Dubravka

    2012-01-01

    Purpose: In this study, the authors investigated whether previous findings of a low phonotactic probability/unfamiliar object word-learning advantage in preschoolers could be replicated, whether this advantage would be apparent at different "stages" of word learning, and whether findings would differ for preschoolers with specific language…

  20. Probability estimation with machine learning methods for dichotomous and multicategory outcome: theory.

    PubMed

    Kruppa, Jochen; Liu, Yufeng; Biau, Gérard; Kohler, Michael; König, Inke R; Malley, James D; Ziegler, Andreas

    2014-07-01

    Probability estimation for binary and multicategory outcome using logistic and multinomial logistic regression has a long-standing tradition in biostatistics. However, biases may occur if the model is misspecified. In contrast, outcome probabilities for individuals can be estimated consistently with machine learning approaches, including k-nearest neighbors (k-NN), bagged nearest neighbors (b-NN), random forests (RF), and support vector machines (SVM). Because machine learning methods are rarely used by applied biostatisticians, the primary goal of this paper is to explain the concept of probability estimation with these methods and to summarize recent theoretical findings. Probability estimation in k-NN, b-NN, and RF can be embedded into the class of nonparametric regression learning machines; therefore, we start with the construction of nonparametric regression estimates and review results on consistency and rates of convergence. In SVMs, outcome probabilities for individuals are estimated consistently by repeatedly solving classification problems. For SVMs we review classification problem and then dichotomous probability estimation. Next we extend the algorithms for estimating probabilities using k-NN, b-NN, and RF to multicategory outcomes and discuss approaches for the multicategory probability estimation problem using SVM. In simulation studies for dichotomous and multicategory dependent variables we demonstrate the general validity of the machine learning methods and compare it with logistic regression. However, each method fails in at least one simulation scenario. We conclude with a discussion of the failures and give recommendations for selecting and tuning the methods. Applications to real data and example code are provided in a companion article (doi:10.1002/bimj.201300077).

  1. Incidental learning of probability information is differentially affected by the type of visual working memory representation.

    PubMed

    van Lamsweerde, Amanda E; Beck, Melissa R

    2015-12-01

    In this study, we investigated whether the ability to learn probability information is affected by the type of representation held in visual working memory. Across 4 experiments, participants detected changes to displays of coloured shapes. While participants detected changes in 1 dimension (e.g., colour), a feature from a second, nonchanging dimension (e.g., shape) predicted which object was most likely to change. In Experiments 1 and 3, items could be grouped by similarity in the changing dimension across items (e.g., colours and shapes were repeated in the display), while in Experiments 2 and 4 items could not be grouped by similarity (all features were unique). Probability information from the predictive dimension was learned and used to increase performance, but only when all of the features within a display were unique (Experiments 2 and 4). When it was possible to group by feature similarity in the changing dimension (e.g., 2 blue objects appeared within an array), participants were unable to learn probability information and use it to improve performance (Experiments 1 and 3). The results suggest that probability information can be learned in a dimension that is not explicitly task-relevant, but only when the probability information is represented with the changing dimension in visual working memory. PMID:26010021

  2. A Cross-Sectional Comparison of the Effects of Phonotactic Probability and Neighborhood Density on Word Learning by Preschool Children

    ERIC Educational Resources Information Center

    Hoover, Jill R.; Storkel, Holly L.; Hogan, Tiffany P.

    2010-01-01

    Two experiments examined the effects of phonotactic probability and neighborhood density on word learning by 3-, 4-, and 5-year-old children. Nonwords orthogonally varying in probability and density were taught with learning and retention measured via picture naming. Experiment 1 used a within story probability/across story density exposure…

  3. A comparison of homonym and novel word learning: The role of phonotactic probability and word frequency

    PubMed Central

    Storkel, Holly L.; Maekawa, Junko

    2006-01-01

    This study compares homonym learning to novel word learning by three- to four-year-old children to determine whether homonyms are learned more rapidly or more slowly than novel words. In addition, the role of form characteristics in homonym learning is examined by manipulating phonotactic probability and word frequency. Thirty-two children were exposed to homonyms and novel words in a story with visual support and learning was measured in two tasks: referent identification; picture naming. Results showed that responses to homonyms were as accurate as responses to novel words in the referent identification task. In contrast, responses to homonyms were more accurate than responses to novel words in the picture-naming task. Furthermore, homonyms composed of common sound sequences were named more accurately than those composed of rare sound sequences. The influence of word frequency was less straightforward. These results may be inconsistent with a one-to-one form-referent bias in word learning. PMID:16429713

  4. The Influence of Phonotactic Probability and Neighborhood Density on Children's Production of Newly Learned Words

    ERIC Educational Resources Information Center

    Heisler, Lori; Goffman, Lisa

    2016-01-01

    A word learning paradigm was used to teach children novel words that varied in phonotactic probability and neighborhood density. The effects of frequency and density on speech production were examined when phonetic forms were nonreferential (i.e., when no referent was attached) and when phonetic forms were referential (i.e., when a referent was…

  5. Influence of Phonotactic Probability/Neighbourhood Density on Lexical Learning in Late Talkers

    ERIC Educational Resources Information Center

    MacRoy-Higgins, Michelle; Schwartz, Richard G.; Shafer, Valerie L.; Marton, Klara

    2013-01-01

    Background: Toddlers who are late talkers demonstrate delays in phonological and lexical skills. However, the influence of phonological factors on lexical acquisition in toddlers who are late talkers has not been examined directly. Aims: To examine the influence of phonotactic probability/neighbourhood density on word learning in toddlers who were…

  6. Blind Students' Learning of Probability through the Use of a Tactile Model

    ERIC Educational Resources Information Center

    Vita, Aida Carvalho; Kataoka, Verônica Yumi

    2014-01-01

    The objective of this paper is to discuss how blind students learn basic concepts of probability using the tactile model proposed by Vita (2012). Among the activities were part of the teaching sequence "Jefferson's Random Walk", in which students built a tree diagram (using plastic trays, foam cards, and toys), and pictograms in 3D…

  7. Effects of Multiple Simulation Presentation among Students of Different Anxiety Levels in the Learning of Probability

    ERIC Educational Resources Information Center

    Fong, Soon Fook; Por, Fei Ping; Tang, Ai Ling

    2012-01-01

    The purpose of this study was to investigate the effects of multiple simulation presentation in interactive multimedia are on the achievement of students with different levels of anxiety in the learning of Probability. The interactive multimedia courseware was developed in two different modes, which were Multiple Simulation Presentation (MSP) and…

  8. Deep learning of support vector machines with class probability output networks.

    PubMed

    Kim, Sangwook; Yu, Zhibin; Kil, Rhee Man; Lee, Minho

    2015-04-01

    Deep learning methods endeavor to learn features automatically at multiple levels and allow systems to learn complex functions mapping from the input space to the output space for the given data. The ability to learn powerful features automatically is increasingly important as the volume of data and range of applications of machine learning methods continues to grow. This paper proposes a new deep architecture that uses support vector machines (SVMs) with class probability output networks (CPONs) to provide better generalization power for pattern classification problems. As a result, deep features are extracted without additional feature engineering steps, using multiple layers of the SVM classifiers with CPONs. The proposed structure closely approaches the ideal Bayes classifier as the number of layers increases. Using a simulation of classification problems, the effectiveness of the proposed method is demonstrated.

  9. Splitting the variance of statistical learning performance: A parametric investigation of exposure duration and transitional probabilities.

    PubMed

    Bogaerts, Louisa; Siegelman, Noam; Frost, Ram

    2016-08-01

    What determines individuals' efficacy in detecting regularities in visual statistical learning? Our theoretical starting point assumes that the variance in performance of statistical learning (SL) can be split into the variance related to efficiency in encoding representations within a modality and the variance related to the relative computational efficiency of detecting the distributional properties of the encoded representations. Using a novel methodology, we dissociated encoding from higher-order learning factors, by independently manipulating exposure duration and transitional probabilities in a stream of visual shapes. Our results show that the encoding of shapes and the retrieving of their transitional probabilities are not independent and additive processes, but interact to jointly determine SL performance. The theoretical implications of these findings for a mechanistic explanation of SL are discussed.

  10. Splitting the variance of statistical learning performance: A parametric investigation of exposure duration and transitional probabilities.

    PubMed

    Bogaerts, Louisa; Siegelman, Noam; Frost, Ram

    2016-08-01

    What determines individuals' efficacy in detecting regularities in visual statistical learning? Our theoretical starting point assumes that the variance in performance of statistical learning (SL) can be split into the variance related to efficiency in encoding representations within a modality and the variance related to the relative computational efficiency of detecting the distributional properties of the encoded representations. Using a novel methodology, we dissociated encoding from higher-order learning factors, by independently manipulating exposure duration and transitional probabilities in a stream of visual shapes. Our results show that the encoding of shapes and the retrieving of their transitional probabilities are not independent and additive processes, but interact to jointly determine SL performance. The theoretical implications of these findings for a mechanistic explanation of SL are discussed. PMID:26743060

  11. Ensemble learning of inverse probability weights for marginal structural modeling in large observational datasets.

    PubMed

    Gruber, Susan; Logan, Roger W; Jarrín, Inmaculada; Monge, Susana; Hernán, Miguel A

    2015-01-15

    Inverse probability weights used to fit marginal structural models are typically estimated using logistic regression. However, a data-adaptive procedure may be able to better exploit information available in measured covariates. By combining predictions from multiple algorithms, ensemble learning offers an alternative to logistic regression modeling to further reduce bias in estimated marginal structural model parameters. We describe the application of two ensemble learning approaches to estimating stabilized weights: super learning (SL), an ensemble machine learning approach that relies on V-fold cross validation, and an ensemble learner (EL) that creates a single partition of the data into training and validation sets. Longitudinal data from two multicenter cohort studies in Spain (CoRIS and CoRIS-MD) were analyzed to estimate the mortality hazard ratio for initiation versus no initiation of combined antiretroviral therapy among HIV positive subjects. Both ensemble approaches produced hazard ratio estimates further away from the null, and with tighter confidence intervals, than logistic regression modeling. Computation time for EL was less than half that of SL. We conclude that ensemble learning using a library of diverse candidate algorithms offers an alternative to parametric modeling of inverse probability weights when fitting marginal structural models. With large datasets, EL provides a rich search over the solution space in less time than SL with comparable results.

  12. Computational Modeling of Statistical Learning: Effects of Transitional Probability versus Frequency and Links to Word Learning

    ERIC Educational Resources Information Center

    Mirman, Daniel; Estes, Katharine Graf; Magnuson, James S.

    2010-01-01

    Statistical learning mechanisms play an important role in theories of language acquisition and processing. Recurrent neural network models have provided important insights into how these mechanisms might operate. We examined whether such networks capture two key findings in human statistical learning. In Simulation 1, a simple recurrent network…

  13. Web-based experiments controlled by JavaScript: an example from probability learning.

    PubMed

    Birnbaum, Michael H; Wakcher, Sandra V

    2002-05-01

    JavaScript programs can be used to control Web experiments. This technique is illustrated by an experiment that tested the effects of advice on performance in the classic probability-learning paradigm. Previous research reported that people tested via the Web or in the lab tended to match the probabilities of their responses to the probabilities that those responses would be reinforced. The optimal strategy, however, is to consistently choose the more frequent event; probability matching produces suboptimal performance. We investigated manipulations we reasoned should improve performance. A horse race scenario in which participants predicted the winner in each of a series of races between two horses was compared with an abstract scenario used previously. Ten groups of learners received different amounts of advice, including all combinations of (1) explicit instructions concerning the optimal strategy, (2) explicit instructions concerning a monetary sum to maximize, and (3) accurate information concerning the probabilities of events. The results showed minimal effects of horse race versus abstract scenario. Both advice concerning the optimal strategy and probability information contributed significantly to performance in the task. This paper includes a brief tutorial on JavaScript, explaining with simple examples how to assemble a browser-based experiment.

  14. More than words: Adults learn probabilities over categories and relationships between them

    PubMed Central

    Hudson Kam, Carla L.

    2009-01-01

    This study examines whether human learners can acquire statistics over abstract categories and their relationships to each other. Adult learners were exposed to miniature artificial languages containing variation in the ordering of the Subject, Object, and Verb constituents. Different orders (e.g. SOV, VSO) occurred in the input with different frequencies, but the occurrence of one order versus another was not predictable. Importantly, the language was constructed such that participants could only match the overall input probabilities if they were tracking statistics over abstract categories, not over individual words. At test, participants reproduced the probabilities present in the input with a high degree of accuracy. Closer examination revealed that learner’s were matching the probabilities associated with individual verbs rather than the category as a whole. However, individual nouns had no impact on word orders produced. Thus, participants learned the probabilities of a particular ordering of the abstract grammatical categories Subject and Object associated with each verb. Results suggest that statistical learning mechanisms are capable of tracking relationships between abstract linguistic categories in addition to individual items. PMID:20161375

  15. Probability-confidence-kernel-based localized multiple kernel learning with lp norm.

    PubMed

    Han, Yina; Liu, Guizhong

    2012-06-01

    Localized multiple kernel learning (LMKL) is an attractive strategy for combining multiple heterogeneous features in terms of their discriminative power for each individual sample. However, models excessively fitting to a specific sample would obstacle the extension to unseen data, while a more general form is often insufficient for diverse locality characterization. Hence, both learning sample-specific local models for each training datum and extending the learned models to unseen test data should be equally addressed in designing LMKL algorithm. In this paper, for an integrative solution, we propose a probability confidence kernel (PCK), which measures per-sample similarity with respect to probabilistic-prediction-based class attribute: The class attribute similarity complements the spatial-similarity-based base kernels for more reasonable locality characterization, and the predefined form of involved class probability density function facilitates the extension to the whole input space and ensures its statistical meaning. Incorporating PCK into support-vectormachine-based LMKL framework, we propose a new PCK-LMKL with arbitrary l(p)-norm constraint implied in the definition of PCKs, where both the parameters in PCK and the final classifier can be efficiently optimized in a joint manner. Evaluations of PCK-LMKL on both benchmark machine learning data sets (ten University of California Irvine (UCI) data sets) and challenging computer vision data sets (15-scene data set and Caltech-101 data set) have shown to achieve state-of-the-art performances.

  16. Impact of Statistical Learning Methods on the Predictive Power of Multivariate Normal Tissue Complication Probability Models

    SciTech Connect

    Xu Chengjian; Schaaf, Arjen van der; Schilstra, Cornelis; Langendijk, Johannes A.; Veld, Aart A. van't

    2012-03-15

    Purpose: To study the impact of different statistical learning methods on the prediction performance of multivariate normal tissue complication probability (NTCP) models. Methods and Materials: In this study, three learning methods, stepwise selection, least absolute shrinkage and selection operator (LASSO), and Bayesian model averaging (BMA), were used to build NTCP models of xerostomia following radiotherapy treatment for head and neck cancer. Performance of each learning method was evaluated by a repeated cross-validation scheme in order to obtain a fair comparison among methods. Results: It was found that the LASSO and BMA methods produced models with significantly better predictive power than that of the stepwise selection method. Furthermore, the LASSO method yields an easily interpretable model as the stepwise method does, in contrast to the less intuitive BMA method. Conclusions: The commonly used stepwise selection method, which is simple to execute, may be insufficient for NTCP modeling. The LASSO method is recommended.

  17. Under the hood of statistical learning: A statistical MMN reflects the magnitude of transitional probabilities in auditory sequences

    PubMed Central

    Koelsch, Stefan; Busch, Tobias; Jentschke, Sebastian; Rohrmeier, Martin

    2016-01-01

    Within the framework of statistical learning, many behavioural studies investigated the processing of unpredicted events. However, surprisingly few neurophysiological studies are available on this topic, and no statistical learning experiment has investigated electroencephalographic (EEG) correlates of processing events with different transition probabilities. We carried out an EEG study with a novel variant of the established statistical learning paradigm. Timbres were presented in isochronous sequences of triplets. The first two sounds of all triplets were equiprobable, while the third sound occurred with either low (10%), intermediate (30%), or high (60%) probability. Thus, the occurrence probability of the third item of each triplet (given the first two items) was varied. Compared to high-probability triplet endings, endings with low and intermediate probability elicited an early anterior negativity that had an onset around 100 ms and was maximal at around 180 ms. This effect was larger for events with low than for events with intermediate probability. Our results reveal that, when predictions are based on statistical learning, events that do not match a prediction evoke an early anterior negativity, with the amplitude of this mismatch response being inversely related to the probability of such events. Thus, we report a statistical mismatch negativity (sMMN) that reflects statistical learning of transitional probability distributions that go beyond auditory sensory memory capabilities. PMID:26830652

  18. Learning probabilities from random observables in high dimensions: the maximum entropy distribution and others

    NASA Astrophysics Data System (ADS)

    Obuchi, Tomoyuki; Cocco, Simona; Monasson, Remi

    We consider the problem of learning a target probability distribution over a set of N binary variables from the knowledge of the expectation values (with this target distribution) of M observables, drawn uniformly at random. The space of all probability distributions compatible with these M expectation values within some fixed accuracy, called version space, is studied. We introduce a biased measure over the version space, which gives a boost with the entropy of the distributions and with an arbitrary `temperature'. The choice of the temperature allows us to interpolate between the flat measure over all the distributions and the pointwise measure concentrated at the maximum entropy distribution. Using the replica method we compute the volume of the version space and other quantities of interest, such as the distance R between the target distribution and the center-of-mass distribution over the version space. Some phase transitions are found, corresponding to qualitative improvements in the learning of the target distribution and to the decrease of the distance R. However, the distance R does not vary with the temperature, meaning that the maximum entropy distribution is not closer to the target distribution than any others. I am a member of one of the reciprocal societies, The Physical Society of Japan (JPS), and put the ID of JPS above.

  19. The Effect of Incremental Changes in Phonotactic Probability and Neighborhood Density on Word Learning by Preschool Children

    ERIC Educational Resources Information Center

    Storkel, Holly L.; Bontempo, Daniel E.; Aschenbrenner, Andrew J.; Maekawa, Junko; Lee, Su-Yeon

    2013-01-01

    Purpose: Phonotactic probability or neighborhood density has predominately been defined through the use of gross distinctions (i.e., low vs. high). In the current studies, the authors examined the influence of finer changes in probability (Experiment 1) and density (Experiment 2) on word learning. Method: The authors examined the full range of…

  20. Triggering word learning in children with Language Impairment: the effect of phonotactic probability and neighbourhood density.

    PubMed

    McKean, Cristina; Letts, Carolyn; Howard, David

    2014-11-01

    The effect of phonotactic probability (PP) and neighbourhood density (ND) on triggering word learning was examined in children with Language Impairment (3;04-6;09) and compared to Typically Developing children. Nonwords, varying PP and ND orthogonally, were presented in a story context and their learning tested using a referent identification task. Group comparisons with receptive vocabulary as a covariate found no group differences in overall scores or in the influence of PP or ND. Therefore, there was no evidence of atypical lexical or phonological processing. 'Convergent' PP/ND (High PP/High ND; Low PP/Low ND) was optimal for word learning in both groups. This bias interacted with vocabulary knowledge. 'Divergent' PP/ND word scores (High PP/Low ND; Low PP/High ND) were positively correlated with vocabulary so the 'divergence disadvantage' reduced as vocabulary knowledge grew; an interaction hypothesized to represent developmental changes in lexical-phonological processing linked to the emergence of phonological representations.

  1. Nonassociative learning processes affecting swimming probability in the seaslug Tritonia diomedea: habituation, sensitization and inhibition.

    PubMed

    Brown, G D

    1998-10-01

    The role of nonassociative learning processes in determining whether or not a chemical stimulus will elicit the Tritonia diomedea swimming response was examined in a variety of conditioning experiments. Iterative presentation of a chemical stimulus resulted in a reduced swimming probability (SP). By the criteria of Thompson and Spencer (Thompson RF, Spencer WA. Psychol. Rev. 1966;73:16-43) and others, this iterative reduction of SP was concluded to be the result of habituation. Site-specificity and a below zero effect implicated sensory pathways in habituation memory storage. The iterative reduction in SP was reversible, confirming that a sensitization-like process can also influence SP. It was further concluded that a short-term decrement in swimming cycle number was most likely due to a constraint in the effector pathway. Experience with a tactile stimulus had a long-lasting decremental effect on SP. This heterostimic reduction of SP was amplified in a multistimic paradigm that included both chemical and tactile stimuli during training. The chemical stimuli alone did not alter SP in this experiment. Multistimic reduction lasted for a week and was reversed temporarily by an excitatory chemical stimulus. The long-lasting reduction of SP by tactile stimulation appears to be the result of a novel nonassociative inhibitory process, which was distinguished from other learning processes by its duration and specificity. A total of three distinct learning processes are postulated to account for the role of simple types of experience in determining SP in Tritonia: habituation, sensitization, and nonassociative inhibition.

  2. Perceptual and Neuronal Boundary Learned from Higher-Order Stimulus Probabilities

    PubMed Central

    Köver, Hania; Gill, Kirt; Tseng, Yi-Ting L.; Bao, Shaowen

    2013-01-01

    During an early epoch of development, the brain is highly adaptive to the stimulus environment. Exposing young animals to a particular tone, for example, leads to an enlarged representation of that tone in primary auditory cortex. While the neural effects of simple tonal environments are well characterized, the principles that guide plasticity in more complex acoustic environments remain unclear. In addition, very little is known about the perceptual consequences of early experience-induced plasticity. To address these questions, we reared juvenile rats in complex multitone environments that differed in terms of the higher-order conditional probabilities between sounds. We found that the development of primary cortical acoustic representations, as well as frequency discrimination ability in adult animals, were shaped by the higher-order stimulus statistics of the early acoustic environment. Our results suggest that early experience-dependent cortical reorganization may mediate perceptual changes through statistical learning of the sensory input. PMID:23426696

  3. Probability weighted ensemble transfer learning for predicting interactions between HIV-1 and human proteins.

    PubMed

    Mei, Suyu

    2013-01-01

    Reconstruction of host-pathogen protein interaction networks is of great significance to reveal the underlying microbic pathogenesis. However, the current experimentally-derived networks are generally small and should be augmented by computational methods for less-biased biological inference. From the point of view of computational modelling, data scarcity, data unavailability and negative data sampling are the three major problems for host-pathogen protein interaction networks reconstruction. In this work, we are motivated to address the three concerns and propose a probability weighted ensemble transfer learning model for HIV-human protein interaction prediction (PWEN-TLM), where support vector machine (SVM) is adopted as the individual classifier of the ensemble model. In the model, data scarcity and data unavailability are tackled by homolog knowledge transfer. The importance of homolog knowledge is measured by the ROC-AUC metric of the individual classifiers, whose outputs are probability weighted to yield the final decision. In addition, we further validate the assumption that only the homolog knowledge is sufficient to train a satisfactory model for host-pathogen protein interaction prediction. Thus the model is more robust against data unavailability with less demanding data constraint. As regards with negative data construction, experiments show that exclusiveness of subcellular co-localized proteins is unbiased and more reliable than random sampling. Last, we conduct analysis of overlapped predictions between our model and the existing models, and apply the model to novel host-pathogen PPIs recognition for further biological research.

  4. Decision forests for learning prostate cancer probability maps from multiparametric MRI

    NASA Astrophysics Data System (ADS)

    Ehrenberg, Henry R.; Cornfeld, Daniel; Nawaf, Cayce B.; Sprenkle, Preston C.; Duncan, James S.

    2016-03-01

    Objectives: Advances in multiparametric magnetic resonance imaging (mpMRI) and ultrasound/MRI fusion imaging offer a powerful alternative to the typical undirected approach to diagnosing prostate cancer. However, these methods require the time and expertise needed to interpret mpMRI image scenes. In this paper, a machine learning framework for automatically detecting and localizing cancerous lesions within the prostate is developed and evaluated. Methods: Two studies were performed to gather MRI and pathology data. The 12 patients in the first study underwent an MRI session to obtain structural, diffusion-weighted, and dynamic contrast enhanced image vol- umes of the prostate, and regions suspected of being cancerous from the MRI data were manually contoured by radiologists. Whole-mount slices of the prostate were obtained for the patients in the second study, in addition to structural and diffusion-weighted MRI data, for pathology verification. A 3-D feature set for voxel-wise appear- ance description combining intensity data, textural operators, and zonal approximations was generated. Voxels in a test set were classified as normal or cancer using a decision forest-based model initialized using Gaussian discriminant analysis. A leave-one-patient-out cross-validation scheme was used to assess the predictions against the expert manual segmentations confirmed as cancer by biopsy. Results: We achieved an area under the average receiver-operator characteristic curve of 0.923 for the first study, and visual assessment of the probability maps showed 21 out of 22 tumors were identified while a high level of specificity was maintained. In addition to evaluating the model against related approaches, the effects of the individual MRI parameter types were explored, and pathological verification using whole-mount slices from the second study was performed. Conclusions: The results of this paper show that the

  5. Activity in Inferior Parietal and Medial Prefrontal Cortex Signals the Accumulation of Evidence in a Probability Learning Task

    PubMed Central

    d'Acremont, Mathieu; Fornari, Eleonora; Bossaerts, Peter

    2013-01-01

    In an uncertain environment, probabilities are key to predicting future events and making adaptive choices. However, little is known about how humans learn such probabilities and where and how they are encoded in the brain, especially when they concern more than two outcomes. During functional magnetic resonance imaging (fMRI), young adults learned the probabilities of uncertain stimuli through repetitive sampling. Stimuli represented payoffs and participants had to predict their occurrence to maximize their earnings. Choices indicated loss and risk aversion but unbiased estimation of probabilities. BOLD response in medial prefrontal cortex and angular gyri increased linearly with the probability of the currently observed stimulus, untainted by its value. Connectivity analyses during rest and task revealed that these regions belonged to the default mode network. The activation of past outcomes in memory is evoked as a possible mechanism to explain the engagement of the default mode network in probability learning. A BOLD response relating to value was detected only at decision time, mainly in striatum. It is concluded that activity in inferior parietal and medial prefrontal cortex reflects the amount of evidence accumulated in favor of competing and uncertain outcomes. PMID:23401673

  6. ANNz2: Photometric Redshift and Probability Distribution Function Estimation using Machine Learning

    NASA Astrophysics Data System (ADS)

    Sadeh, I.; Abdalla, F. B.; Lahav, O.

    2016-10-01

    We present ANNz2, a new implementation of the public software for photometric redshift (photo-z) estimation of Collister & Lahav, which now includes generation of full probability distribution functions (PDFs). ANNz2 utilizes multiple machine learning methods, such as artificial neural networks and boosted decision/regression trees. The objective of the algorithm is to optimize the performance of the photo-z estimation, to properly derive the associated uncertainties, and to produce both single-value solutions and PDFs. In addition, estimators are made available, which mitigate possible problems of non-representative or incomplete spectroscopic training samples. ANNz2 has already been used as part of the first weak lensing analysis of the Dark Energy Survey, and is included in the experiment's first public data release. Here we illustrate the functionality of the code using data from the tenth data release of the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. The code is available for download at http://github.com/IftachSadeh/ANNZ.

  7. Computer-Based Graphical Displays for Enhancing Mental Animation and Improving Reasoning in Novice Learning of Probability

    ERIC Educational Resources Information Center

    Kaplan, Danielle E.; Wu, Erin Chia-ling

    2006-01-01

    Our research suggests static and animated graphics can lead to more animated thinking and more correct problem solving in computer-based probability learning. Pilot software modules were developed for graduate online statistics courses and representation research. A study with novice graduate student statisticians compared problem solving in five…

  8. Development and Use of a Computer-Based Interactive Resource for Teaching and Learning Probability in Primary Classrooms

    ERIC Educational Resources Information Center

    Trigueros, Maria; Lozano, Maria Dolores; Lage, Ana Elisa

    2006-01-01

    "Enciclomedia" is a Mexican project for primary school teaching using computers in the classroom. Within this project, and following an enactivist theoretical perspective and methodology, we have designed a computer-based package called "Dados", which, together with teaching guides, is intended to support the teaching and learning of probability.…

  9. Using Rasch Analysis to Explore What Students Learn about Probability Concepts

    ERIC Educational Resources Information Center

    Mahmud, Zamalia; Porter, Anne

    2015-01-01

    Students' understanding of probability concepts have been investigated from various different perspectives. This study was set out to investigate perceived understanding of probability concepts of forty-four students from the STAT131 Understanding Uncertainty and Variation course at the University of Wollongong, NSW. Rasch measurement which is…

  10. Calibrating perceived understanding and competency in probability concepts: A diagnosis of learning difficulties based on Rasch probabilistic model

    NASA Astrophysics Data System (ADS)

    Mahmud, Zamalia; Porter, Anne; Salikin, Masniyati; Ghani, Nor Azura Md

    2015-12-01

    Students' understanding of probability concepts have been investigated from various different perspectives. Competency on the other hand is often measured separately in the form of test structure. This study was set out to show that perceived understanding and competency can be calibrated and assessed together using Rasch measurement tools. Forty-four students from the STAT131 Understanding Uncertainty and Variation course at the University of Wollongong, NSW have volunteered to participate in the study. Rasch measurement which is based on a probabilistic model is used to calibrate the responses from two survey instruments and investigate the interactions between them. Data were captured from the e-learning platform Moodle where students provided their responses through an online quiz. The study shows that majority of the students perceived little understanding about conditional and independent events prior to learning about it but tend to demonstrate a slightly higher competency level afterward. Based on the Rasch map, there is indication of some increase in learning and knowledge about some probability concepts at the end of the two weeks lessons on probability concepts.

  11. Value and probability coding in a feedback-based learning task utilizing food rewards.

    PubMed

    Tricomi, Elizabeth; Lempert, Karolina M

    2015-01-01

    For the consequences of our actions to guide behavior, the brain must represent different types of outcome-related information. For example, an outcome can be construed as negative because an expected reward was not delivered or because an outcome of low value was delivered. Thus behavioral consequences can differ in terms of the information they provide about outcome probability and value. We investigated the role of the striatum in processing probability-based and value-based negative feedback by training participants to associate cues with food rewards and then employing a selective satiety procedure to devalue one food outcome. Using functional magnetic resonance imaging, we examined brain activity related to receipt of expected rewards, receipt of devalued outcomes, omission of expected rewards, omission of devalued outcomes, and expected omissions of an outcome. Nucleus accumbens activation was greater for rewarding outcomes than devalued outcomes, but activity in this region did not correlate with the probability of reward receipt. Activation of the right caudate and putamen, however, was largest in response to rewarding outcomes relative to expected omissions of reward. The dorsal striatum (caudate and putamen) at the time of feedback also showed a parametric increase correlating with the trialwise probability of reward receipt. Our results suggest that the ventral striatum is sensitive to the motivational relevance, or subjective value, of the outcome, while the dorsal striatum codes for a more complex signal that incorporates reward probability. Value and probability information may be integrated in the dorsal striatum, to facilitate action planning and allocation of effort.

  12. Simulation of rat behavior by a reinforcement learning algorithm in consideration of appearance probabilities of reinforcement signals.

    PubMed

    Murakoshi, Kazushi; Noguchi, Takuya

    2005-04-01

    Brown and Wanger [Brown, R.T., Wanger, A.R., 1964. Resistance to punishment and extinction following training with shock or nonreinforcement. J. Exp. Psychol. 68, 503-507] investigated rat behaviors with the following features: (1) rats were exposed to reward and punishment at the same time, (2) environment changed and rats relearned, and (3) rats were stochastically exposed to reward and punishment. The results are that exposure to nonreinforcement produces resistance to the decremental effects of behavior after stochastic reward schedule and that exposure to both punishment and reinforcement produces resistance to the decremental effects of behavior after stochastic punishment schedule. This paper aims to simulate the rat behaviors by a reinforcement learning algorithm in consideration of appearance probabilities of reinforcement signals. The former algorithms of reinforcement learning were unable to simulate the behavior of the feature (3). We improve the former reinforcement learning algorithms by controlling learning parameters in consideration of the acquisition probabilities of reinforcement signals. The proposed algorithm qualitatively simulates the result of the animal experiment of Brown and Wanger. PMID:15740837

  13. Simulation of rat behavior by a reinforcement learning algorithm in consideration of appearance probabilities of reinforcement signals.

    PubMed

    Murakoshi, Kazushi; Noguchi, Takuya

    2005-04-01

    Brown and Wanger [Brown, R.T., Wanger, A.R., 1964. Resistance to punishment and extinction following training with shock or nonreinforcement. J. Exp. Psychol. 68, 503-507] investigated rat behaviors with the following features: (1) rats were exposed to reward and punishment at the same time, (2) environment changed and rats relearned, and (3) rats were stochastically exposed to reward and punishment. The results are that exposure to nonreinforcement produces resistance to the decremental effects of behavior after stochastic reward schedule and that exposure to both punishment and reinforcement produces resistance to the decremental effects of behavior after stochastic punishment schedule. This paper aims to simulate the rat behaviors by a reinforcement learning algorithm in consideration of appearance probabilities of reinforcement signals. The former algorithms of reinforcement learning were unable to simulate the behavior of the feature (3). We improve the former reinforcement learning algorithms by controlling learning parameters in consideration of the acquisition probabilities of reinforcement signals. The proposed algorithm qualitatively simulates the result of the animal experiment of Brown and Wanger.

  14. We Can Still Learn About Probability by Rolling Dice and Tossing Coins

    ERIC Educational Resources Information Center

    Dunn, Peter K.

    2005-01-01

    Rolling dice and tossing coins can still be used to teach probability even if students know (or think they know) what happens in these experiments. This article considers many simple variations of these experiments which are interesting, potentially enjoyable and challenging. Using these variations can cause students (and teachers) to think again…

  15. Learning in Reverse: Eight-Month-Old Infants Track Backward Transitional Probabilities

    ERIC Educational Resources Information Center

    Pelucchi, Bruna; Hay, Jessica F.; Saffran, Jenny R.

    2009-01-01

    Numerous recent studies suggest that human learners, including both infants and adults, readily track sequential statistics computed between adjacent elements. One such statistic, transitional probability, is typically calculated as the likelihood that one element predicts another. However, little is known about whether listeners are sensitive to…

  16. Mice plan decision strategies based on previously learned time intervals, locations, and probabilities.

    PubMed

    Tosun, Tuğçe; Gür, Ezgi; Balcı, Fuat

    2016-01-19

    Animals can shape their timed behaviors based on experienced probabilistic relations in a nearly optimal fashion. On the other hand, it is not clear if they adopt these timed decisions by making computations based on previously learnt task parameters (time intervals, locations, and probabilities) or if they gradually develop their decisions based on trial and error. To address this question, we tested mice in the timed-switching task, which required them to anticipate when (after a short or long delay) and at which of the two delay locations a reward would be presented. The probability of short trials differed between test groups in two experiments. Critically, we first trained mice on relevant task parameters by signaling the active trial with a discriminative stimulus and delivered the corresponding reward after the associated delay without any response requirement (without inducing switching behavior). During the test phase, both options were presented simultaneously to characterize the emergence and temporal characteristics of the switching behavior. Mice exhibited timed-switching behavior starting from the first few test trials, and their performance remained stable throughout testing in the majority of the conditions. Furthermore, as the probability of the short trial increased, mice waited longer before switching from the short to long location (experiment 1). These behavioral adjustments were in directions predicted by reward maximization. These results suggest that rather than gradually adjusting their time-dependent choice behavior, mice abruptly adopted temporal decision strategies by directly integrating their previous knowledge of task parameters into their timed behavior, supporting the model-based representational account of temporal risk assessment. PMID:26733674

  17. Unification of field theory and maximum entropy methods for learning probability densities.

    PubMed

    Kinney, Justin B

    2015-09-01

    The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

  18. The Influence of Part-Word Phonotactic Probability/Neighborhood Density on Word Learning by Preschool Children Varying in Expressive Vocabulary

    ERIC Educational Resources Information Center

    Storkel, Holly L.; Hoover, Jill R.

    2011-01-01

    The goal of this study was to examine the influence of part-word phonotactic probability/neighborhood density on word learning by preschool children with normal vocabularies that varied in size. Ninety-eight children (age 2 ; 11-6 ; 0) were taught consonant-vowel-consonant (CVC) nonwords orthogonally varying in the probability/density of the CV…

  19. A Study of Students' Learning Styles, Discipline Attitudes and Knowledge Acquisition in Technology-Enhanced Probability and Statistics Education.

    PubMed

    Christou, Nicolas; Dinov, Ivo D

    2010-09-01

    Many modern technological advances have direct impact on the format, style and efficacy of delivery and consumption of educational content. For example, various novel communication and information technology tools and resources enable efficient, timely, interactive and graphical demonstrations of diverse scientific concepts. In this manuscript, we report on a meta-study of 3 controlled experiments of using the Statistics Online Computational Resources in probability and statistics courses. Web-accessible SOCR applets, demonstrations, simulations and virtual experiments were used in different courses as treatment and compared to matched control classes utilizing traditional pedagogical approaches. Qualitative and quantitative data we collected for all courses included Felder-Silverman-Soloman index of learning styles, background assessment, pre and post surveys of attitude towards the subject, end-point satisfaction survey, and varieties of quiz, laboratory and test scores. Our findings indicate that students' learning styles and attitudes towards a discipline may be important confounds of their final quantitative performance. The observed positive effects of integrating information technology with established pedagogical techniques may be valid across disciplines within the broader spectrum courses in the science education curriculum. The two critical components of improving science education via blended instruction include instructor training, and development of appropriate activities, simulations and interactive resources.

  20. The influence of part-word phonotactic probability/neighborhood density on word learning by preschool children varying in expressive vocabulary.

    PubMed

    Storkel, Holly L; Hoover, Jill R

    2011-06-01

    The goal of this study was to examine the influence of part-word phonotactic probability/neighborhood density on word learning by preschool children with normal vocabularies that varied in size. Ninety-eight children (age 2 ; 11-6 ; 0) were taught consonant-vowel-consonant (CVC) nonwords orthogonally varying in the probability/density of the CV (i.e. body) and VC (i.e. rhyme). Learning was measured via picture naming. Children with the lowest expressive vocabulary scores showed no effect of either CV or VC probability/density, although floor effects could not be ruled out. In contrast, children with low or high expressive vocabulary scores demonstrated sensitivity to part-word probability/density with the nature of the effect varying by group. Children with the highest expressive vocabulary scores displayed yet a third pattern of part-word probability/density effects. Taken together, word learning by preschool children was influenced by part-word probability/density but the nature of this influence appeared to depend on the size of the lexicon.

  1. Effect of Phonotactic Probability and Neighborhood Density on Word-Learning Configuration by Preschoolers with Typical Development and Specific Language Impairment

    ERIC Educational Resources Information Center

    Gray, Shelley; Pittman, Andrea; Weinhold, Juliet

    2014-01-01

    Purpose: In this study, the authors assessed the effects of phonotactic probability and neighborhood density on word-learning configuration by preschoolers with specific language impairment (SLI) and typical language development (TD). Method: One hundred thirty-one children participated: 48 with SLI, 44 with TD matched on age and gender, and 39…

  2. Induced Probabilities.

    ERIC Educational Resources Information Center

    Neel, John H.

    Induced probabilities have been largely ignored by educational researchers. Simply stated, if a new or random variable is defined in terms of a first random variable, then induced probability is the probability or density of the new random variable that can be found by summation or integration over the appropriate domains of the original random…

  3. Probability Theory

    NASA Astrophysics Data System (ADS)

    Jaynes, E. T.; Bretthorst, G. Larry

    2003-04-01

    Foreword; Preface; Part I. Principles and Elementary Applications: 1. Plausible reasoning; 2. The quantitative rules; 3. Elementary sampling theory; 4. Elementary hypothesis testing; 5. Queer uses for probability theory; 6. Elementary parameter estimation; 7. The central, Gaussian or normal distribution; 8. Sufficiency, ancillarity, and all that; 9. Repetitive experiments, probability and frequency; 10. Physics of 'random experiments'; Part II. Advanced Applications: 11. Discrete prior probabilities, the entropy principle; 12. Ignorance priors and transformation groups; 13. Decision theory: historical background; 14. Simple applications of decision theory; 15. Paradoxes of probability theory; 16. Orthodox methods: historical background; 17. Principles and pathology of orthodox statistics; 18. The Ap distribution and rule of succession; 19. Physical measurements; 20. Model comparison; 21. Outliers and robustness; 22. Introduction to communication theory; References; Appendix A. Other approaches to probability theory; Appendix B. Mathematical formalities and style; Appendix C. Convolutions and cumulants.

  4. Word learning, phonological short-term memory, phonotactic probability and long-term memory: towards an integrated framework

    PubMed Central

    Gupta, Prahlad; Tisdale, Jamie

    2009-01-01

    Word learning is studied in a multitude of ways, and it is often not clear what the relationship is between different phenomena. In this article, we begin by outlining a very simple functional framework that despite its simplicity can serve as a useful organizing scheme for thinking about various types of studies of word learning. We then review a number of themes that in recent years have emerged as important topics in the study of word learning, and relate them to the functional framework, noting nevertheless that these topics have tended to be somewhat separate areas of study. In the third part of the article, we describe a recent computational model and discuss how it offers a framework that can integrate and relate these various topics in word learning to each other. We conclude that issues that have typically been studied as separate topics can perhaps more fruitfully be thought of as closely integrated, with the present framework offering several suggestions about the nature of such integration. PMID:19933144

  5. Probability workshop to be better in probability topic

    NASA Astrophysics Data System (ADS)

    Asmat, Aszila; Ujang, Suriyati; Wahid, Sharifah Norhuda Syed

    2015-02-01

    The purpose of the present study was to examine whether statistics anxiety and attitudes towards probability topic among students in higher education level have an effect on their performance. 62 fourth semester science students were given statistics anxiety questionnaires about their perception towards probability topic. Result indicated that students' performance in probability topic is not related to anxiety level, which means that the higher level in statistics anxiety will not cause lower score in probability topic performance. The study also revealed that motivated students gained from probability workshop ensure that their performance in probability topic shows a positive improvement compared before the workshop. In addition there exists a significance difference in students' performance between genders with better achievement among female students compared to male students. Thus, more initiatives in learning programs with different teaching approaches is needed to provide useful information in improving student learning outcome in higher learning institution.

  6. Adapting machine learning techniques to censored time-to-event health record data: A general-purpose approach using inverse probability of censoring weighting.

    PubMed

    Vock, David M; Wolfson, Julian; Bandyopadhyay, Sunayan; Adomavicius, Gediminas; Johnson, Paul E; Vazquez-Benitez, Gabriela; O'Connor, Patrick J

    2016-06-01

    Models for predicting the probability of experiencing various health outcomes or adverse events over a certain time frame (e.g., having a heart attack in the next 5years) based on individual patient characteristics are important tools for managing patient care. Electronic health data (EHD) are appealing sources of training data because they provide access to large amounts of rich individual-level data from present-day patient populations. However, because EHD are derived by extracting information from administrative and clinical databases, some fraction of subjects will not be under observation for the entire time frame over which one wants to make predictions; this loss to follow-up is often due to disenrollment from the health system. For subjects without complete follow-up, whether or not they experienced the adverse event is unknown, and in statistical terms the event time is said to be right-censored. Most machine learning approaches to the problem have been relatively ad hoc; for example, common approaches for handling observations in which the event status is unknown include (1) discarding those observations, (2) treating them as non-events, (3) splitting those observations into two observations: one where the event occurs and one where the event does not. In this paper, we present a general-purpose approach to account for right-censored outcomes using inverse probability of censoring weighting (IPCW). We illustrate how IPCW can easily be incorporated into a number of existing machine learning algorithms used to mine big health care data including Bayesian networks, k-nearest neighbors, decision trees, and generalized additive models. We then show that our approach leads to better calibrated predictions than the three ad hoc approaches when applied to predicting the 5-year risk of experiencing a cardiovascular adverse event, using EHD from a large U.S. Midwestern healthcare system.

  7. Adapting machine learning techniques to censored time-to-event health record data: A general-purpose approach using inverse probability of censoring weighting.

    PubMed

    Vock, David M; Wolfson, Julian; Bandyopadhyay, Sunayan; Adomavicius, Gediminas; Johnson, Paul E; Vazquez-Benitez, Gabriela; O'Connor, Patrick J

    2016-06-01

    Models for predicting the probability of experiencing various health outcomes or adverse events over a certain time frame (e.g., having a heart attack in the next 5years) based on individual patient characteristics are important tools for managing patient care. Electronic health data (EHD) are appealing sources of training data because they provide access to large amounts of rich individual-level data from present-day patient populations. However, because EHD are derived by extracting information from administrative and clinical databases, some fraction of subjects will not be under observation for the entire time frame over which one wants to make predictions; this loss to follow-up is often due to disenrollment from the health system. For subjects without complete follow-up, whether or not they experienced the adverse event is unknown, and in statistical terms the event time is said to be right-censored. Most machine learning approaches to the problem have been relatively ad hoc; for example, common approaches for handling observations in which the event status is unknown include (1) discarding those observations, (2) treating them as non-events, (3) splitting those observations into two observations: one where the event occurs and one where the event does not. In this paper, we present a general-purpose approach to account for right-censored outcomes using inverse probability of censoring weighting (IPCW). We illustrate how IPCW can easily be incorporated into a number of existing machine learning algorithms used to mine big health care data including Bayesian networks, k-nearest neighbors, decision trees, and generalized additive models. We then show that our approach leads to better calibrated predictions than the three ad hoc approaches when applied to predicting the 5-year risk of experiencing a cardiovascular adverse event, using EHD from a large U.S. Midwestern healthcare system. PMID:26992568

  8. What is Learned in Probability Learning

    ERIC Educational Resources Information Center

    Sullivan, Frank J.; Ross, Bruce M.

    1970-01-01

    Examines Weir's hypothesis of a U-shaped relationship between age and terminal level of correct responding; studies use of alternation patterning as a response strategy; investigates extent to which immediate reinforcement controlled the subjects' choices. The results reported here are based on part of a doctoral dissertation submitted by the…

  9. Probability 1/e

    ERIC Educational Resources Information Center

    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.

  10. On Probability Domains III

    NASA Astrophysics Data System (ADS)

    Frič, Roman; Papčo, Martin

    2015-12-01

    Domains of generalized probability have been introduced in order to provide a general construction of random events, observables and states. It is based on the notion of a cogenerator and the properties of product. We continue our previous study and show how some other quantum structures fit our categorical approach. We discuss how various epireflections implicitly used in the classical probability theory are related to the transition to fuzzy probability theory and describe the latter probability theory as a genuine categorical extension of the former. We show that the IF-probability can be studied via the fuzzy probability theory. We outline a "tensor modification" of the fuzzy probability theory.

  11. The Role of Cooperative Learning Type Team Assisted Individualization to Improve the Students' Mathematics Communication Ability in the Subject of Probability Theory

    ERIC Educational Resources Information Center

    Tinungki, Georgina Maria

    2015-01-01

    The importance of learning mathematics can not be separated from its role in all aspects of life. Communicating ideas by using mathematics language is even more practical, systematic, and efficient. In order to overcome the difficulties of students who have insufficient understanding of mathematics material, good communications should be built in…

  12. Probability on a Budget.

    ERIC Educational Resources Information Center

    Ewbank, William A.; Ginther, John L.

    2002-01-01

    Describes how to use common dice numbered 1-6 for simple mathematical situations including probability. Presents a lesson using regular dice and specially marked dice to explore some of the concepts of probability. (KHR)

  13. Is quantum probability rational?

    PubMed

    Houston, Alasdair I; Wiesner, Karoline

    2013-06-01

    We concentrate on two aspects of the article by Pothos & Busemeyer (P&B): the relationship between classical and quantum probability and quantum probability as a basis for rational decisions. We argue that the mathematical relationship between classical and quantum probability is not quite what the authors claim. Furthermore, it might be premature to regard quantum probability as the best practical rational scheme for decision making.

  14. Predicted probabilities' relationship to inclusion probabilities.

    PubMed

    Fang, Di; Chong, Jenny; Wilson, Jeffrey R

    2015-05-01

    It has been shown that under a general multiplicative intercept model for risk, case-control (retrospective) data can be analyzed by maximum likelihood as if they had arisen prospectively, up to an unknown multiplicative constant, which depends on the relative sampling fraction. (1) With suitable auxiliary information, retrospective data can also be used to estimate response probabilities. (2) In other words, predictive probabilities obtained without adjustments from retrospective data will likely be different from those obtained from prospective data. We highlighted this using binary data from Medicare to determine the probability of readmission into the hospital within 30 days of discharge, which is particularly timely because Medicare has begun penalizing hospitals for certain readmissions. (3).

  15. Racing To Understand Probability.

    ERIC Educational Resources Information Center

    Van Zoest, Laura R.; Walker, Rebecca K.

    1997-01-01

    Describes a series of lessons designed to supplement textbook instruction of probability by addressing the ideas of "equally likely,""not equally likely," and "fairness," as well as to introduce the difference between theoretical and experimental probability. Presents four lessons using The Wind Racer games to study probability. (ASK)

  16. Dependent Probability Spaces

    ERIC Educational Resources Information Center

    Edwards, William F.; Shiflett, Ray C.; Shultz, Harris

    2008-01-01

    The mathematical model used to describe independence between two events in probability has a non-intuitive consequence called dependent spaces. The paper begins with a very brief history of the development of probability, then defines dependent spaces, and reviews what is known about finite spaces with uniform probability. The study of finite…

  17. Searching with probabilities

    SciTech Connect

    Palay, A.J.

    1985-01-01

    This book examines how probability distributions can be used as a knowledge representation technique. It presents a mechanism that can be used to guide a selective search algorithm to solve a variety of tactical chess problems. Topics covered include probabilities and searching the B algorithm and chess probabilities - in practice, examples, results, and future work.

  18. In All Probability, Probability is not All

    ERIC Educational Resources Information Center

    Helman, Danny

    2004-01-01

    The national lottery is often portrayed as a game of pure chance with no room for strategy. This misperception seems to stem from the application of probability instead of expectancy considerations, and can be utilized to introduce the statistical concept of expectation.

  19. Probability of satellite collision

    NASA Technical Reports Server (NTRS)

    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.

  20. Normal tissue complication probability (NTCP) modelling using spatial dose metrics and machine learning methods for severe acute oral mucositis resulting from head and neck radiotherapy

    PubMed Central

    Dean, Jamie A; Wong, Kee H; Welsh, Liam C; Jones, Ann-Britt; Schick, Ulrike; Newbold, Kate L; Bhide, Shreerang A; Harrington, Kevin J; Nutting, Christopher M; Gulliford, Sarah L

    2016-01-01

    Background and Purpose Severe acute mucositis commonly results from head and neck (chemo)radiotherapy. A predictive model of mucositis could guide clinical decision-making and inform treatment planning. We aimed to generate such a model using spatial dose metrics and machine learning. Material and Methods Predictive models of severe acute mucositis were generated using radiotherapy dose (dose-volume and spatial dose metrics) and clinical data. Penalised logistic regression, support vector classification and random forest classification (RFC) models were generated and compared. Internal validation was performed (with 100-iteration cross-validation), using multiple metrics, including area under the receiver operating characteristic curve (AUC) and calibration slope, to assess performance. Associations between covariates and severe mucositis were explored using the models. Results The dose-volume-based models (standard) performed equally to those incorporating spatial information. Discrimination was similar between models, but the RFCstandard had the best calibration. The mean AUC and calibration slope for this model were 0.71 (s.d.=0.09) and 3.9 (s.d.=2.2), respectively. The volumes of oral cavity receiving intermediate and high doses were associated with severe mucositis. Conclusions The RFCstandard model performance is modest-to-good, but should be improved, and requires external validation. Reducing the volumes of oral cavity receiving intermediate and high doses may reduce mucositis incidence. PMID:27240717

  1. Probability, statistics, and computational science.

    PubMed

    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.

  2. A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

    ERIC Educational Resources Information Center

    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…

  3. Estimation of State Transition Probabilities: A Neural Network Model

    NASA Astrophysics Data System (ADS)

    Saito, Hiroshi; Takiyama, Ken; Okada, Masato

    2015-12-01

    Humans and animals can predict future states on the basis of acquired knowledge. This prediction of the state transition is important for choosing the best action, and the prediction is only possible if the state transition probability has already been learned. However, how our brains learn the state transition probability is unknown. Here, we propose a simple algorithm for estimating the state transition probability by utilizing the state prediction error. We analytically and numerically confirmed that our algorithm is able to learn the probability completely with an appropriate learning rate. Furthermore, our learning rule reproduced experimentally reported psychometric functions and neural activities in the lateral intraparietal area in a decision-making task. Thus, our algorithm might describe the manner in which our brains learn state transition probabilities and predict future states.

  4. Abstract Models of Probability

    NASA Astrophysics Data System (ADS)

    Maximov, V. M.

    2001-12-01

    Probability theory presents a mathematical formalization of intuitive ideas of independent events and a probability as a measure of randomness. It is based on axioms 1-5 of A.N. Kolmogorov 1 and their generalizations 2. Different formalized refinements were proposed for such notions as events, independence, random value etc., 2,3, whereas the measure of randomness, i.e. numbers from [0,1], remained unchanged. To be precise we mention some attempts of generalization of the probability theory with negative probabilities 4. From another side the physicists tryed to use the negative and even complex values of probability to explain some paradoxes in quantum mechanics 5,6,7. Only recently, the necessity of formalization of quantum mechanics and their foundations 8 led to the construction of p-adic probabilities 9,10,11, which essentially extended our concept of probability and randomness. Therefore, a natural question arises how to describe algebraic structures whose elements can be used as a measure of randomness. As consequence, a necessity arises to define the types of randomness corresponding to every such algebraic structure. Possibly, this leads to another concept of randomness that has another nature different from combinatorical - metric conception of Kolmogorov. Apparenly, discrepancy of real type of randomness corresponding to some experimental data lead to paradoxes, if we use another model of randomness for data processing 12. Algebraic structure whose elements can be used to estimate some randomness will be called a probability set Φ. Naturally, the elements of Φ are the probabilities.

  5. Probability with Roulette

    ERIC Educational Resources Information Center

    Marshall, Jennings B.

    2007-01-01

    This article describes how roulette can be used to teach basic concepts of probability. Various bets are used to illustrate the computation of expected value. A betting system shows variations in patterns that often appear in random events.

  6. Quantum computing and probability.

    PubMed

    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.

  7. Launch Collision Probability

    NASA Technical Reports Server (NTRS)

    Bollenbacher, Gary; Guptill, James D.

    1999-01-01

    This report analyzes the probability of a launch vehicle colliding with one of the nearly 10,000 tracked objects orbiting the Earth, given that an object on a near-collision course with the launch vehicle has been identified. Knowledge of the probability of collision throughout the launch window can be used to avoid launching at times when the probability of collision is unacceptably high. The analysis in this report assumes that the positions of the orbiting objects and the launch vehicle can be predicted as a function of time and therefore that any tracked object which comes close to the launch vehicle can be identified. The analysis further assumes that the position uncertainty of the launch vehicle and the approaching space object can be described with position covariance matrices. With these and some additional simplifying assumptions, a closed-form solution is developed using two approaches. The solution shows that the probability of collision is a function of position uncertainties, the size of the two potentially colliding objects, and the nominal separation distance at the point of closest approach. ne impact of the simplifying assumptions on the accuracy of the final result is assessed and the application of the results to the Cassini mission, launched in October 1997, is described. Other factors that affect the probability of collision are also discussed. Finally, the report offers alternative approaches that can be used to evaluate the probability of collision.

  8. Experimental Probability in Elementary School

    ERIC Educational Resources Information Center

    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.

  9. Univariate Probability Distributions

    ERIC Educational Resources Information Center

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

    2012-01-01

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

  10. Approximating Integrals Using Probability

    ERIC Educational Resources Information Center

    Maruszewski, Richard F., Jr.; Caudle, Kyle A.

    2005-01-01

    As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

  11. A Unifying Probability Example.

    ERIC Educational Resources Information Center

    Maruszewski, Richard F., Jr.

    2002-01-01

    Presents an example from probability and statistics that ties together several topics including the mean and variance of a discrete random variable, the binomial distribution and its particular mean and variance, the sum of independent random variables, the mean and variance of the sum, and the central limit theorem. Uses Excel to illustrate these…

  12. Probability & Perception: The Representativeness Heuristic in Action

    ERIC Educational Resources Information Center

    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®…

  13. On Probability Domains

    NASA Astrophysics Data System (ADS)

    Frič, Roman; Papčo, Martin

    2010-12-01

    Motivated by IF-probability theory (intuitionistic fuzzy), we study n-component probability domains in which each event represents a body of competing components and the range of a state represents a simplex S n of n-tuples of possible rewards-the sum of the rewards is a number from [0,1]. For n=1 we get fuzzy events, for example a bold algebra, and the corresponding fuzzy probability theory can be developed within the category ID of D-posets (equivalently effect algebras) of fuzzy sets and sequentially continuous D-homomorphisms. For n=2 we get IF-events, i.e., pairs ( μ, ν) of fuzzy sets μ, ν∈[0,1] X such that μ( x)+ ν( x)≤1 for all x∈ X, but we order our pairs (events) coordinatewise. Hence the structure of IF-events (where ( μ 1, ν 1)≤( μ 2, ν 2) whenever μ 1≤ μ 2 and ν 2≤ ν 1) is different and, consequently, the resulting IF-probability theory models a different principle. The category ID is cogenerated by I=[0,1] (objects of ID are subobjects of powers I X ), has nice properties and basic probabilistic notions and constructions are categorical. For example, states are morphisms. We introduce the category S n D cogenerated by Sn=\\{(x1,x2,ldots ,xn)in In;sum_{i=1}nxi≤ 1\\} carrying the coordinatewise partial order, difference, and sequential convergence and we show how basic probability notions can be defined within S n D.

  14. Bayesian Probability Theory

    NASA Astrophysics Data System (ADS)

    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.

  15. Fractal probability laws.

    PubMed

    Eliazar, Iddo; Klafter, Joseph

    2008-06-01

    We explore six classes of fractal probability laws defined on the positive half-line: Weibull, Frechét, Lévy, hyper Pareto, hyper beta, and hyper shot noise. Each of these classes admits a unique statistical power-law structure, and is uniquely associated with a certain operation of renormalization. All six classes turn out to be one-dimensional projections of underlying Poisson processes which, in turn, are the unique fixed points of Poissonian renormalizations. The first three classes correspond to linear Poissonian renormalizations and are intimately related to extreme value theory (Weibull, Frechét) and to the central limit theorem (Lévy). The other three classes correspond to nonlinear Poissonian renormalizations. Pareto's law--commonly perceived as the "universal fractal probability distribution"--is merely a special case of the hyper Pareto class.

  16. Waste Package Misload Probability

    SciTech Connect

    J.K. Knudsen

    2001-11-20

    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.

  17. Learning.

    ERIC Educational Resources Information Center

    Glaser, Robert

    A report on learning psychology and its relationship to the study of school learning emphasizes the increasing interaction between theorists and educational practitioners, particularly in attempting to learn which variables influence the instructional process and to find an appropriate methodology to measure and evaluate learning. "Learning…

  18. Nucleosomes, transcription, and probability

    PubMed Central

    Boeger, Hinrich

    2014-01-01

    Speaking of current measurements on single ion channel molecules, David Colquhoun wrote in 2006, “Individual molecules behave randomly, so suddenly we had to learn how to deal with stochastic processes.” Here I describe theoretical efforts to understand recent experimental observations on the chromatin structure of single gene molecules, a molecular biologist's path toward probabilistic theories. PMID:25368419

  19. Regional flood probabilities

    USGS Publications Warehouse

    Troutman, B.M.; Karlinger, M.R.

    2003-01-01

    The T-year annual maximum flood at a site is defined to be that streamflow, that has probability 1/T of being exceeded in any given year, and for a group of sites the corresponding regional flood probability (RFP) is the probability that at least one site will experience a T-year flood in any given year. The RFP depends on the number of sites of interest and on the spatial correlation of flows among the sites. We present a Monte Carlo method for obtaining the RFP and demonstrate that spatial correlation estimates used in this method may be obtained with rank transformed data and therefore that knowledge of the at-site peak flow distribution is not necessary. We examine the extent to which the estimates depend on specification of a parametric form for the spatial correlation function, which is known to be nonstationary for peak flows. It is shown in a simulation study that use of a stationary correlation function to compute RFPs yields satisfactory estimates for certain nonstationary processes. Application of asymptotic extreme value theory is examined, and a methodology for separating channel network and rainfall effects on RFPs is suggested. A case study is presented using peak flow data from the state of Washington. For 193 sites in the Puget Sound region it is estimated that a 100-year flood will occur on the average every 4,5 years.

  20. Stimulus probability effects in absolute identification.

    PubMed

    Kent, Christopher; Lamberts, Koen

    2016-05-01

    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 presentation probability on both proportion correct and response times. The effects were moderated by the ubiquitous stimulus position effect. The accuracy and response time data were predicted by an exemplar-based model of perceptual cognition (Kent & Lamberts, 2005). The bow in discriminability was also attenuated when presentation probability for middle items was relatively high, an effect that will constrain future model development. The study provides evidence for item-specific learning in absolute identification. Implications for other theories of absolute identification are discussed. (PsycINFO Database Record

  1. Seismicity alert probabilities at Parkfield, California, revisited

    USGS Publications Warehouse

    Michael, A.J.; Jones, L.M.

    1998-01-01

    For a decade, the US Geological Survey has used the Parkfield Earthquake Prediction Experiment scenario document to estimate the probability that earthquakes observed on the San Andreas fault near Parkfield will turn out to be foreshocks followed by the expected magnitude six mainshock. During this time, we have learned much about the seismogenic process at Parkfield, about the long-term probability of the Parkfield mainshock, and about the estimation of these types of probabilities. The probabilities for potential foreshocks at Parkfield are reexamined and revised in light of these advances. As part of this process, we have confirmed both the rate of foreshocks before strike-slip earthquakes in the San Andreas physiographic province and the uniform distribution of foreshocks with magnitude proposed by earlier studies. Compared to the earlier assessment, these new estimates of the long-term probability of the Parkfield mainshock are lower, our estimate of the rate of background seismicity is higher, and we find that the assumption that foreshocks at Parkfield occur in a unique way is not statistically significant at the 95% confidence level. While the exact numbers vary depending on the assumptions that are made, the new alert probabilities are lower than previously estimated. Considering the various assumptions and the statistical uncertainties in the input parameters, we also compute a plausible range for the probabilities. The range is large, partly due to the extra knowledge that exists for the Parkfield segment, making us question the usefulness of these numbers.

  2. Emptiness Formation Probability

    NASA Astrophysics Data System (ADS)

    Crawford, Nicholas; Ng, Stephen; Starr, Shannon

    2016-08-01

    We present rigorous upper and lower bounds on the emptiness formation probability for the ground state of a spin-1/2 Heisenberg XXZ quantum spin system. For a d-dimensional system we find a rate of decay of the order {exp(-c L^{d+1})} where L is the sidelength of the box in which we ask for the emptiness formation event to occur. In the {d=1} case this confirms previous predictions made in the integrable systems community, though our bounds do not achieve the precision predicted by Bethe ansatz calculations. On the other hand, our bounds in the case {d ≥ 2} are new. The main tools we use are reflection positivity and a rigorous path integral expansion, which is a variation on those previously introduced by Toth, Aizenman-Nachtergaele and Ueltschi.

  3. People's conditional probability judgments follow probability theory (plus noise).

    PubMed

    Costello, Fintan; Watts, Paul

    2016-09-01

    A common view in current psychology is that people estimate probabilities using various 'heuristics' or rules of thumb that do not follow the normative rules of probability theory. We present a model where people estimate conditional probabilities such as P(A|B) (the probability of A given that B has occurred) by a process that follows standard frequentist probability theory but is subject to random noise. This model accounts for various results from previous studies of conditional probability judgment. This model predicts that people's conditional probability judgments will agree with a series of fundamental identities in probability theory whose form cancels the effect of noise, while deviating from probability theory in other expressions whose form does not allow such cancellation. Two experiments strongly confirm these predictions, with people's estimates on average agreeing with probability theory for the noise-cancelling identities, but deviating from probability theory (in just the way predicted by the model) for other identities. This new model subsumes an earlier model of unconditional or 'direct' probability judgment which explains a number of systematic biases seen in direct probability judgment (Costello & Watts, 2014). This model may thus provide a fully general account of the mechanisms by which people estimate probabilities.

  4. People's conditional probability judgments follow probability theory (plus noise).

    PubMed

    Costello, Fintan; Watts, Paul

    2016-09-01

    A common view in current psychology is that people estimate probabilities using various 'heuristics' or rules of thumb that do not follow the normative rules of probability theory. We present a model where people estimate conditional probabilities such as P(A|B) (the probability of A given that B has occurred) by a process that follows standard frequentist probability theory but is subject to random noise. This model accounts for various results from previous studies of conditional probability judgment. This model predicts that people's conditional probability judgments will agree with a series of fundamental identities in probability theory whose form cancels the effect of noise, while deviating from probability theory in other expressions whose form does not allow such cancellation. Two experiments strongly confirm these predictions, with people's estimates on average agreeing with probability theory for the noise-cancelling identities, but deviating from probability theory (in just the way predicted by the model) for other identities. This new model subsumes an earlier model of unconditional or 'direct' probability judgment which explains a number of systematic biases seen in direct probability judgment (Costello & Watts, 2014). This model may thus provide a fully general account of the mechanisms by which people estimate probabilities. PMID:27570097

  5. Familiarity and preference for pitch probability profiles.

    PubMed

    Cui, Anja-Xiaoxing; Collett, Meghan J; Troje, Niko F; Cuddy, Lola L

    2015-05-01

    We investigated familiarity and preference judgments of participants toward a novel musical system. We exposed participants to tone sequences generated from a novel pitch probability profile. Afterward, we either asked participants to identify more familiar or we asked participants to identify preferred tone sequences in a two-alternative forced-choice task. The task paired a tone sequence generated from the pitch probability profile they had been exposed to and a tone sequence generated from another pitch probability profile at three levels of distinctiveness. We found that participants identified tone sequences as more familiar if they were generated from the same pitch probability profile which they had been exposed to. However, participants did not prefer these tone sequences. We interpret this relationship between familiarity and preference to be consistent with an inverted U-shaped relationship between knowledge and affect. The fact that participants identified tone sequences as even more familiar if they were generated from the more distinctive (caricatured) version of the pitch probability profile which they had been exposed to suggests that the statistical learning of the pitch probability profile is involved in gaining of musical knowledge. PMID:25838257

  6. Probability distributions for magnetotellurics

    SciTech Connect

    Stodt, John A.

    1982-11-01

    Estimates of the magnetotelluric transfer functions can be viewed as ratios of two complex random variables. It is assumed that the numerator and denominator are governed approximately by a joint complex normal distribution. Under this assumption, probability distributions are obtained for the magnitude, squared magnitude, logarithm of the squared magnitude, and the phase of the estimates. Normal approximations to the distributions are obtained by calculating mean values and variances from error propagation, and the distributions are plotted with their normal approximations for different percentage errors in the numerator and denominator of the estimates, ranging from 10% to 75%. The distribution of the phase is approximated well by a normal distribution for the range of errors considered, while the distribution of the logarithm of the squared magnitude is approximated by a normal distribution for a much larger range of errors than is the distribution of the squared magnitude. The distribution of the squared magnitude is most sensitive to the presence of noise in the denominator of the estimate, in which case the true distribution deviates significantly from normal behavior as the percentage errors exceed 10%. In contrast, the normal approximation to the distribution of the logarithm of the magnitude is useful for errors as large as 75%.

  7. A "Virtual Spin" on the Teaching of Probability

    ERIC Educational Resources Information Center

    Beck, Shari A.; Huse, Vanessa E.

    2007-01-01

    This article, which describes integrating virtual manipulatives with the teaching of probability at the elementary level, puts a "virtual spin" on the teaching of probability to provide more opportunities for students to experience successful learning. The traditional use of concrete manipulatives is enhanced with virtual coins and spinners from…

  8. Visualizing and Understanding Probability and Statistics: Graphical Simulations Using Excel

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.; Gordon, Florence S.

    2009-01-01

    The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…

  9. A Tale of Two Probabilities

    ERIC Educational Resources Information Center

    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.

  10. The Probability of Causal Conditionals

    ERIC Educational Resources Information Center

    Over, David E.; Hadjichristidis, Constantinos; Evans, Jonathan St. B. T.; Handley, Simon J.; Sloman, Steven A.

    2007-01-01

    Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q [such that] p). We report three experiments on…

  11. Unders and Overs: Using a Dice Game to Illustrate Basic Probability Concepts

    ERIC Educational Resources Information Center

    McPherson, Sandra Hanson

    2015-01-01

    In this paper, the dice game "Unders and Overs" is described and presented as an active learning exercise to introduce basic probability concepts. The implementation of the exercise is outlined and the resulting presentation of various probability concepts are described.

  12. Propensity, Probability, and Quantum Theory

    NASA Astrophysics Data System (ADS)

    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.

  13. PROBABILITY SURVEYS, CONDITIONAL PROBABILITIES, AND ECOLOGICAL RISK ASSESSMENT

    EPA Science Inventory

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

  14. PROBABILITY SURVEYS , CONDITIONAL PROBABILITIES AND ECOLOGICAL RISK ASSESSMENT

    EPA Science Inventory

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

  15. Probability Surveys, Conditional Probability, and Ecological Risk Assessment

    EPA Science Inventory

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

  16. The relationship between species detection probability and local extinction probability

    USGS Publications Warehouse

    Alpizar-Jara, R.; Nichols, J.D.; Hines, J.E.; Sauer, J.R.; Pollock, K.H.; Rosenberry, C.S.

    2004-01-01

    In community-level ecological studies, generally not all species present in sampled areas are detected. Many authors have proposed the use of estimation methods that allow detection probabilities that are <1 and that are heterogeneous among species. These methods can also be used to estimate community-dynamic parameters such as species local extinction probability and turnover rates (Nichols et al. Ecol Appl 8:1213-1225; Conserv Biol 12:1390-1398). Here, we present an ad hoc approach to estimating community-level vital rates in the presence of joint heterogeneity of detection probabilities and vital rates. The method consists of partitioning the number of species into two groups using the detection frequencies and then estimating vital rates (e.g., local extinction probabilities) for each group. Estimators from each group are combined in a weighted estimator of vital rates that accounts for the effect of heterogeneity. Using data from the North American Breeding Bird Survey, we computed such estimates and tested the hypothesis that detection probabilities and local extinction probabilities were negatively related. Our analyses support the hypothesis that species detection probability covaries negatively with local probability of extinction and turnover rates. A simulation study was conducted to assess the performance of vital parameter estimators as well as other estimators relevant to questions about heterogeneity, such as coefficient of variation of detection probabilities and proportion of species in each group. Both the weighted estimator suggested in this paper and the original unweighted estimator for local extinction probability performed fairly well and provided no basis for preferring one to the other.

  17. Probability Interpretation of Quantum Mechanics.

    ERIC Educational Resources Information Center

    Newton, Roger G.

    1980-01-01

    This paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the "paradoxical" aspects of quantum mechanics lose their counterintuitive character.…

  18. The Probabilities of Conditionals Revisited

    ERIC Educational Resources Information Center

    Douven, Igor; Verbrugge, Sara

    2013-01-01

    According to what is now commonly referred to as "the Equation" in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of…

  19. Minimizing the probable maximum flood

    SciTech Connect

    Woodbury, M.S.; Pansic, N. ); Eberlein, D.T. )

    1994-06-01

    This article examines Wisconsin Electric Power Company's efforts to determine an economical way to comply with Federal Energy Regulatory Commission requirements at two hydroelectric developments on the Michigamme River. Their efforts included refinement of the area's probable maximum flood model based, in part, on a newly developed probable maximum precipitation estimate.

  20. Updating: Learning versus Supposing

    ERIC Educational Resources Information Center

    Zhao, Jiaying; Crupi, Vincenzo; Tentori, Katya; Fitelson, Branden; Osherson, Daniel

    2012-01-01

    Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event "A" after learning "B" should equal the conditional probability of "A" given "B" prior to learning "B". We examine whether ordinary judgment conforms to the orthodox view. In three experiments we found substantial…

  1. Holographic probabilities in eternal inflation.

    PubMed

    Bousso, Raphael

    2006-11-10

    In the global description of eternal inflation, probabilities for vacua are notoriously ambiguous. The local point of view is preferred by holography and naturally picks out a simple probability measure. It is insensitive to large expansion factors or lifetimes and so resolves a recently noted paradox. Any cosmological measure must be complemented with the probability for observers to emerge in a given vacuum. In lieu of anthropic criteria, I propose to estimate this by the entropy that can be produced in a local patch. This allows for prior-free predictions.

  2. Logic, probability, and human reasoning.

    PubMed

    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.

  3. Dinosaurs, Dinosaur Eggs, and Probability.

    ERIC Educational Resources Information Center

    Teppo, Anne R.; Hodgson, Ted

    2001-01-01

    Outlines several recommendations for teaching probability in the secondary school. Offers an activity that employs simulation by hand and using a programmable calculator in which geometry, analytical geometry, and discrete mathematics are explored. (KHR)

  4. The Probabilities of Unique Events

    PubMed Central

    Khemlani, Sangeet S.; Lotstein, Max; Johnson-Laird, Phil

    2012-01-01

    Many theorists argue that the probabilities of unique events, even real possibilities such as President Obama's re-election, are meaningless. As a consequence, psychologists have seldom investigated them. We propose a new theory (implemented in a computer program) in which such estimates depend on an intuitive non-numerical system capable only of simple procedures, and a deliberative system that maps intuitions into numbers. The theory predicts that estimates of the probabilities of conjunctions should often tend to split the difference between the probabilities of the two conjuncts. We report two experiments showing that individuals commit such violations of the probability calculus, and corroborating other predictions of the theory, e.g., individuals err in the same way even when they make non-numerical verbal estimates, such as that an event is highly improbable. PMID:23056224

  5. Joint probabilities and quantum cognition

    SciTech Connect

    Acacio de Barros, J.

    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.

  6. Joint probabilities and quantum cognition

    NASA Astrophysics Data System (ADS)

    de Barros, J. Acacio

    2012-12-01

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

  7. A Quantum Probability Model of Causal Reasoning

    PubMed Central

    Trueblood, Jennifer S.; Busemeyer, Jerome R.

    2012-01-01

    People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause) with diagnostic judgments (i.e., the conditional probability of a cause given an effect). The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment. PMID:22593747

  8. Joint probability distributions for projection probabilities of random orthonormal states

    NASA Astrophysics Data System (ADS)

    Alonso, L.; Gorin, T.

    2016-04-01

    The quantum chaos conjecture applied to a finite dimensional quantum system implies that such a system has eigenstates that show similar statistical properties as the column vectors of random orthogonal or unitary matrices. Here, we consider the different probabilities for obtaining a specific outcome in a projective measurement, provided the system is in one of its eigenstates. We then give analytic expressions for the joint probability density for these probabilities, with respect to the ensemble of random matrices. In the case of the unitary group, our results can be applied, also, to the phenomenon of universal conductance fluctuations, where the same mathematical quantities describe partial conductances in a two-terminal mesoscopic scattering problem with a finite number of modes in each terminal.

  9. Cognitive Snapshots of the Stochastic River--A Review of "Chance Encounters: Probability in Education," edited by Ramesh Kapadia and Manfred Borovcnik.

    ERIC Educational Resources Information Center

    Shaughnessy, J. Michael

    1993-01-01

    Reviews chapters of this book on probability in mathematics education. Topics discussed in the chapters include a historical perspective of probability, an epistemological perspective of probability, an overview of the psychological research on probability learning, computers in probability education, and an analysis of the probability curriculum.…

  10. Imprecise probabilities in engineering analyses

    NASA Astrophysics Data System (ADS)

    Beer, Michael; Ferson, Scott; Kreinovich, Vladik

    2013-05-01

    Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical differences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved. This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another. This paper was especially prepared for this special issue and reflects, in various ways, the thinking and presentation preferences of the authors, who are also the guest editors for this special issue.

  11. Normal probability plots with confidence.

    PubMed

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

    2015-01-01

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

  12. Children's understanding of posterior probability.

    PubMed

    Girotto, Vittorio; Gonzalez, Michel

    2008-01-01

    Do young children have a basic intuition of posterior probability? Do they update their decisions and judgments in the light of new evidence? We hypothesized that they can do so extensionally, by considering and counting the various ways in which an event may or may not occur. The results reported in this paper showed that from the age of five, children's decisions under uncertainty (Study 1) and judgments about random outcomes (Study 2) are correctly affected by posterior information. From the same age, children correctly revise their decisions in situations in which they face a single, uncertain event, produced by an intentional agent (Study 3). The finding that young children have some understanding of posterior probability supports the theory of naive extensional reasoning, and contravenes some pessimistic views of probabilistic reasoning, in particular the evolutionary claim that the human mind cannot deal with single-case probability. PMID:17391661

  13. Interference of probabilities in dynamics

    SciTech Connect

    Zak, Michail

    2014-08-15

    A new class of dynamical systems with a preset type of interference of probabilities is introduced. It is obtained from the extension of the Madelung equation by replacing the quantum potential with a specially selected feedback from the Liouville equation. It has been proved that these systems are different from both Newtonian and quantum systems, but they can be useful for modeling spontaneous collective novelty phenomena when emerging outputs are qualitatively different from the weighted sum of individual inputs. Formation of language and fast decision-making process as potential applications of the probability interference is discussed.

  14. Knowledge typology for imprecise probabilities.

    SciTech Connect

    Wilson, G. D.; Zucker, L. 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.

  15. Stretching Probability Explorations with Geoboards

    ERIC Educational Resources Information Center

    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…

  16. GPS: Geometry, Probability, and Statistics

    ERIC Educational Resources Information Center

    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…

  17. Some Surprising Probabilities from Bingo.

    ERIC Educational Resources Information Center

    Mercer, Joseph O.

    1993-01-01

    Investigates the probability of winning the largest prize at Bingo through a series of five simpler problems. Investigations are conducted with the aid of either BASIC computer programs, spreadsheets, or a computer algebra system such as Mathematica. Provides sample data tables to illustrate findings. (MDH)

  18. Probability Simulation in Middle School.

    ERIC Educational Resources Information Center

    Lappan, Glenda; Winter, M. J.

    1980-01-01

    Two simulations designed to teach probability to middle-school age pupils are presented. The first simulates the one-on-one foul shot simulation in basketball; the second deals with collecting a set of six cereal box prizes by buying boxes containing one toy each. (MP)

  19. Comments on quantum probability theory.

    PubMed

    Sloman, Steven

    2014-01-01

    Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness.

  20. Genetics as a Context for the Study of Probability.

    ERIC Educational Resources Information Center

    Brahier, Daniel J.

    1999-01-01

    Presents an activity in which students develop a handy strategy for exploring probability as applied in the life sciences by learning to use the Punnett square, an effective tool that helps students visualize sample spaces and determine the likelihood of events. (ASK)

  1. Teaching Probability with the Support of the R Statistical Software

    ERIC Educational Resources Information Center

    dos Santos Ferreira, Robson; Kataoka, Verônica Yumi; Karrer, Monica

    2014-01-01

    The objective of this paper is to discuss aspects of high school students' learning of probability in a context where they are supported by the statistical software R. We report on the application of a teaching experiment, constructed using the perspective of Gal's probabilistic literacy and Papert's constructionism. The results…

  2. Understanding Y haplotype matching probability.

    PubMed

    Brenner, Charles H

    2014-01-01

    The Y haplotype population-genetic terrain is better explored from a fresh perspective rather than by analogy with the more familiar autosomal ideas. For haplotype matching probabilities, versus for autosomal matching probabilities, explicit attention to modelling - such as how evolution got us where we are - is much more important while consideration of population frequency is much less so. This paper explores, extends, and explains some of the concepts of "Fundamental problem of forensic mathematics - the evidential strength of a rare haplotype match". That earlier paper presented and validated a "kappa method" formula for the evidential strength when a suspect matches a previously unseen haplotype (such as a Y-haplotype) at the crime scene. Mathematical implications of the kappa method are intuitive and reasonable. Suspicions to the contrary raised in rest on elementary errors. Critical to deriving the kappa method or any sensible evidential calculation is understanding that thinking about haplotype population frequency is a red herring; the pivotal question is one of matching probability. But confusion between the two is unfortunately institutionalized in much of the forensic world. Examples make clear why (matching) probability is not (population) frequency and why uncertainty intervals on matching probabilities are merely confused thinking. Forensic matching calculations should be based on a model, on stipulated premises. The model inevitably only approximates reality, and any error in the results comes only from error in the model, the inexactness of the approximation. Sampling variation does not measure that inexactness and hence is not helpful in explaining evidence and is in fact an impediment. Alternative haplotype matching probability approaches that various authors have considered are reviewed. Some are based on no model and cannot be taken seriously. For the others, some evaluation of the models is discussed. Recent evidence supports the adequacy of

  3. Knot probabilities in random diagrams

    NASA Astrophysics Data System (ADS)

    Cantarella, Jason; Chapman, Harrison; Mastin, Matt

    2016-10-01

    We consider a natural model of random knotting—choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to compute exact probabilities for knots in this model. As expected, most diagrams with 10 and fewer crossings are unknots (about 78% of the roughly 1.6 billion 10 crossing diagrams). For these crossing numbers, the unknot fraction is mostly explained by the prevalence of ‘tree-like’ diagrams which are unknots for any assignment of over/under information at crossings. The data shows a roughly linear relationship between the log of knot type probability and the log of the frequency rank of the knot type, analogous to Zipf’s law for word frequency. The complete tabulation and all knot frequencies are included as supplementary data.

  4. Probability distributions for multimeric systems.

    PubMed

    Albert, Jaroslav; Rooman, Marianne

    2016-01-01

    We propose a fast and accurate method of obtaining the equilibrium mono-modal joint probability distributions for multimeric systems. The method necessitates only two assumptions: the copy number of all species of molecule may be treated as continuous; and, the probability density functions (pdf) are well-approximated by multivariate skew normal distributions (MSND). Starting from the master equation, we convert the problem into a set of equations for the statistical moments which are then expressed in terms of the parameters intrinsic to the MSND. Using an optimization package on Mathematica, we minimize a Euclidian distance function comprising of a sum of the squared difference between the left and the right hand sides of these equations. Comparison of results obtained via our method with those rendered by the Gillespie algorithm demonstrates our method to be highly accurate as well as efficient.

  5. Probability, Information and Statistical Physics

    NASA Astrophysics Data System (ADS)

    Kuzemsky, A. L.

    2016-03-01

    In this short survey review we discuss foundational issues of the probabilistic approach to information theory and statistical mechanics from a unified standpoint. Emphasis is on the inter-relations between theories. The basic aim is tutorial, i.e. to carry out a basic introduction to the analysis and applications of probabilistic concepts to the description of various aspects of complexity and stochasticity. We consider probability as a foundational concept in statistical mechanics and review selected advances in the theoretical understanding of interrelation of the probability, information and statistical description with regard to basic notions of statistical mechanics of complex systems. It includes also a synthesis of past and present researches and a survey of methodology. The purpose of this terse overview is to discuss and partially describe those probabilistic methods and approaches that are used in statistical mechanics with the purpose of making these ideas easier to understanding and to apply.

  6. A Lakatosian Encounter with Probability

    ERIC Educational Resources Information Center

    Chick, Helen

    2010-01-01

    There is much to be learned and pondered by reading "Proofs and Refutations" by Imre Lakatos (Lakatos, 1976). It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning…

  7. Objective Probability and Quantum Fuzziness

    NASA Astrophysics Data System (ADS)

    Mohrhoff, U.

    2009-02-01

    This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and the claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which

  8. Probability for Weather and Climate

    NASA Astrophysics Data System (ADS)

    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

  9. The Black Hole Formation Probability

    NASA Astrophysics Data System (ADS)

    Clausen, Drew R.; Piro, Anthony; 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. Using the observed BH mass distribution from Galactic X-ray binaries, we investigate the probability that a star will make a BH as a function of its ZAMS mass. Although the shape of the black hole formation probability function is poorly constrained by current measurements, we believe that this framework is an important new step toward better understanding BH formation. We also consider some of the implications of this probability distribution, from its impact on the chemical enrichment from massive stars, to its connection with the structure of the core at the time of collapse, to the birth kicks that black holes receive. A probabilistic description of BH formation will be a useful 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.

  10. Persistence probabilities for stream populations.

    PubMed

    Samia, Yasmine; Lutscher, Frithjof

    2012-07-01

    Individuals in streams and rivers are constantly at risk of being washed downstream and thereby lost to their population. The possibility of diffusion-mediated persistence of populations in advective environments has been the focus of a multitude of recent modeling efforts. Most of these recent models are deterministic, and they predict the existence of a critical advection velocity, above which a population cannot persist. In this work, we present a stochastic approach to the persistence problem in streams and rivers. We use the dominant eigenvalue of the advection-diffusion operator to transition from a spatially explicit description to a spatially implicit birth-death process, in which individual washout from the domain appears as an additional death term. We find that the deterministic persistence threshold is replaced by a smooth transition from almost sure persistence to extinction as advection velocity increases. More interestingly, we explore how temporal variation in flow rate and other parameters affect the persistence probability. In line with general expectations, we find that temporal variation often decreases the persistence probability, and we focus on a few examples of how variation can increase population persistence.

  11. Lectures on probability and statistics

    SciTech Connect

    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.

  12. MSPI False Indication Probability Simulations

    SciTech Connect

    Dana Kelly; Kurt Vedros; Robert Youngblood

    2011-03-01

    This paper examines false indication probabilities in the context of the Mitigating System Performance Index (MSPI), in order to investigate the pros and cons of different approaches to resolving two coupled issues: (1) sensitivity to the prior distribution used in calculating the Bayesian-corrected unreliability contribution to the MSPI, and (2) whether (in a particular plant configuration) to model the fuel oil transfer pump (FOTP) as a separate component, or integrally to its emergency diesel generator (EDG). False indication probabilities were calculated for the following situations: (1) all component reliability parameters at their baseline values, so that the true indication is green, meaning that an indication of white or above would be false positive; (2) one or more components degraded to the extent that the true indication would be (mid) white, and “false” would be green (negative) or yellow (negative) or red (negative). In key respects, this was the approach taken in NUREG-1753. The prior distributions examined were the constrained noninformative (CNI) prior used currently by the MSPI, a mixture of conjugate priors, the Jeffreys noninformative prior, a nonconjugate log(istic)-normal prior, and the minimally informative prior investigated in (Kelly et al., 2010). The mid-white performance state was set at ?CDF = ?10 ? 10-6/yr. For each simulated time history, a check is made of whether the calculated ?CDF is above or below 10-6/yr. If the parameters were at their baseline values, and ?CDF > 10-6/yr, this is counted as a false positive. Conversely, if one or all of the parameters are set to values corresponding to ?CDF > 10-6/yr but that time history’s ?CDF < 10-6/yr, this is counted as a false negative indication. The false indication (positive or negative) probability is then estimated as the number of false positive or negative counts divided by the number of time histories (100,000). Results are presented for a set of base case parameter values

  13. Lévy laws in free probability

    PubMed Central

    Barndorff-Nielsen, Ole E.; Thorbjørnsen, Steen

    2002-01-01

    This article and its sequel outline recent developments in the theory of infinite divisibility and Lévy processes in free probability, a subject area belonging to noncommutative (or quantum) probability. The present paper discusses the classes of infinitely divisible probability measures in classical and free probability, respectively, via a study of the Bercovici–Pata bijection between these classes. PMID:12473744

  14. Associativity and normative credal probability.

    PubMed

    Snow, P

    2002-01-01

    Cox's Theorem is a widely cited motivation for probabilistic models of uncertain belief. The theorem relates the associativity of the logical connectives to that of the arithmetic operations of probability. Recent questions about the correctness of Cox's Theorem have been resolved, but there are new questions about one functional equation used by Cox in 1946. This equation is missing from his later work. Advances in knowledge since 1946 and changes in Cox's research interests explain the equation's disappearance. Other associativity-based motivations avoid functional equations altogether, and so may be more transparently applied to finite domains and discrete beliefs. A discrete counterpart of Cox's Theorem can be assembled from results that have been in the literature since 1959. PMID:18238098

  15. Imprecise probability for non-commuting observables

    NASA Astrophysics Data System (ADS)

    Allahverdyan, Armen E.

    2015-08-01

    It is known that non-commuting observables in quantum mechanics do not have joint probability. This statement refers to the precise (additive) probability model. I show that the joint distribution of any non-commuting pair of variables can be quantified via upper and lower probabilities, i.e. the joint probability is described by an interval instead of a number (imprecise probability). I propose transparent axioms from which the upper and lower probability operators follow. The imprecise probability depend on the non-commuting observables, is linear over the state (density matrix) and reverts to the usual expression for commuting observables.

  16. Fusion probability in heavy nuclei

    NASA Astrophysics Data System (ADS)

    Banerjee, Tathagata; Nath, S.; Pal, Santanu

    2015-03-01

    Background: Fusion between two massive nuclei is a very complex process and is characterized by three stages: (a) capture inside the potential barrier, (b) formation of an equilibrated compound nucleus (CN), and (c) statistical decay of the CN leading to a cold evaporation residue (ER) or fission. The second stage is the least understood of the three and is the most crucial in predicting yield of superheavy elements (SHE) formed in complete fusion reactions. Purpose: A systematic study of average fusion probability, , is undertaken to obtain a better understanding of its dependence on various reaction parameters. The study may also help to clearly demarcate onset of non-CN fission (NCNF), which causes fusion probability, PCN, to deviate from unity. Method: ER excitation functions for 52 reactions leading to CN in the mass region 170-220, which are available in the literature, have been compared with statistical model (SM) calculations. Capture cross sections have been obtained from a coupled-channels code. In the SM, shell corrections in both the level density and the fission barrier have been included. for these reactions has been extracted by comparing experimental and theoretical ER excitation functions in the energy range ˜5 %-35% above the potential barrier, where known effects of nuclear structure are insignificant. Results: has been shown to vary with entrance channel mass asymmetry, η (or charge product, ZpZt ), as well as with fissility of the CN, χCN. No parameter has been found to be adequate as a single scaling variable to determine . Approximate boundaries have been obtained from where starts deviating from unity. Conclusions: This study quite clearly reveals the limits of applicability of the SM in interpreting experimental observables from fusion reactions involving two massive nuclei. Deviation of from unity marks the beginning of the domain of dynamical models of fusion. Availability of precise ER cross

  17. THE BLACK HOLE FORMATION PROBABILITY

    SciTech Connect

    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 {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.

  18. The Black Hole Formation Probability

    NASA Astrophysics Data System (ADS)

    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.

  19. The Probability Distribution for a Biased Spinner

    ERIC Educational Resources Information Center

    Foster, Colin

    2012-01-01

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

  20. Lévy processes in free probability

    PubMed Central

    Barndorff-Nielsen, Ole E.; Thorbjørnsen, Steen

    2002-01-01

    This is the continuation of a previous article that studied the relationship between the classes of infinitely divisible probability measures in classical and free probability, respectively, via the Bercovici–Pata bijection. Drawing on the results of the preceding article, the present paper outlines recent developments in the theory of Lévy processes in free probability. PMID:12473745

  1. Using Playing Cards to Differentiate Probability Interpretations

    ERIC Educational Resources Information Center

    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.

  2. Pre-Service Teachers' Conceptions of Probability

    ERIC Educational Resources Information Center

    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…

  3. Teaching Probabilities and Statistics to Preschool Children

    ERIC Educational Resources Information Center

    Pange, Jenny

    2003-01-01

    This study considers the teaching of probabilities and statistics to a group of preschool children using traditional classroom activities and Internet games. It was clear from this study that children can show a high level of understanding of probabilities and statistics, and demonstrate high performance in probability games. The use of Internet…

  4. The Cognitive Substrate of Subjective Probability

    ERIC Educational Resources Information Center

    Nilsson, Hakan; Olsson, Henrik; Juslin, Peter

    2005-01-01

    The prominent cognitive theories of probability judgment were primarily developed to explain cognitive biases rather than to account for the cognitive processes in probability judgment. In this article the authors compare 3 major theories of the processes and representations in probability judgment: the representativeness heuristic, implemented as…

  5. Illustrating Basic Probability Calculations Using "Craps"

    ERIC Educational Resources Information Center

    Johnson, Roger W.

    2006-01-01

    Instructors may use the gambling game of craps to illustrate the use of a number of fundamental probability identities. For the "pass-line" bet we focus on the chance of winning and the expected game length. To compute these, probabilities of unions of disjoint events, probabilities of intersections of independent events, conditional probabilities…

  6. Subjective and objective probabilities in quantum mechanics

    SciTech Connect

    Srednicki, Mark

    2005-05-15

    We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

  7. Dynamic encoding of speech sequence probability in human temporal cortex.

    PubMed

    Leonard, Matthew K; Bouchard, Kristofer E; Tang, Claire; Chang, Edward F

    2015-05-01

    Sensory processing involves identification of stimulus features, but also integration with the surrounding sensory and cognitive context. Previous work in animals and humans has shown fine-scale sensitivity to context in the form of learned knowledge about the statistics of the sensory environment, including relative probabilities of discrete units in a stream of sequential auditory input. These statistics are a defining characteristic of one of the most important sequential signals humans encounter: speech. For speech, extensive exposure to a language tunes listeners to the statistics of sound sequences. To address how speech sequence statistics are neurally encoded, we used high-resolution direct cortical recordings from human lateral superior temporal cortex as subjects listened to words and nonwords with varying transition probabilities between sound segments. In addition to their sensitivity to acoustic features (including contextual features, such as coarticulation), we found that neural responses dynamically encoded the language-level probability of both preceding and upcoming speech sounds. Transition probability first negatively modulated neural responses, followed by positive modulation of neural responses, consistent with coordinated predictive and retrospective recognition processes, respectively. Furthermore, transition probability encoding was different for real English words compared with nonwords, providing evidence for online interactions with high-order linguistic knowledge. These results demonstrate that sensory processing of deeply learned stimuli involves integrating physical stimulus features with their contextual sequential structure. Despite not being consciously aware of phoneme sequence statistics, listeners use this information to process spoken input and to link low-level acoustic representations with linguistic information about word identity and meaning.

  8. Calibrating Subjective Probabilities Using Hierarchical Bayesian Models

    NASA Astrophysics Data System (ADS)

    Merkle, Edgar C.

    A body of psychological research has examined the correspondence between a judge's subjective probability of an event's outcome and the event's actual outcome. The research generally shows that subjective probabilities are noisy and do not match the "true" probabilities. However, subjective probabilities are still useful for forecasting purposes if they bear some relationship to true probabilities. The purpose of the current research is to exploit relationships between subjective probabilities and outcomes to create improved, model-based probabilities for forecasting. Once the model has been trained in situations where the outcome is known, it can then be used in forecasting situations where the outcome is unknown. These concepts are demonstrated using experimental psychology data, and potential applications are discussed.

  9. The uncertainty in earthquake conditional probabilities

    USGS Publications Warehouse

    Savage, J.C.

    1992-01-01

    The Working Group on California Earthquake Probabilities (WGCEP) questioned the relevance of uncertainty intervals assigned to earthquake conditional probabilities on the basis that the uncertainty in the probability estimate seemed to be greater the smaller the intrinsic breadth of the recurrence-interval distribution. It is shown here that this paradox depends upon a faulty measure of uncertainty in the conditional probability and that with a proper measure of uncertainty no paradox exists. The assertion that the WGCEP probability assessment in 1988 correctly forecast the 1989 Loma Prieta earthquake is also challenged by showing that posterior probability of rupture inferred after the occurrence of the earthquake from the prior WGCEP probability distribution reverts to a nearly informationless distribution. -Author

  10. Integrated statistical modelling of spatial landslide probability

    NASA Astrophysics Data System (ADS)

    Mergili, M.; Chu, H.-J.

    2015-09-01

    Statistical methods are commonly employed to estimate spatial probabilities of landslide release at the catchment or regional scale. Travel distances and impact areas are often computed by means of conceptual mass point models. The present work introduces a fully automated procedure extending and combining both concepts to compute an integrated spatial landslide probability: (i) the landslide inventory is subset into release and deposition zones. (ii) We employ a simple statistical approach to estimate the pixel-based landslide release probability. (iii) We use the cumulative probability density function of the angle of reach of the observed landslide pixels to assign an impact probability to each pixel. (iv) We introduce the zonal probability i.e. the spatial probability that at least one landslide pixel occurs within a zone of defined size. We quantify this relationship by a set of empirical curves. (v) The integrated spatial landslide probability is defined as the maximum of the release probability and the product of the impact probability and the zonal release probability relevant for each pixel. We demonstrate the approach with a 637 km2 study area in southern Taiwan, using an inventory of 1399 landslides triggered by the typhoon Morakot in 2009. We observe that (i) the average integrated spatial landslide probability over the entire study area corresponds reasonably well to the fraction of the observed landside area; (ii) the model performs moderately well in predicting the observed spatial landslide distribution; (iii) the size of the release zone (or any other zone of spatial aggregation) influences the integrated spatial landslide probability to a much higher degree than the pixel-based release probability; (iv) removing the largest landslides from the analysis leads to an enhanced model performance.

  11. Simple artificial neural networks that match probability and exploit and explore when confronting a multiarmed bandit.

    PubMed

    Dawson, Michael R W; Dupuis, Brian; Spetch, Marcia L; Kelly, Debbie M

    2009-08-01

    The matching law (Herrnstein 1961) states that response rates become proportional to reinforcement rates; this is related to the empirical phenomenon called probability matching (Vulkan 2000). Here, we show that a simple artificial neural network generates responses consistent with probability matching. This behavior was then used to create an operant procedure for network learning. We use the multiarmed bandit (Gittins 1989), a classic problem of choice behavior, to illustrate that operant training balances exploiting the bandit arm expected to pay off most frequently with exploring other arms. Perceptrons provide a medium for relating results from neural networks, genetic algorithms, animal learning, contingency theory, reinforcement learning, and theories of choice.

  12. Simple artificial neural networks that match probability and exploit and explore when confronting a multiarmed bandit.

    PubMed

    Dawson, Michael R W; Dupuis, Brian; Spetch, Marcia L; Kelly, Debbie M

    2009-08-01

    The matching law (Herrnstein 1961) states that response rates become proportional to reinforcement rates; this is related to the empirical phenomenon called probability matching (Vulkan 2000). Here, we show that a simple artificial neural network generates responses consistent with probability matching. This behavior was then used to create an operant procedure for network learning. We use the multiarmed bandit (Gittins 1989), a classic problem of choice behavior, to illustrate that operant training balances exploiting the bandit arm expected to pay off most frequently with exploring other arms. Perceptrons provide a medium for relating results from neural networks, genetic algorithms, animal learning, contingency theory, reinforcement learning, and theories of choice. PMID:19596631

  13. Machine Learning

    NASA Astrophysics Data System (ADS)

    Hoffmann, Achim; Mahidadia, Ashesh

    human comprehension as it is essentially a large collection of probability values. In Sect. 9, we present a generic method for improving accuracy of a given learner by generatingmultiple classifiers using variations of the training data. While this works well in most cases, the resulting classifiers have significantly increased complexity and, hence, tend to destroy the human readability of the learning result that a single learner may produce. Section 10 contains a summary, mentions briefly other techniques not discussed in this chapter and presents outlook on the potential of machine learning in the future.

  14. Bell Could Become the Copernicus of Probability

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2016-07-01

    Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.

  15. Probability and Quantum Paradigms: the Interplay

    NASA Astrophysics Data System (ADS)

    Kracklauer, A. F.

    2007-12-01

    Since the introduction of Born's interpretation of quantum wave functions as yielding the probability density of presence, Quantum Theory and Probability have lived in a troubled symbiosis. Problems arise with this interpretation because quantum probabilities exhibit features alien to usual probabilities, namely non Boolean structure and non positive-definite phase space probability densities. This has inspired research into both elaborate formulations of Probability Theory and alternate interpretations for wave functions. Herein the latter tactic is taken and a suggested variant interpretation of wave functions based on photo detection physics proposed, and some empirical consequences are considered. Although incomplete in a few details, this variant is appealing in its reliance on well tested concepts and technology.

  16. Probability and Quantum Paradigms: the Interplay

    SciTech Connect

    Kracklauer, A. F.

    2007-12-03

    Since the introduction of Born's interpretation of quantum wave functions as yielding the probability density of presence, Quantum Theory and Probability have lived in a troubled symbiosis. Problems arise with this interpretation because quantum probabilities exhibit features alien to usual probabilities, namely non Boolean structure and non positive-definite phase space probability densities. This has inspired research into both elaborate formulations of Probability Theory and alternate interpretations for wave functions. Herein the latter tactic is taken and a suggested variant interpretation of wave functions based on photo detection physics proposed, and some empirical consequences are considered. Although incomplete in a few details, this variant is appealing in its reliance on well tested concepts and technology.

  17. Entropy analysis of systems exhibiting negative probabilities

    NASA Astrophysics Data System (ADS)

    Tenreiro Machado, J. A.

    2016-07-01

    This paper addresses the concept of negative probability and its impact upon entropy. An analogy between the probability generating functions, in the scope of quasiprobability distributions, and the Grünwald-Letnikov definition of fractional derivatives, is explored. Two distinct cases producing negative probabilities are formulated and their distinct meaning clarified. Numerical calculations using the Shannon entropy characterize further the characteristics of the two limit cases.

  18. Calculating the CEP (Circular Error Probable)

    NASA Technical Reports Server (NTRS)

    1987-01-01

    This report compares the probability contained in the Circular Error Probable associated with an Elliptical Error Probable to that of the EEP at a given confidence level. The levels examined are 50 percent and 95 percent. The CEP is found to be both more conservative and less conservative than the associated EEP, depending on the eccentricity of the ellipse. The formulas used are derived in the appendix.

  19. Psychophysics of the probability weighting function

    NASA Astrophysics Data System (ADS)

    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(-() (0<α<1 and w(0)=1,w(1e)=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.

  20. Is probability of frequency too narrow?

    SciTech Connect

    Martz, H.F.

    1993-10-01

    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.

  1. Conditional probability density function estimation with sigmoidal neural networks.

    PubMed

    Sarajedini, A; Hecht-Nielsen, R; Chau, P M

    1999-01-01

    Real-world problems can often be couched in terms of conditional probability density function estimation. In particular, pattern recognition, signal detection, and financial prediction are among the multitude of applications requiring conditional density estimation. Previous developments in this direction have used neural nets to estimate statistics of the distribution or the marginal or joint distributions of the input-output variables. We have modified the joint distribution estimating sigmoidal neural network to estimate the conditional distribution. Thus, the probability density of the output conditioned on the inputs is estimated using a neural network. We have derived and implemented the learning laws to train the network. We show that this network has computational advantages over a brute force ratio of joint and marginal distributions. We also compare its performance to a kernel conditional density estimator in a larger scale (higher dimensional) problem simulating more realistic conditions.

  2. Neural correlates of the divergence of instrumental probability distributions.

    PubMed

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

    2013-07-24

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

  3. Neural Correlates of the Divergence of Instrumental Probability Distributions

    PubMed Central

    Wang, Shuo; Zhang, June; O'Doherty, John P.

    2013-01-01

    Flexible action selection requires knowledge about how alternative actions impact the environment: a “cognitive map” of instrumental contingencies. Reinforcement learning theories formalize this map as a set of stochastic relationships between actions and states, such that for any given action considered in a current state, a probability distribution is specified over possible outcome states. Here, we show that activity in the human inferior parietal lobule correlates with the divergence of such outcome distributions–a measure that reflects whether discrimination between alternative actions increases the controllability of the future–and, further, that this effect is dissociable from those of other information theoretic and motivational variables, such as outcome entropy, action values, and outcome utilities. Our results suggest that, although ultimately combined with reward estimates to generate action values, outcome probability distributions associated with alternative actions may be contrasted independently of valence computations, to narrow the scope of the action selection problem. PMID:23884955

  4. Lattice Duality: The Origin of Probability and Entropy

    NASA Technical Reports Server (NTRS)

    Knuth, Kevin H.

    2004-01-01

    Bayesian probability theory is an inference calculus, which originates from a generalization of inclusion on the Boolean lattice of logical assertions to a degree of inclusion represented by a real number. Dual to this lattice is the distributive lattice of questions constructed from the ordered set of down-sets of assertions, which forms the foundation of the calculus of inquiry-a generalization of information theory. In this paper we introduce this novel perspective on these spaces in which machine learning is performed and discuss the relationship between these results and several proposed generalizations of information theory in the literature.

  5. Executable Code Recognition in Network Flows Using Instruction Transition Probabilities

    NASA Astrophysics Data System (ADS)

    Kim, Ikkyun; Kang, Koohong; Choi, Yangseo; Kim, Daewon; Oh, Jintae; Jang, Jongsoo; Han, Kijun

    The ability to recognize quickly inside network flows to be executable is prerequisite for malware detection. For this purpose, we introduce an instruction transition probability matrix (ITPX) which is comprised of the IA-32 instruction sets and reveals the characteristics of executable code's instruction transition patterns. And then, we propose a simple algorithm to detect executable code inside network flows using a reference ITPX which is learned from the known Windows Portable Executable files. We have tested the algorithm with more than thousands of executable and non-executable codes. The results show that it is very promising enough to use in real world.

  6. Stimulus Probability Effects in Absolute Identification

    ERIC Educational Resources Information Center

    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…

  7. Probability: A Matter of Life and Death

    ERIC Educational Resources Information Center

    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…

  8. Average Transmission Probability of a Random Stack

    ERIC Educational Resources Information Center

    Lu, Yin; Miniatura, Christian; Englert, Berthold-Georg

    2010-01-01

    The transmission through a stack of identical slabs that are separated by gaps with random widths is usually treated by calculating the average of the logarithm of the transmission probability. We show how to calculate the average of the transmission probability itself with the aid of a recurrence relation and derive analytical upper and lower…

  9. Teaching Probability: A Socio-Constructivist Perspective

    ERIC Educational Resources Information Center

    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.

  10. Probability Simulations by Non-Lipschitz Chaos

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    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. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

  11. 47 CFR 1.1623 - Probability calculation.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... computed to no less than three significant digits. Probabilities will be truncated to the number of significant digits used in a particular lottery. (b) Divide the total number of applicants into 1.00 to... than .40, then multiply each such intermediate probability by the ratio of .40 to such sum. Divide...

  12. Correlation as Probability of Common Descent.

    ERIC Educational Resources Information Center

    Falk, Ruma; Well, Arnold D.

    1996-01-01

    One interpretation of the Pearson product-moment correlation ("r"), correlation as the probability of originating from common descent, important to the genetic measurement of inbreeding, is examined. The conditions under which "r" can be interpreted as the probability of "identity by descent" are specified, and the possibility of generalizing this…

  13. Phonotactic Probabilities in Young Children's Speech Production

    ERIC Educational Resources Information Center

    Zamuner, Tania S.; Gerken, Louann; Hammond, Michael

    2004-01-01

    This research explores the role of phonotactic probability in two-year-olds' production of coda consonants. Twenty-nine children were asked to repeat CVC non-words that were used as labels for pictures of imaginary animals. The CVC non-words were controlled for their phonotactic probabilities, neighbourhood densities, word-likelihood ratings, and…

  14. 47 CFR 1.1623 - Probability calculation.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 47 Telecommunication 1 2012-10-01 2012-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants by Random Selection Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a)...

  15. Simulations of Probabilities for Quantum Computing

    NASA Technical Reports Server (NTRS)

    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.

  16. Probability Issues in without Replacement Sampling

    ERIC Educational Resources Information Center

    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…

  17. Teenagers' Perceived and Actual Probabilities of Pregnancy.

    ERIC Educational Resources Information Center

    Namerow, Pearila Brickner; And Others

    1987-01-01

    Explored adolescent females' (N=425) actual and perceived probabilities of pregnancy. Subjects estimated their likelihood of becoming pregnant the last time they had intercourse, and indicated the dates of last intercourse and last menstrual period. Found that the distributions of perceived probability of pregnancy were nearly identical for both…

  18. 47 CFR 1.1623 - Probability calculation.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 47 Telecommunication 1 2014-10-01 2014-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants by Random Selection Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a)...

  19. 47 CFR 1.1623 - Probability calculation.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 47 Telecommunication 1 2013-10-01 2013-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants by Random Selection Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a)...

  20. Laboratory-Tutorial Activities for Teaching Probability

    ERIC Educational Resources Information Center

    Wittmann, Michael C.; Morgan, Jeffrey T.; Feeley, Roger E.

    2006-01-01

    We report on the development of students' ideas of probability and probability density in a University of Maine laboratory-based general education physics course called "Intuitive Quantum Physics". Students in the course are generally math phobic with unfavorable expectations about the nature of physics and their ability to do it. We describe a…

  1. 47 CFR 1.1623 - Probability calculation.

    Code of Federal Regulations, 2010 CFR

    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...

  2. Time-dependent landslide probability mapping

    USGS Publications Warehouse

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

    1993-01-01

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

  3. Alternative probability theories for cognitive psychology.

    PubMed

    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.

  4. Quantum probability assignment limited by relativistic causality

    PubMed Central

    Han, Yeong Deok; Choi, Taeseung

    2016-01-01

    Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment. PMID:26971717

  5. Multinomial mixture model with heterogeneous classification probabilities

    USGS Publications Warehouse

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

    2011-01-01

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

  6. Assessment of the probability of contaminating Mars

    NASA Technical Reports Server (NTRS)

    Judd, B. R.; North, D. W.; Pezier, J. P.

    1974-01-01

    New methodology is proposed to assess the probability that the planet Mars will by biologically contaminated by terrestrial microorganisms aboard a spacecraft. Present NASA methods are based on the Sagan-Coleman formula, which states that the probability of contamination is the product of the expected microbial release and a probability of growth. The proposed new methodology extends the Sagan-Coleman approach to permit utilization of detailed information on microbial characteristics, the lethality of release and transport mechanisms, and of other information about the Martian environment. Three different types of microbial release are distinguished in the model for assessing the probability of contamination. The number of viable microbes released by each mechanism depends on the bio-burden in various locations on the spacecraft and on whether the spacecraft landing is accomplished according to plan. For each of the three release mechanisms a probability of growth is computed, using a model for transport into an environment suited to microbial growth.

  7. Survival probability in patients with liver trauma.

    PubMed

    Buci, Skender; Kukeli, Agim

    2016-08-01

    Purpose - The purpose of this paper is to assess the survival probability among patients with liver trauma injury using the anatomical and psychological scores of conditions, characteristics and treatment modes. Design/methodology/approach - A logistic model is used to estimate 173 patients' survival probability. Data are taken from patient records. Only emergency room patients admitted to University Hospital of Trauma (former Military Hospital) in Tirana are included. Data are recorded anonymously, preserving the patients' privacy. Findings - When correctly predicted, the logistic models show that survival probability varies from 70.5 percent up to 95.4 percent. The degree of trauma injury, trauma with liver and other organs, total days the patient was hospitalized, and treatment method (conservative vs intervention) are statistically important in explaining survival probability. Practical implications - The study gives patients, their relatives and physicians ample and sound information they can use to predict survival chances, the best treatment and resource management. Originality/value - This study, which has not been done previously, explores survival probability, success probability for conservative and non-conservative treatment, and success probability for single vs multiple injuries from liver trauma.

  8. Liquefaction probability curves for surficial geologic deposits

    USGS Publications Warehouse

    Holzer, Thomas L.; Noce, Thomas E.; Bennett, Michael J.

    2011-01-01

    Liquefaction probability curves that predict the probability of surface manifestations of earthquake-induced liquefaction are developed for 14 different types of surficial geologic units. The units consist of alluvial fan, beach ridge, river delta topset and foreset beds, eolian dune, point bar, flood basin, natural river and alluvial fan levees, abandoned river channel, deep-water lake, lagoonal, sandy artificial fill, and valley train deposits. Probability is conditioned on earthquake magnitude and peak ground acceleration. Curves are developed for water table depths of 1.5 and 5.0 m. Probabilities are derived from complementary cumulative frequency distributions of the liquefaction potential index (LPI) that were computed from 927 cone penetration tests. For natural deposits with a water table at 1.5 m and subjected to a M7.5 earthquake with peak ground acceleration (PGA)  =  0.25g, probabilities range from 0.5 for beach ridge, point bar, and deltaic deposits. The curves also were used to assign ranges of liquefaction probabilities to the susceptibility categories proposed previously for different geologic deposits. For the earthquake described here, probabilities for susceptibility categories have ranges of 0–0.08 for low, 0.09–0.30 for moderate, 0.31–0.62 for high, and 0.63–1.00 for very high. Retrospective predictions of liquefaction during historical earthquakes based on the curves compare favorably to observations.

  9. Survival probability in patients with liver trauma.

    PubMed

    Buci, Skender; Kukeli, Agim

    2016-08-01

    Purpose - The purpose of this paper is to assess the survival probability among patients with liver trauma injury using the anatomical and psychological scores of conditions, characteristics and treatment modes. Design/methodology/approach - A logistic model is used to estimate 173 patients' survival probability. Data are taken from patient records. Only emergency room patients admitted to University Hospital of Trauma (former Military Hospital) in Tirana are included. Data are recorded anonymously, preserving the patients' privacy. Findings - When correctly predicted, the logistic models show that survival probability varies from 70.5 percent up to 95.4 percent. The degree of trauma injury, trauma with liver and other organs, total days the patient was hospitalized, and treatment method (conservative vs intervention) are statistically important in explaining survival probability. Practical implications - The study gives patients, their relatives and physicians ample and sound information they can use to predict survival chances, the best treatment and resource management. Originality/value - This study, which has not been done previously, explores survival probability, success probability for conservative and non-conservative treatment, and success probability for single vs multiple injuries from liver trauma. PMID:27477933

  10. The Animism Controversy Revisited: A Probability Analysis

    ERIC Educational Resources Information Center

    Smeets, Paul M.

    1973-01-01

    Considers methodological issues surrounding the Piaget-Huang controversy. A probability model, based on the difference between the expected and observed animistic and deanimistic responses is applied as an improved technique for the assessment of animism. (DP)

  11. Classical and Quantum Spreading of Position Probability

    ERIC Educational Resources Information Center

    Farina, J. E. G.

    1977-01-01

    Demonstrates that the standard deviation of the position probability of a particle moving freely in one dimension is a function of the standard deviation of its velocity distribution and time in classical or quantum mechanics. (SL)

  12. Inclusion probability with dropout: an operational formula.

    PubMed

    Milot, E; Courteau, J; Crispino, F; Mailly, F

    2015-05-01

    In forensic genetics, a mixture of two or more contributors to a DNA profile is often interpreted using the inclusion probabilities theory. In this paper, we present a general formula for estimating the probability of inclusion (PI, also known as the RMNE probability) from a subset of visible alleles when dropouts are possible. This one-locus formula can easily be extended to multiple loci using the cumulative probability of inclusion. We show that an exact formulation requires fixing the number of contributors, hence to slightly modify the classic interpretation of the PI. We discuss the implications of our results for the enduring debate over the use of PI vs likelihood ratio approaches within the context of low template amplifications.

  13. The cognitive substrate of subjective probability.

    PubMed

    Nilsson, Håkan; Olsson, Henrik; Juslin, Peter

    2005-07-01

    The prominent cognitive theories of probability judgment were primarily developed to explain cognitive biases rather than to account for the cognitive processes in probability judgment. In this article the authors compare 3 major theories of the processes and representations in probability judgment: the representativeness heuristic, implemented as prototype similarity, relative likelihood, or evidential support accumulation (ESAM; D. J. Koehler, C. M. White, & R. Grondin, 2003); cue-based relative frequency; and exemplar memory, implemented by probabilities from exemplars (PROBEX; P. Juslin & M. Persson, 2002). Three experiments with different task structures consistently demonstrate that exemplar memory is the best account of the data whereas the results are inconsistent with extant formulations of the representativeness heuristic and cue-based relative frequency. PMID:16060768

  14. Rare Gases Transition Probabilities for Plasma Diagnostics

    SciTech Connect

    Katsonis, K.; Siskos, A.; Ndiaye, A.; Clark, R. E. H.; Cornille, M.; Abdallah, J. Jr.

    2006-01-15

    Evaluation of Ar and Xe transition probabilities to be used in Collisional-Radiative models for plasma diagnostics is addressed. Partial results are given for the typical case of the 4p <- 4d Ar III multiplet.

  15. Teaching Elementary Probability Through its History.

    ERIC Educational Resources Information Center

    Kunoff, Sharon; Pines, Sylvia

    1986-01-01

    Historical problems are presented which can readily be solved by students once some elementary probability concepts are developed. The Duke of Tuscany's Problem; the problem of points; and the question of proportions, divination, and Bertrand's Paradox are included. (MNS)

  16. Determining Probabilities by Examining Underlying Structure.

    ERIC Educational Resources Information Center

    Norton, Robert M.

    2001-01-01

    Discusses how dice games pose fairness issues that appeal to students and examines a structure for three games involving two dice in a way that leads directly to the theoretical probabilities for all possible outcomes. (YDS)

  17. On Convergent Probability of a Random Walk

    ERIC Educational Resources Information Center

    Lee, Y.-F.; Ching, W.-K.

    2006-01-01

    This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

  18. Robust location and spread measures for nonparametric probability density function estimation.

    PubMed

    López-Rubio, Ezequiel

    2009-10-01

    Robustness against outliers is a desirable property of any unsupervised learning scheme. In particular, probability density estimators benefit from incorporating this feature. A possible strategy to achieve this goal is to substitute the sample mean and the sample covariance matrix by more robust location and spread estimators. Here we use the L1-median to develop a nonparametric probability density function (PDF) estimator. We prove its most relevant properties, and we show its performance in density estimation and classification applications.

  19. Non-Gaussian Photon Probability Distribution

    NASA Astrophysics Data System (ADS)

    Solomon, Benjamin T.

    2010-01-01

    This paper investigates the axiom that the photon's probability distribution is a Gaussian distribution. The Airy disc empirical evidence shows that the best fit, if not exact, distribution is a modified Gamma mΓ distribution (whose parameters are α = r, βr/√u ) in the plane orthogonal to the motion of the photon. This modified Gamma distribution is then used to reconstruct the probability distributions along the hypotenuse from the pinhole, arc from the pinhole, and a line parallel to photon motion. This reconstruction shows that the photon's probability distribution is not a Gaussian function. However, under certain conditions, the distribution can appear to be Normal, thereby accounting for the success of quantum mechanics. This modified Gamma distribution changes with the shape of objects around it and thus explains how the observer alters the observation. This property therefore places additional constraints to quantum entanglement experiments. This paper shows that photon interaction is a multi-phenomena effect consisting of the probability to interact Pi, the probabilistic function and the ability to interact Ai, the electromagnetic function. Splitting the probability function Pi from the electromagnetic function Ai enables the investigation of the photon behavior from a purely probabilistic Pi perspective. The Probabilistic Interaction Hypothesis is proposed as a consistent method for handling the two different phenomena, the probability function Pi and the ability to interact Ai, thus redefining radiation shielding, stealth or cloaking, and invisibility as different effects of a single phenomenon Pi of the photon probability distribution. Sub wavelength photon behavior is successfully modeled as a multi-phenomena behavior. The Probabilistic Interaction Hypothesis provides a good fit to Otoshi's (1972) microwave shielding, Schurig et al. (2006) microwave cloaking, and Oulton et al. (2008) sub wavelength confinement; thereby providing a strong case that

  20. Probability distribution of the vacuum energy density

    SciTech Connect

    Duplancic, Goran; Stefancic, Hrvoje; Glavan, Drazen

    2010-12-15

    As the vacuum state of a quantum field is not an eigenstate of the Hamiltonian density, the vacuum energy density can be represented as a random variable. We present an analytical calculation of the probability distribution of the vacuum energy density for real and complex massless scalar fields in Minkowski space. The obtained probability distributions are broad and the vacuum expectation value of the Hamiltonian density is not fully representative of the vacuum energy density.

  1. Robust satisficing and the probability of survival

    NASA Astrophysics Data System (ADS)

    Ben-Haim, Yakov

    2014-01-01

    Concepts of robustness are sometimes employed when decisions under uncertainty are made without probabilistic information. We present a theorem that establishes necessary and sufficient conditions for non-probabilistic robustness to be equivalent to the probability of satisfying the specified outcome requirements. When this holds, probability is enhanced (or maximised) by enhancing (or maximising) robustness. Two further theorems establish important special cases. These theorems have implications for success or survival under uncertainty. Applications to foraging and finance are discussed.

  2. When probability trees don't work

    NASA Astrophysics Data System (ADS)

    Chan, K. C.; Lenard, C. T.; Mills, T. M.

    2016-08-01

    Tree diagrams arise naturally in courses on probability at high school or university, even at an elementary level. Often they are used to depict outcomes and associated probabilities from a sequence of games. A subtle issue is whether or not the Markov condition holds in the sequence of games. We present two examples that illustrate the importance of this issue. Suggestions as to how these examples may be used in a classroom are offered.

  3. The spline probability hypothesis density filter

    NASA Astrophysics Data System (ADS)

    Sithiravel, Rajiv; Tharmarasa, Ratnasingham; McDonald, Mike; Pelletier, Michel; Kirubarajan, Thiagalingam

    2012-06-01

    The Probability Hypothesis Density Filter (PHD) is a multitarget tracker for recursively estimating the number of targets and their state vectors from a set of observations. The PHD filter is capable of working well in scenarios with false alarms and missed detections. Two distinct PHD filter implementations are available in the literature: the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters. The SMC-PHD filter uses particles to provide target state estimates, which can lead to a high computational load, whereas the GM-PHD filter does not use particles, but restricts to linear Gaussian mixture models. The SMC-PHD filter technique provides only weighted samples at discrete points in the state space instead of a continuous estimate of the probability density function of the system state and thus suffers from the well-known degeneracy problem. This paper proposes a B-Spline based Probability Hypothesis Density (S-PHD) filter, which has the capability to model any arbitrary probability density function. The resulting algorithm can handle linear, non-linear, Gaussian, and non-Gaussian models and the S-PHD filter can also provide continuous estimates of the probability density function of the system state. In addition, by moving the knots dynamically, the S-PHD filter ensures that the splines cover only the region where the probability of the system state is significant, hence the high efficiency of the S-PHD filter is maintained at all times. Also, unlike the SMC-PHD filter, the S-PHD filter is immune to the degeneracy problem due to its continuous nature. The S-PHD filter derivations and simulations are provided in this paper.

  4. Infants Segment Continuous Events Using Transitional Probabilities

    ERIC Educational Resources Information Center

    Stahl, Aimee E.; Romberg, Alexa R.; Roseberry, Sarah; Golinkoff, Roberta Michnick; Hirsh-Pasek, Kathryn

    2014-01-01

    Throughout their 1st year, infants adeptly detect statistical structure in their environment. However, little is known about whether statistical learning is a primary mechanism for event segmentation. This study directly tests whether statistical learning alone is sufficient to segment continuous events. Twenty-eight 7- to 9-month-old infants…

  5. Site occupancy models with heterogeneous detection probabilities

    USGS Publications Warehouse

    Royle, J. Andrew

    2006-01-01

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

  6. Probability Forecasting Using Monte Carlo Simulation

    NASA Astrophysics Data System (ADS)

    Duncan, M.; Frisbee, J.; Wysack, J.

    2014-09-01

    Space Situational Awareness (SSA) is defined as the knowledge and characterization of all aspects of space. SSA is now a fundamental and critical component of space operations. Increased dependence on our space assets has in turn lead to a greater need for accurate, near real-time knowledge of all space activities. With the growth of the orbital debris population, satellite operators are performing collision avoidance maneuvers more frequently. Frequent maneuver execution expends fuel and reduces the operational lifetime of the spacecraft. Thus the need for new, more sophisticated collision threat characterization methods must be implemented. The collision probability metric is used operationally to quantify the collision risk. The collision probability is typically calculated days into the future, so that high risk and potential high risk conjunction events are identified early enough to develop an appropriate course of action. As the time horizon to the conjunction event is reduced, the collision probability changes. A significant change in the collision probability will change the satellite mission stakeholder's course of action. So constructing a method for estimating how the collision probability will evolve improves operations by providing satellite operators with a new piece of information, namely an estimate or 'forecast' of how the risk will change as time to the event is reduced. Collision probability forecasting is a predictive process where the future risk of a conjunction event is estimated. The method utilizes a Monte Carlo simulation that produces a likelihood distribution for a given collision threshold. Using known state and state uncertainty information, the simulation generates a set possible trajectories for a given space object pair. Each new trajectory produces a unique event geometry at the time of close approach. Given state uncertainty information for both objects, a collision probability value can be computed for every trail. This yields a

  7. Tsunami probability in the Caribbean Region

    USGS Publications Warehouse

    Parsons, T.; Geist, E.L.

    2008-01-01

    We calculated tsunami runup probability (in excess of 0.5 m) at coastal sites throughout the Caribbean region. We applied a Poissonian probability model because of the variety of uncorrelated tsunami sources in the region. Coastlines were discretized into 20 km by 20 km cells, and the mean tsunami runup rate was determined for each cell. The remarkable ???500-year empirical record compiled by O'Loughlin and Lander (2003) was used to calculate an empirical tsunami probability map, the first of three constructed for this study. However, it is unclear whether the 500-year record is complete, so we conducted a seismic moment-balance exercise using a finite-element model of the Caribbean-North American plate boundaries and the earthquake catalog, and found that moment could be balanced if the seismic coupling coefficient is c = 0.32. Modeled moment release was therefore used to generate synthetic earthquake sequences to calculate 50 tsunami runup scenarios for 500-year periods. We made a second probability map from numerically-calculated runup rates in each cell. Differences between the first two probability maps based on empirical and numerical-modeled rates suggest that each captured different aspects of tsunami generation; the empirical model may be deficient in primary plate-boundary events, whereas numerical model rates lack backarc fault and landslide sources. We thus prepared a third probability map using Bayesian likelihood functions derived from the empirical and numerical rate models and their attendant uncertainty to weight a range of rates at each 20 km by 20 km coastal cell. Our best-estimate map gives a range of 30-year runup probability from 0 - 30% regionally. ?? irkhaueser 2008.

  8. The Problem with Probability: Why rare hazards feel even rarer

    NASA Astrophysics Data System (ADS)

    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

  9. Computing Earthquake Probabilities on Global Scales

    NASA Astrophysics Data System (ADS)

    Holliday, James R.; Graves, William R.; Rundle, John B.; Turcotte, Donald L.

    2016-03-01

    Large devastating events in systems such as earthquakes, typhoons, market crashes, electricity grid blackouts, floods, droughts, wars and conflicts, and landslides can be unexpected and devastating. Events in many of these systems display frequency-size statistics that are power laws. Previously, we presented a new method for calculating probabilities for large events in systems such as these. This method counts the number of small events since the last large event and then converts this count into a probability by using a Weibull probability law. We applied this method to the calculation of large earthquake probabilities in California-Nevada, USA. In that study, we considered a fixed geographic region and assumed that all earthquakes within that region, large magnitudes as well as small, were perfectly correlated. In the present article, we extend this model to systems in which the events have a finite correlation length. We modify our previous results by employing the correlation function for near mean field systems having long-range interactions, an example of which is earthquakes and elastic interactions. We then construct an application of the method and show examples of computed earthquake probabilities.

  10. The role of probabilities in physics.

    PubMed

    Le Bellac, Michel

    2012-09-01

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

  11. Approximation of Failure Probability Using Conditional Sampling

    NASA Technical Reports Server (NTRS)

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

    2008-01-01

    In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.

  12. Classical and Quantum Probability for Biologists - Introduction

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei.

    2010-01-01

    The aim of this review (oriented to biologists looking for applications of QM) is to provide a detailed comparative analysis of classical (Kolmogorovian) and quantum (Dirac-von Neumann) models. We will stress differences in the definition of conditional probability and as a consequence in the structures of matrices of transition probabilities, especially the condition of double stochasticity which arises naturally in QM. One of the most fundamental differences between two models is deformation of the classical formula of total probability (FTP) which plays an important role in statistics and decision making. An additional term appears in the QM-version of FTP - so called interference term. Finally, we discuss Bell's inequality and show that the common viewpoint that its violation induces either nonlocality or "death of realism" has not been completely justified. For us it is merely a sign of non-Kolmogorovianity of probabilistic data collected in a few experiments with incompatible setups of measurement devices.

  13. Detection probability of EBPSK-MODEM system

    NASA Astrophysics Data System (ADS)

    Yao, Yu; Wu, Lenan

    2016-07-01

    Since the impacting filter-based receiver is able to transform phase modulation into amplitude peak, a simple threshold decision can detect the Extend-Binary Phase Shift Keying (EBPSK) modulated ranging signal in noise environment. In this paper, an analysis of the EBPSK-MODEM system output gives the probability density function for EBPSK modulated signals plus noise. The equation of detection probability (pd) for fluctuating and non-fluctuating targets has been deduced. Also, a comparison of the pd for the EBPSK-MODEM system and pulse radar receiver is made, and some results are plotted. Moreover, the probability curves of such system with several modulation parameters are analysed. When modulation parameter is not smaller than 6, the detection performance of EBPSK-MODEM system is more excellent than traditional radar system. In addition to theoretical considerations, computer simulations are provided for illustrating the performance.

  14. Transition Probabilities for Hydrogen-Like Atoms

    NASA Astrophysics Data System (ADS)

    Jitrik, Oliverio; Bunge, Carlos F.

    2004-12-01

    E1, M1, E2, M2, E3, and M3 transition probabilities for hydrogen-like atoms are calculated with point-nucleus Dirac eigenfunctions for Z=1-118 and up to large quantum numbers l=25 and n=26, increasing existing data more than a thousandfold. A critical evaluation of the accuracy shows a higher reliability with respect to previous works. Tables for hydrogen containing a subset of the results are given explicitly, listing the states involved in each transition, wavelength, term energies, statistical weights, transition probabilities, oscillator strengths, and line strengths. The complete results, including 1 863 574 distinct transition probabilities, lifetimes, and branching fractions are available at http://www.fisica.unam.mx/research/tables/spectra/1el

  15. Independent events in elementary probability theory

    NASA Astrophysics Data System (ADS)

    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): 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. 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.

  16. Local Directed Percolation Probability in Two Dimensions

    NASA Astrophysics Data System (ADS)

    Inui, Norio; Konno, Norio; Komatsu, Genichi; Kameoka, Koichi

    1998-01-01

    Using the series expansion method and Monte Carlo simulation,we study the directed percolation probability on the square lattice Vn0=\\{ (x,y) \\in {Z}2:x+y=even, 0 ≤ y ≤ n, - y ≤ x ≤ y \\}.We calculate the local percolationprobability Pnl defined as the connection probability between theorigin and a site (0,n). The critical behavior of P∞lis clearly different from the global percolation probability P∞g characterized by a critical exponent βg.An analysis based on the Padé approximants shows βl=2βg.In addition, we find that the series expansion of P2nl can be expressed as a function of Png.

  17. Sampling Quantum Nonlocal Correlations with High Probability

    NASA Astrophysics Data System (ADS)

    González-Guillén, C. E.; Jiménez, C. H.; Palazuelos, C.; Villanueva, I.

    2016-05-01

    It is well known that quantum correlations for bipartite dichotomic measurements are those of the form {γ=(< u_i,v_jrangle)_{i,j=1}^n}, where the vectors u i and v j are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of {α=m/n}, where the previous vectors are sampled according to the Haar measure in the unit sphere of {R^m}. In particular, we prove the existence of an {α_0 > 0} such that if {α≤ α_0}, {γ} is nonlocal with probability tending to 1 as {n→ ∞}, while for {α > 2}, {γ} is local with probability tending to 1 as {n→ ∞}.

  18. Match probabilities in racially admixed populations.

    PubMed

    Lange, K

    1993-02-01

    The calculation of match probabilities is the most contentious issue dividing prosecution and defense experts in the forensic applications of DNA fingerprinting. In particular, defense experts question the applicability of the population genetic laws of Hardy-Weinberg and linkage equilibrium to racially admixed American populations. Linkage equilibrium justifies the product rule for computing match probabilities across loci. The present paper suggests a method of bounding match probabilities that depends on modeling gene descent from ancestral populations to contemporary populations under the assumptions of Hardy-Weinberg and linkage equilibrium only in the ancestral populations. Although these bounds are conservative from the defendant's perspective, they should be small enough in practice to satisfy prosecutors.

  19. Genotypic probabilities for pairs of inbred relatives.

    PubMed

    Liu, Wenlei; Weir, B S

    2005-07-29

    Expressions for the joint genotypic probabilities of two related individuals are used in many population and quantitative genetic analyses. These expressions, resting on a set of 15 probabilities of patterns of identity by descent among the four alleles at a locus carried by the relatives, are generally well known. There has been recent interest in special cases where the two individuals are both related and inbred, although there have been differences among published results. Here, we return to the original 15-probability treatment and show appropriate reductions for relatives when they are drawn from a population that itself is inbred or when the relatives have parents who are related. These results have application in affected-relative tests for linkage, and in methods for interpreting forensic genetic profiles.

  20. Steering in spin tomographic probability representation

    NASA Astrophysics Data System (ADS)

    Man'ko, V. I.; Markovich, L. A.

    2016-09-01

    The steering property known for two-qubit state in terms of specific inequalities for the correlation function is translated for the state of qudit with the spin j = 3 / 2. Since most steering detection inequalities are based on the correlation functions we introduce analogs of such functions for the single qudit systems. The tomographic probability representation for the qudit states is applied. The connection between the correlation function in the two-qubit system and the single qudit is presented in an integral form with an intertwining kernel calculated explicitly in tomographic probability terms.

  1. Conditional Probabilities and Collapse in Quantum Measurements

    NASA Astrophysics Data System (ADS)

    Laura, Roberto; Vanni, Leonardo

    2008-09-01

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

  2. Survival probability for the stadium billiard

    NASA Astrophysics Data System (ADS)

    Dettmann, Carl P.; Georgiou, Orestis

    2009-12-01

    We consider the open stadium billiard, consisting of two semicircles joined by parallel straight sides with one hole situated somewhere on one of the sides. Due to the hyperbolic nature of the stadium billiard, the initial decay of trajectories, due to loss through the hole, appears exponential. However, some trajectories (bouncing ball orbits) persist and survive for long times and therefore form the main contribution to the survival probability function at long times. Using both numerical and analytical methods, we concur with previous studies that the long-time survival probability for a reasonably small hole drops like Constant×(; here we obtain an explicit expression for the Constant.

  3. Does Probability Interference Exist In Social Science?

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei Yu.; Haven, Emmanuel

    2007-02-01

    In this paper we discuss the rationale why sub(super)-additive probabilities in a psychological setting could be explained via the use of quantum probability interference. We propose to measure the complementarity of two variables: i) time of processing (by experiment participants) of (non-moving) images and ii) the ability (by experiment participants) of recognizing deformations of (non-moving) pictures. We argue in the paper why we can not find this complementarity using the Heisenberg Uncertainty Principle. The paper provides for the details on the experimental set up to test the complementarity.

  4. Random walks with similar transition probabilities

    NASA Astrophysics Data System (ADS)

    Schiefermayr, Klaus

    2003-04-01

    We consider random walks on the nonnegative integers with a possible absorbing state at -1. A random walk is called [alpha]-similar to a random walk if there exist constants Cij such that for the corresponding n-step transition probabilities , i,j[greater-or-equal, slanted]0, hold. We give necessary and sufficient conditions for the [alpha]-similarity of two random walks both in terms of the parameters and in terms of the corresponding spectral measures which appear in the spectral representation of the n-step transition probabilities developed by Karlin and McGregor.

  5. Quantum probability and quantum decision-making.

    PubMed

    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.

  6. Nonstationary envelope process and first excursion probability.

    NASA Technical Reports Server (NTRS)

    Yang, J.-N.

    1972-01-01

    The definition of stationary random envelope proposed by Cramer and Leadbetter, is extended to the envelope of nonstationary random process possessing evolutionary power spectral densities. The density function, the joint density function, the moment function, and the crossing rate of a level of the nonstationary envelope process are derived. Based on the envelope statistics, approximate solutions to the first excursion probability of nonstationary random processes are obtained. In particular, applications of the first excursion probability to the earthquake engineering problems are demonstrated in detail.

  7. Probabilities for separating sets of order statistics.

    PubMed

    Glueck, D H; Karimpour-Fard, A; Mandel, J; Muller, K E

    2010-04-01

    Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution functions. The probability that these order statistics fall in disjoint, ordered intervals and that of the smallest statistics, a certain number come from the first populations is given in terms of the two distribution functions. The result is applied to computing the joint probability of the number of rejections and the number of false rejections for the Benjamini-Hochberg false discovery rate procedure.

  8. Electric quadrupole transition probabilities for atomic lithium

    SciTech Connect

    Çelik, Gültekin; Gökçe, Yasin; Yıldız, Murat

    2014-05-15

    Electric quadrupole transition probabilities for atomic lithium have been calculated using the weakest bound electron potential model theory (WBEPMT). We have employed numerical non-relativistic Hartree–Fock wavefunctions for expectation values of radii and the necessary energy values have been taken from the compilation at NIST. The results obtained with the present method agree very well with the Coulomb approximation results given by Caves (1975). Moreover, electric quadrupole transition probability values not existing in the literature for some highly excited levels have been obtained using the WBEPMT.

  9. Non-Gaussian Photon Probability Distribution

    SciTech Connect

    Solomon, Benjamin T.

    2010-01-28

    This paper investigates the axiom that the photon's probability distribution is a Gaussian distribution. The Airy disc empirical evidence shows that the best fit, if not exact, distribution is a modified Gamma mGAMMA distribution (whose parameters are alpha = r, betar/sq root(u)) in the plane orthogonal to the motion of the photon. This modified Gamma distribution is then used to reconstruct the probability distributions along the hypotenuse from the pinhole, arc from the pinhole, and a line parallel to photon motion. This reconstruction shows that the photon's probability distribution is not a Gaussian function. However, under certain conditions, the distribution can appear to be Normal, thereby accounting for the success of quantum mechanics. This modified Gamma distribution changes with the shape of objects around it and thus explains how the observer alters the observation. This property therefore places additional constraints to quantum entanglement experiments. This paper shows that photon interaction is a multi-phenomena effect consisting of the probability to interact P{sub i}, the probabilistic function and the ability to interact A{sub i}, the electromagnetic function. Splitting the probability function P{sub i} from the electromagnetic function A{sub i} enables the investigation of the photon behavior from a purely probabilistic P{sub i} perspective. The Probabilistic Interaction Hypothesis is proposed as a consistent method for handling the two different phenomena, the probability function P{sub i} and the ability to interact A{sub i}, thus redefining radiation shielding, stealth or cloaking, and invisibility as different effects of a single phenomenon P{sub i} of the photon probability distribution. Sub wavelength photon behavior is successfully modeled as a multi-phenomena behavior. The Probabilistic Interaction Hypothesis provides a good fit to Otoshi's (1972) microwave shielding, Schurig et al.(2006) microwave cloaking, and Oulton et al.(2008) sub

  10. Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces

    SciTech Connect

    Vourdas, A.

    2014-08-15

    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{sub 1},H{sub 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{sub 1}),P(H{sub 2}), to the subspaces H{sub 1}, H{sub 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.

  11. Technique for Evaluating Multiple Probability Occurrences /TEMPO/

    NASA Technical Reports Server (NTRS)

    Mezzacappa, M. A.

    1970-01-01

    Technique is described for adjustment of engineering response information by broadening the application of statistical subjective stimuli theory. The study is specifically concerned with a mathematical evaluation of the expected probability of relative occurrence which can be identified by comparison rating techniques.

  12. The Smart Potential behind Probability Matching

    ERIC Educational Resources Information Center

    Gaissmaier, Wolfgang; Schooler, Lael J.

    2008-01-01

    Probability matching is a classic choice anomaly that has been studied extensively. While many approaches assume that it is a cognitive shortcut driven by cognitive limitations, recent literature suggests that it is not a strategy per se, but rather another outcome of people's well-documented misperception of randomness. People search for patterns…

  13. Assessing Schematic Knowledge of Introductory Probability Theory

    ERIC Educational Resources Information Center

    Birney, Damian P.; Fogarty, Gerard J.; Plank, Ashley

    2005-01-01

    The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to…

  14. Automatic Item Generation of Probability Word Problems

    ERIC Educational Resources Information Center

    Holling, Heinz; Bertling, Jonas P.; Zeuch, Nina

    2009-01-01

    Mathematical word problems represent a common item format for assessing student competencies. Automatic item generation (AIG) is an effective way of constructing many items with predictable difficulties, based on a set of predefined task parameters. The current study presents a framework for the automatic generation of probability word problems…

  15. Probable Bright Supernovae discovered by PSST

    NASA Astrophysics Data System (ADS)

    Smith, K. W.; Wright, D.; Smartt, S. J.; Huber, M.; Chambers, K. C.; Flewelling, H.; Willman, M.; Primak, N.; Schultz, A.; Gibson, B.; Magnier, E.; Waters, C.; Tonry, J.; Wainscoat, R. J.; Foley, R. J.; Jha, S. W.; Rest, A.; Scolnic, D.

    2016-01-01

    Three bright transients, which are probable supernovae, have been discovered as part of the Pan-STARRS Survey for Transients (PSST). Information on all objects discovered by the Pan-STARRS Survey for Transients is available at http://star.pst.qub.ac.uk/ps1threepi/ (see Huber et al. ATel #7153).

  16. Probable Bright Supernova discovered by PSST

    NASA Astrophysics Data System (ADS)

    Smith, K. W.; Wright, D.; Smartt, S. J.; Young, D. R.; Huber, M.; Chambers, K. C.; Flewelling, H.; Willman, M.; Primak, N.; Schultz, A.; Gibson, B.; Magnier, E.; Waters, C.; Tonry, J.; Wainscoat, R. J.; Foley, R. J.; Jha, S. W.; Rest, A.; Scolnic, D.

    2016-09-01

    A bright transient, which is a probable supernova, has been discovered as part of the Pan-STARRS Survey for Transients (PSST). Information on all objects discovered by the Pan-STARRS Survey for Transients is available at http://star.pst.qub.ac.uk/ps1threepi/ (see Huber et al. ATel #7153).

  17. Probability distribution functions in turbulent convection

    NASA Technical Reports Server (NTRS)

    Balachandar, S.; Sirovich, L.

    1991-01-01

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

  18. Confusion between Odds and Probability, a Pandemic?

    ERIC Educational Resources Information Center

    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…

  19. Posterior Probabilities for a Consensus Ordering.

    ERIC Educational Resources Information Center

    Fligner, Michael A.; Verducci, Joseph S.

    1990-01-01

    The concept of consensus ordering is defined, and formulas for exact and approximate posterior probabilities for consensus ordering are developed under the assumption of a generalized Mallows' model with a diffuse conjugate prior. These methods are applied to a data set concerning 98 college students. (SLD)

  20. Quantum temporal probabilities in tunneling systems

    NASA Astrophysics Data System (ADS)

    Anastopoulos, Charis; Savvidou, Ntina

    2013-09-01

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

  1. Teaching Mathematics with Technology: Probability Simulations.

    ERIC Educational Resources Information Center

    Bright, George W.

    1989-01-01

    Discussed are the use of probability simulations in a mathematics classroom. Computer simulations using regular dice and special dice are described. Sample programs used to generate 100 rolls of a pair of dice in BASIC and Logo languages are provided. (YP)

  2. Conceptual Variation and Coordination in Probability Reasoning

    ERIC Educational Resources Information Center

    Nilsson, Per

    2009-01-01

    This study investigates students' conceptual variation and coordination among theoretical and experimental interpretations of probability. In the analysis we follow how Swedish students (12-13 years old) interact with a dice game, specifically designed to offer the students opportunities to elaborate on the logic of sample space,…

  3. Probability in Action: The Red Traffic Light

    ERIC Educational Resources Information Center

    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…

  4. Independent Events in Elementary Probability Theory

    ERIC Educational Resources Information Center

    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],…

  5. Large Deviations: Advanced Probability for Undergrads

    ERIC Educational Resources Information Center

    Rolls, David A.

    2007-01-01

    In the branch of probability called "large deviations," rates of convergence (e.g. of the sample mean) are considered. The theory makes use of the moment generating function. So, particularly for sums of independent and identically distributed random variables, the theory can be made accessible to senior undergraduates after a first course in…

  6. Monte Carlo methods to calculate impact probabilities

    NASA Astrophysics Data System (ADS)

    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

  7. There Once Was a 9-Block ...--A Middle-School Design for Probability and Statistics

    ERIC Educational Resources Information Center

    Abrahamson, Dor; Janusz, Ruth M.; Wilensky, Uri

    2006-01-01

    ProbLab is a probability-and-statistics unit developed at the Center for Connected Learning and Computer-Based Modeling, Northwestern University. Students analyze the combinatorial space of the 9-block, a 3-by-3 grid of squares, in which each square can be either green or blue. All 512 possible 9-blocks are constructed and assembled in a "bar…

  8. Chance and Probability: What Do They Mean to University Engineering Students?

    ERIC Educational Resources Information Center

    Barragues, J. I.; Guisasola, J.; Morais, A.

    2006-01-01

    The great interest aroused by the incorporation of Statistics and Probability into curricular projects has been accompanied by considerable evidence of significant difficulties in the meaningful learning and application of the concepts. These difficulties have been the subject of many studies, mostly concerning secondary school students. This…

  9. Developing a Model and Applications for Probabilities of Student Success: A Case Study of Predictive Analytics

    ERIC Educational Resources Information Center

    Calvert, Carol Elaine

    2014-01-01

    This case study relates to distance learning students on open access courses. It demonstrates the use of predictive analytics to generate a model of the probabilities of success and retention at different points, or milestones, in a student journey. A core set of explanatory variables has been established and their varying relative importance at…

  10. Phonotactic Probabilities at the Onset of Language Development: Speech Production and Word Position

    ERIC Educational Resources Information Center

    Zamuner, Tania S.

    2009-01-01

    Purpose: To examine the role of phonotactic probabilities at the onset of language development, in a new language (Dutch), while controlling for word position. Method: Using a nonword imitation task, 64 Dutch-learning children (age 2;2-2;8 [years;months]) were tested on how they imitated segments in low- and high-phonotactic probability…

  11. A Computational Model of Word Segmentation from Continuous Speech Using Transitional Probabilities of Atomic Acoustic Events

    ERIC Educational Resources Information Center

    Rasanen, Okko

    2011-01-01

    Word segmentation from continuous speech is a difficult task that is faced by human infants when they start to learn their native language. Several studies indicate that infants might use several different cues to solve this problem, including intonation, linguistic stress, and transitional probabilities between subsequent speech sounds. In this…

  12. The Independent Effects of Phonotactic Probability and Neighbourhood Density on Lexical Acquisition by Preschool Children

    ERIC Educational Resources Information Center

    Storkel, Holly L.; Lee, Su-Yeon

    2011-01-01

    The goal of this research was to disentangle effects of phonotactic probability, the likelihood of occurrence of a sound sequence, and neighbourhood density, the number of phonologically similar words, in lexical acquisition. Two-word learning experiments were conducted with 4-year-old children. Experiment 1 manipulated phonotactic probability…

  13. Quantum temporal probabilities in tunneling systems

    SciTech Connect

    Anastopoulos, Charis Savvidou, Ntina

    2013-09-15

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

  14. The albedo effect on neutron transmission probability.

    PubMed

    Khanouchi, A; Sabir, A; Boulkheir, M; Ichaoui, R; Ghassoun, J; Jehouani, A

    1997-01-01

    The aim of this study is to evaluate the albedo effect on the neutron transmission probability through slab shields. For this reason we have considered an infinite homogeneous slab having a fixed thickness equal to 20 lambda (lambda is the mean free path of the neutron in the slab). This slab is characterized by the factor Ps (scattering probability) and contains a vacuum channel which is formed by two horizontal parts and an inclined one (David, M. C. (1962) Duc and Voids in shields. In Reactor Handbook, Vol. III, Part B, p. 166). The thickness of the vacuum channel is taken equal to 2 lambda. An infinite plane source of neutrons is placed on the first of the slab (left face) and detectors, having windows equal to 2 lambda, are placed on the second face of the slab (right face). Neutron histories are sampled by the Monte Carlo method (Booth, T. E. and Hendricks, J. S. (1994) Nuclear Technology 5) using exponential biasing in order to increase the Monte Carlo calculation efficiency (Levitt, L. B. (1968) Nuclear Science and Engineering 31, 500-504; Jehouani, A., Ghassoun, J. and Abouker, A. (1994) In Proceedings of the 6th International Symposium on Radiation Physics, Rabat, Morocco) and we have applied the statistical weight method which supposes that the neutron is born at the source with a unit statistical weight and after each collision this weight is corrected. For different values of the scattering probability and for different slopes of the inclined part of the channel we have calculated the neutron transmission probability for different positions of the detectors versus the albedo at the vacuum channel-medium interface. Some analytical representations are also presented for these transmission probabilities. PMID:9463883

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

    ERIC Educational Resources Information Center

    Satake, Eiki; Amato, Philip P.

    2008-01-01

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

  16. Killeen's Probability of Replication and Predictive Probabilities: How to Compute, Use, and Interpret Them

    ERIC Educational Resources Information Center

    Lecoutre, Bruno; Lecoutre, Marie-Paule; Poitevineau, Jacques

    2010-01-01

    P. R. Killeen's (2005a) probability of replication ("p[subscript rep]") of an experimental result is the fiducial Bayesian predictive probability of finding a same-sign effect in a replication of an experiment. "p[subscript rep]" is now routinely reported in "Psychological Science" and has also begun to appear in other journals. However, there is…

  17. You Say "Probable" and I Say "Likely": Improving Interpersonal Communication With Verbal Probability Phrases

    ERIC Educational Resources Information Center

    Karelitz, Tzur M.; Budescu, David V.

    2004-01-01

    When forecasters and decision makers describe uncertain events using verbal probability terms, there is a risk of miscommunication because people use different probability phrases and interpret them in different ways. In an effort to facilitate the communication process, the authors investigated various ways of converting the forecasters' verbal…

  18. Using High-Probability Foods to Increase the Acceptance of Low-Probability Foods

    ERIC Educational Resources Information Center

    Meier, Aimee E.; Fryling, Mitch J.; Wallace, Michele D.

    2012-01-01

    Studies have evaluated a range of interventions to treat food selectivity in children with autism and related developmental disabilities. The high-probability instructional sequence is one intervention with variable results in this area. We evaluated the effectiveness of a high-probability sequence using 3 presentations of a preferred food on…

  19. VOLCANIC RISK ASSESSMENT - PROBABILITY AND CONSEQUENCES

    SciTech Connect

    G.A. Valentine; F.V. Perry; S. Dartevelle

    2005-08-26

    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

  20. Approaches to Evaluating Probability of Collision Uncertainty

    NASA Technical Reports Server (NTRS)

    Hejduk, Matthew D.; Johnson, Lauren C.

    2016-01-01

    While the two-dimensional probability of collision (Pc) calculation has served as the main input to conjunction analysis risk assessment for over a decade, it has done this mostly as a point estimate, with relatively little effort made to produce confidence intervals on the Pc value based on the uncertainties in the inputs. The present effort seeks to try to carry these uncertainties through the calculation in order to generate a probability density of Pc results rather than a single average value. Methods for assessing uncertainty in the primary and secondary objects' physical sizes and state estimate covariances, as well as a resampling approach to reveal the natural variability in the calculation, are presented; and an initial proposal for operationally-useful display and interpretation of these data for a particular conjunction is given.

  1. Estimation of transition probabilities of credit ratings

    NASA Astrophysics Data System (ADS)

    Peng, Gan Chew; Hin, Pooi Ah

    2015-12-01

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

  2. Conflict Probability Estimation for Free Flight

    NASA Technical Reports Server (NTRS)

    Paielli, Russell A.; Erzberger, Heinz

    1996-01-01

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

  3. A quantum probability perspective on borderline vagueness.

    PubMed

    Blutner, Reinhard; Pothos, Emmanuel M; Bruza, Peter

    2013-10-01

    The term "vagueness" describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon. PMID:24039093

  4. Approximate probability distributions of the master equation

    NASA Astrophysics Data System (ADS)

    Thomas, Philipp; Grima, Ramon

    2015-07-01

    Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.

  5. Earthquake probabilities: theoretical assessments and reality

    NASA Astrophysics Data System (ADS)

    Kossobokov, V. G.

    2013-12-01

    It is of common knowledge that earthquakes are complex phenomena which classification and sizing remain serious problems of the contemporary seismology. In general, their frequency-magnitude distribution exhibit power law scaling. This scaling differs significantly when different time and/or space domains are considered. At the scale of a particular earthquake rupture zone the frequency of similar size events is usually estimated to be about once in several hundred years. Evidently, contemporary seismology does not possess enough reported instrumental data for any reliable quantification of an earthquake probability at a given place of expected event. Regretfully, most of the state-of-the-art theoretical approaches to assess probability of seismic events are based on trivial (e.g. Poisson, periodic, etc) or, conversely, delicately-designed (e.g. STEP, ETAS, etc) models of earthquake sequences. Some of these models are evidently erroneous, some can be rejected by the existing statistics, and some are hardly testable in our life-time. Nevertheless such probabilistic counts including seismic hazard assessment and earthquake forecasting when used on practice eventually mislead to scientifically groundless advices communicated to decision makers and inappropriate decisions. As a result, the population of seismic regions continues facing unexpected risk and losses. The international project Global Earthquake Model (GEM) is on the wrong track, if it continues to base seismic risk estimates on the standard, mainly probabilistic, methodology to assess seismic hazard. It is generally accepted that earthquakes are infrequent, low-probability events. However, they keep occurring at earthquake-prone areas with 100% certainty. Given the expectation of seismic event once per hundred years, the daily probability of occurrence on a certain date may range from 0 to 100% depending on a choice of probability space (which is yet unknown and, therefore, made by a subjective lucky chance

  6. Cheating Probabilities on Multiple Choice Tests

    NASA Astrophysics Data System (ADS)

    Rizzuto, Gaspard T.; Walters, Fred

    1997-10-01

    This paper is strictly based on mathematical statistics and as such does not depend on prior performance and assumes the probability of each choice to be identical. In a real life situation, the probability of two students having identical responses becomes larger the better the students are. However the mathematical model is developed for all responses, both correct and incorrect, and provides a baseline for evaluation. David Harpp and coworkers (2, 3) at McGill University have evaluated ratios of exact errors in common (EEIC) to errors in common (EIC) and differences (D). In pairings where the ratio EEIC/EIC was greater than 0.75, the pair had unusually high odds against their answer pattern being random. Detection of copying of the EEIC/D ratios at values >1.0 indicate that pairs of these students were seated adjacent to one another and copied from one another. The original papers should be examined for details.

  7. A quantum probability perspective on borderline vagueness.

    PubMed

    Blutner, Reinhard; Pothos, Emmanuel M; Bruza, Peter

    2013-10-01

    The term "vagueness" describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon.

  8. Multiple model cardinalized probability hypothesis density filter

    NASA Astrophysics Data System (ADS)

    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.

  9. Nuclear data uncertainties: I, Basic concepts of probability

    SciTech Connect

    Smith, D.L.

    1988-12-01

    Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs.

  10. Non-signalling Theories and Generalized Probability

    NASA Astrophysics Data System (ADS)

    Tylec, Tomasz I.; Kuś, Marek; Krajczok, Jacek

    2016-09-01

    We provide mathematically rigorous justification of using term probability in connection to the so called non-signalling theories, known also as Popescu's and Rohrlich's box worlds. No only do we prove correctness of these models (in the sense that they describe composite system of two independent subsystems) but we obtain new properties of non-signalling boxes and expose new tools for further investigation. Moreover, it allows strightforward generalization to more complicated systems.

  11. Probability of photoassociation from a quasicontinuum approach

    NASA Astrophysics Data System (ADS)

    Javanainen, Juha; Mackie, Matt

    1998-08-01

    We examine photoassociation by using a quasicontinuum to describe the colliding atoms. The quasicontinuum system is analyzed using methods adapted from the theory of laser spectroscopy and quantum optics, and a continuum limit is then taken. In a degenerate gas the equilibrium probability of photoassociation may be close to unity. In the continuum limit, for a thermal atomic sample, the stimulated Raman adiabatic passage (STIRAP) mechanism cannot be employed to eliminate unwanted spontaneous transitions.

  12. Neural coding of uncertainty and probability.

    PubMed

    Ma, Wei Ji; Jazayeri, Mehrdad

    2014-01-01

    Organisms must act in the face of sensory, motor, and reward uncertainty stemming from a pandemonium of stochasticity and missing information. In many tasks, organisms can make better decisions if they have at their disposal a representation of the uncertainty associated with task-relevant variables. We formalize this problem using Bayesian decision theory and review recent behavioral and neural evidence that the brain may use knowledge of uncertainty, confidence, and probability.

  13. Computational methods for probability of instability calculations

    NASA Technical Reports Server (NTRS)

    Wu, Y.-T.; Burnside, O. H.

    1990-01-01

    This paper summarizes the development of the methods and a computer program to compute the probability of instability of a dynamic system than can be represented by a system of second-order ordinary linear differential equations. Two instability criteria based upon the roots of the characteristics equation or Routh-Hurwitz test functions are investigated. Computational methods based on system reliability analysis methods and importance sampling concepts are proposed to perform efficient probabilistic analysis. Numerical examples are provided to demonstrate the methods.

  14. Probability and Statistics in Aerospace Engineering

    NASA Technical Reports Server (NTRS)

    Rheinfurth, M. H.; Howell, L. W.

    1998-01-01

    This monograph was prepared to give the practicing engineer a clear understanding of probability and statistics with special consideration to problems frequently encountered in aerospace engineering. It is conceived to be both a desktop reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject.

  15. Neural coding of uncertainty and probability.

    PubMed

    Ma, Wei Ji; Jazayeri, Mehrdad

    2014-01-01

    Organisms must act in the face of sensory, motor, and reward uncertainty stemming from a pandemonium of stochasticity and missing information. In many tasks, organisms can make better decisions if they have at their disposal a representation of the uncertainty associated with task-relevant variables. We formalize this problem using Bayesian decision theory and review recent behavioral and neural evidence that the brain may use knowledge of uncertainty, confidence, and probability. PMID:25032495

  16. Sampling probability distributions of lesions in mammograms

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

  17. Probability with Collaborative Data Visualization Software

    ERIC Educational Resources Information Center

    Willis, Melinda B. N.; Hay, Sue; Martin, Fred G.; Scribner-MacLean, Michelle; Rudnicki, Ivan

    2015-01-01

    Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

  18. Probability Explorations in a Multicultural Context

    ERIC Educational Resources Information Center

    Naresh, Nirmala; Harper, Suzanne R.; Keiser, Jane M.; Krumpe, Norm

    2014-01-01

    Mathematical ideas exist and develop in many different cultures. From this multicultural perspective, teachers can use a variety of approaches to acknowledge the role of culture in the teaching and learning of mathematics. Curricular materials that "emphasize both the mathematical and sociocultural aspects" not only help teachers achieve…

  19. Finding Possibility and Probability Lessons in Sports

    ERIC Educational Resources Information Center

    Busadee, Nutjira; Laosinchai, Parames; Panijpan, Bhinyo

    2011-01-01

    Today's students demand that their lessons be real, interesting, relevant, and manageable. Mathematics is one subject that eludes many students partly because its traditional presentation lacks those elements that encourage students to learn. Easy accessibility through electronic media has exposed people all over the world to a variety of sports…

  20. Understanding Deutsch's probability in a deterministic multiverse

    NASA Astrophysics Data System (ADS)

    Greaves, H.

    2004-09-01

    Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from 'probability' without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular rationality principle. The decision-theoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future Everettian measurement outcome is subjective uncertainty. I argue that subjective uncertainty is not available to the Everettian, but I offer an alternative: we can justify the Everettian application of decision theory on the basis that an Everettian should care about all her future branches. The probabilities appearing in the decision-theoretic representation theorem can then be interpreted as the degrees to which the rational agent cares about each future branch. This reinterpretation, however, reduces the intuitive plausibility of one of the Deutsch-Wallace axioms (measurement neutrality).

  1. The Probability Distribution of Daily Streamflow

    NASA Astrophysics Data System (ADS)

    Blum, A.; Vogel, R. M.

    2015-12-01

    Flow duration curves (FDCs) are a graphical illustration of the cumulative distribution of streamflow. Daily streamflows often range over many orders of magnitude, making it extremely challenging to find a probability distribution function (pdf) which can mimic the steady state or period of record FDC (POR-FDC). Median annual FDCs (MA-FDCs) describe the pdf of daily streamflow in a typical year. For POR- and MA-FDCs, Lmoment diagrams, visual assessments of FDCs and Quantile-Quantile probability plot correlation coefficients are used to evaluate goodness of fit (GOF) of candidate probability distributions. FDCs reveal that both four-parameter kappa (KAP) and three-parameter generalized Pareto (GP3) models result in very high GOF for the MA-FDC and a relatively lower GOF for POR-FDCs at over 500 rivers across the coterminous U.S. Physical basin characteristics, such as baseflow index as well as hydroclimatic indices such as the aridity index and the runoff ratio are found to be correlated with one of the shape parameters (kappa) of the KAP and GP3 pdfs. Our work also reveals several important areas for future research including improved parameter estimators for the KAP pdf, as well as increasing our understanding of the conditions which give rise to improved GOF of analytical pdfs to large samples of daily streamflows.

  2. Detection probabilities in fuel cycle oriented safeguards

    SciTech Connect

    Canty, J.J.; Stein, G.; Avenhaus, R. )

    1987-01-01

    An intensified discussion of evaluation criteria for International Atomic Energy Agency (IAEA) safeguards effectiveness is currently under way. Considerations basic to the establishment of such criteria are derived from the model agreement INFCIRC/153 and include threshold amounts, strategic significance, conversion times, required assurances, cost-effectiveness, and nonintrusiveness. In addition to these aspects, the extent to which fuel cycle characteristics are taken into account in safeguards implementations (Article 81c of INFCIRC/153) will be reflected in the criteria. The effectiveness of safeguards implemented under given manpower constraints is evaluated. As the significant quantity and timeliness criteria have established themselves within the safeguards community, these are taken as fixed. Detection probabilities, on the other hand, still provide a certain degree of freedom in interpretation. The problem of randomization of inspection activities across a fuel cycle, or portions thereof, is formalized as a two-person zero-sum game, the payoff function of which is the detection probability achieved by the inspectorate. It is argued, from the point of view of risk of detection, that fuel cycle-independent, minimally accepted threshold criteria for such detection probabilities cannot and should not be applied.

  3. Augmenting Transition Probabilities for Neutral Atomic Nitrogen

    NASA Technical Reports Server (NTRS)

    Terrazas-Salines, Imelda; Park, Chul; Strawa, Anthony W.; Hartman, G. Joseph (Technical Monitor)

    1996-01-01

    The transition probability values for a number of neutral atomic nitrogen (NI) lines in the visible wavelength range are determined in order to augment those given in the National Bureau of Standards Tables. These values are determined from experimentation as well as by using the published results of other investigators. The experimental determination of the lines in the 410 to 430 nm range was made from the observation of the emission from the arc column of an arc-heated wind tunnel. The transition probability values of these NI lines are determined to an accuracy of +/- 30% by comparison of their measured intensities with those of the atomic oxygen (OI) multiplet at around 615 nm. The temperature of the emitting medium is determined both using a multiple-layer model, based on a theoretical model of the flow in the arc column, and an empirical single-layer model. The results show that the two models lead to the same values of transition probabilities for the NI lines.

  4. Bacteria survival probability in bactericidal filter paper.

    PubMed

    Mansur-Azzam, Nura; Hosseinidoust, Zeinab; Woo, Su Gyeong; Vyhnalkova, Renata; Eisenberg, Adi; van de Ven, Theo G M

    2014-05-01

    Bactericidal filter papers offer the simplicity of gravity filtration to simultaneously eradicate microbial contaminants and particulates. We previously detailed the development of biocidal block copolymer micelles that could be immobilized on a filter paper to actively eradicate bacteria. Despite the many advantages offered by this system, its widespread use is hindered by its unknown mechanism of action which can result in non-reproducible outcomes. In this work, we sought to investigate the mechanism by which a certain percentage of Escherichia coli cells survived when passing through the bactericidal filter paper. Through the process of elimination, the possibility that the bacterial survival probability was controlled by the initial bacterial load or the existence of resistant sub-populations of E. coli was dismissed. It was observed that increasing the thickness or the number of layers of the filter significantly decreased bacterial survival probability for the biocidal filter paper but did not affect the efficiency of the blank filter paper (no biocide). The survival probability of bacteria passing through the antibacterial filter paper appeared to depend strongly on the number of collision between each bacterium and the biocide-loaded micelles. It was thus hypothesized that during each collision a certain number of biocide molecules were directly transferred from the hydrophobic core of the micelle to the bacterial lipid bilayer membrane. Therefore, each bacterium must encounter a certain number of collisions to take up enough biocide to kill the cell and cells that do not undergo the threshold number of collisions are expected to survive.

  5. Learning to Learn

    ERIC Educational Resources Information Center

    Roberts, Dominic

    2010-01-01

    Everyone learns in a different way--for some, learning comes naturally, but for others it can be a real struggle. Many negative experiences of education are a result of individuals not knowing how they learn most effectively, or believing that they do not have the capacity to learn well. Addressing the issues of how individuals learn can help…

  6. Instability of Wave Trains and Wave Probabilities

    NASA Astrophysics Data System (ADS)

    Babanin, Alexander

    2013-04-01

    Centre for Ocean Engineering, Science and Technology, Swinburne University of Technology, Melbourne, Australia, ababanin@swin.edu.au Design criteria in ocean engineering, whether this is one in 50 years or one in 5000 years event, are hardly ever based on measurements, and rather on statistical distributions of relevant metocean properties. Of utmost interest is the tail of distribution, that is rare events such as the highest waves with low probability. Engineers have long since realised that the superposition of linear waves with narrow-banded spectrum as depicted by the Rayleigh distribution underestimates the probability of extreme wave heights and crests, which is a critical shortcoming as far as the engineering design is concerned. Ongoing theoretical and experimental efforts have been under way for decades to address this issue. Typical approach is the treating all possible waves in the ocean or at a particular location as a single ensemble for which some comprehensive solution can be obtained. The oceanographic knowledge, however, now indicates that no single and united comprehensive solution is available. We would expect the probability distributions of wave height to depend on a) whether the waves are at the spectral peak or at the tail; b) on wave spectrum and mean steepness in the wave field; c) on the directional distribution of the peak waves; d) on whether the waves are in deep water, in intermediate depth or in shallow water; e) on wave breaking; f) on the wind, particularly if it is very strong, and on the currents if they have suitable horizontal gradients. Probability distributions in the different circumstances according to these groups of conditions should be different, and by combining them together the inevitable scatter is introduced. The scatter and the accuracy will not improve by increasing the bulk data quality and quantity, and it hides the actual distribution of extremes. The groups have to be separated and their probability

  7. Determination of riverbank erosion probability using Locally Weighted Logistic Regression

    NASA Astrophysics Data System (ADS)

    Ioannidou, Elena; Flori, Aikaterini; Varouchakis, Emmanouil A.; Giannakis, Georgios; Vozinaki, Anthi Eirini K.; Karatzas, George P.; Nikolaidis, Nikolaos

    2015-04-01

    erosion occurrence probability can be calculated in conjunction with the model deviance regarding the independent variables tested. The most straightforward measure for goodness of fit is the G statistic. It is a simple and effective way to study and evaluate the Logistic Regression model efficiency and the reliability of each independent variable. The developed statistical model is applied to the Koiliaris River Basin on the island of Crete, Greece. Two datasets of river bank slope, river cross-section width and indications of erosion were available for the analysis (12 and 8 locations). Two different types of spatial dependence functions, exponential and tricubic, were examined to determine the local spatial dependence of the independent variables at the measurement locations. The results show a significant improvement when the tricubic function is applied as the erosion probability is accurately predicted at all eight validation locations. Results for the model deviance show that cross-section width is more important than bank slope in the estimation of erosion probability along the Koiliaris riverbanks. The proposed statistical model is a useful tool that quantifies the erosion probability along the riverbanks and can be used to assist managing erosion and flooding events. Acknowledgements This work is part of an on-going THALES project (CYBERSENSORS - High Frequency Monitoring System for Integrated Water Resources Management of Rivers). The project has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.

  8. Probability sampling in legal cases: Kansas cellphone users

    NASA Astrophysics Data System (ADS)

    Kadane, Joseph B.

    2012-10-01

    Probability sampling is a standard statistical technique. This article introduces the basic ideas of probability sampling, and shows in detail how probability sampling was used in a particular legal case.

  9. CPROB: A COMPUTATIONAL TOOL FOR CONDUCTING CONDITIONAL PROBABILITY ANALYSIS

    EPA Science Inventory

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

  10. Taking the easy way out? Increasing implementation effort reduces probability maximizing under cognitive load.

    PubMed

    Schulze, Christin; Newell, Ben R

    2016-07-01

    Cognitive load has previously been found to have a positive effect on strategy selection in repeated risky choice. Specifically, whereas inferior probability matching often prevails under single-task conditions, optimal probability maximizing sometimes dominates when a concurrent task competes for cognitive resources. We examined the extent to which this seemingly beneficial effect of increased task demands hinges on the effort required to implement each of the choice strategies. Probability maximizing typically involves a simple repeated response to a single option, whereas probability matching requires choice proportions to be tracked carefully throughout a sequential choice task. Here, we flipped this pattern by introducing a manipulation that made the implementation of maximizing more taxing and, at the same time, allowed decision makers to probability match via a simple repeated response to a single option. The results from two experiments showed that increasing the implementation effort of probability maximizing resulted in decreased adoption rates of this strategy. This was the case both when decision makers simultaneously learned about the outcome probabilities and responded to a dual task (Exp. 1) and when these two aspects were procedurally separated in two distinct stages (Exp. 2). We conclude that the effort involved in implementing a choice strategy is a key factor in shaping repeated choice under uncertainty. Moreover, highlighting the importance of implementation effort casts new light on the sometimes surprising and inconsistent effects of cognitive load that have previously been reported in the literature.

  11. Taking the easy way out? Increasing implementation effort reduces probability maximizing under cognitive load.

    PubMed

    Schulze, Christin; Newell, Ben R

    2016-07-01

    Cognitive load has previously been found to have a positive effect on strategy selection in repeated risky choice. Specifically, whereas inferior probability matching often prevails under single-task conditions, optimal probability maximizing sometimes dominates when a concurrent task competes for cognitive resources. We examined the extent to which this seemingly beneficial effect of increased task demands hinges on the effort required to implement each of the choice strategies. Probability maximizing typically involves a simple repeated response to a single option, whereas probability matching requires choice proportions to be tracked carefully throughout a sequential choice task. Here, we flipped this pattern by introducing a manipulation that made the implementation of maximizing more taxing and, at the same time, allowed decision makers to probability match via a simple repeated response to a single option. The results from two experiments showed that increasing the implementation effort of probability maximizing resulted in decreased adoption rates of this strategy. This was the case both when decision makers simultaneously learned about the outcome probabilities and responded to a dual task (Exp. 1) and when these two aspects were procedurally separated in two distinct stages (Exp. 2). We conclude that the effort involved in implementing a choice strategy is a key factor in shaping repeated choice under uncertainty. Moreover, highlighting the importance of implementation effort casts new light on the sometimes surprising and inconsistent effects of cognitive load that have previously been reported in the literature. PMID:26884088

  12. [Subjective probability of reward receipt and the magnitude effect in probability discounting].

    PubMed

    Isomura, Mieko; Aoyama, Kenjiro

    2008-06-01

    Previous research suggested that larger probabilistic rewards were discounted more steeply than smaller probabilistic rewards (the magnitude effect). This research tests the hypothesis that the magnitude effect reflects the extent to which individuals distrust the stated probability of receiving different amounts of rewards. The participants were 105 college students. Probability discounting of two different amounts of rewards (5 000 yen and 100 000 yen) and the subjective probability of reward receipt of the different amounts (5 000 yen, 100 000 yen and 1 000 000 yen) were measured. The probabilistic 100 000 yen was discounted more steeply than the probabilistic 5 000 yen. The subjective probability of reward receipt was higher in the 5 000 yen than in the 100 000 yen condition. The proportion of subjective probability of receiving 5 000 yen to that of receiving 100 000 yen was significantly correlated with the proportion of degree of probability discounting for 5 000 yen to that for 100 000 yen. These results were consistent with the hypothesis stated above.

  13. On the universality of knot probability ratios

    NASA Astrophysics Data System (ADS)

    Janse van Rensburg, E. J.; Rechnitzer, A.

    2011-04-01

    Let pn denote the number of self-avoiding polygons of length n on a regular three-dimensional lattice, and let pn(K) be the number which have knot type K. The probability that a random polygon of length n has knot type K is pn(K)/pn 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 pn(K), but there is substantial numerical evidence (Orlandini et al 1988 J. Phys. A: Math. Gen. 31 5953-67, Marcone et al 2007 Phys. Rev. E 75 41105, Rawdon et al 2008 Macromolecules 41 4444-51, Janse van Rensburg and Rechnitzer 2008 J. Phys. A: Math. Theor. 41 105002) that pn(K) grows as p_n(K) \\simeq C_K \\mu _\\emptyset ^n n^{\\alpha -3+N_K}, \\qquad as\\quad n \\rightarrow \\infty, where NK is the number of prime components of the knot type K. It is believed that the entropic exponent, α, is universal, while the exponential growth rate, μ∅, is independent of the knot type but varies with the lattice. The amplitude, CK, 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 is \\frac{p_n(K)/p_n}{p_n(L)/p_n} = \\frac{p_n(K)}{p_n(L)} \\simeq \\left[ \\frac{C_K}{C_L} \\right].\\\\[-8pt] 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

  14. Snell Envelope with Small Probability Criteria

    SciTech Connect

    Del Moral, Pierre Hu, Peng; Oudjane, Nadia

    2012-12-15

    We present a new algorithm to compute the Snell envelope in the specific case where the criteria to optimize is associated with a small probability or a rare event. This new approach combines the Stochastic Mesh approach of Broadie and Glasserman with a particle approximation scheme based on a specific change of measure designed to concentrate the computational effort in regions pointed out by the criteria. The theoretical analysis of this new algorithm provides non asymptotic convergence estimates. Finally, the numerical tests confirm the practical interest of this approach.

  15. Modulation Based on Probability Density Functions

    NASA Technical Reports Server (NTRS)

    Williams, Glenn L.

    2009-01-01

    A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.

  16. Symmetry, probability, and recognition in face space.

    PubMed

    Sirovich, Lawrence; Meytlis, Marsha

    2009-04-28

    The essential midline symmetry of human faces is shown to play a key role in facial coding and recognition. This also has deep and important connections with recent explorations of the organization of primate cortex, as well as human psychophysical experiments. Evidence is presented that the dimension of face recognition space for human faces is dramatically lower than previous estimates. One result of the present development is the construction of a probability distribution in face space that produces an interesting and realistic range of (synthetic) faces. Another is a recognition algorithm that by reasonable criteria is nearly 100% accurate.

  17. The Prediction of Spatial Aftershock Probabilities (PRESAP)

    NASA Astrophysics Data System (ADS)

    McCloskey, J.

    2003-12-01

    It is now widely accepted that the goal of deterministic earthquake prediction is unattainable in the short term and may even be forbidden by nonlinearity in the generating dynamics. This nonlinearity does not, however, preclude the estimation of earthquake probability and, in particular, how this probability might change in space and time; earthquake hazard estimation might be possible in the absence of earthquake prediction. Recently, there has been a major development in the understanding of stress triggering of earthquakes which allows accurate calculation of the spatial variation of aftershock probability following any large earthquake. Over the past few years this Coulomb stress technique (CST) has been the subject of intensive study in the geophysics literature and has been extremely successful in explaining the spatial distribution of aftershocks following several major earthquakes. The power of current micro-computers, the great number of local, telemeter seismic networks, the rapid acquisition of data from satellites coupled with the speed of modern telecommunications and data transfer all mean that it may be possible that these new techniques could be applied in a forward sense. In other words, it is theoretically possible today to make predictions of the likely spatial distribution of aftershocks in near-real-time following a large earthquake. Approximate versions of such predictions could be available within, say, 0.1 days after the mainshock and might be continually refined and updated over the next 100 days. The European Commission has recently provided funding for a project to assess the extent to which it is currently possible to move CST predictions into a practically useful time frame so that low-confidence estimates of aftershock probability might be made within a few hours of an event and improved in near-real-time, as data of better quality become available over the following day to tens of days. Specifically, the project aim is to assess the

  18. Mapping probability of shipping sound exposure level.

    PubMed

    Gervaise, Cédric; Aulanier, Florian; Simard, Yvan; Roy, Nathalie

    2015-06-01

    Mapping vessel noise is emerging as one method of identifying areas where sound exposure due to shipping noise could have negative impacts on aquatic ecosystems. The probability distribution function (pdf) of sound exposure levels (SEL) is an important metric for identifying areas of concern. In this paper a probabilistic shipping SEL modeling method is described to obtain the pdf of SEL using the sonar equation and statistical relations linking the pdfs of ship traffic density, source levels, and transmission losses to their products and sums.

  19. Probability of detection calculations using MATLAB

    NASA Astrophysics Data System (ADS)

    Wei, Yung-Chung

    1993-06-01

    A set of highly efficient computer programs based on the Marcum and Swerling's analysis on radar detection has been written in MATLAB to evaluate the probability of detection. The programs are based on accurate methods unlike the detectability method which is based on approximation. This thesis also outlines radar detection theory and target models as a background. The goal of this effort is to provide a set of efficient computer programs for student usage and teacher's aid. Programs are designed to be user friendly and run on personal computers.

  20. Uncertainty analysis for Probable Maximum Precipitation estimates

    NASA Astrophysics Data System (ADS)

    Micovic, Zoran; Schaefer, Melvin G.; Taylor, George H.

    2015-02-01

    An analysis of uncertainty associated with Probable Maximum Precipitation (PMP) estimates is presented. The focus of the study is firmly on PMP estimates derived through meteorological analyses and not on statistically derived PMPs. Theoretical PMP cannot be computed directly and operational PMP estimates are developed through a stepwise procedure using a significant degree of subjective professional judgment. This paper presents a methodology for portraying the uncertain nature of PMP estimation by analyzing individual steps within the PMP derivation procedure whereby for each parameter requiring judgment, a set of possible values is specified and accompanied by expected probabilities. The resulting range of possible PMP values can be compared with the previously derived operational single-value PMP, providing measures of the conservatism and variability of the original estimate. To our knowledge, this is the first uncertainty analysis conducted for a PMP derived through meteorological analyses. The methodology was tested on the La Joie Dam watershed in British Columbia. The results indicate that the commonly used single-value PMP estimate could be more than 40% higher when possible changes in various meteorological variables used to derive the PMP are considered. The findings of this study imply that PMP estimates should always be characterized as a range of values recognizing the significant uncertainties involved in PMP estimation. In fact, we do not know at this time whether precipitation is actually upper-bounded, and if precipitation is upper-bounded, how closely PMP estimates approach the theoretical limit.

  1. On the probability of matching DNA fingerprints.

    PubMed

    Risch, N J; Devlin, B

    1992-02-01

    Forensic scientists commonly assume that DNA fingerprint patterns are infrequent in the general population and that genotypes are independent across loci. To test these assumptions, the number of matching DNA patterns in two large databases from the Federal Bureau of Investigation (FBI) and from Lifecodes was determined. No deviation from independence across loci in either database was apparent. For the Lifecodes database, the probability of a three-locus match ranges from 1 in 6,233 in Caucasians to 1 in 119,889 in Blacks. When considering all trios of five loci in the FBI database, there was only a single match observed out of more than 7.6 million comparisons. If independence is assumed, the probability of a five-locus match ranged from 1.32 x 10(-12) in Southeast Hispanics to 5.59 x 10(-14) in Blacks, implying that the minimum number of possible patterns for each ethnic group is several orders of magnitude greater than their corresponding population sizes in the United States. The most common five-locus pattern can have a frequency no greater than about 10(-6). Hence, individual five-locus DNA profiles are extremely uncommon, if not unique. PMID:1738844

  2. Estimating flood exceedance probabilities in estuarine regions

    NASA Astrophysics Data System (ADS)

    Westra, Seth; Leonard, Michael

    2016-04-01

    Flood events in estuarine regions can arise from the interaction of extreme rainfall and storm surge. Determining flood level exceedance probabilities in these regions is complicated by the dependence of these processes for extreme events. A comprehensive study of tide and rainfall gauges along the Australian coastline was conducted to determine the dependence of these extremes using a bivariate logistic threshold-excess model. The dependence strength is shown to vary as a function of distance over many hundreds of kilometres indicating that the dependence arises due to synoptic scale meteorological forcings. It is also shown to vary as a function of storm burst duration, time lag between the extreme rainfall and the storm surge event. The dependence estimates are then used with a bivariate design variable method to determine flood risk in estuarine regions for a number of case studies. Aspects of the method demonstrated in the case studies include, the resolution and range of the hydraulic response table, fitting of probability distributions, computational efficiency, uncertainty, potential variation in marginal distributions due to climate change, and application to two dimensional output from hydraulic models. Case studies are located on the Swan River (Western Australia), Nambucca River and Hawkesbury Nepean River (New South Wales).

  3. Probably maximum flood of the Sava River

    NASA Astrophysics Data System (ADS)

    Brilly, Mitja; Vidmar, Andrej; Raj, Mojca Å.

    2010-05-01

    The Nuclear Power Plant Krško (NEK) situated on the left bank of the Save River close to the border of Croatia. Probably Maximum Flood, on the location of the NEK could result in combination of probably maximum precipitation, sequential storm before PMP or snowmelt on the Sava River watershed. Mediterranean climate characterises very high precipitation and temporary high snow pack. The HBV-96 model as Integrated Hydrological Modelling System (IHMS) used for modelling. Model was calibrated and verification for daily time step at first for time period 1190-2006. Calibration and verification for hourly time step was done for period 1998-1999. The stream routing parameters were calibrated for flood event in years 1998 and 2007 and than verification for flood event in 1990. Discharge routing data analysis shown that possible inundation of Ljubljana and Savinja valley was not properly estimated. The flood areas are protected with levees and water does not spread over flooded areas in events used for calibration. Inundated areas in Ljubljana valley and Savinja valley are protected by levees and model could not simulate properly inundation of PMF. We recalibrate parameters controlled inundation on those areas for the worst scenario. Calculated PMF values drop down tramendosly after recalibration.

  4. The Human Bathtub: Safety and Risk Predictions Including the Dynamic Probability of Operator Errors

    SciTech Connect

    Duffey, Romney B.; Saull, John W.

    2006-07-01

    Reactor safety and risk are dominated by the potential and major contribution for human error in the design, operation, control, management, regulation and maintenance of the plant, and hence to all accidents. Given the possibility of accidents and errors, now we need to determine the outcome (error) probability, or the chance of failure. Conventionally, reliability engineering is associated with the failure rate of components, or systems, or mechanisms, not of human beings in and interacting with a technological system. The probability of failure requires a prior knowledge of the total number of outcomes, which for any predictive purposes we do not know or have. Analysis of failure rates due to human error and the rate of learning allow a new determination of the dynamic human error rate in technological systems, consistent with and derived from the available world data. The basis for the analysis is the 'learning hypothesis' that humans learn from experience, and consequently the accumulated experience defines the failure rate. A new 'best' equation has been derived for the human error, outcome or failure rate, which allows for calculation and prediction of the probability of human error. We also provide comparisons to the empirical Weibull parameter fitting used in and by conventional reliability engineering and probabilistic safety analysis methods. These new analyses show that arbitrary Weibull fitting parameters and typical empirical hazard function techniques cannot be used to predict the dynamics of human errors and outcomes in the presence of learning. Comparisons of these new insights show agreement with human error data from the world's commercial airlines, the two shuttle failures, and from nuclear plant operator actions and transient control behavior observed in transients in both plants and simulators. The results demonstrate that the human error probability (HEP) is dynamic, and that it may be predicted using the learning hypothesis and the minimum

  5. Measures, Probability and Holography in Cosmology

    NASA Astrophysics Data System (ADS)

    Phillips, Daniel

    This dissertation compiles four research projects on predicting values for cosmological parameters and models of the universe on the broadest scale. The first examines the Causal Entropic Principle (CEP) in inhomogeneous cosmologies. The CEP aims to predict the unexpectedly small value of the cosmological constant Lambda using a weighting by entropy increase on causal diamonds. The original work assumed a purely isotropic and homogeneous cosmology. But even the level of inhomogeneity observed in our universe forces reconsideration of certain arguments about entropy production. In particular, we must consider an ensemble of causal diamonds associated with each background cosmology and we can no longer immediately discard entropy production in the far future of the universe. Depending on our choices for a probability measure and our treatment of black hole evaporation, the prediction for Lambda may be left intact or dramatically altered. The second related project extends the CEP to universes with curvature. We have found that curvature values larger than rho k = 40rhom are disfavored by more than $99.99% and a peak value at rhoLambda = 7.9 x 10-123 and rhok =4.3rho m for open universes. For universes that allow only positive curvature or both positive and negative curvature, we find a correlation between curvature and dark energy that leads to an extended region of preferred values. Our universe is found to be disfavored to an extent depending the priors on curvature. We also provide a comparison to previous anthropic constraints on open universes and discuss future directions for this work. The third project examines how cosmologists should formulate basic questions of probability. We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically verified fully classical theory of probability. We

  6. Learning How To Learn.

    ERIC Educational Resources Information Center

    Barnett, Demian

    2000-01-01

    In one California high school, learning to learn is a measurable outcome assessed by all students' participation in graduation by exhibition. Students must meet state requirements and demonstrate learning prowess by publicly exhibiting their skills in math, science, language arts, social science, service learning, and postgraduation planning. (MLH)

  7. Significance of "high probability/low damage" versus "low probability/high damage" flood events

    NASA Astrophysics Data System (ADS)

    Merz, B.; Elmer, F.; Thieken, A. H.

    2009-06-01

    The need for an efficient use of limited resources fosters the application of risk-oriented design in flood mitigation. Flood defence measures reduce future damage. Traditionally, this benefit is quantified via the expected annual damage. We analyse the contribution of "high probability/low damage" floods versus the contribution of "low probability/high damage" events to the expected annual damage. For three case studies, i.e. actual flood situations in flood-prone communities in Germany, it is shown that the expected annual damage is dominated by "high probability/low damage" events. Extreme events play a minor role, even though they cause high damage. Using typical values for flood frequency behaviour, flood plain morphology, distribution of assets and vulnerability, it is shown that this also holds for the general case of river floods in Germany. This result is compared to the significance of extreme events in the public perception. "Low probability/high damage" events are more important in the societal view than it is expressed by the expected annual damage. We conclude that the expected annual damage should be used with care since it is not in agreement with societal priorities. Further, risk aversion functions that penalise events with disastrous consequences are introduced in the appraisal of risk mitigation options. It is shown that risk aversion may have substantial implications for decision-making. Different flood mitigation decisions are probable, when risk aversion is taken into account.

  8. Economic choices reveal probability distortion in macaque monkeys.

    PubMed

    Stauffer, William R; Lak, Armin; Bossaerts, Peter; Schultz, Wolfram

    2015-02-18

    Economic choices are largely determined by two principal elements, reward value (utility) and probability. Although nonlinear utility functions have been acknowledged for centuries, nonlinear probability weighting (probability distortion) was only recently recognized as a ubiquitous aspect of real-world choice behavior. Even when outcome probabilities are known and acknowledged, human decision makers often overweight low probability outcomes and underweight high probability outcomes. Whereas recent studies measured utility functions and their corresponding neural correlates in monkeys, it is not known whether monkeys distort probability in a manner similar to humans. Therefore, we investigated economic choices in macaque monkeys for evidence of probability distortion. We trained two monkeys to predict reward from probabilistic gambles with constant outcome values (0.5 ml or nothing). The probability of winning was conveyed using explicit visual cues (sector stimuli). Choices between the gambles revealed that the monkeys used the explicit probability information to make meaningful decisions. Using these cues, we measured probability distortion from choices between the gambles and safe rewards. Parametric modeling of the choices revealed classic probability weighting functions with inverted-S shape. Therefore, the animals overweighted low probability rewards and underweighted high probability rewards. Empirical investigation of the behavior verified that the choices were best explained by a combination of nonlinear value and nonlinear probability distortion. Together, these results suggest that probability distortion may reflect evolutionarily preserved neuronal processing.

  9. Economic Choices Reveal Probability Distortion in Macaque Monkeys

    PubMed Central

    Lak, Armin; Bossaerts, Peter; Schultz, Wolfram

    2015-01-01

    Economic choices are largely determined by two principal elements, reward value (utility) and probability. Although nonlinear utility functions have been acknowledged for centuries, nonlinear probability weighting (probability distortion) was only recently recognized as a ubiquitous aspect of real-world choice behavior. Even when outcome probabilities are known and acknowledged, human decision makers often overweight low probability outcomes and underweight high probability outcomes. Whereas recent studies measured utility functions and their corresponding neural correlates in monkeys, it is not known whether monkeys distort probability in a manner similar to humans. Therefore, we investigated economic choices in macaque monkeys for evidence of probability distortion. We trained two monkeys to predict reward from probabilistic gambles with constant outcome values (0.5 ml or nothing). The probability of winning was conveyed using explicit visual cues (sector stimuli). Choices between the gambles revealed that the monkeys used the explicit probability information to make meaningful decisions. Using these cues, we measured probability distortion from choices between the gambles and safe rewards. Parametric modeling of the choices revealed classic probability weighting functions with inverted-S shape. Therefore, the animals overweighted low probability rewards and underweighted high probability rewards. Empirical investigation of the behavior verified that the choices were best explained by a combination of nonlinear value and nonlinear probability distortion. Together, these results suggest that probability distortion may reflect evolutionarily preserved neuronal processing. PMID:25698750

  10. Model estimates hurricane wind speed probabilities

    NASA Astrophysics Data System (ADS)

    Mumane, Richard J.; Barton, Chris; Collins, Eric; Donnelly, Jeffrey; Eisner, James; Emanuel, Kerry; Ginis, Isaac; Howard, Susan; Landsea, Chris; Liu, Kam-biu; Malmquist, David; McKay, Megan; Michaels, Anthony; Nelson, Norm; O Brien, James; Scott, David; Webb, Thompson, III

    In the United States, intense hurricanes (category 3, 4, and 5 on the Saffir/Simpson scale) with winds greater than 50 m s -1 have caused more damage than any other natural disaster [Pielke and Pielke, 1997]. Accurate estimates of wind speed exceedance probabilities (WSEP) due to intense hurricanes are therefore of great interest to (re)insurers, emergency planners, government officials, and populations in vulnerable coastal areas.The historical record of U.S. hurricane landfall is relatively complete only from about 1900, and most model estimates of WSEP are derived from this record. During the 1899-1998 period, only two category-5 and 16 category-4 hurricanes made landfall in the United States. The historical record therefore provides only a limited sample of the most intense hurricanes.

  11. Audio feature extraction using probability distribution function

    NASA Astrophysics Data System (ADS)

    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.

  12. Probability of Brownian motion hitting an obstacle

    SciTech Connect

    Knessl, C.; Keller, J.B.

    2000-02-01

    The probability p(x) that Brownian motion with drift, starting at x, hits an obstacle is analyzed. The obstacle {Omega} is a compact subset of R{sup n}. It is shown that p(x) is expressible in terms of the field U(x) scattered by {Omega} when it is hit by plane wave. Therefore results for U(x), and methods for finding U(x) can be used to determine p(x). The authors illustrate this by obtaining exact and asymptotic results for p(x) when {Omega} is a slit in R{sup 2}, and asymptotic results when {Omega} is a disc in R{sup 3}.

  13. Carrier Modulation Via Waveform Probability Density Function

    NASA Technical Reports Server (NTRS)

    Williams, Glenn L.

    2004-01-01

    Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital ONEs or ZEROs. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental natural laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.

  14. On the probability of dinosaur fleas.

    PubMed

    Dittmar, Katharina; Zhu, Qiyun; Hastriter, Michael W; Whiting, Michael F

    2016-01-11

    Recently, a set of publications described flea fossils from Jurassic and Early Cretaceous geological strata in northeastern China, which were suggested to have parasitized feathered dinosaurs, pterosaurs, and early birds or mammals. In support of these fossils being fleas, a recent publication in BMC Evolutionary Biology described the extended abdomen of a female fossil specimen as due to blood feeding.We here comment on these findings, and conclude that the current interpretation of the evolutionary trajectory and ecology of these putative dinosaur fleas is based on appeal to probability, rather than evidence. Hence, their taxonomic positioning as fleas, or stem fleas, as well as their ecological classification as ectoparasites and blood feeders is not supported by currently available data.

  15. Parabolic Ejecta Features on Titan? Probably Not

    NASA Astrophysics Data System (ADS)

    Lorenz, R. D.; Melosh, H. J.

    1996-03-01

    Radar mapping of Venus by Magellan indicated a number of dark parabolic features, associated with impact craters. A suggested mechanism for generating such features is that ejecta from the impact event is 'winnowed' by the zonal wind field, with smaller ejecta particles falling out of the atmosphere more slowly, and hence drifting further. What discriminates such features from simple wind streaks is the 'stingray' or parabolic shape. This is due to the ejecta's spatial distribution prior to being winnowed during fallout, and this distribution is generated by the explosion plume of the impact piercing the atmosphere, allowing the ejecta to disperse pseudoballistically before re-entering the atmosphere, decelerating to terminal velocity and then being winnowed. Here we apply this model to Titan, which has a zonal wind field similar to that of Venus. We find that Cassini will probably not find parabolic features, as the winds stretch the deposition so far that ejecta will form streaks or bands instead.

  16. Trending in Probability of Collision Measurements

    NASA Technical Reports Server (NTRS)

    Vallejo, J. J.; Hejduk, M. D.; Stamey, J. D.

    2015-01-01

    A simple model is proposed to predict the behavior of Probabilities of Collision (P(sub c)) for conjunction events. The model attempts to predict the location and magnitude of the peak P(sub c) value for an event by assuming the progression of P(sub c) values can be modeled to first order by a downward-opening parabola. To incorporate prior information from a large database of past conjunctions, the Bayes paradigm is utilized; and the operating characteristics of the model are established through a large simulation study. Though the model is simple, it performs well in predicting the temporal location of the peak (P(sub c)) and thus shows promise as a decision aid in operational conjunction assessment risk analysis.

  17. Quantum probabilities for inflation from holography

    SciTech Connect

    Hartle, James B.; Hawking, S.W.; Hertog, Thomas E-mail: S.W.Hawking@damtp.cam.ac.uk

    2014-01-01

    The evolution of the universe is determined by its quantum state. The wave function of the universe obeys the constraints of general relativity and in particular the Wheeler-DeWitt equation (WDWE). For non-zero Λ, we show that solutions of the WDWE at large volume have two domains in which geometries and fields are asymptotically real. In one the histories are Euclidean asymptotically anti-de Sitter, in the other they are Lorentzian asymptotically classical de Sitter. Further, the universal complex semiclassical asymptotic structure of solutions of the WDWE implies that the leading order in h-bar quantum probabilities for classical, asymptotically de Sitter histories can be obtained from the action of asymptotically anti-de Sitter configurations. This leads to a promising, universal connection between quantum cosmology and holography.

  18. Carrier Modulation Via Waveform Probability Density Function

    NASA Technical Reports Server (NTRS)

    Williams, Glenn L.

    2006-01-01

    Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital one's or zero's. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental physical laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.

  19. 5426 Sharp: A Probable Hungaria Binary

    NASA Astrophysics Data System (ADS)

    Warner, Brian D.; Benishek, Vladimir; Ferrero, Andrea

    2015-07-01

    Initial CCD photometry observations of the Hungaria asteroid 5426 Sharp in 2014 December and 2015 January at the Center of Solar System Studies-Palmer Divide Station in Landers, CA, showed attenuations from the general lightcurve, indicating the possibility of the asteroid being a binary system. The secondary period was almost exactly an Earth day, prompting a collaboration to be formed with observers in Europe, which eventually allowed establishing two periods: P1 = 4.5609 ± 0.0003 h, A1 = 0.18 ± 0.01 mag and P2 = 24.22 ± 0.02 h, A2 = 0.08 ± 0.01 mag. No mutual events, i.e., occultations and/or eclipses, were seen, therefore the asteroid is considered a probable and not confirmed binary

  20. On the probability of dinosaur fleas.

    PubMed

    Dittmar, Katharina; Zhu, Qiyun; Hastriter, Michael W; Whiting, Michael F

    2016-01-01

    Recently, a set of publications described flea fossils from Jurassic and Early Cretaceous geological strata in northeastern China, which were suggested to have parasitized feathered dinosaurs, pterosaurs, and early birds or mammals. In support of these fossils being fleas, a recent publication in BMC Evolutionary Biology described the extended abdomen of a female fossil specimen as due to blood feeding.We here comment on these findings, and conclude that the current interpretation of the evolutionary trajectory and ecology of these putative dinosaur fleas is based on appeal to probability, rather than evidence. Hence, their taxonomic positioning as fleas, or stem fleas, as well as their ecological classification as ectoparasites and blood feeders is not supported by currently available data. PMID:26754250

  1. Evolution probabilities and phylogenetic distance of dinucleotides.

    PubMed

    Michel, Christian J

    2007-11-21

    We develop here an analytical evolution model based on a dinucleotide mutation matrix 16 x 16 with six substitution parameters associated with the three types of substitutions in the two dinucleotide sites. It generalizes the previous models based on the nucleotide mutation matrices 4 x 4. It determines at some time t the exact occurrence probabilities of dinucleotides mutating randomly according to these six substitution parameters. Furthermore, several properties and two applications of this model allow to derive 16 evolutionary analytical solutions of dinucleotides and also a dinucleotide phylogenetic distance. Finally, based on this mathematical model, the SED (Stochastic Evolution of Dinucleotides) web server has been developed for deriving evolutionary analytical solutions of dinucleotides.

  2. Decision from Models: Generalizing Probability Information to Novel Tasks

    PubMed Central

    Zhang, Hang; Paily, Jacienta T.; Maloney, Laurence T.

    2014-01-01

    We investigate a new type of decision under risk where—to succeed—participants must generalize their experience in one set of tasks to a novel set of tasks. We asked participants to trade distance for reward in a virtual minefield where each successive step incurred the same fixed probability of failure (referred to as hazard). With constant hazard, the probability of success (the survival function) decreases exponentially with path length. On each trial, participants chose between a shorter path with smaller reward and a longer (more dangerous) path with larger reward. They received feedback in 160 training trials: encountering a mine along their chosen path resulted in zero reward and successful completion of the path led to the reward associated with the path chosen. They then completed 600 no-feedback test trials with novel combinations of path length and rewards. To maximize expected gain, participants had to learn the correct exponential model in training and generalize it to the test conditions. We compared how participants discounted reward with increasing path length to the predictions of nine choice models including the correct exponential model. The choices of a majority of the participants were best accounted for by a model of the correct exponential form although with marked overestimation of the hazard rate. The decision-from-models paradigm differs from experience-based decision paradigms such as decision-from-sampling in the importance assigned to generalizing experience-based information to novel tasks. The task itself is representative of everyday tasks involving repeated decisions in stochastically invariant environments. PMID:25621287

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

    PubMed

    Dinov, Ivo D; Kamino, Scott; Bhakhrani, Bilal; Christou, Nicolas

    2013-01-01

    Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students' understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference.

  4. Homonymous Hemianopsia Associated with Probable Alzheimer's Disease.

    PubMed

    Ishiwata, Akiko; Kimura, Kazumi

    2016-01-01

    Posterior cortical atrophy (PCA) is a rare neurodegenerative disorder that has cerebral atrophy in the parietal, occipital, or occipitotemporal cortices and is characterized by visuospatial and visuoperceptual impairments. The most cases are pathologically compatible with Alzheimer's disease (AD). We describe a case of PCA in which a combination of imaging methods, in conjunction with symptoms and neurological and neuropsychological examinations, led to its being diagnosed and to AD being identified as its probable cause. Treatment with donepezil for 6 months mildly improved alexia symptoms, but other symptoms remained unchanged. A 59-year-old Japanese woman with progressive alexia, visual deficit, and mild memory loss was referred to our neurologic clinic for the evaluation of right homonymous hemianopsia. Our neurological examination showed alexia, constructional apraxia, mild disorientation, short-term memory loss, and right homonymous hemianopsia. These findings resulted in a score of 23 (of 30) points on the Mini-Mental State Examination. Occipital atrophy was identified, with magnetic resonance imaging (MRI) showing left-side dominance. The MRI data were quantified with voxel-based morphometry, and PCA was diagnosed on the basis of these findings. Single photon emission computed tomography with (123)I-N-isopropyl-p-iodoamphetamine showed hypoperfusion in the corresponding voxel-based morphometry occipital lobes. Additionally, the finding of hypoperfusion in the posterior associate cortex, posterior cingulate gyrus, and precuneus was consistent with AD. Therefore, the PCA was considered to be a result of AD. We considered Lewy body dementia as a differential diagnosis because of the presence of hypoperfusion in the occipital lobes. However, the patient did not meet the criteria for Lewy body dementia during the course of the disease. We therefore consider including PCA in the differential diagnoses to be important for patients with visual deficit, cognitive

  5. Repetition probability effects for inverted faces.

    PubMed

    Grotheer, Mareike; Hermann, Petra; Vidnyánszky, Zoltán; Kovács, Gyula

    2014-11-15

    It has been shown, that the repetition related reduction of the blood-oxygen level dependent (BOLD) signal is modulated by the probability of repetitions (P(rep)) for faces (Summerfield et al., 2008), providing support for the predictive coding (PC) model of visual perception (Rao and Ballard, 1999). However, the stage of face processing where repetition suppression (RS) is modulated by P(rep) is still unclear. Face inversion is known to interrupt higher level configural/holistic face processing steps and if modulation of RS by P(rep) takes place at these stages of face processing, P(rep) effects are expected to be reduced for inverted when compared to upright faces. Therefore, here we aimed at investigating whether P(rep) effects on RS observed for face stimuli originate at the higher-level configural/holistic stages of face processing by comparing these effects for upright and inverted faces. Similarly to previous studies, we manipulated P(rep) for pairs of stimuli in individual blocks of fMRI recordings. This manipulation significantly influenced repetition suppression in the posterior FFA, the OFA and the LO, independently of stimulus orientation. Our results thus reveal that RS in the ventral visual stream is modulated by P(rep) even in the case of face inversion and hence strongly compromised configural/holistic face processing. An additional whole-brain analysis could not identify any areas where the modulatory effect of probability was orientation specific either. These findings imply that P(rep) effects on RS might originate from the earlier stages of face processing.

  6. Practical implementation of joint multitarget probabilities

    NASA Astrophysics Data System (ADS)

    Musick, Stanton; Kastella, Keith D.; Mahler, Ronald P. S.

    1998-07-01

    A Joint Multitarget Probability (JMP) is a posterior probability density pT(x1,...,xTZ) that there are T targets (T an unknown number) with unknown locations specified by the multitarget state X equals (x1,...,xT)T conditioned on a set of observations Z. This paper presents a numerical approximation for implementing JMP in detection, tracking and sensor management applications. A problem with direct implementation of JMP is that, if each xt, t equals 1,...,T, is discretized on a grid of N elements, NT variables are required to represent JMP on the T-target sector. This produces a large computational requirement even for small values of N and T. However, when the sensor easily separates targets, the resulting JMP factorizes and can be approximated by a product representation requiring only O(T2N) variables. Implementation of JMP for multitarget tracking requires a Bayes' rule step for measurement update and a Markov transition step for time update. If the measuring sensor is only influenced by the cell it observes, the JMP product representation is preserved under measurement update. However, the product form is not quite preserved by the Markov time update, but can be restored using a minimum discrimination approach. All steps for the approximation can be performed with O(N) effort. This notion is developed and demonstrated in numerical examples with at most two targets in a 1-dimensional surveillance region. In this case, numerical results for detection and tracking for the product approximation and the full JMP are very similar.

  7. Probability matching involves rule-generating ability: a neuropsychological mechanism dealing with probabilities.

    PubMed

    Unturbe, Jesús; Corominas, Josep

    2007-09-01

    Probability matching is a nonoptimal strategy consisting of selecting each alternative in proportion to its reinforcement contingency. However, matching is related to hypothesis testing in an incidental, marginal, and methodologically disperse manner. Although some authors take it for granted, the relationship has not been demonstrated. Fifty-eight healthy participants performed a modified, bias-free probabilistic two-choice task, the Simple Prediction Task (SPT). Self-reported spurious rules were recorded and then graded by two independent judges. Participants who produced the most complex rules selected the probability matching strategy and were therefore less successful than those who did not produce rules. The close relationship between probability matching and rule generating makes SPT a complementary instrument for studying decision making, which might throw some light on the debate about irrationality. The importance of the reaction times, both before and after responding, is also discussed.

  8. Mixture Modeling of Individual Learning Curves

    ERIC Educational Resources Information Center

    Streeter, Matthew

    2015-01-01

    We show that student learning can be accurately modeled using a mixture of learning curves, each of which specifies error probability as a function of time. This approach generalizes Knowledge Tracing [7], which can be viewed as a mixture model in which the learning curves are step functions. We show that this generality yields order-of-magnitude…

  9. Detecting Learning Moment-by-Moment

    ERIC Educational Resources Information Center

    Baker, Ryan S. J. D.; Goldstein, Adam B.; Heffernan, Neil T.

    2011-01-01

    Intelligent tutors have become increasingly accurate at detecting whether a student knows a skill, or knowledge component (KC), at a given time. However, current student models do not tell us exactly at which point a KC is learned. In this paper, we present a machine-learned model that assesses the probability that a student learned a KC at a…

  10. Towards an Emergent View of Learning Work

    ERIC Educational Resources Information Center

    Johnsson, Mary C.; Boud, David

    2010-01-01

    The purpose of this paper is to challenge models of workplace learning that seek to isolate or manipulate a limited set of features to increase the probability of learning. Such models typically attribute learning (or its absence) to individual engagement, manager expectations or organizational affordances and are therefore at least implicitly…

  11. Learning from Our Students

    ERIC Educational Resources Information Center

    Noddings, Nel

    2004-01-01

    Most teachers have been good students. Some students are fast learners and attain the required knowledge and skills easily; others are obedient, hard workers. In either case, teachers are likely to believe that if students really try, they will do well. Listening to students over many years, the author has learned that this is probably not true.…

  12. Motivation through Mastery Learning

    ERIC Educational Resources Information Center

    Josten, Denice

    2006-01-01

    Every developmental education teacher would probably agree that motivation to complete assignments is one of the biggest obstacles to getting students to practice necessary skills. Short stories and other types of recreational reading might help motivate students, but they need to learn specific skills to help them cope with college textbook…

  13. Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal

    SciTech Connect

    Helton, J.C.

    1996-03-01

    A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S{sub st}, S{sub st}, p{sub st}) for stochastic uncertainty, a probability space (S{sub su}, S{sub su}, p{sub su}) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S{sub st}, S{sub st}, p{sub st}) and (S{sub su}, S{sub su}, p{sub su}). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the U.S. Environmental Protection Agency`s standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems.

  14. Exercise in probability and statistics, or the probability of winning at tennis

    NASA Astrophysics Data System (ADS)

    Fischer, Gaston

    1980-01-01

    The relationships between the probabilities p, x, s, and M, of winning, respectively, a point, a game, a set, or a match have been derived. The calculations are carried out under the assumption that these probabilities are averages. For example, x represents an average probability of winning a game when serving and receiving, and the same value of x is assumed to hold also for tie-break games. The formulas derived are for sets played with a tie-break game at the level of 6-6, as well as for the traditional rule requiring an advantage of two games to win a set. Matches to the best of three and five sets are considered. As is to be expected, a small advantage in the probability p of winning a point leads to advantages which are amplified by large factors : 2.5 for games, 7.1 for sets with tie-break at 6-6, 10.6 for matches to the best of three sets, and 13.3 for matches to the best of five sets. When sets are decided according to the traditional rule, the last three factors become, respectively, 7.4, 11.1, and 13.8. The theoretical calculations are compared with real and synthetic tennis scores and good agreement is found. The scatter of the data is seen to obey the predictions of a normal distribution. Some classroom problems are suggested at the end.

  15. Enhanced awakening probability of repetitive impulse sounds.

    PubMed

    Vos, Joos; Houben, Mark M J

    2013-09-01

    In the present study relations between the level of impulse sounds and the observed proportion of behaviorally confirmed awakening reactions were determined. The sounds (shooting sounds, bangs produced by door slamming or by container transshipment, aircraft landings) were presented by means of loudspeakers in the bedrooms of 50 volunteers. The fragments for the impulse sounds consisted of single or multiple events. The sounds were presented during a 6-h period that started 75 min after the subjects wanted to sleep. In order to take account of habituation, each subject participated during 18 nights. At equal indoor A-weighted sound exposure levels, the proportion of awakening for the single impulse sounds was equal to that for the aircraft sounds. The proportion of awakening induced by the multiple impulse sounds, however, was significantly higher. For obtaining the same rate of awakening, the sound level of each of the successive impulses in a fragment had to be about 15-25 dB lower than the level of one single impulse. This level difference was largely independent of the degree of habituation. Various explanations for the enhanced awakening probability are discussed. PMID:23967934

  16. Lectures on probability and statistics. Revision

    SciTech Connect

    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.

  17. The probability of finding suitable directed donors.

    PubMed

    Kanter, M; Selvin, S; Myhre, B A

    1989-02-01

    A series of tables based on mathematical calculations is given as guidelines for the number of directed donors needed by members of various ethnic/racial groups to provide a desired number of units of blood with a selected probability of achieving this result. From these tables, certain conclusions can be drawn. Unrelated donors who do not know their blood type are an inefficient source of directed donors. Rh-negative patients are unlikely to obtain enough directed-donor units from either related or unrelated donors with confidence unless these donors known their blood type. In general, siblings, parents, and offspring are the most efficient directed donors from the standpoint of compatibility. Cousins, uncles, aunts, nieces, and nephews are not much more likely to be compatible than unrelated donors are. It is easier to obtain suitable directed-donor units among Hispanics than among whites, blacks, or Asians, due to their skewed blood group frequencies. In general, using O-negative directed donors for Rh-positive recipients does not significantly increase the likelihood of finding suitable donors.

  18. Probability of rupture of multiple fault segments

    USGS Publications Warehouse

    Andrews, D.J.; Schwerer, E.

    2000-01-01

    Fault segments identified from geologic and historic evidence have sometimes been adopted as features limiting the likely extends of earthquake ruptures. There is no doubt that individual segments can sometimes join together to produce larger earthquakes. This work is a trial of an objective method to determine the probability of multisegment ruptures. The frequency of occurrence of events on all conjectured combinations of adjacent segments in northern California is found by fitting to both geologic slip rates and to an assumed distribution of event sizes for the region as a whole. Uncertainty in the shape of the distribution near the maximum magnitude has a large effect on the solution. Frequencies of individual events cannot be determined, but it is possible to find a set of frequencies to fit a model closely. A robust conclusion for the San Francisco Bay region is that large multisegment events occur on the San Andreas and San Gregorio faults, but single-segment events predominate on the extended Hayward and Calaveras strands of segments.

  19. Essays on probability elicitation scoring rules

    NASA Astrophysics Data System (ADS)

    Firmino, Paulo Renato A.; dos Santos Neto, Ademir B.

    2012-10-01

    In probability elicitation exercises it has been usual to considerer scoring rules (SRs) to measure the performance of experts when inferring about a given unknown, Θ, for which the true value, θ*, is (or will shortly be) known to the experimenter. Mathematically, SRs quantify the discrepancy between f(θ) (the distribution reflecting the expert's uncertainty about Θ) and d(θ), a zero-one indicator function of the observation θ*. Thus, a remarkable characteristic of SRs is to contrast expert's beliefs with the observation θ*. The present work aims at extending SRs concepts and formulas for the cases where Θ is aleatory, highlighting advantages of goodness-of-fit and entropy-like measures. Conceptually, it is argued that besides of evaluating the personal performance of the expert, SRs may also play a role when comparing the elicitation processes adopted to obtain f(θ). Mathematically, it is proposed to replace d(θ) by g(θ), the distribution that model the randomness of Θ, and do also considerer goodness-of-fit and entropylike metrics, leading to SRs that measure the adherence of f(θ) to g(θ). The implications of this alternative perspective are discussed and illustrated by means of case studies based on the simulation of controlled experiments. The usefulness of the proposed approach for evaluating the performance of experts and elicitation processes is investigated.

  20. Atomic Transition Probabilities for Neutral Cerium

    NASA Astrophysics Data System (ADS)

    Lawler, J. E.; den Hartog, E. A.; Wood, M. P.; Nitz, D. E.; Chisholm, J.; Sobeck, J.

    2009-10-01

    The spectra of neutral cerium (Ce I) and singly ionized cerium (Ce II) are more complex than spectra of other rare earth species. The resulting high density of lines in the visible makes Ce ideal for use in metal halide (MH) High Intensity Discharge (HID) lamps. Inclusion of cerium-iodide in a lamp dose can improve both the Color Rendering Index and luminous efficacy of a MH-HID lamp. Basic spectroscopic data including absolute atomic transition probabilities for Ce I and Ce II are needed for diagnosing and modeling these MH-HID lamps. Recent work on Ce II [1] is now being augmented with similar work on Ce I. Radiative lifetimes from laser induced fluorescence measurements [2] on neutral Ce are being combined with emission branching fractions from spectra recorded using a Fourier transform spectrometer. A total of 14 high resolution spectra are being analyzed to determine branching fractions for 2000 to 3000 lines from 153 upper levels in neutral Ce. Representative data samples and progress to date will be presented. [4pt] [1] J. E. Lawler, C. Sneden, J. J. Cowan, I. I. Ivans, and E. A. Den Hartog, Astrophys. J. Suppl. Ser. 182, 51-79 (2009). [0pt] [2] E. A. Den Hartog, K. P. Buettner, and J. E. Lawler, J. Phys. B: Atomic, Molecular & Optical Physics 42, 085006 (7pp) (2009).

  1. Do aftershock probabilities decay with time?

    USGS Publications Warehouse

    Michael, Andrew J.

    2012-01-01

    So, do aftershock probabilities decay with time? Consider a thought experiment in which we are at the time of the mainshock and ask how many aftershocks will occur a day, week, month, year, or even a century from now. First we must decide how large a window to use around each point in time. Let's assume that, as we go further into the future, we are asking a less precise question. Perhaps a day from now means 1 day 10% of a day, a week from now means 1 week 10% of a week, and so on. If we ignore c because it is a small fraction of a day (e.g., Reasenberg and Jones, 1989, hereafter RJ89), and set p = 1 because it is usually close to 1 (its value in the original Omori law), then the rate of earthquakes (K=t) decays at 1=t. If the length of the windows being considered increases proportionally to t, then the number of earthquakes at any time from now is the same because the rate decrease is canceled by the increase in the window duration. Under these conditions we should never think "It's a bit late for this to be an aftershock."

  2. Parametric probability distributions for anomalous change detection

    SciTech Connect

    Theiler, James P; Foy, Bernard R; Wohlberg, Brendt E; Scovel, James C

    2010-01-01

    The problem of anomalous change detection arises when two (or possibly more) images are taken of the same scene, but at different times. The aim is to discount the 'pervasive differences' that occur thoughout the imagery, due to the inevitably different conditions under which the images were taken (caused, for instance, by differences in illumination, atmospheric conditions, sensor calibration, or misregistration), and to focus instead on the 'anomalous changes' that actually take place in the scene. In general, anomalous change detection algorithms attempt to model these normal or pervasive differences, based on data taken directly from the imagery, and then identify as anomalous those pixels for which the model does not hold. For many algorithms, these models are expressed in terms of probability distributions, and there is a class of such algorithms that assume the distributions are Gaussian. By considering a broader class of distributions, however, a new class of anomalous change detection algorithms can be developed. We consider several parametric families of such distributions, derive the associated change detection algorithms, and compare the performance with standard algorithms that are based on Gaussian distributions. We find that it is often possible to significantly outperform these standard algorithms, even using relatively simple non-Gaussian models.

  3. Probability judgments under ambiguity and conflict

    PubMed Central

    Smithson, Michael

    2015-01-01

    Whether conflict and ambiguity are distinct kinds of uncertainty remains an open question, as does their joint impact on judgments of overall uncertainty. This paper reviews recent advances in our understanding of human judgment and decision making when both ambiguity and conflict are present, and presents two types of testable models of judgments under conflict and ambiguity. The first type concerns estimate-pooling to arrive at “best” probability estimates. The second type is models of subjective assessments of conflict and ambiguity. These models are developed for dealing with both described and experienced information. A framework for testing these models in the described-information setting is presented, including a reanalysis of a multi-nation data-set to test best-estimate models, and a study of participants' assessments of conflict, ambiguity, and overall uncertainty reported by Smithson (2013). A framework for research in the experienced-information setting is then developed, that differs substantially from extant paradigms in the literature. This framework yields new models of “best” estimates and perceived conflict. The paper concludes with specific suggestions for future research on judgment and decision making under conflict and ambiguity. PMID:26042081

  4. Quantum reinforcement learning.

    PubMed

    Dong, Daoyi; Chen, Chunlin; Li, Hanxiong; Tarn, Tzyh-Jong

    2008-10-01

    The key approaches for machine learning, particularly learning in unknown probabilistic environments, are new representations and computation mechanisms. In this paper, a novel quantum reinforcement learning (QRL) method is proposed by combining quantum theory and reinforcement learning (RL). Inspired by the state superposition principle and quantum parallelism, a framework of a value-updating algorithm is introduced. The state (action) in traditional RL is identified as the eigen state (eigen action) in QRL. The state (action) set can be represented with a quantum superposition state, and the eigen state (eigen action) can be obtained by randomly observing the simulated quantum state according to the collapse postulate of quantum measurement. The probability of the eigen action is determined by the probability amplitude, which is updated in parallel according to rewards. Some related characteristics of QRL such as convergence, optimality, and balancing between exploration and exploitation are also analyzed, which shows that this approach makes a good tradeoff between exploration and exploitation using the probability amplitude and can speedup learning through the quantum parallelism. To evaluate the performance and practicability of QRL, several simulated experiments are given, and the results demonstrate the effectiveness and superiority of the QRL algorithm for some complex problems. This paper is also an effective exploration on the application of quantum computation to artificial intelligence.

  5. Quantum reinforcement learning.

    PubMed

    Dong, Daoyi; Chen, Chunlin; Li, Hanxiong; Tarn, Tzyh-Jong

    2008-10-01

    The key approaches for machine learning, particularly learning in unknown probabilistic environments, are new representations and computation mechanisms. In this paper, a novel quantum reinforcement learning (QRL) method is proposed by combining quantum theory and reinforcement learning (RL). Inspired by the state superposition principle and quantum parallelism, a framework of a value-updating algorithm is introduced. The state (action) in traditional RL is identified as the eigen state (eigen action) in QRL. The state (action) set can be represented with a quantum superposition state, and the eigen state (eigen action) can be obtained by randomly observing the simulated quantum state according to the collapse postulate of quantum measurement. The probability of the eigen action is determined by the probability amplitude, which is updated in parallel according to rewards. Some related characteristics of QRL such as convergence, optimality, and balancing between exploration and exploitation are also analyzed, which shows that this approach makes a good tradeoff between exploration and exploitation using the probability amplitude and can speedup learning through the quantum parallelism. To evaluate the performance and practicability of QRL, several simulated experiments are given, and the results demonstrate the effectiveness and superiority of the QRL algorithm for some complex problems. This paper is also an effective exploration on the application of quantum computation to artificial intelligence. PMID:18784007

  6. Semi-supervised dimensionality reduction using estimated class membership probabilities

    NASA Astrophysics Data System (ADS)

    Li, Wei; Ruan, Qiuqi; Wan, Jun

    2012-10-01

    In solving pattern-recognition tasks with partially labeled training data, the semi-supervised dimensionality reduction method, which considers both labeled and unlabeled data, is preferable for improving the classification and generalization capability of the testing data. Among such techniques, graph-based semi-supervised learning methods have attracted a lot of attention due to their appealing properties in discovering discriminative structure and geometric structure of data points. Although they have achieved remarkable success, they cannot promise good performance when the size of the labeled data set is small, as a result of inaccurate class matrix variance approximated by insufficient labeled training data. In this paper, we tackle this problem by combining class membership probabilities estimated from unlabeled data and ground-truth class information associated with labeled data to more precisely characterize the class distribution. Therefore, it is expected to enhance performance in classification tasks. We refer to this approach as probabilistic semi-supervised discriminant analysis (PSDA). The proposed PSDA is applied to face and facial expression recognition tasks and is evaluated using the ORL, Extended Yale B, and CMU PIE face databases and the Cohn-Kanade facial expression database. The promising experimental results demonstrate the effectiveness of our proposed method.

  7. Levetiracetam: Probably Associated Diurnal Frequent Urination.

    PubMed

    Ju, Jun; Zou, Li-Ping; Shi, Xiu-Yu; Hu, Lin-Yan; Pang, Ling-Yu

    2016-01-01

    Diurnal frequent urination is a common condition in elementary school children who are especially at risk for associated somatic and behavioral problems. Levetiracetam (LEV) is a broad-spectrum antiepileptic drug that has been used in both partial and generalized seizures and less commonly adverse effects including psychiatric and behavioral problems. Diurnal frequent urination is not a well-known adverse effect of LEV. Here, we reported 2 pediatric cases with epilepsy that developed diurnal frequent urination after LEV administration. Case 1 was a 6-year-old male patient who presented urinary frequency and urgency in the daytime since the third day after LEV was given as adjunctive therapy. Symptoms increased accompanied by the raised dosage of LEV. Laboratory tests and auxiliary examinations did not found evidence of organic disease. Diurnal frequent urination due to LEV was suspected, and then the drug was discontinued. As expected, his frequency of urination returned to normal levels. Another 13-year-old female patient got similar clinical manifestations after oral LEV monotherapy and the symptoms became aggravated while in stress state. Since the most common causes of frequent micturition had been ruled out, the patient was considered to be diagnosed with LEV-associated psychogenic frequent urination. The dosage of LEV was reduced to one-third, and the frequency of urination was reduced by 60%. Both patients got the Naranjo score of 6, which indicated that LEV was a "probable" cause of diurnal frequent urination. Although a definite causal link between LEV and diurnal urinary frequency in the 2 cases remains to be established, we argue that diurnal frequent urination associated with LEV deserves clinician's attention. PMID:26938751

  8. What is preexisting strength? Predicting free association probabilities, similarity ratings, and cued recall probabilities.

    PubMed

    Nelson, Douglas L; Dyrdal, Gunvor M; Goodmon, Leilani B

    2005-08-01

    Measuring lexical knowledge poses a challenge to the study of the influence of preexisting knowledge on the retrieval of new memories. Many tasks focus on word pairs, but words are embedded in associative networks, so how should preexisting pair strength be measured? It has been measured by free association, similarity ratings, and co-occurrence statistics. Researchers interpret free association response probabilities as unbiased estimates of forward cue-to-target strength. In Study 1, analyses of large free association and extralist cued recall databases indicate that this interpretation is incorrect. Competitor and backward strengths bias free association probabilities, and as with other recall tasks, preexisting strength is described by a ratio rule. In Study 2, associative similarity ratings are predicted by forward and backward, but not by competitor, strength. Preexisting strength is not a unitary construct, because its measurement varies with method. Furthermore, free association probabilities predict extralist cued recall better than do ratings and co-occurrence statistics. The measure that most closely matches the criterion task may provide the best estimate of the identity of preexisting strength. PMID:16447386

  9. Prospect evaluation as a function of numeracy and probability denominator.

    PubMed

    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.

  10. Prospect evaluation as a function of numeracy and probability denominator.

    PubMed

    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. PMID:25704578

  11. On lacunary statistical convergence of order α in probability

    NASA Astrophysics Data System (ADS)

    Işık, Mahmut; Et, Kübra Elif

    2015-09-01

    In this study, we examine the concepts of lacunary statistical convergence of order α in probability and Nθ—convergence of order α in probability. We give some relations connected to these concepts.

  12. Probability-summation model of multiple laser-exposure effects.

    PubMed

    Menendez, A R; Cheney, F E; Zuclich, J A; Crump, P

    1993-11-01

    A probability-summation model is introduced to provide quantitative criteria for discriminating independent from interactive effects of multiple laser exposures on biological tissue. Data that differ statistically from predictions of the probability-summation model indicate the action of sensitizing (synergistic/positive) or desensitizing (hardening/negative) biophysical interactions. Interactions are indicated when response probabilities vary with changes in the spatial or temporal separation of exposures. In the absence of interactions, probability-summation parsimoniously accounts for "cumulative" effects. Data analyzed using the probability-summation model show instances of both sensitization and desensitization of retinal tissue by laser exposures. Other results are shown to be consistent with probability-summation. The relevance of the probability-summation model to previous laser-bioeffects studies, models, and safety standards is discussed and an appeal is made for improved empirical estimates of response probabilities for single exposures.

  13. Probability in Theories With Complex Dynamics and Hardy's Fifth Axiom

    NASA Astrophysics Data System (ADS)

    Burić, Nikola

    2010-08-01

    L. Hardy has formulated an axiomatization program of quantum mechanics and generalized probability theories that has been quite influential. In this paper, properties of typical Hamiltonian dynamical systems are used to argue that there are applications of probability in physical theories of systems with dynamical complexity that require continuous spaces of pure states. Hardy’s axiomatization program does not deal with such theories. In particular Hardy’s fifth axiom does not differentiate between such applications of classical probability and quantum probability.

  14. Pretest probability assessment derived from attribute matching

    PubMed Central

    Kline, Jeffrey A; Johnson, Charles L; Pollack, Charles V; Diercks, Deborah B; Hollander, Judd E; Newgard, Craig D; Garvey, J Lee

    2005-01-01

    Background Pretest probability (PTP) assessment plays a central role in diagnosis. This report compares a novel attribute-matching method to generate a PTP for acute coronary syndrome (ACS). We compare the new method with a validated logistic regression equation (LRE). Methods Eight clinical variables (attributes) were chosen by classification and regression tree analysis of a prospectively collected reference database of 14,796 emergency department (ED) patients evaluated for possible ACS. For attribute matching, a computer program identifies patients within the database who have the exact profile defined by clinician input of the eight attributes. The novel method was compared with the LRE for ability to produce PTP estimation <2% in a validation set of 8,120 patients evaluated for possible ACS and did not have ST segment elevation on ECG. 1,061 patients were excluded prior to validation analysis because of ST-segment elevation (713), missing data (77) or being lost to follow-up (271). Results In the validation set, attribute matching produced 267 unique PTP estimates [median PTP value 6%, 1st–3rd quartile 1–10%] compared with the LRE, which produced 96 unique PTP estimates [median 24%, 1st–3rd quartile 10–30%]. The areas under the receiver operating characteristic curves were 0.74 (95% CI 0.65 to 0.82) for the attribute matching curve and 0.68 (95% CI 0.62 to 0.77) for LRE. The attribute matching system categorized 1,670 (24%, 95% CI = 23–25%) patients as having a PTP < 2.0%; 28 developed ACS (1.7% 95% CI = 1.1–2.4%). The LRE categorized 244 (4%, 95% CI = 3–4%) with PTP < 2.0%; four developed ACS (1.6%, 95% CI = 0.4–4.1%). Conclusion Attribute matching estimated a very low PTP for ACS in a significantly larger proportion of ED patients compared with a validated LRE. PMID:16095534

  15. Pig Data and Bayesian Inference on Multinomial Probabilities

    ERIC Educational Resources Information Center

    Kern, John C.

    2006-01-01

    Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…

  16. Factors influencing reporting and harvest probabilities in North American geese

    USGS Publications Warehouse

    Zimmerman, G.S.; Moser, T.J.; Kendall, W.L.; Doherty, P.F.; White, Gary C.; Caswell, D.F.

    2009-01-01

    We assessed variation in reporting probabilities of standard bands among species, populations, harvest locations, and size classes of North American geese to enable estimation of unbiased harvest probabilities. We included reward (US10,20,30,50, or100) and control (0) banded geese from 16 recognized goose populations of 4 species: Canada (Branta canadensis), cackling (B. hutchinsii), Ross's (Chen rossii), and snow geese (C. caerulescens). We incorporated spatially explicit direct recoveries and live recaptures into a multinomial model to estimate reporting, harvest, and band-retention probabilities. We compared various models for estimating harvest probabilities at country (United States vs. Canada), flyway (5 administrative regions), and harvest area (i.e., flyways divided into northern and southern sections) scales. Mean reporting probability of standard bands was 0.73 (95 CI 0.690.77). Point estimates of reporting probabilities for goose populations or spatial units varied from 0.52 to 0.93, but confidence intervals for individual estimates overlapped and model selection indicated that models with species, population, or spatial effects were less parsimonious than those without these effects. Our estimates were similar to recently reported estimates for mallards (Anas platyrhynchos). We provide current harvest probability estimates for these populations using our direct measures of reporting probability, improving the accuracy of previous estimates obtained from recovery probabilities alone. Goose managers and researchers throughout North America can use our reporting probabilities to correct recovery probabilities estimated from standard banding operations for deriving spatially explicit harvest probabilities.

  17. 28 CFR 2.101 - Probable cause hearing and determination.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 28 Judicial Administration 1 2013-07-01 2013-07-01 false Probable cause hearing and determination... Parolees § 2.101 Probable cause hearing and determination. (a) Hearing. A parolee who is retaken and held... convicted of a new crime, shall be given a probable cause hearing by an examiner of the Commission no...

  18. 28 CFR 2.214 - Probable cause hearing and determination.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 28 Judicial Administration 1 2012-07-01 2012-07-01 false Probable cause hearing and determination... § 2.214 Probable cause hearing and determination. (a) Hearing. A supervised releasee who is retaken... been convicted of a new crime, shall be given a probable cause hearing by an examiner of the...

  19. 28 CFR 2.214 - Probable cause hearing and determination.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 28 Judicial Administration 1 2013-07-01 2013-07-01 false Probable cause hearing and determination... § 2.214 Probable cause hearing and determination. (a) Hearing. A supervised releasee who is retaken... been convicted of a new crime, shall be given a probable cause hearing by an examiner of the...

  20. 21 CFR 1316.10 - Administrative probable cause.

    Code of Federal Regulations, 2014 CFR

    2014-04-01

    ... 21 Food and Drugs 9 2014-04-01 2014-04-01 false Administrative probable cause. 1316.10 Section..., PRACTICES, AND PROCEDURES Administrative Inspections § 1316.10 Administrative probable cause. If the judge or magistrate is satisfied that “administrative probable cause,” as defined in section 510(d)(1)...

  1. 28 CFR 2.101 - Probable cause hearing and determination.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 28 Judicial Administration 1 2011-07-01 2011-07-01 false Probable cause hearing and determination... Parolees § 2.101 Probable cause hearing and determination. (a) Hearing. A parolee who is retaken and held... convicted of a new crime, shall be given a probable cause hearing by an examiner of the Commission no...

  2. 21 CFR 1316.10 - Administrative probable cause.

    Code of Federal Regulations, 2013 CFR

    2013-04-01

    ... 21 Food and Drugs 9 2013-04-01 2013-04-01 false Administrative probable cause. 1316.10 Section..., PRACTICES, AND PROCEDURES Administrative Inspections § 1316.10 Administrative probable cause. If the judge or magistrate is satisfied that “administrative probable cause,” as defined in section 510(d)(1)...

  3. 21 CFR 1316.10 - Administrative probable cause.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 21 Food and Drugs 9 2010-04-01 2010-04-01 false Administrative probable cause. 1316.10 Section..., PRACTICES, AND PROCEDURES Administrative Inspections § 1316.10 Administrative probable cause. If the judge or magistrate is satisfied that “administrative probable cause,” as defined in section 510(d)(1)...

  4. 28 CFR 2.214 - Probable cause hearing and determination.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 28 Judicial Administration 1 2014-07-01 2014-07-01 false Probable cause hearing and determination... § 2.214 Probable cause hearing and determination. (a) Hearing. A supervised releasee who is retaken... been convicted of a new crime, shall be given a probable cause hearing by an examiner of the...

  5. 21 CFR 1316.10 - Administrative probable cause.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... 21 Food and Drugs 9 2012-04-01 2012-04-01 false Administrative probable cause. 1316.10 Section..., PRACTICES, AND PROCEDURES Administrative Inspections § 1316.10 Administrative probable cause. If the judge or magistrate is satisfied that “administrative probable cause,” as defined in section 510(d)(1)...

  6. 28 CFR 2.101 - Probable cause hearing and determination.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 28 Judicial Administration 1 2014-07-01 2014-07-01 false Probable cause hearing and determination... Parolees § 2.101 Probable cause hearing and determination. (a) Hearing. A parolee who is retaken and held... convicted of a new crime, shall be given a probable cause hearing by an examiner of the Commission no...

  7. 28 CFR 2.101 - Probable cause hearing and determination.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 28 Judicial Administration 1 2012-07-01 2012-07-01 false Probable cause hearing and determination... Parolees § 2.101 Probable cause hearing and determination. (a) Hearing. A parolee who is retaken and held... convicted of a new crime, shall be given a probable cause hearing by an examiner of the Commission no...

  8. 28 CFR 2.214 - Probable cause hearing and determination.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 28 Judicial Administration 1 2011-07-01 2011-07-01 false Probable cause hearing and determination... § 2.214 Probable cause hearing and determination. (a) Hearing. A supervised releasee who is retaken... been convicted of a new crime, shall be given a probable cause hearing by an examiner of the...

  9. 28 CFR 2.214 - Probable cause hearing and determination.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Probable cause hearing and determination... § 2.214 Probable cause hearing and determination. (a) Hearing. A supervised releasee who is retaken... been convicted of a new crime, shall be given a probable cause hearing by an examiner of the...

  10. 28 CFR 2.101 - Probable cause hearing and determination.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Probable cause hearing and determination... Parolees § 2.101 Probable cause hearing and determination. (a) Hearing. A parolee who is retaken and held... convicted of a new crime, shall be given a probable cause hearing by an examiner of the Commission no...

  11. 21 CFR 1316.10 - Administrative probable cause.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... 21 Food and Drugs 9 2011-04-01 2011-04-01 false Administrative probable cause. 1316.10 Section..., PRACTICES, AND PROCEDURES Administrative Inspections § 1316.10 Administrative probable cause. If the judge or magistrate is satisfied that “administrative probable cause,” as defined in section 510(d)(1)...

  12. Contingency bias in probability judgement may arise from ambiguity regarding additional causes.

    PubMed

    Mitchell, Chris J; Griffiths, Oren; More, Pranjal; Lovibond, Peter F

    2013-09-01

    In laboratory contingency learning tasks, people usually give accurate estimates of the degree of contingency between a cue and an outcome. However, if they are asked to estimate the probability of the outcome in the presence of the cue, they tend to be biased by the probability of the outcome in the absence of the cue. This bias is often attributed to an automatic contingency detection mechanism, which is said to act via an excitatory associative link to activate the outcome representation at the time of testing. We conducted 3 experiments to test alternative accounts of contingency bias. Participants were exposed to the same outcome probability in the presence of the cue, but different outcome probabilities in the absence of the cue. Phrasing the test question in terms of frequency rather than probability and clarifying the test instructions reduced but did not eliminate contingency bias. However, removal of ambiguity regarding the presence of additional causes during the test phase did eliminate contingency bias. We conclude that contingency bias may be due to ambiguity in the test question, and therefore it does not require postulation of a separate associative link-based mechanism.

  13. Pattern formation, logistics, and maximum path probability

    NASA Astrophysics Data System (ADS)

    Kirkaldy, J. S.

    1985-05-01

    The concept of pattern formation, which to current researchers is a synonym for self-organization, carries the connotation of deductive logic together with the process of spontaneous inference. Defining a pattern as an equivalence relation on a set of thermodynamic objects, we establish that a large class of irreversible pattern-forming systems, evolving along idealized quasisteady paths, approaches the stable steady state as a mapping upon the formal deductive imperatives of a propositional function calculus. In the preamble the classical reversible thermodynamics of composite systems is analyzed as an externally manipulated system of space partitioning and classification based on ideal enclosures and diaphragms. The diaphragms have discrete classification capabilities which are designated in relation to conserved quantities by descriptors such as impervious, diathermal, and adiabatic. Differentiability in the continuum thermodynamic calculus is invoked as equivalent to analyticity and consistency in the underlying class or sentential calculus. The seat of inference, however, rests with the thermodynamicist. In the transition to an irreversible pattern-forming system the defined nature of the composite reservoirs remains, but a given diaphragm is replaced by a pattern-forming system which by its nature is a spontaneously evolving volume partitioner and classifier of invariants. The seat of volition or inference for the classification system is thus transferred from the experimenter or theoretician to the diaphragm, and with it the full deductive facility. The equivalence relations or partitions associated with the emerging patterns may thus be associated with theorems of the natural pattern-forming calculus. The entropy function, together with its derivatives, is the vehicle which relates the logistics of reservoirs and diaphragms to the analog logistics of the continuum. Maximum path probability or second-order differentiability of the entropy in isolation are

  14. Probability Distribution for Flowing Interval Spacing

    SciTech Connect

    S. Kuzio

    2004-09-22

    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

  15. Total probabilities of ensemble runoff forecasts

    NASA Astrophysics Data System (ADS)

    Olav Skøien, Jon; Bogner, Konrad; Salamon, Peter; Smith, Paul; Pappenberger, Florian

    2016-04-01

    Ensemble forecasting has for a long time been used as a method in meteorological modelling to indicate the uncertainty of the forecasts. However, as the ensembles often exhibit both bias and dispersion errors, it is necessary to calibrate and post-process them. Two of the most common methods for this are Bayesian Model Averaging (Raftery et al., 2005) and Ensemble Model Output Statistics (EMOS) (Gneiting et al., 2005). There are also methods for regionalizing these methods (Berrocal et al., 2007) and for incorporating the correlation between lead times (Hemri et al., 2013). Engeland and Steinsland Engeland and Steinsland (2014) developed a framework which can estimate post-processing parameters which are different in space and time, but still can give a spatially and temporally consistent output. However, their method is computationally complex for our larger number of stations, and cannot directly be regionalized in the way we would like, so we suggest a different path below. The target of our work is to create a mean forecast with uncertainty bounds for a large number of locations in the framework of the European Flood Awareness System (EFAS - http://www.efas.eu) We are therefore more interested in improving the forecast skill for high-flows rather than the forecast skill of lower runoff levels. EFAS uses a combination of ensemble forecasts and deterministic forecasts from different forecasters to force a distributed hydrologic model and to compute runoff ensembles for each river pixel within the model domain. Instead of showing the mean and the variability of each forecast ensemble individually, we will now post-process all model outputs to find a total probability, the post-processed mean and uncertainty of all ensembles. The post-processing parameters are first calibrated for each calibration location, but assuring that they have some spatial correlation, by adding a spatial penalty in the calibration process. This can in some cases have a slight negative

  16. Three Dimensional Probability Distributions of the Interplanetary Magnetic Field

    NASA Astrophysics Data System (ADS)

    Podesta, J. J.

    2014-12-01

    Empirical probability density functions (PDFs) of the interplanetary magnetic field (IMF) have been derived from spacecraft data since the early years of the space age. A survey of the literature shows that past studies have investigated the separate Cartesian components of the magnetic field, the vector magnitude, and the direction of the IMF by means of one-dimensional or two-dimensional PDFs. But, to my knowledge, there exist no studies which investigate the three dimensional nature of the IMF by means of three dimensional PDFs, either in (Bx,By,Bz)(B_x,B_y,B_z)-coordinates or (BR,BT,BN)(B_R,B_T,B_N)-coordinates or some other appropriate system of coordinates. Likewise, there exist no studies which investigate three dimensional PDFs of magnetic field fluctuations, that is, vector differences bmB(t+τ)-bmB(t)bm{B}(t+tau)-bm{B}(t). In this talk, I shall present examples of three dimensional PDFs obtained from spacecraft data that demonstrate the solar wind magnetic field possesses a very interesting spatial structure that, to my knowledge, has not previously been identified. Perhaps because of the well known model of Barnes (1981) in which the magnitude of the IMF remains constant, it may be commonly believed that there is nothing new to learn from a full three dimensional PDF. To the contrary, there is much to learn from the investigation of three dimensional PDFs of the solar wind plasma velocity and the magnetic field, as well as three dimensional PDFs of their fluctuations. Knowledge of these PDFs will not only improve understanding of solar wind physics, it is an essential prerequisite for the construction of realistic models of the stochastic time series measured by a single spacecraft, one of the longstanding goals of space physics research. In addition, three dimensional PDFs contain valuable information about the anisotropy of solar wind fluctuations in three dimensional physical space, information that may help identify the reason why the three

  17. Learning foraging thresholds for lizards

    SciTech Connect

    Goldberg, L.A.; Hart, W.E.; Wilson, D.B.

    1996-01-12

    This work gives a proof of convergence for a randomized learning algorithm that describes how anoles (lizards found in the Carribean) learn a foraging threshold distance. This model assumes that an anole will pursue a prey if and only if it is within this threshold of the anole`s perch. This learning algorithm was proposed by the biologist Roughgarden and his colleagues. They experimentally confirmed that this algorithm quickly converges to the foraging threshold that is predicted by optimal foraging theory our analysis provides an analytic confirmation that the learning algorithm converses to this optimal foraging threshold with high probability.

  18. Surprisingly rational: probability theory plus noise explains biases in judgment.

    PubMed

    Costello, Fintan; Watts, Paul

    2014-07-01

    The systematic biases seen in people's probability judgments are typically taken as evidence that people do not use the rules of probability theory when reasoning about probability but instead use heuristics, which sometimes yield reasonable judgments and sometimes yield systematic biases. This view has had a major impact in economics, law, medicine, and other fields; indeed, the idea that people cannot reason with probabilities has become a truism. We present a simple alternative to this view, where people reason about probability according to probability theory but are subject to random variation or noise in the reasoning process. In this account the effect of noise is canceled for some probabilistic expressions. Analyzing data from 2 experiments, we find that, for these expressions, people's probability judgments are strikingly close to those required by probability theory. For other expressions, this account produces systematic deviations in probability estimates. These deviations explain 4 reliable biases in human probabilistic reasoning (conservatism, subadditivity, conjunction, and disjunction fallacies). These results suggest that people's probability judgments embody the rules of probability theory and that biases in those judgments are due to the effects of random noise. PMID:25090427

  19. Probability shapes perceptual precision: A study in orientation estimation.

    PubMed

    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."

  20. On the shape of the probability weighting function.

    PubMed

    Gonzalez, R; Wu, G

    1999-02-01

    Empirical studies have shown that decision makers do not usually treat probabilities linearly. Instead, people tend to overweight small probabilities and underweight large probabilities. One way to model such distortions in decision making under risk is through a probability weighting function. We present a nonparametric estimation procedure for assessing the probability weighting function and value function at the level of the individual subject. The evidence in the domain of gains supports a two-parameter weighting function, where each parameter is given a psychological interpretation: one parameter measures how the decision maker discriminates probabilities, and the other parameter measures how attractive the decision maker views gambling. These findings are consistent with a growing body of empirical and theoretical work attempting to establish a psychological rationale for the probability weighting function. PMID:10090801

  1. Nonlinear Neurobiological Probability Weighting Functions For Aversive Outcomes

    PubMed Central

    Berns, Gregory S.; Capra, C. Monica; Chappelow, Jonathan; Moore, Sara; Noussair, Charles

    2008-01-01

    While mainstream economic models assume that individuals treat probabilities objectively, many people tend to overestimate the likelihood of improbable events and underestimate the likelihood of probable events. However, a biological account for why probabilities would be treated this way does not yet exist. While undergoing fMRI, we presented individuals with a series of lotteries, defined by the voltage of an impending cutaneous electric shock and the probability with which the shock would be received. During the prospect phase, neural activity that tracked the probability of the expected outcome was observed in a circumscribed network of brain regions that included the anterior cingulate, visual, parietal, and temporal cortices. Most of these regions displayed responses to probabilities consistent with nonlinear probability weighting. The neural responses to passive lotteries predicted 79% of subsequent decisions when individuals were offered choices between different lotteries, and exceeded that predicted by behavior alone near the indifference point. PMID:18060809

  2. Conditional Probabilities for Large Events Estimated by Small Earthquake Rate

    NASA Astrophysics Data System (ADS)

    Wu, Yi-Hsuan; Chen, Chien-Chih; Li, Hsien-Chi

    2016-01-01

    We examined forecasting quiescence and activation models to obtain the conditional probability that a large earthquake will occur in a specific time period on different scales in Taiwan. The basic idea of the quiescence and activation models is to use earthquakes that have magnitudes larger than the completeness magnitude to compute the expected properties of large earthquakes. We calculated the probability time series for the whole Taiwan region and for three subareas of Taiwan—the western, eastern, and northeastern Taiwan regions—using 40 years of data from the Central Weather Bureau catalog. In the probability time series for the eastern and northeastern Taiwan regions, a high probability value is usually yielded in cluster events such as events with foreshocks and events that all occur in a short time period. In addition to the time series, we produced probability maps by calculating the conditional probability for every grid point at the time just before a large earthquake. The probability maps show that high probability values are yielded around the epicenter before a large earthquake. The receiver operating characteristic (ROC) curves of the probability maps demonstrate that the probability maps are not random forecasts, but also suggest that lowering the magnitude of a forecasted large earthquake may not improve the forecast method itself. From both the probability time series and probability maps, it can be observed that the probability obtained from the quiescence model increases before a large earthquake and the probability obtained from the activation model increases as the large earthquakes occur. The results lead us to conclude that the quiescence model has better forecast potential than the activation model.

  3. Young Star Probably Ejected From Triple System

    NASA Astrophysics Data System (ADS)

    2003-01-01

    Astronomers analyzing nearly 20 years of data from the National Science Foundation's Very Large Array radio telescope have discovered that a small star in a multiple-star system in the constellation Taurus probably has been ejected from the system after a close encounter with one of the system's more-massive components, presumed to be a compact double star. This is the first time any such event has been observed. Path of Small Star, 1983-2001 "Our analysis shows a drastic change in the orbit of this young star after it made a close approach to another object in the system," said Luis Rodriguez of the Institute of Astronomy of the National Autonomous University of Mexico (UNAM). "The young star was accelerated to a large velocity by the close approach, and certainly now is in a very different, more remote orbit, and may even completely escape its companions," said Laurent Loinard, leader of the research team that also included Monica Rodriguez in addition to Luis Rodriguez. The UNAM astronomers presented their findings at the American Astronomical Society's meeting in Seattle, WA. The discovery of this chaotic event will be important for advancing our understanding of classical dynamic astronomy and of how stars evolve, including possibly providing an explanation for the production of the mysterious "brown dwarfs," the astronomers said. The scientists analyzed VLA observations of T Tauri, a multiple system of young stars some 450 light-years from Earth. The observations were made from 1983 to 2001. The T Tauri system includes a "Northern" star, the famous star that gives its name to the class of young visible stars, and a "Southern" system of stars, all orbiting each other. The VLA data were used to track the orbit of the smaller Southern star around the larger Southern object, presumed to be a pair of stars orbiting each other closely. The astronomers' plot of the smaller star's orbit shows that it followed an apparently elliptical orbit around its twin companions

  4. A physical-space approach for the probability hypothesis density and cardinalized probability hypothesis density filters

    NASA Astrophysics Data System (ADS)

    Erdinc, Ozgur; Willett, Peter; Bar-Shalom, Yaakov

    2006-05-01

    The probability hypothesis density (PHD) filter, an automatically track-managed multi-target tracker, is attracting increasing but cautious attention. Its derivation is elegant and mathematical, and thus of course many engineers fear it; perhaps that is currently limiting the number of researchers working on the subject. In this paper, we explore a physical-space approach - a bin model - which leads us to arrive the same filter equations as the PHD. Unlike the original derivation of the PHD filter, the concepts used are the familiar ones of conditional probability. The original PHD suffers from a "target-death" problem in which even a single missed detection can lead to the apparent disappearance of a target. To obviate this, PHD originator Mahler has recently developed a new "cardinalized" version of PHD (CPHD). We are able to extend our physical-space derivation to the CPHD case as well. We stress that the original derivations are mathematically correct, and need no embellishment from us; our contribution here is to offer an alternative derivation, one that we find appealing.

  5. GNSS integer ambiguity validation based on posterior probability

    NASA Astrophysics Data System (ADS)

    Wu, Zemin; Bian, Shaofeng

    2015-10-01

    GNSS integer ambiguity validation is considered to be a challenge task for decades. Several kinds of validation tests are developed and widely used in these years, but theoretical basis is their weakness. Ambiguity validation theoretically is an issue of hypothesis test. In the frame of Bayesian hypothesis testing, posterior probability is the canonical standard that statistical decision should be based on. In this contribution, (i) we derive the posterior probability of the fixed ambiguity based on the Bayesian principle and modify it for practice ambiguity validation. (ii) The optimal property of the posterior probability test is proved based on an extended Neyman-Pearson lemma. Since validation failure rate is the issue users most concerned about, (iii) we derive the failure rate upper bound of the posterior probability test, so the user can use the posterior probability test either in the fixed posterior probability or in the fixed failure rate way. Simulated as well as real observed data are used for experimental validations. The results show that (i) the posterior probability test is the most effective within the R-ratio test, difference test, ellipsoidal integer aperture test and posterior probability test, (ii) the posterior probability test is computational efficient and (iii) the failure rate estimation for posterior probability test is useful.

  6. Dynamics of opinion formation with strengthen selection probability

    NASA Astrophysics Data System (ADS)

    Zhang, Haifeng; Jin, Zhen; Wang, Binghong

    2014-04-01

    The local majority rule is extensively accepted as a paradigmatic model to reflect the formation of opinion. In this paper, we study a model of opinion formation where opinion update rule is not based on the majority rule or linear selection probability but on a strengthen selection probability controlled by an adjustable parameter β. In particular, our proposed probability function can proximately fit the two extreme cases-linear probability function and majority rule or in between the two cases under different values of β. By studying such model on different kinds of networks, including different regular networks and complex networks, we find that there exists an optimal value of β giving the most efficient convergence to consensus regardless of the topology of networks. This work reveals that, compared with the majority rule and linear selection probability, the strengthen selection probability might be a more proper model in understanding the formation of opinions in society.

  7. Learning to Learn Cooperatively

    ERIC Educational Resources Information Center

    Byrd, Anne Hammond

    2009-01-01

    Cooperative learning, put quite simply, is a type of instruction whereby students work together in small groups to achieve a common goal. Cooperative learning has become increasingly popular as a feature of Communicative Language Teaching (CLT) with benefits that include increased student interest due to the quick pace of cooperative tasks,…

  8. Learning about Learning

    ERIC Educational Resources Information Center

    Siegler, Robert S.

    2004-01-01

    The field of children's learning was thriving when the Merrill-Palmer Quarterly was launched; the field later went into eclipse and now is in the midst of a resurgence. This commentary examines reasons for these trends, and describes the emerging field of children's learning. In particular, the new field is seen as differing from the old in its…

  9. Measurement outcomes and probability in Everettian quantum mechanics

    NASA Astrophysics Data System (ADS)

    Baker, David J.

    The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.

  10. Path probability of stochastic motion: A functional approach

    NASA Astrophysics Data System (ADS)

    Hattori, Masayuki; Abe, Sumiyoshi

    2016-06-01

    The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.

  11. Learning to aid learning.

    PubMed

    Richards, Jacqui

    2016-01-01

    The National Health Service (NHS) is one of the largest employers in the world and, with 1.3 million staff, the biggest employer in Europe. With over three hundred different careers on offer (NHS 2015), the acquisition of skills and qualifications, through academic and clinical training, is an integral part of day-to-day life in the health service. As such, mentoring has become a significant feature in the preparation of healthcare professionals, to support students and ensure learning needs and experiences are appropriate to competency. This article examines the mentor's role, in relation to a teaching innovation designed to address students' identified learning needs to meet the requirements of the multi-professional learning and assessment in practice course NM6156. The effectiveness of the aids to learning will be assessed through an online quiz, and its usefulness will be analysed with reference to educational theories of learning and development.

  12. Learning to aid learning.

    PubMed

    Richards, Jacqui

    2016-01-01

    The National Health Service (NHS) is one of the largest employers in the world and, with 1.3 million staff, the biggest employer in Europe. With over three hundred different careers on offer (NHS 2015), the acquisition of skills and qualifications, through academic and clinical training, is an integral part of day-to-day life in the health service. As such, mentoring has become a significant feature in the preparation of healthcare professionals, to support students and ensure learning needs and experiences are appropriate to competency. This article examines the mentor's role, in relation to a teaching innovation designed to address students' identified learning needs to meet the requirements of the multi-professional learning and assessment in practice course NM6156. The effectiveness of the aids to learning will be assessed through an online quiz, and its usefulness will be analysed with reference to educational theories of learning and development. PMID:26975128

  13. Code System to Calculate Pressure Vessel Failure Probabilities.

    2001-03-27

    Version 00 OCTAVIA (Operationally Caused Transients And Vessel Integrity Analysis) calculates the probability of pressure vessel failure from operationally-caused pressure transients which can occur in a pressurized water reactor (PWR). For specified vessel and operating environment characteristics the program computes the failure pressure at which the vessel will fail for different-sized flaws existing in the beltline and the probability of vessel failure per reactor year due to the flaw. The probabilities are summed over themore » various flaw sizes to obtain the total vessel failure probability. Sensitivity studies can be performed to investigate different vessel or operating characteristics in the same computer run.« less

  14. Probability forecast of the suspended sediment concentration using copula

    NASA Astrophysics Data System (ADS)

    Yu, Kun-xia; Li, Peng; Li, Zhanbin

    2016-04-01

    An approach for probability forecast of the suspended sediment loads is presented in our research. Probability forecast model is established based on the joint probability distribution of water discharge and suspended sediment concentration. The conditional distribution function of suspended sediment concentration given water discharge is evaluated provided the joint probability distribution between water discharge and suspended sediment concentration is constructed, and probability forecast of suspended sediment concentration is implemented in terms of conditional probability function. This approach is exemplified using annual data set of ten watersheds in the middle Yellow River which is characterized by heavy sediment. The three-parameter Gamma distribution is employed to fit the marginal distribution of annual water discharge and annual suspended sediment concentration, and the Gumbel copula can well describe the dependence structure between annual water discharge and annual suspended sediment concentration. Annual suspended sediment concentration estimated from the conditional distribution function with forecast probability of 50 percent agree better with the observed suspended sediment concentration values than the traditional sediment rating curve method given water discharge values. The overwhelming majority of observed suspended sediment concentration points lie between the forecast probability of 5 percent and 95 percent, which can be considered as the lower and upper 95th percent uncertainty bound of the predicted observation respectively. The results indicate that probability forecast on the basis of conditional distribution function is a potential alternative in suspended sediment and other hydrological variables estimation.

  15. Anytime synthetic projection: Maximizing the probability of goal satisfaction

    NASA Technical Reports Server (NTRS)

    Drummond, Mark; Bresina, John L.

    1990-01-01

    A projection algorithm is presented for incremental control rule synthesis. The algorithm synthesizes an initial set of goal achieving control rules using a combination of situation probability and estimated remaining work as a search heuristic. This set of control rules has a certain probability of satisfying the given goal. The probability is incrementally increased by synthesizing additional control rules to handle 'error' situations the execution system is likely to encounter when following the initial control rules. By using situation probabilities, the algorithm achieves a computationally effective balance between the limited robustness of triangle tables and the absolute robustness of universal plans.

  16. Oscillations in probability distributions for stochastic gene expression

    SciTech Connect

    Petrosyan, K. G. Hu, Chin-Kun

    2014-05-28

    The phenomenon of oscillations in probability distribution functions of number of components is found for a model of stochastic gene expression. It takes place in cases of low levels of molecules or strong intracellular noise. The oscillations distinguish between more probable even and less probable odd number of particles. The even-odd symmetry restores as the number of molecules increases with the probability distribution function tending to Poisson distribution. We discuss the possibility of observation of the phenomenon in gene, protein, and mRNA expression experiments.

  17. Challenges for Enriching the Curriculum: Statistics and Probability.

    ERIC Educational Resources Information Center

    Swift, Jim

    1983-01-01

    Three probability problems designed to challenge students are presented: Liars and Diamonds, Heads Wins, and Random Walks. Other statistic problems are suggested that could involve computer simulations. (MNS)

  18. Methods for fitting a parametric probability distribution to most probable number data.

    PubMed

    Williams, Michael S; Ebel, Eric D

    2012-07-01

    Every year hundreds of thousands, if not millions, of samples are collected and analyzed to assess microbial contamination in food and water. The concentration of pathogenic organisms at the end of the production process is low for most commodities, so a highly sensitive screening test is used to determine whether the organism of interest is present in a sample. In some applications, samples that test positive are subjected to quantitation. The most probable number (MPN) technique is a common method to quantify the level of contamination in a sample because it is able to provide estimates at low concentrations. This technique uses a series of dilution count experiments to derive estimates of the concentration of the microorganism of interest. An application for these data is food-safety risk assessment, where the MPN concentration estimates can be fitted to a parametric distribution to summarize the range of potential exposures to the contaminant. Many different methods (e.g., substitution methods, maximum likelihood and regression on order statistics) have been proposed to fit microbial contamination data to a distribution, but the development of these methods rarely considers how the MPN technique influences the choice of distribution function and fitting method. An often overlooked aspect when applying these methods is whether the data represent actual measurements of the average concentration of microorganism per milliliter or the data are real-valued estimates of the average concentration, as is the case with MPN data. In this study, we propose two methods for fitting MPN data to a probability distribution. The first method uses a maximum likelihood estimator that takes average concentration values as the data inputs. The second is a Bayesian latent variable method that uses the counts of the number of positive tubes at each dilution to estimate the parameters of the contamination distribution. The performance of the two fitting methods is compared for two

  19. Student Understanding of Probability and Introductory Statistical Physics in Upper-division Courses on Thermal Physics

    NASA Astrophysics Data System (ADS)

    Loverude, Michael E.

    2006-12-01

    This talk describes part of an ongoing investigation of student learning in the context of upper-division courses in thermal physics. In particular, we will examine student understanding of the fundamental concepts of statistical physics, and the underlying mathematics of probability. Our results suggest that students lack a deep understanding of the statistics of binary systems like coin flips, calling into question their ability to apply these results to simple physical systems. We will provide examples of student responses and written explanations and discuss implications for instruction.

  20. Hit Expansion from Screening Data Based upon Conditional Probabilities of Activity Derived from SAR Matrices.

    PubMed

    Gupta-Ostermann, Disha; Balfer, Jenny; Bajorath, Jürgen

    2015-02-01

    A new methodology for activity prediction of compounds from SAR matrices is introduced that is based upon conditional probabilities of activity. The approach has low computational complexity, is primarily designed for hit expansion from biological screening data, and accurately predicts both active and inactive compounds. Its performance is comparable to state-of-the-art machine learning methods such as support vector machines or Bayesian classification. Matrix-based activity prediction of virtual compounds further extends the spectrum of computational methods for compound design.

  1. Hit Expansion from Screening Data Based upon Conditional Probabilities of Activity Derived from SAR Matrices.

    PubMed

    Gupta-Ostermann, Disha; Balfer, Jenny; Bajorath, Jürgen

    2015-02-01

    A new methodology for activity prediction of compounds from SAR matrices is introduced that is based upon conditional probabilities of activity. The approach has low computational complexity, is primarily designed for hit expansion from biological screening data, and accurately predicts both active and inactive compounds. Its performance is comparable to state-of-the-art machine learning methods such as support vector machines or Bayesian classification. Matrix-based activity prediction of virtual compounds further extends the spectrum of computational methods for compound design. PMID:27490036

  2. Learning about Sounds Contributes to Learning about Words: Effects of Prosody and Phonotactics on Infant Word Learning

    ERIC Educational Resources Information Center

    Estes, Katharine Graf; Bowen, Sara

    2013-01-01

    This research investigates how early learning about native language sound structure affects how infants associate sounds with meanings during word learning. Infants (19-month-olds) were presented with bisyllabic labels with high or low phonotactic probability (i.e., sequences of frequent or infrequent phonemes in English). The labels were produced…

  3. How Can Histograms Be Useful for Introducing Continuous Probability Distributions?

    ERIC Educational Resources Information Center

    Derouet, Charlotte; Parzysz, Bernard

    2016-01-01

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

  4. 14 CFR 417.224 - Probability of failure analysis.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ..., DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH SAFETY Flight Safety Analysis § 417.224 Probability of failure analysis. (a) General. All flight safety analyses for a launch, regardless of hazard or phase of flight... probability estimate must use accurate data, scientific principles, and a method that is statistically...

  5. 14 CFR 417.224 - Probability of failure analysis.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ..., DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH SAFETY Flight Safety Analysis § 417.224 Probability of failure analysis. (a) General. All flight safety analyses for a launch, regardless of hazard or phase of flight... probability estimate must use accurate data, scientific principles, and a method that is statistically...

  6. 14 CFR 417.224 - Probability of failure analysis.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ..., DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH SAFETY Flight Safety Analysis § 417.224 Probability of failure analysis. (a) General. All flight safety analyses for a launch, regardless of hazard or phase of flight... probability estimate must use accurate data, scientific principles, and a method that is statistically...

  7. 14 CFR 417.224 - Probability of failure analysis.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ..., DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH SAFETY Flight Safety Analysis § 417.224 Probability of failure analysis. (a) General. All flight safety analyses for a launch, regardless of hazard or phase of flight... probability estimate must use accurate data, scientific principles, and a method that is statistically...

  8. 14 CFR 417.224 - Probability of failure analysis.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ..., DEPARTMENT OF TRANSPORTATION LICENSING LAUNCH SAFETY Flight Safety Analysis § 417.224 Probability of failure analysis. (a) General. All flight safety analyses for a launch, regardless of hazard or phase of flight... probability estimate must use accurate data, scientific principles, and a method that is statistically...

  9. Multiple-event probability in general-relativistic quantum mechanics

    SciTech Connect

    Hellmann, Frank; Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo

    2007-04-15

    We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

  10. Preservice Elementary Teachers and the Fundamentals of Probability

    ERIC Educational Resources Information Center

    Dollard, Clark

    2011-01-01

    This study examined how preservice elementary teachers think about situations involving probability. Twenty-four preservice elementary teachers who had not yet studied probability as part of their preservice elementary mathematics coursework were interviewed using a task-based interview. The participants' responses showed a wide variety of…

  11. The Probability Approach to English If-Conditional Sentences

    ERIC Educational Resources Information Center

    Wu, Mei

    2012-01-01

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

  12. The Influence of Phonotactic Probability on Word Recognition in Toddlers

    ERIC Educational Resources Information Center

    MacRoy-Higgins, Michelle; Shafer, Valerie L.; Schwartz, Richard G.; Marton, Klara

    2014-01-01

    This study examined the influence of phonotactic probability on word recognition in English-speaking toddlers. Typically developing toddlers completed a preferential looking paradigm using familiar words, which consisted of either high or low phonotactic probability sound sequences. The participants' looking behavior was recorded in response…

  13. Public Attitudes toward Stuttering in Turkey: Probability versus Convenience Sampling

    ERIC Educational Resources Information Center

    Ozdemir, R. Sertan; St. Louis, Kenneth O.; Topbas, Seyhun

    2011-01-01

    Purpose: A Turkish translation of the "Public Opinion Survey of Human Attributes-Stuttering" ("POSHA-S") was used to compare probability versus convenience sampling to measure public attitudes toward stuttering. Method: A convenience sample of adults in Eskisehir, Turkey was compared with two replicates of a school-based, probability cluster…

  14. A New Way to Evaluate the Probability and Fresnel Integrals

    ERIC Educational Resources Information Center

    Khalili, Parviz

    2007-01-01

    In this article, we show how "Laplace Transform" may be used to evaluate variety of nontrivial improper integrals, including "Probability" and "Fresnel" integrals. The algorithm we have developed here to evaluate "Probability, Fresnel" and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals…

  15. Misconceptions in Rational Numbers, Probability, Algebra, and Geometry

    ERIC Educational Resources Information Center

    Rakes, Christopher R.

    2010-01-01

    In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

  16. Generalized emptiness formation probability in the six-vertex model

    NASA Astrophysics Data System (ADS)

    Colomo, F.; Pronko, A. G.; Sportiello, A.

    2016-10-01

    In the six-vertex model with domain wall boundary conditions, the emptiness formation probability is the probability that a rectangular region in the top left corner of the lattice is frozen. We generalize this notion to the case where the frozen region has the shape of a generic Young diagram. We derive here a multiple integral representation for this correlation function.

  17. Prizes in Cereal Boxes: An Application of Probability.

    ERIC Educational Resources Information Center

    Litwiller, Bonnie H.; Duncan, David R.

    1992-01-01

    Presents four cases of real-world probabilistic situations to promote more effective teaching of probability. Calculates the probability of obtaining six of six different prizes successively in six, seven, eight, and nine boxes of cereal, generalizes the problem to n boxes of cereal, and offers suggestions to extend the problem. (MDH)

  18. On the Provenance of Judgments of Conditional Probability

    ERIC Educational Resources Information Center

    Zhao, Jiaying; Shah, Anuj; Osherson, Daniel

    2009-01-01

    In standard treatments of probability, Pr(A[vertical bar]B) is defined as the ratio of Pr(A[intersection]B) to Pr(B), provided that Pr(B) greater than 0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr(A[vertical bar]B) arise in the mind via implicit calculation of…

  19. Probabilities of Natural Events Occurring at Savannah River Plant

    SciTech Connect

    Huang, J.C.

    2001-07-17

    This report documents the comprehensive evaluation of probability models of natural events which are applicable to Savannah River Plant. The probability curves selected for these natural events are recommended to be used by all SRP/SRL safety analysts. This will ensure a consistency in analysis methodology for postulated SAR incidents involving natural phenomena.

  20. A Probability Model of Accuracy in Deception Detection Experiments.

    ERIC Educational Resources Information Center

    Park, Hee Sun; Levine, Timothy R.

    2001-01-01

    Extends the recent work on the veracity effect in deception detection. Explains the probabilistic nature of a receiver's accuracy in detecting deception and analyzes a receiver's detection of deception in terms of set theory and conditional probability. Finds that accuracy is shown to be a function of the relevant conditional probability and the…

  1. Probability Theory, Not the Very Guide of Life

    ERIC Educational Resources Information Center

    Juslin, Peter; Nilsson, Hakan; Winman, Anders

    2009-01-01

    Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive…

  2. Use of External Visual Representations in Probability Problem Solving

    ERIC Educational Resources Information Center

    Corter, James E.; Zahner, Doris C.

    2007-01-01

    We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use self-generated…

  3. 49 CFR 209.105 - Notice of probable violation.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Hazardous Materials Penalties Civil Penalties § 209.105 Notice of probable violation. (a) FRA, through the Chief Counsel, begins a civil penalty proceeding by serving a notice of probable violation on a person charging him or her...

  4. 49 CFR 209.105 - Notice of probable violation.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Hazardous Materials Penalties Civil Penalties § 209.105 Notice of probable violation. (a) FRA, through the Chief Counsel, begins a civil penalty proceeding by serving a notice of probable violation on a person charging him or her...

  5. Decision-Making Processes: Sensitivity to Sequentially Experienced Outcome Probabilities

    ERIC Educational Resources Information Center

    Boyer, Ty W.

    2007-01-01

    A computerized sequential event sampling decision-making task was administered to 187 5- to 10-year-olds and adults. Participants made a series of choices between alternatives that differed in win probability (Study 1) or win and loss probability (Study 2). Intuitive and more explicit measures were used. Study 1 revealed that, across ages,…

  6. 49 CFR 209.105 - Notice of probable violation.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Hazardous Materials Penalties Civil Penalties § 209.105 Notice of probable violation. (a) FRA, through the Chief Counsel, begins a civil penalty proceeding by serving a notice of probable violation on a person charging him or her...

  7. 49 CFR 209.105 - Notice of probable violation.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Hazardous Materials Penalties Civil Penalties § 209.105 Notice of probable violation. (a) FRA, through the Chief Counsel, begins a civil penalty proceeding by serving a notice of probable violation on a person charging him or her...

  8. A Quantum Theoretical Explanation for Probability Judgment Errors

    ERIC Educational Resources Information Center

    Busemeyer, Jerome R.; Pothos, Emmanuel M.; Franco, Riccardo; Trueblood, Jennifer S.

    2011-01-01

    A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector…

  9. Fisher classifier and its probability of error estimation

    NASA Technical Reports Server (NTRS)

    Chittineni, C. B.

    1979-01-01

    Computationally efficient expressions are derived for estimating the probability of error using the leave-one-out method. The optimal threshold for the classification of patterns projected onto Fisher's direction is derived. A simple generalization of the Fisher classifier to multiple classes is presented. Computational expressions are developed for estimating the probability of error of the multiclass Fisher classifier.

  10. 49 CFR 209.105 - Notice of probable violation.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... ADMINISTRATION, DEPARTMENT OF TRANSPORTATION RAILROAD SAFETY ENFORCEMENT PROCEDURES Hazardous Materials Penalties Civil Penalties § 209.105 Notice of probable violation. (a) FRA, through the Chief Counsel, begins a civil penalty proceeding by serving a notice of probable violation on a person charging him or her...

  11. Objective probability-like things with and without objective indeterminism

    NASA Astrophysics Data System (ADS)

    Szabó, László E.

    I shall argue that there is no such property of an event as its "probability". This is why standard interpretations cannot give a sound definition in empirical terms of what "probability" is, and this is why empirical sciences like physics can manage without such a definition. "Probability" is a collective term, the meaning of which varies from context to context: it means different-dimensionless [ 0, 1 ] -valued-physical quantities characterising the different particular situations. In other words, probability is a reducible concept, supervening on physical quantities characterising the state of affairs corresponding to the event in question. On the other hand, however, these "probability-like" physical quantities correspond to objective features of the physical world, and are objectively related to measurable quantities like relative frequencies of physical events based on finite samples-no matter whether the world is objectively deterministic or indeterministic.

  12. Oil spill contamination probability in the southeastern Levantine basin.

    PubMed

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

    2015-02-15

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

  13. A discussion on the origin of quantum probabilities

    SciTech Connect

    Holik, Federico; Sáenz, Manuel; Plastino, Angel

    2014-01-15

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

  14. Probability theory, not the very guide of life.

    PubMed

    Juslin, Peter; Nilsson, Håkan; Winman, Anders

    2009-10-01

    Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive integration, in part, at least, because of well-known capacity constraints on controlled thought. In this article, the authors show with computer simulations that when based on approximate knowledge of probabilities, as is routinely the case in natural environments, linear additive integration can yield as accurate estimates, and as good average decision returns, as estimates based on probability theory. It is proposed that in natural environments people have little opportunity or incentive to induce the normative rules of probability theory and, given their cognitive constraints, linear additive integration may often offer superior bounded rationality. PMID:19839686

  15. Decision-making processes: sensitivity to sequentially experienced outcome probabilities.

    PubMed

    Boyer, Ty W

    2007-05-01

    A computerized sequential event sampling decision-making task was administered to 187 5- to 10-year-olds and adults Participants made a series of choices between alternatives that differed in win probability (Study 1) or win and loss probability (Study 2). Intuitive and more explicit measures were used. Study 1 revealed that, across ages, participants demonstrated intuitive sensitivity to probability; however, adult participants evidenced greater sensitivity than did children, and younger children failed to demonstrate more explicit understanding of probability. Study 2 also revealed that children were intuitively sensitive to probability; however, the inclusion of loss had limited impact on decision processes. These findings and their relevance to cognitive developmental theory are discussed.

  16. Probability in the Many-Worlds Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Vaidman, Lev

    It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.

  17. Individual Values, Learning Routines and Academic Procrastination

    ERIC Educational Resources Information Center

    Dietz, Franziska; Hofer, Manfred; Fries, Stefan

    2007-01-01

    Background: Academic procrastination, the tendency to postpone learning activities, is regarded as a consequence of postmodern values that are prominent in post-industrialized societies. When students strive for leisure goals and have no structured routines for academic tasks, delaying strenuous learning activities becomes probable. Aims: The…

  18. Situated Learning in Young Romanian Roma Successful Learning Biographies

    ERIC Educational Resources Information Center

    Nistor, Nicolae; Stanciu, Dorin; Vanea, Cornelia; Sasu, Virginia Maria; Dragota, Maria

    2014-01-01

    European Roma are often associated with social problems and conflicts due to poverty and low formal education. Nevertheless, Roma communities traditionally develop expertise in ethnically specific domains, probably by alternative, informal ways, such as situated learning in communities of practice. Although predictable, empirical evidence of…

  19. Stimulus probability effects on temporal bisection performance of mice (Mus musculus).

    PubMed

    Akdoğan, Başak; Balcı, Fuat

    2016-01-01

    In the temporal bisection task, participants classify experienced stimulus durations as short or long based on their temporal similarity to previously learned reference durations. Temporal decision making in this task should be influenced by the experienced probabilities of the reference durations for adaptiveness. In this study, we tested the temporal bisection performance of mice (Mus musculus) under different short and long reference duration probability conditions implemented across two experimental phases. In Phase 1, the proportion of reference durations (compared to probe durations) was 0.5, whereas in Phase 2 it was increased to 0.8 to further examine the adjustment of choice behavior with more frequent reference duration presentations (under higher reinforcement rate). Our findings suggest that mice developed adaptive biases in their choice behaviors. These adjustments in choice behavior were nearly optimal as the mice maximized their gain to a great extent which required them to monitor stimulus probabilities as well as the level of variability in their temporal judgments. We further found that short but not long categorization response times were sensitive to stimulus probability manipulations, which in turn suggests an asymmetry between short and long categorizations. Finally, we investigated the latent decision processes underlying the bias manifested in subjects' choice behavior within the diffusion model framework. Our results revealed that probabilistic information influenced the starting point and the rate of evidence accumulation process. Overall, the stimulus probability effects on choice behavior were modulated by the reinforcement rate. Our findings illustrate that mice can adapt their temporal behaviors with respect to the probabilistic contingencies in the environment.

  20. Stimulus probability effects on temporal bisection performance of mice (Mus musculus).

    PubMed

    Akdoğan, Başak; Balcı, Fuat

    2016-01-01

    In the temporal bisection task, participants classify experienced stimulus durations as short or long based on their temporal similarity to previously learned reference durations. Temporal decision making in this task should be influenced by the experienced probabilities of the reference durations for adaptiveness. In this study, we tested the temporal bisection performance of mice (Mus musculus) under different short and long reference duration probability conditions implemented across two experimental phases. In Phase 1, the proportion of reference durations (compared to probe durations) was 0.5, whereas in Phase 2 it was increased to 0.8 to further examine the adjustment of choice behavior with more frequent reference duration presentations (under higher reinforcement rate). Our findings suggest that mice developed adaptive biases in their choice behaviors. These adjustments in choice behavior were nearly optimal as the mice maximized their gain to a great extent which required them to monitor stimulus probabilities as well as the level of variability in their temporal judgments. We further found that short but not long categorization response times were sensitive to stimulus probability manipulations, which in turn suggests an asymmetry between short and long categorizations. Finally, we investigated the latent decision processes underlying the bias manifested in subjects' choice behavior within the diffusion model framework. Our results revealed that probabilistic information influenced the starting point and the rate of evidence accumulation process. Overall, the stimulus probability effects on choice behavior were modulated by the reinforcement rate. Our findings illustrate that mice can adapt their temporal behaviors with respect to the probabilistic contingencies in the environment. PMID:26242608

  1. Learning Disabilities

    MedlinePlus

    ... Enhancing Diversity Find People About NINDS NINDS Learning Disabilities Information Page Table of Contents (click to jump ... Español Additional resources from MedlinePlus What are Learning Disabilities? Learning disabilities are disorders that affect the ability ...

  2. Approach to learning disability.

    PubMed

    Kulkarni, M; Kalantre, S; Upadhye, S; Karande, S; Ahuja, S

    2001-06-01

    Learning disabilities (LD) is one of the important causes of poor academic performance in school going children. Learning disabilities are developmental disorders that usually manifest during the period of normal education. These disabilities create a significant gap between the true potential and day to day performance of an individual. Dyslexia, dysgraphia and dyscalculia denote the problem related to reading, writing and mathematics. Perinatal problems are certain neurological conditions, known to be associated with LD; however, genetic predisposition seems to be the most probable etiological factors. Evaluation of a child suspected to be having LD consists of medical examination, vision and hearing test analysis of school performance. The psycho-behaviour assessment and education testing are essential in the process of diagnosis. The experienced persons in the field of LD should interpret the results of such tests. With Individualized Remedial Education Plan (IEP) most children learn to cope up with disability and may get integrated in a regular steam. PMID:11450386

  3. Electrofishing capture probability of smallmouth bass in streams

    USGS Publications Warehouse

    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.

  4. Two-slit experiment: quantum and classical probabilities

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2015-06-01

    Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum-classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane).

  5. Naive Probability: Model-Based Estimates of Unique Events.

    PubMed

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

    2015-08-01

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

  6. Naive Probability: Model-Based Estimates of Unique Events.

    PubMed

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

    2015-08-01

    We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning. PMID:25363706

  7. MLZ: Machine Learning for photo-Z

    NASA Astrophysics Data System (ADS)

    Carrasco Kind, Matias; Brunner, Robert

    2014-03-01

    The parallel Python framework MLZ (Machine Learning and photo-Z) computes fast and robust photometric redshift PDFs using Machine Learning algorithms. It uses a supervised technique with prediction trees and random forest through TPZ that can be used for a regression or a classification problem, or a unsupervised methods with self organizing maps and random atlas called SOMz. These machine learning implementations can be efficiently combined into a more powerful one resulting in robust and accurate probability distributions for photometric redshifts.

  8. Fitness Probability Distribution of Bit-Flip Mutation.

    PubMed

    Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

    2015-01-01

    Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis. PMID:24885680

  9. Visualizing RNA base-pairing probabilities with RNAbow diagrams.

    PubMed

    Aalberts, Daniel P; Jannen, William K

    2013-04-01

    There are many effective ways to represent a minimum free energy RNA secondary structure that make it easy to locate its helices and loops. It is a greater challenge to visualize the thermal average probabilities of all folds in a partition function sum; dot plot representations are often puzzling. Therefore, we introduce the RNAbows visualization tool for RNA base pair probabilities. RNAbows represent base pair probabilities with line thickness and shading, yielding intuitive diagrams. RNAbows aid in disentangling incompatible structures, allow comparisons between clusters of folds, highlight differences between wild-type and mutant folds, and are also rather beautiful.

  10. [Probable flora: an expression mean of ecological gradients in France].

    PubMed

    Garbolino, Emmanuel; De Ruffray, Patrice; Brisse, Henry; Grandjouan, Gilles

    2013-02-01

    The application of the criterion of fidelity of plants to plants over four millions botanical observations in France is considered to characterize the ecology of 215,000 phytosociological surveys. Among those discriminant plants, some are missing of the surveys, but they can have a certain probability of occurrence: these plants are called "probable plants" and they represent the "probable flora" of a territory. The study of their geographical distribution shows ecological gradients of flora across France in a better way than only considering the botanical observations. In fact, this method mitigates the discontinuities of taxa observations whose absence may be due to historical and/or anthropogenic factors.

  11. Calculation of inclusive probabilities from single-particle amplitudes

    NASA Astrophysics Data System (ADS)

    Kürpick, Peter; Lüdde, Hans Jürgen

    1993-04-01

    On the basis of the independent particle model, used to describe collisions between ions and atoms involving many electrons, the formalism of inclusive probabilities allows the computation of many-electron transition probabilities from single-particle amplitudes. The method presented can answer practically any experimental question formulated in terms of a certain number of vacancies and occupancies as can be measured in a typical ion-atom collision experiment. It is specialised to calculate many-particle probabilities with respect to a minimum number of vacancies or occupancies in one or more subshells as obtained e.g. in KLL- or KLM-Auger spectra.

  12. Origin of probabilities and their application to the multiverse

    NASA Astrophysics Data System (ADS)

    Albrecht, Andreas; Phillips, Daniel

    2014-12-01

    We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically verified fully classical theory of probability. We comment on the general implications of this view, and specifically question the application of purely classical probabilities 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.

  13. Quantum correlations in terms of neutrino oscillation probabilities

    NASA Astrophysics Data System (ADS)

    Alok, Ashutosh Kumar; Banerjee, Subhashish; Uma Sankar, S.

    2016-08-01

    Neutrino oscillations provide evidence for the mode entanglement of neutrino mass eigenstates in a given flavour eigenstate. Given this mode entanglement, it is pertinent to consider the relation between the oscillation probabilities and other quantum correlations. In this work, we show that all the well-known quantum correlations, such as the Bell's inequality, are directly related to the neutrino oscillation probabilities. The results of the neutrino oscillation experiments, which measure the neutrino survival probability to be less than unity, imply Bell's inequality violation.

  14. Exact integration of height probabilities in the Abelian Sandpile model

    NASA Astrophysics Data System (ADS)

    Caracciolo, Sergio; Sportiello, Andrea

    2012-09-01

    The height probabilities for the recurrent configurations in the Abelian Sandpile model on the square lattice have analytic expressions, in terms of multidimensional quadratures. At first, these quantities were evaluated numerically with high accuracy and conjectured to be certain cubic rational-coefficient polynomials in π-1. Later their values were determined by different methods. We revert to the direct derivation of these probabilities, by computing analytically the corresponding integrals. Once again, we confirm the predictions on the probabilities, and thus, as a corollary, the conjecture on the average height, <ρ> = 17/8.

  15. Probability Tables: a generic tool for representing and propagating uncertainties

    NASA Astrophysics Data System (ADS)

    Coste-Delclaux, M.; Diop, C. M.; Lahaye, S.

    2014-06-01

    Probability tables are a generic tool that allows representing any random variable whose probability density function is known. In the field of Nuclear Reactor Physics, this tool is currently used to represent the variation of cross-sections versus energy (TRIPOLI4®, MCNP, APOLLO2, ECCO/ERANOS, …). In the present article we show how we can propagate uncertainties, thanks to a probability table representation, through two very simple mathematical problems: an eigenvalue problem (neutron multiplication factor, …) or a depletion problem.

  16. Fitness Probability Distribution of Bit-Flip Mutation.

    PubMed

    Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

    2015-01-01

    Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

  17. Adaptive Learning and Risk Taking

    ERIC Educational Resources Information Center

    Denrell, Jerker

    2007-01-01

    Humans and animals learn from experience by reducing the probability of sampling alternatives with poor past outcomes. Using simulations, J. G. March (1996) illustrated how such adaptive sampling could lead to risk-averse as well as risk-seeking behavior. In this article, the author develops a formal theory of how adaptive sampling influences risk…

  18. A Semantic Web-Based Authoring Tool to Facilitate the Planning of Collaborative Learning Scenarios Compliant with Learning Theories

    ERIC Educational Resources Information Center

    Isotani, Seiji; Mizoguchi, Riichiro; Isotani, Sadao; Capeli, Olimpio M.; Isotani, Naoko; de Albuquerque, Antonio R. P. L.; Bittencourt, Ig. I.; Jaques, Patricia

    2013-01-01

    When the goal of group activities is to support long-term learning, the task of designing well-thought-out collaborative learning (CL) scenarios is an important key to success. To help students adequately acquire and develop their knowledge and skills, a teacher can plan a scenario that increases the probability for learning to occur. Such a…

  19. 10. NORTHWEST END OF WHITSETT PLANT SHOWING PIPELINES PROBABLY FOR ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    10. NORTHWEST END OF WHITSETT PLANT SHOWING PIPELINES PROBABLY FOR FIRE WATER STORAGE, LOOKING SOUTHWEST. - Whitsett Pump Plant, West side of Colorado River, north of Parker Dam, Parker Dam, San Bernardino County, CA

  20. 2. BARN. VIEW LOOKING NORTHWEST. THE ROLLING DOOR PROBABLY REPLACES ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    2. BARN. VIEW LOOKING NORTHWEST. THE ROLLING DOOR PROBABLY REPLACES AN ORIGINAL 4/4 DOUBLE-HUNG WINDOW. - Tonto Ranger Station, Barn, Forest Service Road 65 at Tonto Wash, Skull Valley, Yavapai County, AZ

  1. 42. VIEW EAST OF PLASTIC STACK (PROBABLY PVC) WHICH VENTED ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    42. VIEW EAST OF PLASTIC STACK (PROBABLY PVC) WHICH VENTED FUMES FROM THE DIPPING OPERATIONS IN BUILDING 49A; BUILDING 49 IS AT THE LEFT OF THE PHOTOGRAPH - Scovill Brass Works, 59 Mill Street, Waterbury, New Haven County, CT

  2. Children's Conceptions of Probability--A Psychological and Pedagogical Review.

    ERIC Educational Resources Information Center

    Hawkins, Anne S.; Kapadia, Ramesh

    1984-01-01

    Identifies key questions concerning children's intuitions and conceptions of probabilistic notions. Research on the theoretical framework for probability studies, misconceptions and strategies, and pupil attainment is reviewed, and the methodology is evaluated. Finally, implications for classroom practice are discussed. (MNS)

  3. Adaptive MFR parameter control: fixed vs. variable probabilities of detection

    NASA Astrophysics Data System (ADS)

    Boers, Yvo; Driessen, Hans; Zwaga, Jitse

    2005-09-01

    In this paper an efficient adaptive parameter control scheme for Multi Function Radar (MFR) is used. This scheme has been introduced in.5 The scheme has been designed in such a way that it meets constraints on specific quantities that are relevant for target tracking while minimizing the energy spent. It is shown here, that this optimal scheme leads to a considerable variation of the realized detection probability, even within a single scenario. We also show that constraining or fixing the probability of detection to a certain predefined value leads to a considerable increase in the energy spent on the target. This holds even when one optimizes the fixed probability of detection. The bottom line message is that the detection probability is not a design parameter by itself, but merely the product of an optimal schedule.

  4. Subjective probability intervals: how to reduce overconfidence by interval evaluation.

    PubMed

    Winman, Anders; Hansson, Patrik; Juslin, Peter

    2004-11-01

    Format dependence implies that assessment of the same subjective probability distribution produces different conclusions about over- or underconfidence depending on the assessment format. In 2 experiments, the authors demonstrate that the overconfidence bias that occurs when participants produce intervals for an uncertain quantity is almost abolished when they evaluate the probability that the same intervals include the quantity. The authors successfully apply a method for adaptive adjustment of probability intervals as a debiasing tool and discuss a tentative explanation in terms of a naive sampling model. According to this view, people report their experiences accurately, but they are naive in that they treat both sample proportion and sample dispersion as unbiased estimators, yielding small bias in probability evaluation but strong bias in interval production. PMID:15521796

  5. The role of probability of reinforcement in models of choice.

    PubMed

    Williams, B A

    1994-10-01

    A general account of choice behavior in animals, the cumulative effects model, has been proposed by Davis, Staddon, Machado, and Palmer (1993). Its basic assumptions are that choice occurs in an all-or-none fashion for the response alternative with the highest probability of reinforcement and that the probability of reinforcement for each response alternative is calculated from the entire history of training (total number of reinforced responses/total number of reinforced and nonreinforced responses). The model's reliance on probability of reinforcement as the fundamental variable controlling choice behavior subjects the cumulative effects model to the same criticisms as have been directed toward other related models of choice, notably melioration theory. Several different data sets show that the relative value of a response alternative is not predicted by the obtained probability of reinforcement associated with that alternative. Alternative approaches to choice theory are considered.

  6. Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment

    NASA Technical Reports Server (NTRS)

    Carpenter, James R.; Markley, F Landis

    2014-01-01

    This paper shows how satellite owner/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies tolerances related to targeted false alarm and missed detection rates. This result is independent of the method one uses to compute the probability density that one integrates to compute collision probability. A well-established test case from the literature shows that this test yields acceptable results within the constraints of a typical operational conjunction assessment decision timeline. Another example illustrates the use of the test in a practical conjunction assessment scenario based on operations of the International Space Station.

  7. Quantum Probability Theory and the Foundations of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Fröhlich, Jürg; Schubnel, Baptiste

    By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop "quantum probability theory" into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).

  8. Sculpture, general view looking to the seated lions, probably from ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    Sculpture, general view looking to the seated lions, probably from the American Bungalow - National Park Seminary, Bounded by Capitol Beltway (I-495), Linden Lane, Woodstove Avenue, & Smith Drive, Silver Spring, Montgomery County, MD

  9. 17. Photocopy of photograph (source uncertain; probably the Bucks County ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    17. Photocopy of photograph (source uncertain; probably the Bucks County Historical Society) ca. 1913, photographer unknown SHOWING 1904 SOCIETY HEADQUARTERS AND THE EARLY PHASES OF CONSTRUCTION ON MERCER'S ADDITION - Mercer Museum, Pine & Ashland Streets, Doylestown, Bucks County, PA

  10. Review of Literature for Model Assisted Probability of Detection

    SciTech Connect

    Meyer, Ryan M.; Crawford, Susan L.; Lareau, John P.; Anderson, Michael T.

    2014-09-30

    This is a draft technical letter report for NRC client documenting a literature review of model assisted probability of detection (MAPOD) for potential application to nuclear power plant components for improvement of field NDE performance estimations.

  11. Probable maximum flood at Lake Chippewa near Winter, Wisconsin

    USGS Publications Warehouse

    Krug, William R.

    1976-01-01

    The probable maximum flood was computed for Lake Chippewa, Wisconsin, and routed through the lake to determine maximum lake stage. The peak discharge of the probable maximum flood at Lake Chippewa was computed to be about 75,000 cubic feet per second, primarily caused by rainfall on the lake. A secondary peak of about 41,000 cubic feet per second was due to streamflow entering Lake Chippewa. The 14-day volume of this flood was 450 ,000 acre-feet. Using an assumed operating procedure for Winter Dam, the maximum lake stage for the probable maximum flood was computed to be about 1,318 feet above mean sea level--about 3 feet below the dam crest and 6 feet above the proposed normal summer operating level. The probability of this flood occurring in any year is less than 1 in 10,000. (Woodard-USGS)

  12. Use of Spreadsheets in Introductory Statistics and Probability.

    ERIC Educational Resources Information Center

    Mitchell, Brian S.

    1997-01-01

    Provides details of a course that introduces chemical engineering students to a variety of spreadsheet applications. The course is taken concurrently with stoichiometry and introduces statistical analysis, probability, reliability, and quality control. (DDR)

  13. Exploring Probability through an Evens-Odds Dice Game.

    ERIC Educational Resources Information Center

    Quinn, Robert J.; Wiest, Lynda R.

    1999-01-01

    Presents a dice game that students can use as a basis for exploring mathematical probabilities and making decisions while they also exercise skills in multiplication, pattern identification, proportional thinking, and communication. (ASK)

  14. The use of sequential probabilities in the segmentation of speech.

    PubMed

    van der Lugt, A H

    2001-07-01

    The present investigation addresses the possible utility of sequential probabilities in the segmentation of spoken language. In a series of five word- spotting and two control lexical decision experiments, high- versus low-probability consonant-vowel (Experiments 1, 2, 5, and 7) and vowel-consonant (Experiments 1, 3, 4, and 6) strings were presented either in the nonsense contexts of target words (Experiments 1-3) or within the target words themselves (Experiments 4-7). The results suggest that listeners, at least for sequences in the onset position, indeed use sequential probabilities as cues for segmentation. The probability of a sound sequence influenced segmentation more when the sequence occurred within the target words (Experiments 4-7 vs. Experiments 1-3). Furthermore, the effects were reliable only when the sequences occurred in the onset position (Experiments 1, 2, 5, and 7 vs. Experiments 1, 3, 4, and 6). PMID:11521849

  15. 15. STONE BURR MILL PROBABLY USED FOR GRINDING FEED. ONLY ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    15. STONE BURR MILL PROBABLY USED FOR GRINDING FEED. ONLY REMAINING MILL MACHINERY William E. Barrett, photographer, 1973 - Thomas Shepherd's Grist Mill, High Street Vicinity, Shepherdstown, Jefferson County, WV

  16. Coincidence probabilities for spacecraft gravitational wave experiments - Massive coalescing binaries

    NASA Technical Reports Server (NTRS)

    Tinto, Massimo; Armstrong, J. W.

    1991-01-01

    Massive coalescing binary systems are candidate sources of gravitational radiation in the millihertz frequency band accessible to spacecraft Doppler tracking experiments. This paper discusses signal processing and detection probability for waves from coalescing binaries in the regime where the signal frequency increases linearly with time, i.e., 'chirp' signals. Using known noise statistics, thresholds with given false alarm probabilities are established for one- and two-spacecraft experiments. Given the threshold, the detection probability is calculated as a function of gravitational wave amplitude for both one- and two-spacecraft experiments, assuming random polarization states and under various assumptions about wave directions. This allows quantitative statements about the detection efficiency of these experiments and the utility of coincidence experiments. In particular, coincidence probabilities for two-spacecraft experiments are insensitive to the angle between the directions to the two spacecraft, indicating that near-optical experiments can be done without constraints on spacecraft trajectories.

  17. Applications of the Dirichlet distribution to forensic match probabilities.

    PubMed

    Lange, K

    1995-01-01

    The Dirichlet distribution provides a convenient conjugate prior for Bayesian analyses involving multinomial proportions. In particular, allele frequency estimation can be carried out with a Dirichlet prior. If data from several distinct populations are available, then the parameters characterizing the Dirichlet prior can be estimated by maximum likelihood and then used for allele frequency estimation in each of the separate populations. This empirical Bayes procedure tends to moderate extreme multinomial estimates based on sample proportions. The Dirichlet distribution can also be employed to model the contributions from different ancestral populations in computing forensic match probabilities. If the ancestral populations are in genetic equilibrium, then the product rule for computing match probabilities is valid conditional on the ancestral contributions to a typical person of the reference population. This fact facilitates computation of match probabilities and tight upper bounds to match probabilities.

  18. A Note on the Sequential Probability Ratio Test

    ERIC Educational Resources Information Center

    Thomas, Ewart A. C.

    1975-01-01

    Given reflection symmetry, the moment generating function symmetry is necessary and sufficient for the random walk model to be equivalent to a sequential probability ratio test. For a related article, see TM 501 715. (Author/RC)

  19. Strength of evidence, judged probability, and choice under uncertainty.

    PubMed

    Fox, C R

    1999-02-01

    This paper traces, within subjects, the relationship between assessed strength of evidence, judgments of probability, and decisions under uncertainty. The investigation relies on the theoretical framework provided by support theory (Tversky & Koehler, 1994; Rottenstreich & Tversky, 1997), a nonextensional model of judgment under uncertainty. Fans of professional basketball (N = 50) judged the probability that each of eight teams, four divisions, and two conferences would win the National Basketball Association championship. Additionally, participants rated the relative strength of each team, judged the probability that a given team would win the championship assuming a particular pairing in the finals, priced prospects contingent on the winner of the championship, and made choices between chance prospects. The data conformed to the major tenets of support theory, and the predicted relationships between assessed strength of evidence, hypothetical support, judged probabilities, and choices under uncertainty also held quite well.

  20. Topology of optimally controlled quantum mechanical transition probability landscapes

    SciTech Connect

    Rabitz, H.; Ho, T.-S.; Hsieh, M.; Kosut, R.; Demiralp, M.

    2006-07-15

    An optimally controlled quantum system possesses a search landscape defined by the physical objective as a functional of the control field. This paper particularly explores the topological structure of quantum mechanical transition probability landscapes. The quantum system is assumed to be controllable and the analysis is based on the Euler-Lagrange variational equations derived from a cost function only requiring extremizing the transition probability. It is shown that the latter variational equations are automatically satisfied as a mathematical identity for control fields that either produce transition probabilities of zero or unit value. Similarly, the variational equations are shown to be inconsistent (i.e., they have no solution) for any control field that produces a transition probability different from either of these two extreme values. An upper bound is shown to exist on the norm of the functional derivative of the transition probability with respect to the control field anywhere over the landscape. The trace of the Hessian, evaluated for a control field producing a transition probability of a unit value, is shown to be bounded from below. Furthermore, the Hessian at a transition probability of unit value is shown to have an extensive null space and only a finite number of negative eigenvalues. Collectively, these findings show that (a) the transition probability landscape extrema consists of values corresponding to no control or full control, (b) approaching full control involves climbing a gentle slope with no false traps in the control space and (c) an inherent degree of robustness exists around any full control solution. Although full controllability may not exist in some applications, the analysis provides a basis to understand the evident ease of finding controls that produce excellent yields in simulations and in the laboratory.